B.S., University of Alabama Whi t t lD~AF By

3 iI 4 INST1938 MAR 4 MARI93a LI8BRAR*i lD~AFNTALS OF DSIGNJ 0F SLMIL OIL-FIRED EATING BOILERS By Sidney A. Whit t B.S., University of Alabama 1933 Submitted in Partial ulfillment o the Requirements for the degree of MASTER O SCIENCE from the assachusetts Institute of Technology 1937 A ........... Signature of Author. Department of l.echanical ngineing Signature of Professor in Charge of Research... Signature o Chairman o epartment Committee on Gradu.,ate tuents 4 .................... r I ND EX ,'T"NS" IT-LTAL L T ',ER OF A ACK NO L ED AGEET ' B PREFACE 1 iITRODUCTIO' 4 PART I LI3ERAT IN01 OF HEAT ENIERGY 7 I FUNDAENTAL3S F FUEL OIL UTILIZATION II THE COi.IBUSTION PROCESS III DETERMINATIOIN OF FLAME TEMPERATURE IN COMBUSTION CHA'M.BEROF AN 8 11 26 CIL BURNI1NG BILER IV CONDENSATIOI. OF m?:OISTURE IN' FLUES OF OIL-FIRED AND ITS V EFFECT SELECTION FOR A G UPOCI DESIGN Aj 3IZE MIALL OIL-FIRED HEATING BOILERS A.ND OPERATIOID 33 SHAPE OF A CO,.1BUSTION JiA2HBER iEATING OR FURnTAC iBOILEI 59 PART II RADIANTl TR.,ASFER VI RIAAN' HEAT TSs F OF LIBEeRATED HEAT ERGY ALiONG THE IrT-TER SURFACES 55 OF A COMBUSTIONCHABER VII RADITNT HEAT ALONG EIiR 56 RANtTSFER FROIi GASEOUS PRODUCTS OF COIMBUSTION PATH OF TRAVEL TOUG PART E BCILER III COVriTECTION1 TRANSFER OF LIBERATED HEAT ENERGY VIII COi'TTECTIOCIT IAT ALONG TIR T:SIER 66 80 FROM GASEOUS PRODUCTS OF COMBUSTION PATH OF TRAVEL HROUH THE BOILER 220145 81 PART IV TRANS3FER OF HEAT EERGY IX HEAT TA.NSFER X HEAT TRANSFER TI TC 17JON-BOILIlG TO 93 iATER WATER 95 OCILING WATER 120 PART V SPECIAL PROBLEIMS XI HEAT LOS3 BY RADIATION FROM OUTSIDE 142 SURFACE OF ECBOILER JACKET XII 145 HEAT LOS3 Y N0TURAL 0 ATMOSPPERIC AIR BOILER JACKET XIII ITrTE,TlENT O1.0ECfTION FROM OUTSIDE S'URFACE OF A OPERATION OF SALL 151 OIL-FIRED HEATING OILERS AND ITS EFFECT ON'DESIGN FEATURES 157 PART VI FLUID FLOW XIV ORIFICE XV. FLUID XVI RATIONAL HEATING FLOW OF FLUIDS IN SALL 173 HEATING- BOILERS RICTIOT AND ITS EFTECT ON FLUID FLOii BASIS Oi DESIGN OF WATEIR CIRCULATIONt BOILERS ATUrXILIARY CURVES 186 IN SLL 218 APPENDIX I 170 1Massnchusetts Cnbrid-e, January 14, 1957 Secretary of the Fculty Massachusetts Institute of Technology Cambridge, Massachusetts Dear Sir: In partial fulfillment of the requirements for the Degree of Master of Science I herewith submit a thesis entitled "Fundamentals of Design of Small Oil-Fired Heating Boilers". Respectfully submitted, Sidney A. A h~itt ACKNOWLEDGMENT The writer is indebted to Professor James Holt for the suggestion of the subject of this thesis. It proved to be an invaluable experience, and an incentive for acquiring information and methods of attack on numerous problems in the ever widening fields of heat transfer and thermal engineering. PREFACE In this work the principal aim of the author was to form a scientific basis for analysis and design calculations of small oilfired heating boilers; in particular an effort was made to formulate a method for prediction of performance characteristics. The writer has made no attempt to elaborate upon those phases of the subject which have already been developed in connection with studies of large heating and power boiler designs. The old and well established theories and the data from the field of steam power generation were included in this work only in so far as it was necessary for the logical development of the thesis. After several months of reading and study the writer came to the conclusion that the weakest point in the present state of knowledge concerning design and prediction of performance of small oilfired heating boilers was the lack of quantitative data nd methods of calculation of heat transfer. Bearing this in mind, he devoted most of his efforts to development of a rational method for analysis and calculation of heat transfer processes taking place in various parts of a heating boiler. The fundamentals of heat transfer presented in this work and on which the calculations are based throughout are founded on the original studies and research of the most outstanding investigators in the field of heat transmission. The ultimate selection of data and procedure of computationsmade only after a careful study and comparison from the point of view of authenticity and reliability of material. All information and data -I- s taken from the works of other investigators is acknowledged throughout the text. The most difficult problem in organization nd classification of available fundamentals was the shaping of the contributions of the investigators in various fields of heat transfer into a homogeneous body of principles applicable to the specific problems at hand. The points of view of the chemical engineer, the mechanical engineer, the physicist, and the metalurgical engineer had to be brought to a comrQ~ ~ ~ ~ Mi±iL± +;.~ Laha CU .i-L.%UB L'j.L A +arA~~C IVLy t L L4J.t V d~r WJ.LAqU nAC .LIU V · h~n~l CL "n±.Lr-cWL Wu VaseW 7 The writer believes that as a whole the material presented I. here points accurately to the new phase of ther-malengineering,which i: will be characterized by a wider use of thorough scientific methods of analysis and prediction in accord with the world's effort to prevent i the economic waste of unplanned experimentation. i. THESIS L -3 - INTRODUCTION Analysis Of The Problem Of Small eating Boiler Design The most important fact to bear in mind when attacking the problem of any boiler design is that a boiler is nothing else but a. complex heat exchanger. Any heating boiler can be best described s an apparatus in which the heat energy released during combustion of an oxidizable material is transferred from a high temperature level to a lower level suitable for utilization in heating of dwellings. Tne release and transfer of heat energy in a heating boiler usually goes through the following fundamental steps: (1) A combustible material and air are introduced into a confined space. (2) Conditions in the confined space are so regulated that the combustible material and oxygen in the, air are induced to combine and form a new chemical compound or compounds. (3) Since formation of the new compounds is an exothermic reaction, the chemical energy stored in the original materials is released in the form of heat energy. (4) The heat energy released during combustion raises the temperature of the resulting compounds to a high level- about 2000 to 4000 °F. depending on the conditions. (5) The products of combustion are retained in the boiler for a short period during which the heat is transferred from them through a separating wall to a medium (usually water) which acts as a carrier L -4- of heat to different parts of'the dwelling. (6) As the heat is extracted from the products of combustion, they re expelled from the combustion space and the newly Formed gases take their place. (7) The transfer of heat from the products of combustion to the carrier medium is usually accompanied by a considerable lowering of the temperature level; the difference in temperature, of course, being the potential which causes the flow of heat rom the products of combustion to the carrier medium. (8) The carrier medium transfers the heat to the spaces to be heated. Fig. o. I gives a self explanatory diagram of the basic processes occurring in an elementary heating boiler. Requirements Of An Ideal Heating Boiler Everyday economics give us five fundamental requirements that must be met in design of an ideal heating boiler. First of all, it must be of low initial cost, yet o good and durable construction incorporating such features as safety, reliability, beauty, etc. Secondly, it must be able to use a comparatively inexpensive fuel. Thirdly, it must be subject to automatic operation and regulation. Fourth, it should require a minimum of maintenance. Fifth, it must be as.efficient as possible-- the limit of efficiency being, of course, the point determined by the economic balance Da-5ic Processes o,-4 7-h 01,4yrae"n 4n E/ee7 ta ry iea toz 3o /er farce7,7,frri S2r Zo2Dwe/e///l7y /heea •> Sprace - - - CrroYdiny Comrdwts #' :A-n7 ., - * w K * '1 - r z4 /a 2,/; 1 *. -eat-rarr/ir//?9 A 5eparIa J~-- ------ - - ay I ~ v~~~~~~~~~~~~~~~~ ?f) - 6coofre jj 'rodrc s AirI.. -. · a -, , ..,;' -' . :_ .~.. ,,[; ~,,r~ ~~~~~ ,, , s.: ' -' . ".., -"'."' ;'- ~: ' .... | 84ir~~~I;':' Comn*stroi tAC"10 between the first cost nd the saving in fuel cost during the expected life of the boiler. Meeting The Requirements Of An Ideal Heating Boiler Design In so far as tile engineer is concerned, the basic prerequisites for creation of an ideal heating boiler design are as follows: (A) Thorough understanding in a qualitative way of all physical and chemical phenomena underlying the design of the apparatus, its functioning and regulation. A (B) Comprehensive knowledge of the theories underlying the quantitative relationship amone the variables involved in the phenomena occurring during operation of the apparatus or any of its parts. The division of prerequisite knowledge into qualitative and Quantitative parts is done primarily to indicate that the available stock of information on any subject usually consists in a large measure of qualitative generalities and only in small part of accurate quanti- tativedta. The qualitative information, though not applicable directly to solution of design problems, is invaluable in prescribing the needed quantitative investigations and in interpreting the gathered data. Keeping in mind the two basic prerequisites as outlined above, the subject matter of this thesis is organized around the fundamental functions of a small oil-fired heating boiler and the basic phenomena underlying them. The development of the text in so far as possible follows the logical sequence of events or with respect to each other. -6- s they occur with respect to time II i FR--- I I PART I LIBEIRATION OF HEAT -7- EIERGY r CHAPTER I FUIfDAMENrALS CF FUEL OIL -8L UTILIZATIONi FUNTDAMYTALS OF FUEL OIL UTILIZATO IO Oil Fuel nd Its Prooerties Oil as a fuel in a small heating boiler gives it many unique advantages which are comparable to those incorporated in many other household labor-saving devices. The principal advantages of using oil are as follows: (1) Oil firing lends itself to perfect automatic supply. (2) Oil combustion leaves no residue to be removed. (3) The combustion process is very clean, especially when a b 11 ~~ ~ IUIL'IULII IAZ$ I JttI o _ 1 UVL ; Z5 ' . tllplUYUUU Vil A tILIU A+h\_mn U11U-r,-L U--, + L)U IIrIL-L 0 1n.o Manan nf VI 1,l PUJ%AQ WJ UQ operation without cleaning of gas passages. (4) For equal heat values, the space required for storage of oil is bout 50 ner cent of that required for coal storage. Further- more, oil is stored in a buried tank outside the premises, thus permitting full use of the basement space. (5) here is no loss in heat value due to deterioration while in storage. (6) Stack or flue gas losses are low, because the excess air required for complete combustion is considerably lower than in combustion of coal. (7) There is a much greater adaptability to load variations than canrbe had with coal. (8) Oil firing is adaptable to isolated locations where gaseous fuel can not be had. (9) A much igher combustion efficiency can be obtained with -9- oil fuel than with coal. (10) There are no banking losses. (11) Capacity of a given size boiler can be varied over a considerable range without appreciable loss of overall thermal efficiency. (12) A smaller draft is required than with coal. The principal disadvantage of oil fuel at the present time is its high cost at points of considerable distance from oil fields.However, with increase of cheaper transportation, such as pipe lines and the tank truck delivery, oil will become a strong competitor of coal and natural gas. Another disadvantage of oil fuel utilization is the comparatively high initial cost of installation, but this will become less and less pronounced when oil burning boilers enter the mass production stage. -/0 - IIEr PT II TM-I Co1AgEU5ST:C~xPCZSS - //- i THiECOABUSTION PROCESS -z Introduction Given the definite fuel oil, a desired quantity of air, and the necessary combustion chamber-- the combustion process in a small heating boiler can be analysed in a general manner within the limits prescribed by the theoretical and practical knowledge concerning the r . . subject matter at hand. It is with this view and to this end that the discussion presented below is shaped. ; Chemical Properties of Petroleum Fuel Oils :; The principal chemical property of a fuel oil which must be considered in design of a small heating boiler is its chemical composition in so far as it affects the combustion process, the products of combustion, and consequently heat trensfer. No attempt is made here, of course, to study the effects of different fuel oils on boiler performance, efficiency,or maintenance :: problems. Sole consideration given here to chemical properties of a fuel oil is selection of an average hypothetical fuel oil with a representative ultimate analysis which could be used as a base or starting point in development of combustion nd heat transfer calculations. ' t ' Physical Properties of Petroleum Tuel Oils The principal physical properties of a petroleum fuel oil which heve an important bearing upon the roblems of small heating boiler design are as follows: (1) Higher heating value, Btu./lb. (2) Latent heat of vaporization, Btu./lb. (35)Specific heat, Btu./(lb.)(°F.) (4) Absolute viscosity, lbs./(hr.)(ft.) (5) Specific gravity. Investigations by the United States Bureau of Standards have shown that the first four properties are essentially functions of specific gravity, nd can be expressed with fair degree of accuracy by means of simple empirical relationships. Thus, a single line on Fig.No. 2 attached here represents a practically linear relationship between specific gravity of liquid petroleum roducts and their " higher heating value". It might be noted here that the data on whlichthis relationship is based has an established accuracy of about one per cent. The latentheat of vaporization of fuel oils peratures is given by an approximate equation at various tem- s follows: r = (l/d)(l10.9-0.09t) Vhere: r = Latent heat of vaporization, Btu./lb. d Specific gravity at 600°/600 F. t = Average oil temperature, F. The graphical solution of this equation Is given on Fig. No2The accuracy o the data on wl-ich this equation is based is only within - /X3- I +1 X,,'± w *< s I i i B~ 1 1 i--11- i , 1l 'i:_-15 - : · II . i t t i I i :I 61 I ~~~~~-_ 1 ' - / -- II . r- f 1 Wir I -. 1- -1- t 1-: - - i I i i+ -, l/Wl ii, -. ~'I K ' I 1, I· |~ - Ii~~~~~~ I1' 1 i | } |- I | - 1 ;g 0 - .. I - I.I -I f _ 1 ~~II W~~~~ trt -t -I1' ij -1i r-t-P :X - -I- h :1 I- ~ 1- ! I - :1--i I 1$ 'a', I' I \- - -l r7FT~~~~~~~~~ 11 . ---I ... i e $'j-.---*- *| i 1't| 1Kt' -I.V. 1 - I1- 1 ;- F-rtZ rI Ii''11 1 - T~i- L--,_i i~~i -Fs- I6>.:1;l:l i ii-I !O.,;,,r - ·. I iclrdvi a; iskeic/u~~~i~c - .- 1. 1. ' | ! -- -- tI i' ' i' I ., i W,+ ' { ... i.. 1,- -- _Ii.I I- i.... 1. . ... . . I I ; j'- - - , .4', H+~~~~· i-+ l> :'' a ,i I.~~~~~~~~~~ t~~~~~~ _ -- t 1,,~~~ L+ 1~~ ' 1-L-'I \.4S -I--9' ,-'l1't,~l.1E 1-X--- -I- i Af' , i : I` ,, !I- !97---_,I_.: __ ._. 1 'r' I -'; ': sfi- I I 4/i - 1' \ 1'' : , 1 . -1 ' i 'I m i' ,.s i E_ i [ - I |' ~ |: |I 'i ' -- i , :; 1·X 1· 1 i ' : 1 1 1 1 1i i I. - 10 i : I 12i: ::· 1 1 -2Ž- . '. , .. . : ,. 2|I v- -I -K 1 eb::tII1 I I-_ -1 E ;F1.=1./Zz@29l-AiSL'Ll fl;1S-, 01 i :!:1 ij:1,,10 -i-:1~~~ -1,:1-:--:---i +e:14¢L --VIAX I::, TI~al:7.'~~~~~~~~~~~~~~~~~~~ ::|:·I · ·- 1:: I···- 5 C 3-t;:l| i -I 1iV 1III t - 1-1- 1 _ · !· I - :1 · I--l- 1- -1 K 1 1 · i·- > ·! |II 1 1 ; s1·I i = I· · 1 - m r-liige:E ! .mm 4 t ·i· ie f h 1 i W - I I I L... · 1i ' 1- t· · - · L1re: 1- I I__ 1_. t -·-·~ ~ ~ ~~A 1- t: h >1 :t$: 1 t :-l § i -·- X4 1 I_ I - T. I 1- 1- :1 II i - 1-t::l----li:-ti 1~ i· ,· =1 * 1--I 0g I ··~ -! I- r;-·11 ' ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ -1 -: -: -T :i, ;-l; l-s--;ol-!-- __ L~ 1--i __ jIi Il T t; 11-; ii-.1- ' I Th -l_: 3 i'iL4 1-- -X ' ---1-!---. 1..= _ ' 2 I -1---t-;T,,-9,iif , 4 -il Ii1iIi71; i· I·I-.I ~ · g~ ··· II \C b )~ -iiI tl1i1.fJ'101 ';-1 -C i· :~h 1 11 :1:11.I-t -' .. - ~~~~- 1. , _ . - ~~~ - _ -H"'" ~-i K ~- . X,~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~i ~-m 8-10%J; however, since the quantities of 'heat involved are comparatively small, use of this ecuation will not introduce any appreciable error into combustion or heat transfer calculations to be carried out in this work. Instantaneous specific heat of liquid petroleum products at various temperatures may be given by means of the following equation: .388 8 + .00045t) Sp.Ht.= (/'o, T':here: Sp.Ht. 5 Specific heat, tu./(lb.)(°F.) d = Specific grvity, t = Average at 60°/60'F. oil temrperture, 0F. A graphical solution of this equation is also given on Fig. No.4 attached here. he accuracy of the data on which based is within 5 per cent o the equation is the actual values. Viscosity of petroleum products is given on Fig.No. 56 as a function of specific gravity (60°/600 F.) and temperature,°F. At best these vlues are approximate, because viscosity of mineral oils depends considerably on rmolecular structure, and quite frequently oils of samne density may have entirely different molecular pttern-- and consequently somewhat different viscosities. In general the viscosities estimated from Fig. No. 5 may be expected to be in error as much as 15-20'. The only certin certain way of determining the viscosity of an oil is by measuring it, and then allowin might in one stroke for .ffect it. *14 - 11 variables that 1 - ; I i -- 1 __-_--_I_-_ i _ -- - - r - -- ·----- ·- ---- · ---- `- I `- '--'~---- '- ;~~~ ! - Llr- I i -"`-'-- ----7-F. .,,.. ., i ,i -- - . - -- . -- ---- t - -- 1- -c---L -- - i L i l_ i___ I _ ' ---* . : i f· 4.- - ----- cl-.--.,. 07 Ii ; .-.-- - ._. ; - _I'> * ! . I. . .. I - _ ;, I 1 t_77 i H99llia I - i _ _ . | AT i i r-.---;-- , . __ _I · si-- · i ____ y ^ Y1 ,. 1 10 .! i i ,~ --LI U ::= ·-- -· I' CI - - j' L a . _ i -. t- · LL-PNf ls=r .- I - j . I i L- · i " -------- t ------ i ------I------i-·----;----_i_..__i__ a _ i . o'xC i 7?! - I I /fa -- l i r ___ __- - - : i I - __ , _ -- IC---- - - - - _. _=_ _, - - _ ~/' 7-T ------ -r --_ Z i /-I -t w I ! f IF-W, ._..--_ I 1,S*, - c 1 I _c__c_ ,I f - ' -- -------- .-.-xi.- i.l--.i -i .- L--i i - f __, i----------ILrrJ I-----c--------· i --- i----C---- ; -- ·----- 1 cd;rra ;Itcy ct, ------------ I , i .Î,___ 1·------:I i 'A 0 :-----i __ _ __ , t , 1~~~~~~~~~ I - - i . i I .. _ J ._ I/ /' lw7r _, i i . , j L-c------i 1`1 _ i: eli/"IrTIO-WLPotI~i,~C. , i I' __.1-_ ; ~!k ,- ' ! i...i_ ,._ * _ + -".4, ,; .... 1 13----C-I! ', -L i c rd r- Z Z -L d__~ I _w %n 4 * IL .I-·i------ __ i,-------- __ b , - o--t--- , w _- _' I| __ _ I CI I T r - Ts - I Ii t -r! L t .____i------ | I e !-Ii *, _ _ _- - Z- i · ---*--- --- ; _ _ _ i 1 I i xc----- Il i. i. _ 0g2J3 /, oi ,. 1r i ,,- .~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ - · __ i i i -- ', j - i i . ,, ~~~~~~_ i C 1 I ,i iI ;_:/,. r ; z7>in . · . I I, ; '. f , ..... ,? I ' I ____ - _l i~~~~~~~~~~~~~~~~ I i~~~~~~~~ ti -- 'i LI_ !~-.. -,~ ' - e r---+--i -------- I_ 11111`11171 ____1 i I : : -'7 ;_, V _ _ -j i. I ' -- r- - I I r" i ! i' -- t-- -I.I_. l r iI i _ ! LJi r--- --- t--- --- r----i-i I I I i t· : i .i ·--------,.---- X . Le · ·- t--l -.- ..L--..-I I Ii t-- i F-TorL i ....i _ Y14~~~~~~~~~~~~~~~~ ' I I i ~~~~~~~~~~~~~~~~~~~~~~~~ I i~~ .e i ' I dB4iI I i i I i -1 I i ----- CORI. I i i 1 --s I-: r r i I I 1 - ,--i 4 i I i t i i-fi i ·+- --- i c----- _1. 1 oQ F I·: 1 1 V' r iui t I r i ----------------- t---- -II. 9. --. . -~; + * . X -- T-j--f --t------------ -------;--· · -· -i i il , i 1 I 1 I 1 . ~ ~ - 40 '0,& _ _ 1I 77 _ _ _7 --, __ w i i · f I , ' I -i-1 ti !rp~7rr II ~~~~~~~~~ l - t - ' __ f * - Ti i - __ ,_ 4 -i · !----.-i W- , __ T- . i ___ ---- l , -i I L i I I - -t - -i S --tI---! I -- L ir ' ----- - - ---- - L 1_ t i i ,- - _- L i i i I. 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'~1 f i '~ " '~-:.....> i· HP 60o A0 60 0A? . k$/a'er The Average Fuel Cil (A) Ultimate Analysis In design of the most useful nd widely applicable small oil- fired heating boiler it is, of course, desirable to base the prediction of combustion and heat transfer characteristics on the chemical properties of an average fuel oil available for such purpose, Canvass of much data has established that regardless of source, appearance, or physical characteristics, good fuel oils have ultimate analyses that fall within the following limits: I: Limits, Per Cent Substance Av. Per Cent Carbon 85 to 87% 85% Hydrogen 11 to 14% 12.5% 0.5 ;o 2% 1.25% Nitrogen 0.5 to 2% 1.25% Sulphur 0 to 1% 0.05% Oxygen - Therefore, for the sake of uniformity in computation to be 4· carried out in the text and in order to give a representative practical picture with the limitations involved, a fuel oil will be assumed having the following ultimate analyses: Substance . Per Cent Carbon (C) 85% Hydrogen (H2) 12.5% -1/- Oxygen(02) l.o% Nitrogen (N2 ) 1.0% Sulphur (s) 0.5% (B) Higher Heating Value The higher heating value o the hypothetical average fuel oil selected above can be determined with a fir degree of accuracy (+ or- %) by means of a formula developed by W.Inchley (See:"The Engineer", Vol. III, p. 155). This formula may be written as follows: + 608.90 H Q = 15.000 Where: Q = Higher heating value, Btu./lb. C = Per cent of carbon in given oil. H = Per cent of hydrogen in given oil. Since, 0 = 85% and H = 12.5%; then, for the chosen typical fuel oil, Q =(155.00x85) + (608.90x12.5) = 19,100 Btu./lb. (C) Density From Fig. o. 2 it is seen that an oil with a higher heating value of 19,100 Btu./lb. has a specific gravity of 0.92; hence, this value of specific gravity is assigned to the above chosen hypothetical fuel oil. -/6- Selection Of Air Composition And Air Density For Use In :i Illustrative Problems On Oil Combustion And Heat Transfer (A) Temperature and Humidity For the purpose of predicting the nature of combustion and heat transfer, it will be sufficient for all practical purposes to assume a temperature of 700 F. and relative humidity of 20% for air surrounding the boiler and entering the combustion chamber. The selected temperature of 70 F. is satisfactory from the comlort and utility points of view, and also represents the condition corresponding to the maximum desirable heat loss from the boiler to the space where it is located. If the temperature in the space where the boiler is located rises above 700 F, there being no other source of heat except the boiler casing surface and the piping, it indicates definitei ly that the boiler does not have sufficient insulation. (Today, however, practically all modern boilers come with a thick layer of high grade insulation, and in most cases it is necessary to install direct heating surface in the basement where the boiler is located, so as to maintain a temperature of 700 F.) As far as the assumed relative humidity of 20% is concerned, it represents a higher value than is usually found in most heated but unconditioned spaces during winter months. The usual value of relative humidity is about 10 to 15%, and sometimes less than 5%. This low relative humidity is of course due to.heating outside air from about 00 F.(dry bulb) to say 700 F.(dry bulb). Thus, the 201o relative humidity is a safe figure to use in estimation of heat losses from a small -/17- boiler due to moisture in the ir used for combustion. Besides, at 70°F.(dry bulb) pound of air crries with it only nd 20% relative humidity one bout 0.0050 lbs. of vwater vapor; therefore, for all practical purposes at or near the standard atmoscheric conditions the effect of moisture in the air on the overall efficiency of a heating boiler is negligible. (B) Chemical Composition Chemically -an average sample of dry atmospheric air has the following composition: Substance Per Cent By Volume Oxygen(02) 20.90 % Nitrogen(N2 ) 78.165 Argon 0.90 6 nd other inert gses Carbon Dioxide (CO2 ) 0.04 ?0 For estimation ?nd clculation of combustion and heat transfer, however, dry air can be assumed to have the following approximate composition: Oxygen 20.9% (By volume) Nitrogen 79.1% (By volume) Oxygen 235 (By weight) Nitrogen 77% (y or, weight) -/o- ! (C) Density and Specific Volume Density of dry air at temperature of 700 F. nd barometric pressure of 29.92 inches mercury is 0.07495 lb./cu.ft. Hence the specific volume is equal to 1/0.07495 = 13.34 cu.ft./lb. At temperature of 700 F., 20% relative humidity, and 29.92 inches barometric pressure the specific volume of air is 13.4 cu.ft./lb. which is pproximately 0.45 of one per cent greater than that of dry air. Therefore, it is obvious that in all practical considerations the volume of a given weight of air at above conditions may be regarded as constant for relative humidity variations from 0 and 20 per cent. Average Molecular Weight Of Air And Of The Products 0f Combustion A mixture of gases strictly speaking cannot hve a true ole- cular weight. For ease and simplicity of calculations, however, air and the products of combustion can be assumed to have annapparent ' molecular weight. The general rule for obtaining the apparent molecular weight of a gaseous mixture is as follows: multiply the volume fraction of each gas in the mixture by its molecular weight; add all of these products, and the sum is the average molecular weight. Illustration Taking air to consist as was assumed above of 20.9% oxygen and 79.1% nitrogen by volume; then in one mol-volume of -/9- ir: "Yeightof Oxygen Weight of Nitrogen( (02) ) Weight of one mol of air = 0.209 X 32 = = 0.791 X 28 = = 6.69 lb. 22.15 lb. 28.84 lb. Therefore, average molecular weight of air is equal to 28.84. (Actual value based on accurate chemical composition is 28.97. The result of the example given above does not agree with the true value because the greater molecular weights of argon, carbon dioxide,and other inert gases have been neglected.) For all practical purposes, the value, 29.0, is sufficiently accurate for combustion and heat transfer calculations. In the sme I. obtain the manner, as shown above for air.,it is possible to pperent molecular weight of the products of combustion. Pressure-7olume-Weight Relationship of The Products Of Combustion When the molecular weight of a gas or a mixture of gases is known, its pressure-volume- weight relationship is given, of course, by the Universal Gas Equation which is usually written as follows: P V = (W/m)154 4 T 'here: P = Total pressure to which the gns is subjected, lbs./sq.ft. V = Volume, cu.ft. My= eight o given gas occupying volume(V), lbs. m = molecular weight of given gas, or an pparent molecular weight of a. mixture of gases. T = Absolute temperpture,°F. This equation is suitable for rapid clculation of the volume of products of combustion once their molecular weight is given as on Fig.No./6 ttached here.(The construction nd use of Fig.No./6 re explained elsewhere below). I Quantity Of Air Required For Combustion Of Fuel Oils The quantity of air required to bring about complete combustion of a fuel oil depends on two factors, nmely: (a) The chemical composition of the given fuel oil, in so far as it requires a definite minimum amount of oxygen to oxidize the combustible elements within the fuel, and (b) The design of the combustion chamber since it ffects the ease with which the oxygen molecules may come in contact with the fuel oil molecules, and the rapidity with which they may combine. (A) Theoretical Air Requirement Given sufficient time in proper surroundings, of any given uel oil would require a definite quantity of air to bring about its complete combustion. nis quantity of îr is known as the "theoretical air requirement", and o the nature fixed quantity course depends entirely on nd quantity of oxidizable substances present in the fuel oil. Fig.No.6 resents the old attached here nd well established data on theoretical -ir requirement for combustion of any fuel oil of known ultimate anelysis. The quantities tabulpted on selected Fig.No.6 were nd arranged so as to simplifr the combustion calculations and i -2/ reduce the routine work to the minimum. Its use is, of course, selfevident. (B) Actual Air Requirement As the combustion of fixed uantity of fuel oil with a theoretically correct quantity of air proceeds to a completion, the concentration of oil particles nd air molecules in their concentration the rapidity o a11llsoff, and with reduction combustion reaction also di- minishesr.Thun, since under conditions encountered in actual combustion of fuel oil the time allowed for combustion is limited, the remnants of unburned oil fuel nd unused air may be expelled from the boiler with consequent loss of potential heat energy that their union would represent. To avoid this loss, advantage is tken of what is knovwn in chemistry as the "Loaw of Mlass Action", and more air is supplied in the combustion space than is theoretically necessary; thus increasing the concentration of oxygen at the end o the combustion process and thereby insuring that thlefuel oil molecules and oxygen molecules will collide and combine in the allotted time. The actual air requirement for complete combustion of fuel oil, in what is considered today as well designed heating boilers, is from 25 to 75 per cent greater than the theoretical requirement. The principal factors which determine thleamounts of excess air needed to secure complete combustion are: (a) Degree of oil atomization in the combustion chamber. As a rule, the more complete the atormizationtle less excess air is required. (b) Degree of flume turbulence. The greater the flame turbulence, -2 2- the more intimate is, o course, the intermingling of oil particles and oxygen molecules; therefore, the greater the flame turbulence, the less is the need of excess air. (c) Temperature o the flames. Everything else being equal, less excess air is required to obtain complete combustion when the flames re hot than when they are comparatively cold. (d) Volume of the combustion chamber. Everything else being equal, up to a certain limit, an increase in volume of combustion space results in more complete combustion. Products Of Combustion Resulting From Burning Of A Fuel Oil In Presence Of Atmospheric Air Composition of the ideal products of combustion resulting from burning of a given fuel oil with the minimum theoretical quantity of air is easily determined if the ultimate analysis of the uel oil is known. Fig.No.6 attached here gives the weight and volume of the products of combustion resulting from burnin of individual oxidizable elements of which a greater part of any fuel oil consists. eiglt-Volume-and-"omposition Of Products Of Combustion Resulting From Burning Of The Hypothetical Average Fuel Oil Below are described several charts which present in a graphical manner the story of combustion, and do away with much tedious computation prerequisite to analysis of the combustion and heat transfer "'- t -I- 1.. CII-· N · a/'-7_/ ' .2 '-so9 .,d .n/ %) IQ N /o&' + t¾ pY) zoI K lll= 2 _.~'.7 ? t,'o, j77 N N -1 +. k .7/ ,4.4' j 2 ;71,L IN zZ' ~rze ??/ e9 z 0; m eq oN N N "N I¾ A -Z 7'C 1\ N ~5 -rod N "2(.K)0 I' uN Ila) Ud/r~,,, ;t '~"/- i"7 r-7/ 2.. o, ,ts N. N N Y) q6 N )O QS N N N N 9 tt; Nb \It, eq N ~ZZ 1%) NII -7 'o.i , 1~Q (i , TN 11 N u~ e1) lS4 IN rf) I,-;~e~ 141, $ kj N 06~ N % ZZ3 I:Zr 111 ~r) 1· N N N II 1\ eq lk '5 1u CdI) I ' -IFIt" Z/p,/YZ 9 I II I' k 1 o '-I r5 '1 N 0r *I( -N azz Z: :s fp, CV I-- IN tO qV \t I-b \tV N1 x tr\ 11 ' % III (4 ..ed ~a. 'o .4". 7-~~~~~~- %n N, % '1 il -5- IV ',N \rj (3) II \tc (.·) "Itl N (') - ,-Z, ·~ 7~3/~'~' \o processes. Lased on the 'hypothetical verage fuel oil selected above, which was assumed to have the following properties: (A) Ultiiete Analysis Substance Per Cent Carbon 85 Hydrogen 12.5 % Oxygen 1.0 % Nitrogen 1.0 % Sulphur 0.5 % (B) Higher heating vlue of 19,100 Btu./lb. (C) Specific gravity of 0.92 And tking combustion the representative ir to be supplied for maintenance of s having the following properties: (A) Dry bulb temperature, 700 F. (B) Relative humidity, 20% (C) Density , 0.0746 lb./cu.ft. (D) Specific volume, 13.4 cu.ft./lb. The resulting products of combustion re esily determined if complete combustion of all oxidizable components of the fuel oil is assumed. Thus, Fig.No. 7 attached here ives the total weizht of the products of combustion resulting from the union of one pound of the -2 4 - --- - --L-' .--. A.-.II--'. ---· r-' . .... ! i 1I -*--_ - _ _ : . - " i ' .- ___e L ____ i _I , ! ' .6 - i o6 _ 1_ i ~_- ; X-- C - r. ~II11~IY I L. Ys- _ r . _ L-4 W · !i _ i i _. -- _ _ l i i O -- - , ; I - - '~ " ... s .. _ . _s_ __ i-- j - kze I ··-.-- ····-,..LIc - ,,, ,, ,...i -- -- _ --·- - -- ---- _ -T-e,--e... I I e~u, L_Î·-·-··-= ,L·_ ''*' _ #FW--. 1Ii . he - i i - - A- t i_-- =..; ~ ~ i '/ ~ _ i I. LA I C · i I i .. .1. _ Ii i I j 4-_... --j_ ...... --- t-F ........... //M '..._' _. S ---!-I- -- · c-4-----·~~~~----i -- H ! ~ i i · 1/ zX~~~~~~~~~~~a~~~x~~w~~k ~ i I _L - -a -- S-- i I___ i r -- ; LL_-·_·t-_ -·i- - ~ ~ - i I j,. ' .~ ,.._c___,/_._.._.: I · - L i i i. t II i .''-'.- .... _. -L -- .i i .1~~~~~~1 ........ i-.-4 I ~--I _ ,i 1---- I -- !........ __....... __ ___.... __,................. .._ __ ............... ---- - - 1--- -r 7--- -< . i._i t-go L C ft I : r-- -- I V-·· i ; I - - __ .... T ·--··-··--· --i-- --- ...... I --------- - , ___ ^ | ; I ---- e i -. i_.......... . ^ s o f'i'I '"'/.f; - Y~ ~t,* L,~2/ & -P t-- ' iI '1, I............ .._..? . __._ ... . . . ._ ,. iZrK iNZr- ei~x ' 0 _ '4. s..: : L I i_ _ __ _ _ ] I !- 4i~vA v. A Y._7 -f I I L _ I _ _- ,,- r--- -- - I] Ace - ,1 ·-- - .. ZD - I iazr -- - . ,,,# i I 1l ..... .. .- w.- I .L Z7 t - ......... 32 2?9 ..- ' - T --- " -- AAo-,/ I . I _ _ __ ! CA II. t __ _ lL;- I ! i--- ~ , M ¼'/Y --I today - i s a ; i ~ : , I_ __~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ _ _ __ j ceaL- i · _ _ ,, i i _w _ _ l CI - 7.-- -. '|i .~~~~~ ~~ . ~ _ ._i_-- + _ M ·----·- --- -· Z5 ------------C- -1-- '-i- L: ...... ...., .... . ...... ....... . !i , 1."-.......--..... 'r-. · L-~l-~ -- i !- j j I - . i ~......-...... _-, . · · ' - --: - · , i ---- , :i: .I. 2%h i %.q ",4 , 4 · ~-- "'- - t,% - r----t-' 1' ,p~i I~~~~~~~~~~~~~ ~~~~~~~-"',,'-~··--·- ] , - , -, - - ---, I-' -- ---- ---s- , ; t ^z _ ('$ij _a_i - j '--~·- . , , I' -~ .... s- "I, .~-4 . , -------t--.-= ---------.---- _---~ ----. - 1 !4~ - --- i '--- T - --l''':-' -'··---'-'--f-'----'--', -_ _ _ ..... 4... TL i C ,. 7....... , I ._ H----t A·i-ii' I ~............. 1!..,._.. i5 iv - .3 + i C t-- *..........----- 9 /- ._- i 1 ----. 6- ,% Ico i i t-----·--..I.. ~. 0 /vJ - -- Ik - X _i ;!' i i j . ' i i . 4~~Ae~~' : _ - . . . --.-----.----_ _ . . -- O ·;--- 30 _ _ 4' : : 40: . . 606 .~~~~~~~~~~~~ 7O1 rS)4 "··· i--i··t-- d4*._ .. i. -- --.-------- ----- F-- -·--i/p above selected fuel oil with various quantities of air from the theoretical requirement to excess of 100 per cent. It also gives the weights of the several constituents o the products of combustion. For further simplification of computation procedure, Fig.No.8 presents 7, the composition of the products of combustion given in Fig.No. as weight percentage of total gases involved. Fig.No. 9 lso gives the volune of total products of combustion and that of its individual componentsat 30000F.(Absolute). 7 ~ ---- r i I I I .- !I . /00 90 80 . i !--- 1. , ... f, . i " · : ' .l I-----t- L____.-_ l- i I " I : ii- i i I'. _I ;3LnL)sj i .E I __L _ 11 .12 S 14.4 i -- .--- I I - i t -~- 77 I ., sE iI /'; !;d { I'l- I-C U __ .4U _ 'r / . 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I t ·· !:.1 t',Y A14X _----L----f I I _ I _, <- · · i -- - ,4-- Z .WP i i /tr , i i t----- i 'w , - -i - l . i,> ti--- - _ - - 1-:- Z,~ 1 Iov M _~~~~~~~~~~~~~~~~~~~~~ Gz>>io TE ow i 'r --.",V, ^-- t--X- ; St ' ,~~~' L,, , - -__ I I I t-- -1i _, I------- 1 - · Z_-l' ' , i I 7- --- - . '- ' 'i I . I i .. .I _ ,.42 i I i 7-- _ _ i I I I ... t 'r--T-- Ii ,. . 1'' . I j I , ' I i . I 60 50 d0 1 I ,?IO _ _0 s . I -*- I 7---ri----l_ 7117 I - r :J __t i I --- 20 /O L_ 0 , ~fo,,z Per C~n~i~ Oh - - I -::-- II ,L :·:"' ."71" . 1 -1. p i I 1. 'I · ·-- r·--'- :-r- 7-e 7 !'- :y:: I t- Ii }. I' i. ,I !.I ! I I A -- ---y6L ' II . i- i I ·-·- i · I 1- r . . __- -7- I I ---F--- i·, ... I : ,T ! t i I- 1I' i ·-· -._ I ' -XI :i . 11 -- l-·f-( · i-L- 7 I, I .i. Ie --- I , . I I I · .- ·i-l ·· '-I-' ' -- C · i _r - t I .II I ... -- --- !' !' 1: I .: 11 _Z iv I17'- : _ . t- - r ii; i - 7 -- I· L r·- -I 1 clt`- _ i . I ;... "' r · . L-· .1. I -C r - ---- fI 0- 1- z t-, , I I-Tt- /t I · t.-1.:- Ar _TU. · t-' i I t I I, ·- ·- · : · ' t· r 1" ' i' - -· -·· ·-- .- ·i i- kf~ i ·i r. r 'Ilk 1 ,·· .. - · ·I I-e---- f rr· 6fl k1 4.r AL rL d I · I-·--i-·- ' ' i 1 -C ?.' i' ·-- -i·- 7, -d! i a pi,~ A L~ba_ 77- Ic !-. oclr mrw v yr - r c· de 9, 3 · v 4 6 j_ -rr 1 ... i: 9.17 4c Q1 _B I 0"-'- "4 / 7 - -- f--"e Aa 7/0 Fhii ri2 :% i Iz i · I- .ri i' '' I' Ns I :. L iri: : ·· -· I I: Z ti`n i· · L1 i 7 ·I i -- "li i6 -L,h i71. 22P1 o 1-4 7 -· ;---l-L 401 ·- · -···- L1S1, ·--r; :.i ·· i :----i- I ;-··-l.·r··-I· ;-·- -- r a · 4 1 Co t CiF- :· I I~~ _X-I i I ''' .. I 3 t-CC L-'- t r ""I :-I-·- i _'' i ;· · ' .i-r-l ·---- 1-' - PrA · 1-r- I I A i. i .. ---i ii· ·- · ··- ·- . i.-: i ·-· --i:--1-- iLI 4iL~ "tl:L: ·-·r ·- .- 1 ... i-"l I t ,....... r c·.,-r· -- i -·- Zt-4 ·-, ·1 r -.·)· ·-· · ·--t-·- - 2ZlC ' 5 r ,· .. ;.I -- - i =I . -- --t--- ;' -L-I-- -I 1 I :1 1 Y - l i I - --- .. _.....__..._ -I I- · I /o I I I I 20 I .· . I I I - i I I _-,I II . II 1 7o40 ~c .-I. IIL I ' i' , i: l _I -Z..'i - 'l· o .I _..v. -,e cc·' I.,:. 4.- ___ I 60 __ rJr, llrz Y I I I el AO LY __ PUW I- Itl 70o -o reeove 7"ff-xess·A I ·i · · .,... :l.4t· _I 1. ir -- · : · - i:11 '' ;"' r b.A -Ilt-- -;-1---·" ' ---1-- f. irA i ·- -r- · ....- -·-: : · t ;· rr · . .. :' L · =i M_I1 ·-· ·1(' -1 ·: F!-~ ·-. 7, = _ !I I' I1E;I I 1.47ilwi r I 9o Ir I I I /610 CHAi.PTER III DETEIVIINATIOI OF FLAMeE TElPERTURE IT CODIBUSTIC OIL BUR1ITNGBOILE l:'' ., . ' , · 42' 6 '1 ,_,:'... CHME R OF AN DETE1.RII'ATICOOF FLAME TE,PERATURE I OIL COMElSTION CI3BE OF AN URNIt"G BOILER An important feature of oil burning which must be recognized in order to facilitate determination of flame temperature, is that there are two limiting types of combustion, namely: (A) The instantaneous combustion which oririn.tes and is completed at the point of fuel admission into the coiiustion chamber, and (B) The gradual and uniform combustion during which the whole combustion chamber is filled with a homogeneous mass of flame at uniform temperature. neither of these two types of combustion, of course, exists to the exclusion of the other under actual conditions; however, both are fairly accurate theoretical cal- sufficiently to permit approxinted culation of flame temperature. For either of these two limiting types of combustion or for an actual case lying between the limiting boundaries, the principal factors which govern the temperature of flames are as follows: (1) The higher heating vlue (2) The .amount of excess of the fuel oil. ir reauired to obtain complete combustion of all oxidizable elements in the uel. (3) Mean specific heats of the products of combustion. (4) Radiant and convection heat loss from the flames to the walls of the combustion chamber and water-backed surfaces. () Dissociation of the products of combustion at the flame temperature. (6) Latent heat of vporization of the particular fuel oil. v~.& '' L , matzo_~~~~~~~~~-g"' (7) The temperature at which the fuel oil is supplied to tile burner. (8) The temperature at which the primary and secondary air are supplied to the combustion chamber. Of the above enumerated as.ctorsthe first two have by far the greatest effect on the flame temperature, and with any given fuel oil the amount o excess air supplied to the combustion chamber is the principal factor controlling the.flame temperature. Procedure For Calculation Of Theoretical Flame Temperature (1) The effect of higher heating value of a fuel oil on flame temperature is self evident and does not require any explanation. Higher heating values of fuel oils are determined very closely by means of the following ormula developed by %¥.Inchley (See: "The Engineer", Vol. III, p. 155). Q = 15.00 C + 608.90 H Whe re: Q = Higher heating value, Btu./lb. C = Per cent of carbon in given oil. H = Per cent of hydrogen in given oil. (2) The effect of various amounts of excess air on flame temperature is shown clearly by the curves on Fig.No./t. (5) The mean specific heats of the principal constituents of the roducts of combustion are given on Figs. Nos.0O and /. All that one has to do to obtain gas between any two temperatures is o -28- the mean secific heat of a dd the temperatures in question, I I.--" :... t L:'"t":::t.'' .. ::': .: '" !''.---:"..-.. ,.. : ~ " I::.-..-!' '_ .'..' . i.T;j--. ~ 1-' ' .... ~ ... ,i .. ': . .. ' ' ' .i Ix .. . , ;':-i' ,-.:...-.I .!::*'' I 1'-..:'-'':-: '','::.-J'..1 t ''..I: ..-.. ... .;. :.Zi __ _l'- - 1 1': - - 1- - 1 - i -- !. ·...· ::--f-- .. ' 1I ' . ·i .':i - : I -, .~":. .. . 'o4-' - . i .... ~' '' .. ..... : '...'i::-,, j|I-: ''-----t -. - !..i-i---I:; i:, : t: :': ... ,:' ...... ...., :-] i..,~, , . "~ ~ I ....... '.........-~ -, ..: :. - :i ... - ...... t. · t .~. I ~' _ L·i- ' V 7-.:i7 ; -' . ....... : t T . : -' --;'- i - iA 1 ! '.' -- '" 'h :1t: Z-' i .. . : t':: :.:': .-. ~... .,.......... '...-I . n,: _ X I 's ' i ' :t_.' ':] 1 ii C~.:'.'.-. :_... i 1 ' j N T__1_ - , N .... . 1... . . II...... .......... !:........ [ :_ - KI 1:"t -- : i :... .- . 1. - :: I K t .,....-~--, ---,-. ,', -. i -;. 'i .... .. Y; T~ =i....:; .g i s ,} ... ' 1 i. ...... .!-, :.',.... I.-~".:'_ -_-l';:': ~ .'19 : ,! -, .' I:. \:. 1 -'':'\.' -. ' ' -i," . .1-J .:. ...... l ..:.~ ti...... ,.... .l tl! :0 gt.-1N: . il 1:' ............. .....,... .N i.. . : Ii -1\ : : .. I ....... .~=.:0..... _ _:-_-':~. -Kt7jlj il-·~~ ~ ~ ~ ~ ~ ~ ~ ~~~~~~~~ ::I,:, :;: ...::,· : :" i:! ,.""' i~:~ ::~ ~ ~ ~ ' : ~~-~ ,..~'::~i-'·-"~'-.~ -·-· ' ..r:-:.:.I... ?..... ::"'; :- :::~~: :::~ :. -/ : : ~-: ~ .,F !~~~:._\ ::M - ~ .';.-,-"t :::::::,::. ::~~~ .::-:-·-·-i':: :-4 . -,~ -: ,'' ~ 9o [ ... ~~~:.. i.. ~ .' ~ - .:-- .. 'I::;~,~..... N~ ,-- :·: ~:l .Ij !: ; :~~~~~~~~ ;·" t~~~~~ · ., ' ·· .i .. :~-,i,x' i I~~~~~ , I~~1- .t · ~ i--··t~c· ~ ~ ~ ...... ....... ~.. :,: -::: :~.t\f :-,: ~ :-~:;:; ' · 1' !- :l\:f-- 1I,! · , , .. ,, '" ~ ~ ~~~~~~~~~ '%' :... ,_.· .. ,. : ·· /::,~ ,... ! ~ ~ ~i 1~~ i. :·I- ' - :l-· . i! ., I· . .. t~: :1::: i ~"" · I~~~~ '!ii i~~~~~~~~~~~~~~~~~~~~~~~~~ :·~~~~~~~~~~: i~~~~~~~~~~ U r . l -·· . , , ', , ', -~,.... '~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~I7 'q . . i ! iCL-- 7 ! i I ,~- I . Iij I _ . i 'I 4. I-g_ i E Zp I~ bu I II i I-i K . i i I .. i- 7 I --- T-· 4a -N -- 1 I '-' .-if r. 14 it, tl .i -.-s 7Y . I . "f F.- ' t r . 17 f 34 i ...I -7- i1-: -- i -- --- I r . .. t--l'- :1I .. t ' .. -I- I -- I :. !T1' 4 ,.j I.: !. '%I ' 1, ., ix i\ - -1 1. --- .. . ) 2.. ...... i. .N I I '---1 l'-i I' 'I i. - i . I: L I . ., - I -I! 1-...i --. . i L . .I . , I I; 1 t .. tI t II.- t t1 i --- .1i c--- -- · cl -71 - I (,;. · i .· L. - I' , i.. -, --- 1:1 ;-I~C 1 ' Ii- ' .. . . . 'Ii -· -i-,_.; I-L-- 1 I,% I Ir 'I l-.i U e-- -·--- , :- tla . . i -1- 1 ' Ii I .I.. ' l '' ' I ' -- . [.,. I- I!1 . II. ----. . i i--- ,--- . i -- -Ii''- ''.. I '+L~~~ I - i, 15 .. , L *---i -I -----' I i. . I 241 -1 I' Ii- s . . 'i'' i 1 -- ' -- I --i * ----, --- .j Ll~ ' bI - ; 14 1. L. -' -F-- v I. 13Q t II !j -"-----' 4 I K- i ---- i r l : I. 1--- 1- , -- ---- 1 -,N 1\!' TI I1 i I! "Jj i' "i 1` Li i- -PI- I L] :% IXI .~ I I.,. I~ 9 t I : i !v -I: ,· I ! I ~ i i . I -Ce --- J j lb . .j- I j.:! II -!- ! ' - I 'I. L1-1 1~~~~~~~ ,t I d ;! I -- I. I , p, i . I I i I ._ --I ,A: i, 0---. i . 1. ;v W 1- . , 7- r -i : I ,,t '! T · i i1 -r>! i 1> 1- w~~~~~~~~~~~~~~~~~~~~~~~ L(i - -ILl L i I I' ' I ! : I i __ I_ __ I of srecific heat and read t;e -a:proximatevilue addinz The correctmean secific e,t is obtained and // of Figs.Nos./O to or subtractinc from the a proximate (t, + tb), * on the main ordinates by value corresponding to correctioncorresponding to (ta - tb) as shown on auxiliary ordinates of the same figures.For ex-ample,the mean specific heat of water vapor between 14500 F. and 31000 F. is = equal to 0.6410 + 0.0055 0.6465 Btu./(lb.)(°F.). From Figs.Tos./0 and/ /, Fi.iNo./ was constructed .hich th e mean specific heat of the products of combustion resulting gives from combustion of the hlypothetical average fuel oil with various amounts of excess air. The use of Fig.No./2 is self'explanatory. (4) The effectof radiant nd convection flames on flame heat transfer can be determined only after temperature from the clculation of the theoretical flame temperature. The procedure for determination of influence of heat transfer from flames on their verage effective te:perature depends on the limiting form of combustion pproached by the actual flames. (A) If the combustion is instantaneous rctically nd complete at the point of entry into the combustion chanmber,temperature of flames attnined at that point is equal to the"theoretical flame temperatlure". As the roducts of combustion roceed from the entrance to the exit of the combustion chamber, their temperature flls they continuously 'ns lose heat to the furnace walls. The c.lculation of average effective flame temperature is simple -nd strigchtforward in this case, because the initial of heat flame tempuerature is 'knownwithoutany calculation loss combustion. during Tlle teoretical flame terperature is calculated, and the temperature of gases leavincgthe combustion space is -2 9- ssumed; I I i- I I i 1 . r- l , .. ii . I . I i . ll._ . i i I F -- i I. t- q. k I aU6 ! I' i ·, I I L,J I ,IN J. t_ 1\1 I I I Ik 1-iw -30 -. :- - · I-I I .... ·. . . E- . . . . V l !r u t %J W" .z9- :·: · I . t- -- : i A' A. I r II '' - r L- I. N 1" ci 93 r- I _ M\ \\ '1! ..... 1.t H . ., .. ,K ..... ' ' .i.. i _r .. . - - .1 I . ' IY -e ' ' I .-1 -- _- - t ZS - L\, '· - - . .Ii f i s L. .:\\ . - f .. .. ,I Iq --- F-c II -1 r . ·;i ' 1 I: r I i i I - -- -=L -- i i--JI-;-l -- -- ._tZ I... i --- l-i -I ! · -- _ _- l I _ ! . _ _ _ . - - l _·i_ . · · ______·__ . _ .- .r . . i -rm ,I c1 CO- . - I1 . r. I .... I .... %r ' I . , ; I -1 m.... r1 .* t 4 00 ! t(' lj---- .. *' k I . I - - - t---d ii F.f i~- -I- i -- - .T -· ---- e--- - - : WY 17 : s -8f ___ - _ :: 4:! ----- . I Ad - . -- 1 _ I-tl_ _ I -t .. . I *!. tn 1-7- .= SZ'9C- 1._ I t 7 441P- . , 1 j·- i - . . ' ' ' . .1 I i .a_ - . i -1- - I _ - i ..... E 1 a,. .. II F ' '-t' , i : t · ., . . - ; · , .. .. 1 . : . i1 I -- r I . . ! ' ' .... ... r i t f .'' --- * _1_ - - I --L-l' i iJ I' i_ J -.. I ,... . M. [ .. . - I I ... ·- · · · __ 1 r I ts ¢ I t .'.-19 --- i F | ,Q --c- U 4- s * .i, El ---- I.. 13 k b.1;-s iI ' I ..... t' - -- 1 ..I. f '-I . ilr-l i t I r-~ i--i--i :.,; k _1 . * -- . r j ... .I . ., . .. · I. i- i -·--------I I I . -l t'::.N S4 4: 8 '*.; . _ . .ft J :· 3 - 1% . _ 16.. -1 - Ii ., I i IL I. . ... ... ' ' 1- . t s5 1:-': rlz i . : . .... . ;.-- t-1 . .- . L. 14i I. !\t,\\-\ ;-lj . ! I t \ LAk \ . l iCS- -i -1 N,tI . Ty . I' . t ii 'I I Xo &- a ._ I : r: 1B :. II~ Is - l W i t r--- L- . La 1. -- --i L I 11lIL . cli ... I!iiI N i1. 'i i a, , ii 0 i i I 4j rr II L1 I . I:- tt l .I r~~~~~~~~~~~~~~ i i L- c- 'i Ltim l L- I i I ' I ' i I I i . - --- i I II.. -- i.1- i·· f: L C - - '_ (· 1r il . i I I tI __ !I -I ! = then the heat g-ivenup by flames is obtained (I) by a simple heat balance on the ,roducts of combustion cooling from the theoretical flame temperature to thetenmperature at tle e.-it space, nd (II) by means of a heat-transfer average effectiveflame te-merature. If determined gases in (I) and (II) re ecual, rom the combustion equation involving the eat looses from flames as then the assuxed leaving the combustion chamber and the temperature of verag:e effective flamne temeraeur+e are correct. (B) If te combustion is co-npratively slow, and due to turbulence the flemes filling the same teimerature he combustion chamber are at practically t a11 oints in the chamber; tl-len the actual flame temperature must be determined by a simultaneous calculation of heat innut due to combustion of the combustion case, the cham-ber from the verage effective nd of fuel oil, lames te3i:perture heat during loss to the walls combustion. of the flames In this nd the temperature of the productsof combustionleving the chamber are the same, since the chamber is ssumed to be filled wJithl homogeneous mass of flime. (5) Th'e effect of dissociation of te on flame temirerature is negligible products of combustion t . te..erture below 2500 0 F.; at temperatures above 2500CF., however, crbon dioxide mand water vapor in the products of combustion undergo -rpprecibl e dissociation, ccnsiderable nd cauce lowering- of flame temperature. ?ig.i1o. /3 ives the extent of dissociation of crbon dioxide between temp.eraturesof 2000 to 4'OC DO to 13 itClosr-'eire; while va.ror between tzmperatures ., /4 gives ig.'o. of t Crti 1 Oressure dissociatior data.for wvter 3000 to 4;COO°F., at parti! -3o- romi.05 Pressure __I : I __________ ______ -I j i l ti ' - l I--I- T- X II 1 I I : i - ... I } · i'!- i . _ i II- I_. - I -- _ Y r 1f i 5n C 7O3 4A L -~L- l_ j !I ·----- _ il VL _ "I ', il"1 l 6 r [ /J3 t f-rr r ! I' - .. .- 4 _ _ . t-S- r- I - -C 21 f r 'Id. cl; *,'e 1,2 _ ! -I. . - r r-- ot ci-----I-- Ar s >>r^~~~~~AO I I zJI-I~~~~~~~~~~~ f i f r jCk -,{ . ¢45°.~1 i "I --- Irf .- I _i I c"-L - i IE }/ K"Jr-aw rv4 p-;S ''' iS; .~i~rL~/ . -L--cccccccccccccccccc -l--,.4L- ' ; 0tlC I t Ie .i---- i i I I c-- t I ___ I '-FL- t --- t= 7X0 .4 l i, . --- i i-.I- ?-__ t--- i-- I- - ' i . .t I it i , ._ i, -. ? I I , . _. .. .. __ li t . . ,,I -- il ll . -- I .1: ,1j__ ! ;,~ ----- S- . ,.4. e . ,t: ,. d . . t i __-cc i ·----- ----- _._CI---- I _j ! t L.--------C :- T----I iI ii -- I _ ---- -- r--I -- I ---t -i Tol I-t- .1------51 t- ----- ----- - ---I W\e Ixt----C-- --- ·---- i +----- -· ------- j. 1 I _jif~r: Ii- .- L_ i i If: I In LL P14 -7 is 1: i i t- I _ i. I , i -$-- -'---- I --- I pr r r--- i!IIj t - -i i---- . I IIf I 4-E r-- II I !' -li--^- t--- Js i i ---r--- ---- L--- I_ I. i !, ', , i -fux I rr f. le i ---- T---- I I i | ~ ~~~~1 | I ---- ---- p-- _c- r , . ---- ! I I i, L i: -> i. I ,< . i 8 T t 1_9A 1- I i .'/ 'tf i7 I i . iI I zreTz /' /I / l ' i/ i I I 1 1- -t -I ,. 4. .. ,7 IF - 7 I i ----t-l i -____1 1 ,1 /: il 1i I ·----c, I --- -1 - 1 . . .i "t ---- ___ ci-_ . tL i_. ' I l It 1 I. :; - __. I --- c__l__._,_. i .. j - - - I------- _ i ---- - ; + I _ I~ i 2i 0o0 I i - i - - - I ... · _ I - L .... ..... · . --- WMIko.0 0 . 3r wI I --- I W . S% J ..... _ ,f I i -1 I..=Zllw i t~~~~~~~ I , , I, i .. I ! · hiz i f i I : l30 i i i i ' I I I .. _ , - f ooo~ ·1L, -I A (· i- i -- t---- . f - --i--r ------- ---- , , t .? 1 __ --- c i / ,--i It ,r.f 1 I· i 1, ,: L -1 j i_ ----- I-T~~~~- T I~n-&-' I . i ~~ ~~~, ~ ~ . , i . I ' _ _ 1 - ., . 8 . . I ' i. T ; r -i -T -*--- -- . 1:.. !i l i C ,. i i I . · I ,I ---4- - L- E- .I----- ,_. 7 I -z 1- L_ i _C- _ 7~ I ·: 1- i. i -- . !a t--- r1 t-li-.i i I ---- ,. . I . t - I 31 _ i- I- r : i · - ir i · · · ; -. 1 I t I--·7- I ii i- - T · ' ' 1 , ·1 i t -C·s- : i . .... -- -----I . * i--. i 1 --- r , i ----- - * i .. .. - L1_ i iJo, -- I 7,~j . .. _ , 1 i-s I '!'/ .. ! 0 -.f . /' .J t< .- / -1 t I e I,-j- - ,. . II . I j- !-- - s t . I. i .1 I -I - I . , Ir - .. I- . I· i. . j : ri·I . ? ;i------ I i i--'! . · . i . t' 7--t .. I ! 8 -- I ii -1 . L i ii I i ' . I. -i ' . I .1 .-I I I1 .I ?I L .e z! - I _- t -- . I - ... III I--, cj-r . 1 ii ~__ll.. T- la A '"L(: ! - F11. 7z , I $' h i It -II . 1· . . ..- z X-- P f/l r_ 1... i . i ' I i I , I t.-- .i I · --I · · . I I -- ·' ' t- . .V- . iI- . . 1. I I i i i I... r- r, .] -i . 7--- .I 1 I I l i . . . ---' -- --C_I 1 l'lj i -- 54 i i ! i r II . . a II lip -t. I . S;L"AYt I1 I I ---·e--- I. Y ·-- [-·_ r Ij I' ·---i · c~ -C . .: 12L _- . _t-A. . ìN~ I I - .a~s e-; . I --- - r- --- · ·------- .C? u .. I1. 60.0 ··· ·r I . tA I1' 1-,.I . I ·- r i VVI Lf ii W- l__ jpt -tt r X~ t-3- i. !I I -- -,TI l L w i I .I 1- tr B ..- · --- - .- IIC i r ·- . -i I g. lziT i- IQ&., C- I t II - I . G M I'- · ·--- I.i, : . I: · I , . I' r . _, :I_ L- .. ' ' 1: _ I --- -·-- _ i . i- I 1; --- rZ! . ·· · L---- t LZ - I --- -C-- . ... 1 I PG _ .i r T I ./ nam K ; I I · . t .. ..- . -1 i- I . ! A i1: I.tI V-fmi i r . .l .i , iD' . :I - I I , I . 01 . . t l i W, I ; I. i .I 1':S i .I I. .: 1. i V: i II ._ . I. II _ic 1 ,II i I-t I i : I ..1 ;,- --T7 i --- . ' - i 1- !ill:- .1 I f · : .I ,i' '' I TT -. i.. . ... L . *i.' |. . - l .._-c--·. .;- . . . . - __ i : : I .1 L -- . i! - f I- ! ;~ ~~ ~~~~~~~~~~~I . - . c I from 0.05 to 1.0 tinaosphere. Since upon dissociation, crbon dioxide -nd wa-tervpor ab- sorb the s.me amount of heat that they liberated initielly during form.tion, computation of hent loss from the flames due to dissociation of products of combustion cnsists simply in evaluating the heat of reaction corresponding to the weights of dissociated crbon dioxide and wnter vapor. Fig.T1o./ shows the combined effect of dissociation of carbon dioxide and wter (6) The ltent ve-aoron theoretical flame temperature. he.t of vporization for any given fuel oil can be determined with sufficient-degree of accuracy from Fig.Io.2 , which is based on dnta obtained by the U.S. Bureau of Standards. As cn easily seer from this figure, reduction o be flame tempernture due to heat absorption -ccompanying evaporation of fzel oil is practically negligible. (7) The te'rpernture nt which the burner hs flel oil is supplied to the but a slight effect on temper,.ture of flames. Heat loss from the flames for o ?tomized oil cn oarehletin be estimated esily which gives specific heats of fel tnhe id of Fig21.to. m4 with oils at various temperatures. (8) The effect of ir preheating on flme temper.ature is strai Forward -nd is not described here due to simplicity of clcul:tion; ht- be- sides, a.irDreheating is but very seldom fensible under conditions of operation to which small heatin.gboilers cost of its incorporation into re subjected, boiler is not frequently justifia.ble. Employing Figs. No.Z , 4 , /0, //,12 above results .nd the first /3,rnd /4 , s directed in ?ig.i4o./5 wvhich ives the theoretical flame -3/- temperature L~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ T- ifII _ i r I 1 I-T- -- q I ZiiL)$o i li a 1 . i_ _ _ I ,] i i~~~~~ .. l _------·- a t ll l : - I I! M I. i AreI I k I, II I II 11CI I Y II L - -~~~ _ - -- - - - ~:I -- I~I I- -- .- I ~ , ,-~ - - - I - , J r---` ..LIrl 1,r 1 ._ C #Ao t_| 'el V --lri { II! ---.- -l. _ -- '--- ' I -- I.[i -- ' . _ _ : i Y I - _ --I ;~·~/jf __-__."t.I Ala i V ·I.-rI : , : ' -:P 1Ii;': - i I . . . Ij~ Y ~i- iL) tt1~iI -- IIII1II _ I ILE L ae. I do PED ris.l t4HHoe~S JoPr AirdtY ju2fb .. . r , T i S'x! f 1---- Jf- F~ c inK - h~~~I 1 !----40I7 I~~~~I _ I YÂ,I I _ I I~ Y I._r.. JY_ _- &-- i_L- .7 -7 i . irF 7rF4VF I [ ' I GI ,t ~~t _ L I A .109 /jtOI ---- - - - - - : : I i Z -7- ------- - - it.·; -'-- --^ - - - ---^ - - - 7 - -~- 7ai i , i-I - i i ii----~ ii ---------- q I i-~-- I- I I I ._II- ~ : I T__. I,.A --- 4--- ICI t - -j ......! ~e :_... -- F - i i~I i t -I , t~~~~~~~O1 i I .i i -... i t- ..... t I Ce-rB~ec ~ ---- i !---i - I , In . l~ I -~ i I .l t; ; - - I, ._,_Oe r-----I_A7-'- .n 140'1i r _ _' -aflOO. IIvr · ·-------I -· -·--- - _ . . 7, 6 .i L -·-·--- 1., .... r.---- ...... 14 1.Wi .-'"-li ? t--- +- ._ I_ fI I i . _T " t----- al v' . '1~m-~lqqL ...... --- j _. ._ 4 _ I ... " ._ :14 ,1/P I, I _ _ _ _ , . 24---- f -- --- I i. -Z4 4 _ , I : : , I I-c I .. - - . -- I . , I I ti _..P! II I I!-- i -4-c I -- - t .- 1-_ . _ - _ - _. . --- ! I_ -- .- --- LL ,- .. _ i i ~ _ _ I I !_ · ~ _ _ ~ _ - il I _ r _S I i _O ' do_ :90 po! a '- Ti P l f ! . I I I " t--I 0 ! -10 ; S1- 6o60~7r74 . P _ __ I' & I . _ .; I I _- I [ _- _ _ I Ii 1 ,- , I . ! o _ _ _ _ _ [ ___ l i i VII .. ._i.l_il._..! I 1-F_ · __,~ i i--- 4 i Ii .,A i_._. - i VDv Sl0 i i - .. + I -~i I t , - -I i I i~ 4 , I : i ·----.-- I~~~~~~~~~~~~~~~~~~~~~~~~~ _ , ,_ , , > -A~ - $;_ -1 - i- ---- :- ; I t-t--~~-------- i 5`00i .... uI I l i 0 _: i_ _ .T ! various -< 1~ -midity. quanrtities of excess air at 70°F. Th1edotted curve emerature ~sR outlined on pp. 2Oand 30 .. :;.. · ~~. '~ . :i f- .i . .. ' ai-' . .: , .... :- ·. , -' ... ~. , . nd 0 to 20; relativeu- giveste theoretical fromflame to the wlls , !t. :"' on Fi=-.lo. /5 for dissociation, corrected forhe.t transfer .:' 'nypothetical average fuel oil with ater combustion of resultin ;':' '" flame ut which. nmust be corrected of the combustion cramber CHAPTR IV UCTEDTASTION OF MOISTUE AND ITS ;, EFFECT IN FLUES OF CIL-FIED UPON DESIG-t Ai X.HATITU OPERATIOT- CI LRS O,T,DSA.TI,7 A", ITS .....-. O'SU CO7 .t : 2 E7 FECT UPOTNDESIG Cndenstion fuel TO.F LUS OIL-FIRED HEATITG CPAND PI IC.TIO- of moisture from the arodLuctsof combustion of a oil is one of the rincipal of heat energy libera-teddurinng limitations to comnlete utilization combustion The lowest temperature to ,-ich the -:roducts be routt doln,.,de'ends pFillrily (2) -er cent o torss on three (I) Per centi of hydrogen i the of combustion can -fc ollows: u'e oil excess air suptl iedtor (2 in'vial amountof cisture i n combustion. a ir. Per cent of excess air is the only fa.ctor 'ic; can be con- undler ordias<r-y conditions of combus-tion; since tihe hydrogen in trolled the oil v ries only sit in nrrow liits .rndmois ture in the air is oil), ( .s ixtur- e of several ay" :icl gases t 14i per unit weight of s cangeable Th.e resuI,t of comb-ustion of c- iel L BILERS 1 n7ter cs ooi. n vpor* e weather. .'osaospleric air Figs.os.8 and/6 slo co -rcosition of products o' combustion o - hypoohl-eticalav- erage fuel oil with hydrogoen contenZt off 12.5; oer cent by v-i ght -or all ractical purposes thle 'lue gases cI be asszied to be t at,,mosheric pressure of 29.92 inch.* Hg. Then,ift e prtial s=ureof water vapor in thie lue vgses is (r) inchs , sure of dry flue gases (i.e. inch. less w-ater v-iapor)is euai pres- the par-tiai presto (992 H. Al 1 comronants of t flue ge s or course occupy trhe s.me volpzlne; therefore, themolal ratio of v'ter vcor to dry flue gas is equa to -- / (29.92 - p), nd l ence the ;weig:ht relation be-tween ,,,'ter rd the · : 4:: ' I: .- SJ3X~~r.',. -:, if : i i t ~ 9,LI , ____'_I ' ii i; .... _I_ _' 1-e -. . -i FI i Sd -- <~~~i i 1 : -1 1I-1· . t i 1 i I - . DI: i t. 1 1 i-0:: ,c~ fl -I--++- .... ,i - __ I _ i '--'''-r T i i t I ft t- . ~~~~~~~1 -i-I- 1)' f 1 I eli I $w ': i· 1 t ~ I 1:l i ·: .' :1 . --- 1 I : : 0 2X~ 1q l r L- i .I t fW- _ 4sP f ______ I I 20 I4 I __ ' · I :/ I r i 4~./Qj^ r eS-:£ s ' f 1 i S ·I ' 7 i I · r i ft i I i ir i '''~i-l-~ I,1< r I1 t 1 - f~~~ ,4 ., ,4 ! - r-i-~ !' i' I~~ ~~~~~~ · ,"~~fi f ~iP 0 /a W 930 40~ ~07 60 , -'- , ..I ' , I I· ·i i · I . io, i'l .V 46 Aae 00 / e ses ,is as follows: lb.(H 2 0) / 18.02 P (29.92 - p) 1 lb. / m p lbs.(H20) (29.92 - p) m lb. Dry Gas p = Partial 18.02 pressure of water in flue gas, inch.Hg. m = App.rent molecular weight of bone dry gases. .02 = iolecular weighnt of water. The maximrlmamount of water vpor that ny space can hold of : corresponds to the weight of saturated stemrnat the e space; therefore, when the unsaturated mixture o temperature the products bustion is cooled, condensation of wter vpor occurs at the rature at which partial pressure of wter vpor in the mixture be- equal to saturation pressure of steam at the same temperature. Thus, the equation given bove can be used to determine the temperature at which the products o combustion o a given fuel ty leave a boiler without condensation of moisture in the flue. is accomplished simply as follows: (a) Since: p 18.02 lbs.(H 20) lb. Dry Gas (29.92 - p) m (29.92 lbs.(H 2 0) P = ( lb.Dry Gas Letting, p) m - ( lbs.(H 20) ') 18.02 - lb,. Dry Gas z P 9.92 (81802 2 Zm = 29.92 (. ___ p (% i L9 + 18.02 .92 2 pp.arent iven 'tVem?'hitol Air *-ôlecular 8.02 s on i;sE.tTos. -shenthe composition of O and / 6 (See:"Average on ppid o the Products of Combustionl, 20). Curve t to o Fig.LFo. /6 -ives vlues a.ld of- tle bone dry :.rgeht molecul, 'fcombuStion, is easi y c.lcul-ted the gaseous mixture is - 2 Z mr (b) Th'e trma (m), products 18.02 o (In for various ercent?.ges of eCess , r. ') -areo course esily (c) V-lues of the term Fig.o. 8 , ?nd are given at bottom of ig-.To./8 corresponding to vari- of excess .ercent:ges air. oua . (d) KInoing -rt;il obta'ined fromr the values o tenis (n) and (Z), deterines preasure of -water i n 'the fluecas, as inches of Curve in center o Fi .No sios -the varistion o (p), ercury column. (p) with change in excess ir elivered for combustion"of he hypothetical average fuel oil. (e) 'Then, the telmoerture of flue gases, at which water vpor contained in them berins to condense out, is deterined sply ferring vlues ofI (p) as obtrined rom Fig.Fo. -36- by re- to the data on Fig. 1k*i--() 'g '~~~~~~~c3 ll-:, < -t. t ' 2 . ~~~~~~~ .:~~~~~~~~~~ ...-----... .---,--'...---.-... T _ _ ... I .. ... ....... .. -....... , ~ -.~. ... 'i,-···· i~'i'.:~----I ... .L~ .I.~. ..1~~ --. .. I~i -. i . 1.. *,, .\ N- 1k ',rn~s ~'1°eY:~ -- *<'"'s~ffi E t~'~p~: s229 ' ~*¢ J°~ iJi /, ,t~ 9 ~' i ', i ,s m.--t-*,· i ,: : Ir-·-~-- ·--.~-.-~--; t_---~-i-------------_ __ _ _ _ __ 'IC lz _'- | . .. . . . .. , . . ... ... -----------r - .----- --- -.- -.. .. :- . . . ...... ... -... . . ..... . :- ~~~~~~~~~~~~~~~~~~i-~....... ...... ........ . - t t-· -- 1 ·- .... · - -- ·· ,' t-... --- ....... .\ ' - I. I.,_. __Cl- - IN I--:-----~- -,--- ... .. .. .T .. ,. X __. .- _ L. . ---- -- . ~~~~ _ .. _ - " - I -.. -. . * -·-.-.. I IC- - - 4.-· : - -,_~ ~ ii __~~_ ;_·~_I-^-·L~. __~~·__ --1'-__..~ : I .I.. -t~--`~T~----i`~-'- r..:...~........ .'~ ! *1 II ........ - -- ": …. X .. i ·-- ·· ----·---- , ..........! -?.........t... -- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~'--= :-:-- -,-- ......... - i_ I_ ' _ , _,...___ ....... i~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ "~' ....."':.. · - - '-· . .s. . - .,. : 'II !~~~~~~~ · ' I I i- i---·----·· t............. 1 " . ~-------1-·-t1 .... . .. . . .... -·---. . . X - --- ' · -- '-- ..-- ~~ - - - '- - -·---- ----- -·i V ---- - --. -C...·- I 114 ------ `~----~~S i--i~--i--- -- -+- .. ....- . · t--l I.~-- i~~- ~-~·- ·~ ----'- -- - -- i r .. ' i - ~ - _ '.4.c- .... GI tI x; _:._ __ _. %A : 4 1~ ~~ ~~.---' .... "-`-`r---r---'x.~--~~ I'-~---~I ----~~~~~~~~~~~~~~~~ ...~ ....... I....._........ " ------ ~ %I-z -·i-- " ... i ------ -- . - - - -- --7-l~-;......- 7 f ~...... ~~~~~~~~~~~~~~~~~~~~~~ -- -r-- ~~~~~7' ........... --- --..: ---. -- '--,--- . . i _u 1 - . . . . - - ----- ...... .......... ......-- . ... :_.... ..... . I -. I- .-...--.............. .......... I . j t '? ' ? ~ , ; .........-- ... - , _ Qi~ .---- ......... -_..... ~t ~~~~~~~~~~~~~~~~~~~ ...... i~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ us L - ... i~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ I I I,~, : ··--- · ·---- 7-·-- -- - ·----------------- -------C'C---i-·--·---,-.. b · --L -_ -r--·-- -·L--------·- · -- -----.--- i c ------- , ·-·---L------ ---- ---- · i-. -. . i-- --- - -- t-------·- ·----- ---t i-----·-_-_________ i -.- ; .--.-- ·.....-.-;-- . .-.- i ·- ._. ....- - -c- -... ...-..-1.... . ..-.-. -·e - 1 : i _:___1._ : ._,.___i._,..._.__i.___.,_._j i -- ---·· ;-- ... ·---: r -c·--- ----- ,-I- ----- -·---I---- . ,.. ... . ....--i .. .. ..... . -·-·-----.c-·-,------------·-------·-· i -,--------·-- i i I :tr · .· Z, I4c311 'N N. . N-I 8.IAr3Y;7./rS/ ,;7c?·;CWir: ZBcSCr ...-.. 1..-.....i L_.7 N. :Z ------------ _-. . I I---~--1I 1:i-. ___ i I ~~ ~ ~ ~ ic Ic i I -- - Iia i II ------- - = t _L ek* z|G id -- c--- - P,,,- - Žik~i *7 -I I I II J7 I i . . ; , \- -- ._ I, ,t i I 'L . , I - : --- I---~ t 1, I---I- Ii- LI I . 1% -- T-I--i ; I- L _Z · - 1I I i I V I l- v4e IzrI 1 -A i I. 1~'i . - I i-, ?F s z~ A I-i IN. "4" I ;-._.-._ !'I i IW I l -, T I I~~~~~~~~~~~~ . i i I .vv I r It i I_t-_L I I nAv f 2 /1~1' - I 72r"L - - 4J l - I .. i -. -!, _^ w 1 i iLVi t 1 i 0, J-410 , , 1 - ,11 ,zx-j 1 i m91 r t--- i i~ i . i I I -. Azi- J ! , , iI I Ir. . i 1-: , 1, 1 I i -. IL. 335 I_ --t I t---- L · I -z,* , i i I L ! I _ . I-~- I do 1-4 . FF8!1--r~v w 140e 11 I i -- ------ , I + I i zi i - . i -- i = . i . I II i ------- . i I oI---4- -- - i'- i i i LE__ ------- i11, .i- M -------- ·- .I t- -1 ~L --i I i --"-- -I e---- - ---- ~-_ 8 I·--- --- ·------ i i k .- I I iLI_ L , ___K- i ! -. d- _'_ iI i i ,I - i -L_ -' , i , 1 I- , i _i, L i )V; 31i Ih /Zi -r~ i i iV I - L. ----I -t~O f!OE 4 .Ld1_ 4-- i-7 i,~ 1~~~~· A; 17 ,i eYc , t--t-- W- ..-- I, Ii>kx - i S, ---- ----c- rt· -·-+------' i -1 ie I i O /0 __ ii :____ _ /" 1r O Jo d '----=P`=;~~~~~~~~~~~~~~~~~~~~~~~~~ i· r_ 50 60 70o i 491, . 1:24 (f) The final result is the curve at top of Fig.No. /B which gives the relation between the minimum permissible flue gas temperature and the percentage of excess air, when burning the hypothetical average fuel oil as selected above with air at 70°F. and 0 to 20% relative humidity. It is seen at a glance from Fig. No. / t~·45~ conditions of operation -- , that under ordinary say with 30 to 50 % of excess air, the lowest practicable point to which the temperature o bustion may be reduced without the products of com- running the risk of condensation is about 1250 F. ;· Under usual conditions of operation and with the prevalent -4-4 -- · ~· design of flues and chimneys, however, in order to prevent condensation <4- of water vapor present in the flue gases, their temperature must be *74-4- *1t·. kept considerably above the condensation point until they leave the stack. Quite frequently, keeping the temperature of flue gases say at about 1250 F. until just before they are dissipated into the atmosphere, also means having'their temperature anywhere from 400 to 600 0 F. at the flue connection to the boiler; for losses in temperature occur all along the flue and the stack, depending on thieinsulating qualities of the materials from which they are constructed. A ready measure suggests itself for prevention of heat loss due to high exit temperature of flue gas, in the form of a water heater or an air preheater; however, neither would be practical for the usual small installation due to high first cost. The principal item that makes the first cost of such auxiliary equipment prohibitive is the amount of corrosion resisting metal required for its construction. It is very seldom that a fuel oil can be had without any -3 7- sulphur; there is always at least a trace of it even in the best grades. This presence of sulphur, even in minute quantities, eventually results in accumulation of (02) and (SOS) in the condensed moisture, with consequent corrosion and deterioration o any ordinary steel and even cop- I': _ kjU.-* .J, Q kjUa i .L±Li.LaQo -4 -1 C ti -- A llU ____ LUVLLIUJL C.dV LV U 1o -4. -wIt -o IUWOl1. (±tt, -4 U 1IUVV t U O P' .. A ±L1 1 UULLU U F P: far to be satisfactory for construction of such auxiliary equipment for ~Z;/{s -utilization of heat in the flue gases. Determination of savings in operating cost of a boiler equipped B)s with an economizer as compared to a boiler without such an economizer I.,Zr ..; is an economic problem in determination of the "break even point". It can : .. :, be stated roughly, however, that if the saving in a.nurual cost of fuel . t .i oil is twice as great as the interest and depreciation charges on the v economizer, then incorporation of one in the boiler design is a worth while eature'. ; The quantity of heat saved by means of an economizer can be .. i.3 estimated easily with the aid of Fig.No. /9 which gives the relation - 2 e ship between heat loss to flue gases, their temperature, and the per *:- , cent of excess air used for combustion of the hypothetical.average fuel oil. Fig.No./9 lg; is based on dta presented in Figs.Nos.8 ,/2 and the method of its construction is self evident and is therefore not described here. - 3- - - !,, - :i .I ._ 1 i I -Z .. . 1-: ! .... _ i___ L- Mi -S'; 7 ,,, Ale At Z ----- . .IS I. rs2 - -r -- -. I- 4 1 -4- 4t II iEL i - ... . . F- i. I 1 ,I'. i - I I. ,I- _j . r it-1-- _ 1I' i - - i- !.. i i . i i rr- . · ·1 I- i_ i'- `---~--- ...-. - i- h ;, . i,1 :. .- . : - i- i . e,8' ---I-. - i __ `7--- 1C .14' t rcC II _-,-- I --1-, r::7 ! I -·----- ! . ....... I i----7·19 I ·.- c, .w I .I -i I -- 1- -t -- iI I 1' I __ ; Ii , ' I I i: · ... .. ~ . i --- i----t" ii i--- I d; ; 1~~~ I '. 1I iO-o. I - i - O -LrI I 4-- Alr ' 1 . /I rl , ! I i i ! t I I - -- -- --,-- . .+ -a, A51%S .. . ., -i -b ~tl~~Y r ! I 2 1 . I I I J,O a, Amivjolp_T',, I5 J I - i I f -4r JI iI d~ Ir r G op,6 I cap ~~~~~~~~~~~~~~~~~~ _ I · - i L I0, ! ;0-! c I_ I .! i i A I. . -- I. 4 i C-.- --- ICllfCL Ill I-r I jp--C- . I-' ' -- ·-. 33C--c 1I -1< disawer_-~-~ -r-- ---c i i i _i I1: j_ Be -1?--"-- I . I -.-c__, . S i w 'Woo ! I i . ! i· , 1 -· .e t I I 1 I. ---- 7C' I, I .I , L . Ik/ i i · I F~~rl~~~r :;1 , . fe1. If II iC 7rL ·- ·---- 71 Iii,- I' r , I', I ·- ·----- I. L I. ..T 1 i ii eL--- 1 .i i I 3ei I-i e T I · I .....- T----1 IJ C I' § i_ .i i - 1;· ir7 i : nh-- I , ------I-I I i. · · 1 t1+ i I Ii -- I' Of ---- C---: r I ,. ..... i I ZFji ; i· If , , ia j - - t- 1i' I' t - i I . I . !i I _ r . -_t . I ---+----· C·-I "I , -&- i..i L·· I1: : :: ,IYA I r II r 1 -- I I i- I dCI· I i -. :1 L i · r r 1-L I IA p. II, I, nGftl ak I I; A i. . t I B·atL I r . '. I . . 1 r ;....... I. .. iI 1. t- .- i . I I ak=r , i-t ·-- I --t-tLrh i I . i I L r aib Ar} _ rl - iZ'_ tzd-i_-&e ) aLL L.p L-i I I._ .14 ri·a t -t II4 ._ -t ---I ' AII II - - i i r I' ' r-i- . ml· II f Ii '1 I _C t. - 1 13 9Ie .m. IL ._3r1 _ _ _ - _s I ! i *: 4 49 ¶fl ... .. . +i t _, m 61%' CHAPTR SETECTIOiN CF SIE A1D SAPE V OF A COS FOR A S,1ALL OIL-FIRED -39- .TIO-T, C-;H.BER OR FURNACE HEATING BOILER SELECTION OF SIZE AD FOR A SALL SHAPE OF A COMBUSTION CHAUIBER OR FRNACE OIL-FIRED HEATING BOILER Introduction The three principal factors which control the size and shape of a combustion chamber are s follows: (1) The rate of energy release per cubic foot of combustion space. (2) The leYngthand shape () The quantity of excess air which is expected to be used to o flame which it has to contain. secure complete combustion of fuel. ilinor items overning size and shape of combustion chamber may be as follows: I1) vverall imenslons of tne olIer. (2) Decorative quality. (3) Structural and production limitations. (4) The purpose of the boiler for which the combustion chamber is designed, as for hot water or steam generation. It was not very long ago that the -furnaceand boiler designers were greatly concerned with securing high rtes of energy release in combustion chambers; today their attention is given primarily to providing materials for construction of combustion chambers which can withstand the temperatures resulting from the high rates of energy release that can be obtained with modern 2fel oil burning equipment. The volume of a combustion chamber, everything else being similar, is not the controlling factor either in efficiency of combustion or in overall efficiency of the boiler. This can be seen -fdo- easily upon analysis of performance of any two similar boilers with different combustion chambers; what is more, at times a large combustion chamber increases the overall efficiency and completeness of combustion, while at other instances it diminishes them. Thus it is impossible to lay down an arbitrary rule for selection of a size for a combustion chamber, as there are many other variables in the problem that may upset all hasty conclusions. One of the most interesting and conclusive proofs illustrating the fallacy of the general conception that a large combustion chamber is productive of high boiler efficiencies, is to be found in the thesis on "Effect of Size and Shape of Combustion Chamber Upon Overall Efficiency of a Round C.I. Boiler Adapted to Oil Burning C.L.Svenson and A.L. Hesselschwerdt, conducted at the by ass. Inst. of Technology, 1933. Fig.No.ZO presents conclusively the study of the data in the above mentioned thesis. It shows at a glnce that not only the size of combustion chamber has very little effect on overall boiler efficiency, but that smaller combustion chambers have proved to be even more efficient than larger ones. It is interesting to note that use of Chamber No. 7 which had a volume of about 7 cu.ft. resulted in practically the same overall boiler efficiency as with Chamber No. 6 which had a volume of only 2 cu. ft; as a mtter of fact the efficiency dropped about 5 per cent when the larger chamber was used. The key to the whole performance is in a pair of factors-namely: flame turbulence and "the fraction cold". The "fraction cold" is the name given to the ratio of water backed surfaces that can see -4/- i: ~ ~ _ l ___ _ _ _ r ... ___ A_ .--' , ....1 : i, . _·___ _ ' Ir P.. V, :t i- vt i I !, ...... ___ i ii -.. :,.,. I . i .. ,I: . - ...: . i: :j i i I I I - i-.-' .:._..I , _.. I . 1h. .3 :.c91.L~L . ! d lb .-T' Z . O ... _ * _ , . il t . I . i r j : i. . . . .- I.. .. . .... . _. 0 l _ _ i1 . RJ .- .. f. ¸ " -_ I --i -~ i$ I !i . . i i q,-~-:.. ii: ' t -- j V it. .lll;i t . :. ' r I i e '. . !it .- t- -~--: .. .... I I k I*S_ i :. ili _ ____ a_-c-. *~· k I I .-- _t'~--- ! i.. I .. i K 't,11v - § (is X J e-A;- )il" A- . AI 4-4-Horr 4 N i n---rtt_ . k j, · ;''t ~~~9 · I .·:. 1-! tefa4SA -- .- .c-. I Hi--+- i , : - t · ·- . *;.V EI \1J . I·'C .. _,-C· I'' -· : _-Y _ ~-- :':.I \J.: . Ii - 5- | 5 . , I v - . ll i ' 1 i t t t--: --..4_.__ I i i . . -- -r i .... . iI -, j i i --I !-_+_ -F---- Illi i if ~,: --·--7- :I I . I --· ·-- · ·:----i-·--·-- j- ' - . . . .. i . i i i I - ._ I. : ! i II; --- I -' ' , I . 1 .. I.-- --. . .._.: -j' ..... ": k,4f._t qk;: ..--- . .-.:. :.. --- --- It AT----- j-t--r·- F- --.- ... I- '~~~~~~~~ii -t -- II i-. I I . I. .. · . --- . 4I I . I . I . I..... I _.__ .... __ Y3 . _ _!~~~~~~~~I i "-. , I' i~~ . .. i . : i"- I L..I I ,I -X- ----- ___ -cs~-- ... . ii - m . . I l (A'! ' _i I C_ _ , + .. , : · ,. . 4 r . I :z ..r:S . -- ' -- m~ . _ ..... I 1, .. . !- i- ss__....._ W _ ... . II . . . .. .- :'t : ~11'~ ..... ---.- · ·_C ·I·__I __. . i ---t-------*~---- .: :. ' e.4 '1~¢ W . ., I 1 ~:~:I-:i~ : q . i -I . I I I ... L .'..........{. ...- -'1 ; I .. . .-- r. t . . _ . .- . 1:3 j 2 P ii '' . -- ------- - I · I t N .. _< ' --:- "' , I . .,: P . l .. . .- _ - 9% IN 11 I _ ' ..... . ....i ...... ......... .._.. 1 B la Ihr .d 4. - ... . . N) I u s _ qc :sN; j QI.-.. i. .... :. j-r :I -. - · .i · · --------B -r . . ..1 .. m .' ---k1Y''~~~~~~~~~~~~~~~~~~~I IN : - t· \9 , _ I-c- b 2 ___ T _ - r_ - b~ _ onto_ _ g 9ri · '4- | -" -i '''; N Ir - __ t 5 i jx '· t _._ _ r Ii k, r , 17y6s . - --- __ ... IT I _I_~~~~~~~~~~~~~~ __ __ .. . S_ F r_ t - --- __ I_ _ - -r r ' '. .- ....' ::. I ! - . !] .. ZV i i I - - ...- 9 [-:7 ..... i i ;I -i i .I_._ it lt~-- · · I ,.· t 1'-_. Wol ,__ .,_._i 1 i... :-?Zi- .. . . I' I ... .. I... i ii ci ! I . t - - . . I' I I I ·· · i Y rs I T) 1B I .. . . 4 '- - - ! - - i i :I -''' . ' .. I .i ~~ ~~ ~~ ~~~~~~~~~ a~~ .. . L M , .. . I L, 10 . I In I lr :·":--~~~·'". .7, I ' 4·: i~ the flames, to the total internal surface of the combustion chamber. Turbulence in Chambers Nos. 4,5 and 6 was provided by means of a chequered brick work built into the upper part of the chamber, which also shielded the flames from the water cooled surfaces immediately above the combustion space. Chambers Nos. 1,2,3,7 and 8, however, had their flames exposed fully to the cooling effect of the water backed surface, and had no special provision for creation of flame turbulence. ,i Notwithstanding the radical differences in design of combustion chambers described above, their effect on overall boiler efficiency at no time exceeded per cent above or below the average efficiency for iiiri · .i 1?,.;W is I: i·, .-.;·· · ·-i t;`! r ;Y 1 all eight combustion chambers. ·" This also points to the fact that principal loss of heat during operation with any of the eight combustion chambers was not due to incomplete combustion, but primarily die to low heat transfer efficiency ·"13 of the water backed surface. As was stated elsewhere in this thesis, "·r':I; an oil burning boiler is a heat exchanger as well as a converter of energy, and must be designed with both of these two points in mind in order to secure the highest possible efficiency of operation. Basis For Design Of Small Combustion Chambers Design of combustion chambers for various types of boilers is an art that has reached quite a high state of perfection at the present time, especially so in the field of large power boilers. However, most of the knowledge underlying the present methods of estimation and design of combustion chambers is based primarily on empirical functions, and therefore does not lend itself to correlation and application to design of all sizes and types of combustion chambers. -4z- :,--..~...., 4_.-.7 -. -,_, :Z-~ ,.,.,.... ,... :, !. :.'~ ,. ..~?:'-B-,--.. : ·:~-'"~E,?~':~::.,, r~":.!'.. To meet the above mentioned need of a theoretical foundation for design and prediction of performance of combustion chambers in small oil-fired heating boilers the writer presents below a simplified resume of his studies in several fields of transfer. '~: I , :.,: ":.: .. ''""~ \. ,":. l .'~-,,:~ .~:-t:-.-i : .:.:' ; '. ·~' i'2· :~::.. In general keeping with the main objective of the thesis, the discussion given here is concerned primarily with the calculations and .'.~ theory of thermodynamic and heat transfer phenomena necessary for the rational design basis of combustion chambers in general. Structural details a.redealt with only in so far as the size and shape of com- .'. ,~ _--.,.' bustion chambers are concerned, and physical properties of materials ..'~?::of construction as well as their application are studied principally from the heat transfer point of view. :.':,--·4.i'..' Theory Of Oil Ignition "l~'~~ ....': The basis of the generally accepted theory concerning the igM >'I ::: X nition of fuel oil, is that it proceeds as a series of complex chemical changes -- the final results of which are the products of combustion. The hypothesis underlying the theory is that at a high temperature and in presence of oxygen the surface film on a droplet of oil undergoes so called activation or the formation of activated moloxides (unstable hydrocarbon peroxides); these moloxides are assumed to break or decompose with liberation of sufficient energy to cause the ignition of the remaining hydrocarbons. In short, the moloxides act as primers to the ignition and combustion of the liquid drops. This theory is supported by numerous tests and studies of ignition and combustion of oil in the internal combustion engines. .. :f3 ·.·z EL--· a: ::i ru·: '" i.' -r·"····· E·S,Jbr · i4 aa Regardless of details underlying the theory of ignition and combustion of fuel oil, the following rules have been found almost invariably to hold true in all ordinary instances of combustion of fuel ·-:;;· oils in small and medium size combustion chambers. M"· : -. i:- f""-:·,:i (1) That the rapidity and completeness of . : ;i:'·':,·· ombustion are proportional to the fineness of atmoization of fuel oil. · (2) That the excess of air required for satisfactory combusi;i·rc: i· tion in a correctly designed heating boiler is about 20 to 60 per cent ;· ; B::"··i of the theoretical air requirement-- the per cent of excess air being 1 I-, determined primarily by the combustion rate and partly by the shape of -- I r :,20505- the combustion chamber. (5) That in order to maintain a high degree of completeness of combustion the design of the combustion chamber must be such as to assure complete combustion of all products of oil decomposition before the gases strike the boiler heating surfaces. This requirement is met partly by providing ample combustion space and sufficient distance for flame travel, and partly by lining the inner surfaces of combustion chamber with a high grade of refractory material which prevents the loss of heat from the flames, and thus assists the combustion of oil constituents that require a high temperature for activation or formation of mol-oxides. Rational Method For Determining The Size And Shape Of Combustion Chambers Studies of many investigators in connection with combustion of various fuels in many different applications ranging from internal combustion engines to large power boilers point definitely to three ,I f principal factors which govern the size of a combustion chamber for constant pressure processes, namely: (I) The rate of flame propagation. (II) Flame shape. (III) Flame turbulence. The Rate Of Flame Propagation The first of these factors is important only in cases where there is no appreciable flame turbulence. In typical furnace or combustion chamber of a heating boiler,the effect of rate of flame propagation is negligible compared to flame travel by mnixing convection currents nd eddies generated in the products of combustion by impact andexpansion of air-fuel jet entering the chamber. In general it can be said, however, that for slower rtes of flame propagation, i.e. slow f~lime-fronttravel, the combustion chamber should be lrger to llow a sufficient so as time for combustion to take place in the presence of hot refractory surfaces in order to insure its completeness. Flame Flame shape controls Shape he size of a combustion chamber in two ways: First of all,the length of the chamber along the principal axis of flame travel must be sufficient to prevent the hot portion of the flames from licking the refractory surfaces, thus insuring a long life of the lining. Secondly, the water backed surfaces must be placed at sufficient :?:=Th fistoths!.ctrsi ipot~1;olyincae l.Frhr c·i·.1·?"1;·;!:.`' ,· ·- distance from the flame or shielded from it in order to prevent the ·'lbili " i sh rr·--r· i"::jl? k cooling of gases before the combustion is complete. The length of a flame and its temperature along the principal -&1.. ···· · axis of travel can be calculated with sufficient accuracy for all prac- : ;-; Cli I -.: tical purposes in the following manner: Referring to Fig.No./ . Let: k" r· A' = Cross section area of the jet of primary air-oil mixture ···;· :·I: '-; ·-·; leaving the mouth of the burner and entering the combustion ·-i-a:,.-F· ·. :·:a.· i,:· -;;gr·r···-·: ·,· ;i;..·-.· chamber, sq.ft. W I = Weight of air-oil mixture passing through the area Al, lb./sec. V' = Average velocity at the area A. d = Density of mixture ft./sec. at area A', lb./cu.ft. A" = Cross section area of the jet at the point of mixing where the primary air has mixed with products of combustion to a sufficient degree so as to ignite the oil droplets carried in the primary air. Wi = Weight of gaseous mixture (primary air + oil + products of combustion) flowing through the cross section of the jet at A", lb./sec. V" = Average velocity at area A", ft./sec. d" = Density of the mixture(primary air + oil + products of combustion) at cross section A", just before commencement of combustion, lb./cu.ft. c' Average specific heat of primary air-oil mixture at area A', Btu./(lb.)(°F.) c" Average specific heat of gaseous mixture at area A", Btu./(lb.)(°F.) -15-a- z ! I- K;4 - / **"_ . - /- \ \ -I/ i _- i I / / .;r i I / i i i . I iI 11 I i 14 i i I i ' ii i I I I i / / K1 / i/ / ·. / I\ I·m... f .. - ,i ·· II:. · :· --.. I; ! i .i .·. t' :l:i.SBBP$.:"'-'cr '-:lhB"T! .C .xl· srarac;l:: '-" -;· ii-' ·. = Average temperature of primary air-oil mixture at area A, OF. t" ;il 31· = Average temperature of the gaseous mixture t the area A" just before coirnencenlent of combustion, °F. :···' Now, the volume of primary air-oil mixture of weight () I upon arrival at jet section (A"), has entrained a volume of products of com- I bustion which weighs (W-V' )lbs. per (')lbs. of original jet. The initial temperature of the entrained products o combustion can be assumed i i;-·-:· i ; to have been equal to the average temperature of the flames in the combustion chamber. Thus, the weights of the entrained products of com- ii i; bustion ;; nd the entering primary air-oil milxturehave the following relation to each other: t' WI' + t(w¥" ii;-. ,-. W') = t" W" Where: I t = Average temperature of flames in combustion space, F.; and '"; other smbols I (Note: This relation ·" :: - re as designated above. is, of course, based on the assumption i that specific heats (c') and (c") i:·i·"·`::.' "· wilhin i re equal and remain constant the range of 70 to 6000 F., which is true ceit.) ii; :3 i;;T -1 Also: .Iomentumof jet at area A' is equal to V -· ' and, of jet at IM'omentumn rea A" is equal e· ·1 But, V' W' = V" W" Therefore: V" = (VI W')/W" Since, W' = A ft./sec. V" d" . r- to V" 1'" ithin 4-6 per W"/(v" A" a ) (r + L tan j) 2 But, A Hence: L tan = j = (A"/) ,9= 0 - r Tnere: L = Distance from the mouth of the burner to the cross section of jet (A"), ft. r - angle ,adius of the jet at cross j = An experimental fnction. section (A'), ft. is plotted against the initial velocity cross section area(A'). These values dustrial Frnaces" Knowing by Trirnks,Col. j which angle o22on See: Fig.No. - the jet at the re taken from " In- 1, p. 265.) , (A"r) - r Then: tan .. er w.nv of f`lIaes 1'di-;tance(L) ives the approxim.ate loc.atlion of the'_ti"t from the mouth of the burner. Pst thC-distance (L) the jet loses its conical frml and the flames ssume an irregular shape resembling a pear which tends to float with its blunt end pointing up- Once the combustion has begun, the increase of the cross section of the flame jet due to entraimnrent becomes negligible as compared to its increase due to expansion of the products of combustion withrise of temperature. Simultaneously with increase in crcss section due to expansion, the flame jet begins to turn upward due to buoyancyof the hot products of combustion-- which immediately after generation ave a density of approximately six to seven times less than that of the primary air-oil mA 111 .. · _ _____ __ i , 7-t Fi. ... 'I' .... I"-1: --. !,I-:--7 Ii..- .-I: : / -:.... 24:.:1 __ ____ ~i i ' r .= ._P ,_ . qn ----- _- T]i jj '____ - - .: , I 7 -. I A' ,T _ 'c., , . I _.. --I --- ... . I . - 1_ a· _ . . , e . --- v .' . .. v. . , . . . .. .. - - I: I .-: :.. . :.. :., . ! - il ; I 1 - I 4VA . i'. _ . ·------ ..,.~~ . i~ I'' I t: 1- 7'': : I,. I- 7... , I II. . I . . i I -- . L.-. -. :· 3___ r 1 L I ! :"· i 1 9 t .+ i 8 t:' :i _~-_ 4 . , II * a -I . ::i I. - CI '-- .- :;':, :. - ., , , ti R : t · 1· L - . 40 j .1. It ------------ . .-~' . i 4 -"- . Z. .- - - -I - .. I .- I _ i -,-- · I .II .I: . -, -_ I "-.Al .. % : - -,!. ,- - _ - I, I · ' ~'1 4st-- -- . I . '. ' ~ ;' I t::: !.s' '' t -:I '- | . - i i · · _ i :w- _ , . I .. .-·.i ,..,. . ·;i; i.,, j · - : . . .;r , ., _ tL;li ·" r · · ·-t · 'i 3 "--t"+- : --t· '-- . , i . i 1i ~ ... i-t I . .. . I. , I -.-! . -t'`- ." -r-'----' . . . i i 1--- r- ·--- i·---!------- !----------r i · ·-·- r - ' 'I I, ' t'- j i . -' I2 . . 1-. ·- t--. r .,t . _ . I .{1'e,¢1 r Ir 1 ..i,.· I . ~ + lv - r·-lt I ! : I i ( 'I.... , ' , -- `- ------:- -I r--T jt -----r.I.I ; --. I_ - I : ...I,-..t _.--T- I . r . _ ,0 :l- L , -,-.i i: , r i, I r i ,.~~:.!.!. . I _._ 0 I 1 :..: 'i. . . r ] .,'t .i1 I'- ----. , . - ! ,, J z' i. .I A . - 't i _ : ; 1. ___:I ;. ! _-_-_ : ___,__.. L-_'_. C.------.-- 1 16:: I -----.-I k---c.-·-! , , . rl 1!1 I -!' ~i ~~ ;'--r;': >.i--.::--'-4 . l . i .1 -1 --~:j-;I Z -'S "" X. 1 .I .--m*___ -I -·--·-- -------· --. ,----- -II -. Y 7. - I .. -, I - __ - i Yz"; _ -- I ----- ---- -·--·-------I ' ,:.'T ,. :.' i'. _"- _...... .. ' :._ [..:! - : ii ''' t i-· I _-_-, ,- -4.T N !;.-"-L : i. -! ..' t- -:' u·i -: 1 ;~ .-- . -v-_, ' . ci__ I' _I 6__.. l ' i _:· i ·rJ 1 I . 7 , f·-:"b-'"iie t :,,, i I _ --- _ _! _I I.. i :i .s -I- : ; I . -·i--- i t: · ·-- -II -'s I, ". . . LI .. I: i L: --- L3.- _T ?'s ;AiI! -4,ZU I i I ;-:' "' i li .' I i . 1I `' ' ' -tuz I:I :Lpy ;:-1·i-. 1 7- .: i- iJU' 'h: . . - I i I . ,N --- '--- I i: 1r·. j I t : : c--" .. I i.. I,. i-r w . j : ----- "-- - i I/ 1 . r .:--- - ''| -ctj 42,: I`. · r If 4.--- ·i : 1 1' - ; - j1 _, 'i :/ F-'T - II. ''.. i k.... - -: -1-' t : L pjl .. - -i,- .+.7 - . I ,: .I I r - : I_I ; ) ·. -. i _ I, ;,1 - iilij.i..j.i . ; i fl 1 I 11' '' t t i- t r : - ": .I. ."_ ' -I t ' ' I_ _. . I , . -I :; ._' ;. I I i · Ftj7{..07.=I$se-B '~-. A 041 . L"" q . .: >. : rr TTT- --- )-·----·· -]- I : j __ -!, r----4'_ II : L.. -i -·i 1 · - t.. .. I·it;_L-.;_ i-' : =I i I .,: _:__ . . -:i'·i;· i-,: T .-! . -.-iI i.- 1 '-: i .T -.'' - , j,: .. t 1-I . . . I- P. . I. -- _ - _--r(CI·3PCI·CIT - ' . ? t_- -. .:-:--r . ..7 r'-,.i . ---. I =- I__*_I__ .- ".iI -.1, I - .-. ; i.# ?i -P I 1''-I 1 r !.!. -- ·-- t ------- i; 2_,, t·",i 1- ":--'iI "-'II I . " . -ao -e i--icP1 -r++·U- -U---- ·- i-.. r-- : C i -· C;rii i... .- ___ -- i .i. i:' -. i I ·- ·I-··'1 ^-i---71-·- ·- -1 --- .- c-.- i · i -.- i !. ', r -i- ----- i- -i, 1 -- ·-· -i -- -- - JU t ~ O rl-' t -.... , .. -. I '' / ,? ' ' t, , L r. - -i----. ;i . ----. ... i '-. . ' X'+ : '''il;t w -t- ii ... f . ''t '! "'' 1-- 1-- {-r4 j.... -·; "' ? -.;: .. . - I I III I I it -- . ". t I '- ftW ! I -i------- - --·-- r 'i( --j --· A 1_ ' + j i - | '; ' '~' ' 't ·-··i 1 ~~~i . ...t j... ..... ' /. / .:-jIt.1. .... . i , ,!-: -,- I i t trI* -1 .i/,,, 'i.-- · ' ·-- l.-.--·-L i .,i _.. i· ---- rFcu- i·r; 1 . 'I'i i ·- -- · t --f I Irr · -3n L : i;Ai ..i, i -_·_ t --- ·- i i I- · j' .---.--L_· I]11 /o I I I- I /s' ! i .- :! 20 .. . ·. i r :- -? i ' 30 :· mixture entering the combustion chamber, and 1.1 to 1.7 times less than that of the average products of combustion filling the combustion space. The pproxirmatepath that the flame would take if not restricted by ialls of a combustion chamber may be determined as follows: At distance (L) from the mouth of the burner the flaes have a velocity (V" ) in direction of the horizontal axis of the burner. Let the density of -hl-leproducts of combustion at the center o the flames be equal to (d3 ), while the average density of the gases filling combustion chamber is equal to (d); then, the the uopward force acting on volume ( /ds) is equal to ("/d 3 )(d-d3 ). Since the m-ss of this volume is equal to (W"/g); {_:jj.=:-' The upward acceleration of the flames is iven by the following expression: "(d-d 3 ) a = - orce/mass (g/gW") d3 a = (d - da)/g d3 a = (d/13 - l)/g shere: g = Acceleration of gravity, a = Upward acceleration The shape of the 32.2 ft./(sec.)(sec.) of the flames, ft./(sec.)(sec.) gas stream is, of course, an upward-bent para- bola,coordinates of which are easily calculated. al velocity of the jet is ('V")ft./sec. Thus, if the horizon- after tr.veling distance (L) from the moulh of the burner; thlen, after time (T) seconds the horizontal component of flamepath is equal to (" -49- T), while the vertical component is equal to (a T )/2. This method of determining the shape and size of flame is only approximate and must be used only in conjunction with a good deal of judgement, since the difference in density between the flames and the surrounding gases is not subject to accurate calculations, and entrainment combined with diffusion rapidly obliterates all differences in density after some distance of upward flame travel. At the upper portions of the combustion chamber where the combustionprocessis completeand the mixing is thorough, the principal force creating movement of gases through the passages among the water- backed surfaces is that of draft -- usually induced draft, either by means of a chimney or by means of an induced draft fan. At this point it is appropriate to note that it is not desirable to keep the combustion chamber under positive air pressure for the following reasons: (1) It would cuse exfiltration of flue gases into the space vhere the boiler is located; which would be not only obnoxious, but also fraught ith danger of carbon monoxide poisoning. (2) It would cause infiltration the refractory lining and substructure r soaking of hot gases into of the furnace,thuscausing rapid deterioration. Once the approximate length and shape of the flames have been determined by the method outlined above, the general shape and dimensions of the combustion chamber can be selected so as to contain the flames in a manner that would prevent them from licking unduly the refractory surfaces. Due to structural limitations, however, it will seldom be possible to design a combustion chamber in which at least -.-0- ::r .'L one face is not subject to considerable impingement by flames. In such case the surfaces licked by the flames should be lined with the highest grade of refractory material, and in especially severe instances water-cooled walls should be employed. After the approximate size and shape of the combustion space have been decided on, the next step to consider is whether the performance would be improved by shielding the flames from the waterbacked surfaces or whether some considerations may make shielding unadvisable. ? W: should be employed only when it will promote the completeness of combustion and increase turbulence of the flames. ' '; !"''~?~' In general, the refractory shielding of water-backed surfaces In some cases due to a high rate of heat release in the combustion space it may be definitely advisable not to shield the waterbacked surfaces in order that the average temperature of the refractories may be reduced -- or perhaps only a partial shielding will offer the best solution. III Flame Turbulence As far as relation of flame turbulence to size of a combustion a? i'" chamber is concerned, it can be stated in general that the greater the turbulence the smaller may be the volume of combustion space for the same total energy release. The explanation of this is simple; it lies Zi in the fact that thorough mixing of gases within the combustion space shortens the time required for flame propagation and thus increases the rate of combustion reaction, which in turn results in decrease of time that the gases mu.st remain in the presence of hot refractory surfaces in order to insure completeness of combustion. (Increase in combustion chamber size, while the total heat energy release remains the same, results in lower gs velocities -- which permits the combustion renction to go on for a longer time in the presence of the hot refractory surfaces, thus insuring completeness of oxidation of (CO) to (C02). The rincipal methods that may be used for production of flame turbulence in a combustion chamber are ir-oil miture. (1) Strong jets of primary (2) Strong s follows: jets of secondary air. (3) Construction of combustion chamber so as to induce a.vor- (4) Restriction of pssages in the path tex. so -,sto cause contractions combustion o the products of .nd reexonsions as well as c'hanges of direction. These methods for production of flame turbulence trated by setches on Figs.los.23,2, Fig. No. 2.3 shows spll, flame turbulence is provided by re illus- 5, and 26, round, vertical high velocity boiler in which jet of primary air enterin- a nrrow vertical combustion. Fia.No. 2 #shows . small tubular boiler in .whichflame turbulence is created by srranging the burners so that the flaml jets generate ? vortex in the combustion ch.mber. Also, the narrow openings in the roof w.hichsields tL.e f lai.es from -'he lower ortion of the tubes, create an additional orifice effect. due to teir Wt , ,-~~~~ ~ ~ ~~~ ~ . turbulence in the produ.cts of combustion 'Sy5esZz,9 D2 se Ilot I67U='rB' of7 a Sma / PrnZ JS A #aZ'er 6f/e eO z jilaer ,?&rarj /. 723 C;:4r 'i;~~~~~~~~~~~aT· II I~ Sggeseod es/nr Como c 7ube of74 /Car I I Harner Tcvo- od= ii r 5 eCt/on I "' 4 " i R.&1rle Cros Secton o / . orW IC 2 4 An outstanding advantage of the twin burner set-up is flexi- bility of operation. By proper selection of burners with respect to their capacity, and by use of suitable automatic controls, such a boiler can be operated with an almost flat overall efficiency curve ri: over the range of 50 to 200 per cent of its rated maximum capacity. Fig.No. 2shows a sketch of a large sectional boiler in which the flame turbulence is induced primarily by means of a strong primary ir jet end a fire-brick crest which splits the flame jet into two vertices. Due to impingement of flames on the refractory surfaces, this type of combustion chamber will probably not hve as those shown on Figs. Nos.23 as long a life and2 4 ; however, it is of simple construction and the turbulence crest can be easily relined after a few seasons of operation. Fi.No. 26 shows a boiler furnace in which flame turbulence is created by fourfold means, down-shot burner (arrangement,high velocity jet of primary ir, the turbulence crest at the end of the flame jet travel, and a secondary air supply. The prticular factor in creating'flame turbulence in this setting is the collision of the initial flame jet with the secondary air which enters the combustion chamber through a row of small jets located in the false fire-brick bottom. In general it should be remembered that a higher flame turbulence is lways accompanied by a.higher pressure drop across the combustion chamber. The energy which is generated during combustion exists primarily as kinetic energy of gaseous molecules nd does not contri- bute appreciably to the energy required to overcome the frictional reFE sistance to flow of products of combustion. The only way to utilize directly the energy released during Suggesfed _Dc~~;r/g~o f , LZargte,Se o/er rl I ii I K?/ra c 76-p / 67'A/s 7arr6a/enre 8#wrner Z7roUa A A' //v A/ -, I~ LI c C '4% kS , QJ b>V) C4J KII I-) tz q) br- tl. · z It - : :--, . . :E0;25 combustion, for tile purpose of oercoing f'ric'tionl resiatance flow of products of combustion, of the n-tural is to t-akeadvantage dra.t thatcarn be cre-ted hen liig.L exr'ondedgases ore :, ,-: -- :r;-J :; - ,escape through a stack or chl'neyo j'/: ;., ·.... ,'' :" : :,:, ,' X, ,;,,, :.::f -rtf - to 'er.itted to i: :: L :I ,ll r: -r rART II RADIATT TI',iSFSER OF LIBERATED ~j 2- 1 / I __ . HEAT E'ERGY iTEa Vi Lw- A O0\,:TTI:? -t I;; - _· _'s ; ;i ·_--:i·-. -. ·I, 1-; i .i : i·· 'is;E ·- · ; · -Flk' K ) Cr P '.It II_ 4;i ,.I rz ;· iY a -C · · ·; j:E4 RADIANT HEAT TRAS PER AMONG THE INNER SURFACES OF A 1 r W r COMBUSTION CHAMBER ; Introduction 1.' Radiant heat transfer -t:~~ encountered in combustion chambers of small boilers in general, may be divided into two distinct parts, name' ' ,'ly: (a) That which tkes bustion chamber -": e place among the ier surfaces of the com- including walls, bottom, roof and water-bas.cked surfaces, and !:?" (b) That which takes place between the flames or products of combustion and the solid surfaces. ,~i~.~ ...... . S -. Both o these modes of heat transfer, of course, go on simultaneously; however, for simpliicityof analysis they will be considered as two independent mechanisms -- -' with roper adjust-,entfor such as- ' .... sumption. The subject matter treated here is confined to radiant heat trnsfer q between solid surfaces separated by a non-absorbing medium. At this oint the writer wishes to state that no to theory of radiation is being rmadehere thlnris bsolutely necessary to show the sources and meanings of various constants well .. s their use in the well known equations ore reference nd v.riables, as nd formulae. . :< ~.,-/' ~~Definitions of Terms %~: " .. A brief resume of term definitions is in lace here in order to establish the meaning of all symbols used in the discussion presented below. -S-7- (a) The total eissive -nted s (EA), is defined directions (A), usually ower of a surace desig- s the total radiant energy emitted in all from thatn surface er urnitof time, per unit of rea3, and s --sually given,as tu,/(hr .) (s.ft.) (b) eitted Intensity of radiation is defined s the rdiant energy n:r unit of time, er unit of solid angle with its t;e radiating area, perunrit u norojected radiatinr jected rea-- the -pro- ,to . the d.rectn res beinE on to a l-.anenorr pex at of the rad - -ating beam. (=-) Thrnormo ' o rite ist tevnltenva, of sity when he a.is o (d) The th'lbenm is s3vtrntivit of ioulor t:n-er t he rdiating surface is te fraction of rdiant which energy incident on the srface, "-rbed is of a surfac e iPthe fction (e) Te reflectitv sur- energy incident on the srface, o rdn wich is reflect.d. -(f) iThetrnsis isiity of asubstance P is the frctio o- rdi- etion incident upon it, .hic is trlnsmitted throuh it by rciti..on. ;T.hesu,^ of kbsorrtivit,7+reflectiv-ity '~~ oaoncuesolids of appreciable tFor iroan.te/un :bslt. o , hickness, snO zLsero, rn,tr nsmissivity euals unity. : {.h. ,g) A blc--: od is defined as radiation whJ~%ich-\ falls on it,ai.ad reflects, (hL)The poer t o th t o _no. blc J11 h1e re: ~ %he cntisty surfce trnsits,. ty-- iise`c which absorbs all the an.d scatters none. surface is 'isivuity: tle rt io of its -euissive body, or P = thle trins..,iisSiv-y is equaL A ) tlle....tialy: / (Es) p = Emissivity of surface (A) EA = Total emissive power of surface (A) EB Total emissive power of a black body (i) Kirchhoffs 'Law An important generalization which underlies radiant heat transfer between solid surfaces, known as irc'lhoffs'Law, states that the total emissive power of a surface (Eq),divided by its absorptivity (a) for black body radiation of its oni temperature, is the same for all surfaces at er (B) of a given temperature and is equal to the total emissive pow- black body at that temperature. .Mathematically: (E A ) / a = E Where: EA= Total emissivity of any surface (A) at ra given tenperature, t. EB = Total emissivity of a black body at same ten.perature,t. a = Absorptivity o the.surfacea(A), for blackbody radiation. It is seen, at a glance, from Kirchhoffs'Law that the emissivity of any surface is naerically equal to its absorptivity, at the same temperature. The General Equation For Calculation Of Radiant Heat Interchange Between Two Solid Surfaces The simplest general equation covering most cses of radiant heat transfer between two solid surfaces is usually written in the follo-wing form: r{, -0.172 (A) ((T / 100) - (T2 / 100)) FA)(FE Te ee: -n = Net rate of heat radiation from the hotter surface to the colder, Btu./(hr.) surf,.ces, A= rea of one of theto A T=- Absolute temperature of the sq. ft otter surface, F.kAbs.) T2= Absolute temperature of'the colder surf-ce,°F.(Abs.) F A Factor to allow gorthe verage ?.nle tzhrounout which one surf-ce 'sees" the other. The f.ctor, Pends on tie surface selected o couse, de- for use in term (A). allows or deviation of- the given surfces PFactor wvhvich F from complete blackness, and is a function of their dividui 6emissivties in- k(pz) -nd P2). Application Of The General Equation To Estimation Cf- Radiant Heat Transfer The complexity o rdint surfces In Combustion Chanmbers 'ahe.-tinterlnge of a combustion chamber depends pr.rily hle inner aonc on ter tepera- t-ures. If all surfa.ces are ?t the same temperaeture, which is possible only in the cse of an ideal design, then the net radiant heat transfer f-rom any one of them is of course eual to zero. Such condition is ap- p=roachedonly in small combustion chambers which h.ve the fla,1mes n.id in which the flame is saielded froi tie I,3ape enveloping ter-backed surfaces. In most instances -at different the several surfcces ounding thle 1 fl7ames are temperature -- depending on teir proximity "to the flames, their position in space itlh respect to each other, their emissivity, and the nature of the substance from which they are made. Therefore, the subject metter treated here consists ofmethods for evaluating the equation in order to make it ap- factors (FA) and (FE) in the general plicable under various conditions. On pp. K.li to are presented formulae for calculation of factors (FA) and (FE) for he most common instances of rdiant between solid surfaces; to simplify .transfer heat the computation procedure these formulae are also supplemented by charts on Figs. Nos. 3/ . :, 27 , Z t9, 3£0,,ind ''.j;~ The Concept Of Radinnt Heat Transfer Coefficient The concept o rived esily from the coefficient of radiant heat transfer is de- he general equation given on p. q = 0-172 (A) T 1 / 100) - (T / 100)4 (FA)(FE) may be writte -, q = (A)(FA)(h when thus )(T - T2 ) dofined: h r = (T / 100)4 For ease and simplicity (T2 / 100)41 (o.172)(F7) (T1 - T2 ) of procedure a graphical solution of the coefficient (hr) is given on Fig.No. 3 2 attached here.(Note: on Fig.lo. 32 the term (FE) was ssumed to be equal to unity). -6'-- . · ,* '.. -r-ln C- .... L , ' ...I. ,:. ' ~L, ~.'t , .. -, .... rf.... · . - .. ... I-·· t . f .t : i ' · -- ~... · ! '. ... i .-...: . -- ! ...: i I I i rC--·--------f L. : -- ---i- : E-t---r - ' :· / I r i. . cf , . - ;'4' - . I. . . I. . I. t _L i_ . 4 .I . . - i . _ -t- . _ ' _ . . . . . I I..- .. 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I --;-·-; -r-,- ·-· ....'_ -e X.. _.+ . 4 . .;I . ' .' Si 11! q t - .. -- 4 r t . ... . -;- -1i- -t--' i··· 5 .s . . T I _'h '--~~~~~~~~~~~·~~~~~·h ,-·~~~~~~~~~~~~~~ --.-···t --`' - -- '·.-:-: t. -- t-t C-1" :....t--.- :· ' '' -·- __ , T _ _ .> 1 $, ' -.. ..- :. ,i ;: . -:-+' ti iI . - j: , I | k ; - -t i -; - I. - --_ 0,. | .. 2100 , . -,.F' I, . I · k . -,-· . - - ;. r- -4 I· ... . 4.... i: Fi .!-. I.I...... F71 *'''-li -1 ·r-- . i.. -- 1- ··- · · · -, -C··;-··--·, . .. i .. ..1.... ..: .. i. , i... ·· ·i- r-$ + --L--ce --cci; I- ·L.-._i1-_;-- . j_ I -- --- 1 j _- ".. -?. . I·· _ -It ;.. .- t .' i :... - I 2 .. i : iI _. --- : .- ' . I!::: I 1- ...·. ii. i- -i-·-·' _. . i. ' I ! r. - - -. r-.;..c r .... , ;-c+-. i -.- - i · ·-·--c--c·-- ,· -·r-t '-·i--··-t--''~' i' -_-t-_-r |. i. .~~~ .I - [-- . '1-i i . . a .-.-- t 1'.; i . i___- I 1: ; :_· · i··· I tfp, 1 !F - C _-LzZ ,i.3-.Z.;.n i ' , . , I~~~~~~.,. _ "i'7 ' -; ?_' " I . ... . I 6 I--·-- . . -·----t·--r -1--- -+--··- i --· '; -I--r-·-· --- ···l-C--1· ,-- .. ,-.. .- ;...: .1. .- c-. -- i· ---------- -*-----c-----e . . a i----ec-- '`" "`f t--i-T i--- . -::i ... 9- ._...... I., I . '1 V .'F·· "1t; -e I- -·r ..; ''-· ;- -- r--+ · ---·--t··-·... -:·-f·i· --· +·---r-t i o -I' ' ' ·--I '' --·-· ··I··-L---t..- I -·--·-------- t _L If J 'I I - '.. ..... . i· : I :_I i -`' ,. :. I - . . _- I1 c-- -i---T . t e b - .- '.:': 'I I----+-t3--k-e '"``* -..--c : -------- :i · ·-u ft r ..... , ,, ir : i r CA ll{ ---- ' IT:. r r-· -. ,. .. - e- -ii---t--- j '` .i..,t i. .-e ; - I r-C- t 1 I sa' L I I. - :. 1 ,.. ...,... ' " -i L.I.... ··-!··i - · f - .': "--r--*--ce 7 I · .F., ' . ...... ; ' r ·. I' ' -; qr 1 r ·-- " ' ,I . I..., t I: - ' ' I I I ; i - , : I": i.. ''' i~~~~~~~~~~~~~ . . --.* i - , ' ____s.,..- ':_ ·· i ' : T j. - I - . . ... ·I ~ ~~~~~.. ~~~ ~~~ ~ ~ ~ ~ ~ ~- . ~ ~ .. ' . -_. I . . I r t 1111 i-a , 4 I - i---- 4 4--',; i . il L ; I 1 ;: ' \:% z *j,........ '! Is , ! ' ; ~2&1491 4,0 ............ t--t---ly r t+% i -I .JI 'I - l t ? !: :; Mq I RADIATION BETWEENISOLIDS Below are tabulated 17 fundamental cases of surface arrangement which may occur between solids, and the corresponding factors for equation calculation of radiant heat flow, use in fndamental (Fk(Fi .172(A) t(T±/100) - (T2/100) q As given below: A = The surface to be used in computation; FA The angle factor between the given surfaces; FE= The emissivity factor; p Emissivity; (According to otes by Prof.H.C.Hottel). CASE I: Infinite Dnrallel planes. A Either. I FA~i ;FEl 1l 1 +-1 P. Ps CASE II: Completely enclosed body, small compared with enclosing body. A = That of enclosed body. F= FA 1 1 ;FE= pl CASE III: Completely enclosed body, lrge A = That of enclosed body. FA= 1 FE - compared with enclosing body. 1 1 -1 P1 Ps CASE I7: Intermediate case between (I) and (III) above.(Exact treatment is possible for special shapes only). -62- L ___ _ ______ - - ________ . __I __ __I__ i i I I ! i -- -- ----- ,----- i-----,--- ---- t j i i ..--- ------- i | Xi#, ·- I 1 __ __ - l t S eV I i I ----- I '----'--- I ' , ' '' : --- -;---·;----- ·----- i i ',.-0 -- i ------ ,.-_L.. *---- i __ i : -. .. L.--.-i----l--; I t----r-- :___j ------ Ir-- i __ _1 r. · ...... -· -- 7-lp 1 j ,i ..-- c. -··--- -- - - It. !i. .. i. i.! s1.1 I. ' .I 'izl i 1 i. u. ? ' ? s i ii ,-- i I i I i 1 ii, I i i I n i, i i T- ' i ! -- I r i /fl m - - ; 4 /I i. i i L I . iij !.I'1 : I i I I I I i I I 1 I YJ/r/Y I , I s - - - iI. ...... ,, 1 t--c -. _i : * - i _ ·. .- _ _ . "... t - t- _ __ - } 1,i I_-' I ; . -, ---- ~l i _ _ _ _ II, : t·-- I - i - ._ L_ ---- i t- ------ iIf =r I_ I- ] - -r-- 4 . -s A , I j ; !t r _ _ _- ,-- e i I i I : _ -- -- -__ .! I - I l _j Fl I . !! / - -- r ... ~~~. I 1 i:i , I,.. ..... ,..~ .. t - br L I _ .... i ..,--.~ I 'Ti -' iIe I ii I -;Fn .a~ i. C. F-- 1' ilJ iti o A li ;7.,'--"] 7 7 - ' ,!-.. ,,r' J ., i i LC i I -- - ~I ~ ~i. I I ,J'. I I _ I---· r - --, I i __________ _ -11-~ ' .. 'i" i. z I .---} i . i" l i ,OW _ I I 1 _i ;. . .0t . . __,-- -- i ; I I- I i .! 1 1 i I iJ--~- 1I---] i--- I -L 1 h 7i j:-. ~~~~~~~~~~~i i b-:rx 1 A 1 i i - r' II C-I L L i, : !' .... i 'I .. I 1-''~~~~~~~~~~~~~~~~~i i i I i i --- I'l -I . I i i ! i i I· ~I t. ` I, I r I .. , -- f I i i *t I I I i' Il i. f ....I II .... _~~,.,I . i~ i~ .... -I,-I I~_ii 11,, 4,~~~ i i &;i I i I I' 1 i I/i I i---li----.-- . I i/ I 1 I 1' Ii I --·--, I--~----- '- 7,,.. · __._ _ ,L._ i _ ~i ~! i.;. :T-i -- i I i i /r i x _ ...-. -- c-.-- I ' I i : -~ r~~~~~~~~~~~~~~~~~~~~~~~~~ i,(l i I. . ----- I 1it' t1 -·------i---------- i .-- -. ! I _ i i ------i-' - I ;-t < K r -·-------t---- · tf I ii _------ oi i------I - L._1 _1 _. 4cp I --------- . _..._ .....-.. '+ ' A ---- ... ,c 1 I~~~~~~~ r~~~~~~~~~~~~~~ -----· ---:---------·-i---·--.-i.I -l-i-r -l-- t- .- I... ... L---- .I----. i i , I i i ·----- .- ..... ' ! i i I j I · - I i--+l . .. I i ...... i f ·. - , I- I '; I ,- r- ',, i I ! I i - -- ----- t-t--__ ---k--- I I. - I I 1 tt 1 i ! i II Ii i '' ·--- ··-- i----· I A-- A _. i t X ; r _,__,, ,,_,__ , ; r I I-.--- i- a I ~~~~~~~~~~~i; Gr I .. .. i ~ . ·t ·- · --- T __ II ! ! $ 11" .-- ___ _· · 1. i il __ __ ir v !I '! -- *I . _· ___ __ i -- `-' - ia 2_,~ r ,M jtr0 · w MlF-_ M _.~~~~~~~~~~~~~~~~~~~~_ ~. ....I ir B ;jr; A = That of enclosed body. .a 1 > FE > 1 + Pi P2 p FA= A= 1 r n_ 1 8-; e; CASE V: Concentric spheres or infinite cylinders. II.; fF A = That of enclosed body. A FE FA= 1 i; s: E-p 1 1; A 2 P2 A,= Surface of enclosed body. A2 = Surface of surroundings. jir " A)and area A 2 . CASE VI: Surface element 1 m In general, A = dA Xfr FA= dw c ; F (p )(p') ;ji Cases VII,VIII, IX, and X are special applications of Case VI. (Note: a more complete treatment can be found in an article by H. C. a: L" -i i: i: Hottel,Trans.Amer. Soc. Mech. Eng.,FSP 5-196,1951). CASE VII: Element(dA)and rectangular surface above and parallel to it, with one corner of rectangle contained in normal to(dA). 3 T I A = dA i FA= See secial graph on Fig.No. 2 8. FE= ()(P2) i x s CASE VIII: Element(dA) and any rectangular surface above and parallel to it.Method: divide the rectangle into four rectangles having a common corner above (dA) c r- nd treat as in case VII. A = dA FA= Sum of four FA' ; FE= (pl)(p2) CASE IX: Element (dA) and circular disk in plane parallel to plane of 1i· 1- c , (dA). For complete treatment see reference given in Case VI. For approxi- No I /1 -i C.2 .. .,1 % :^,L - 7 Cz a;3 --: Iz, < 49 0,ZV,, s aq/ / U.; /cr i F __ I_ - II l : _ . _ 7 ___ P_ ,,..-.. - ? 44++- . L.---~. ,__ ___ . 'Mt- _e 1 I i ____ _. II I .% 1-ii . l - _ -I w--- - . -r -- __I '1 _ ,_ I!12 Of _ V* I1. I I l t I -- I | . \ 4~ -L-- - ____ _- l 0N L cl Ia _ -i i )'~---- L--j I I tS i --- i [.: ------- - k i·ll ,. U 14 -- \ 1i1 I ii 1--- ---i . ri , i -t J I II r i I ''.I. , i I -i.! ! _t_ I . 1 KN.. -t i_ . Iht aV% .'.q A 01~ · ---. 1 ' .i : I i ;b --i L1 ii .,1 1 . i , I I I 1 r :i ------- c--i I. I I1i -L !Q . .. _ ---- E I· t t_ =:1 -. 1 : \ ·I I I r It> -Ba t· i 1 ^, I/ 4,K- ' i /, . /-~/ k7rr , I I i I ;_-4 I ~ I I, I II i g Ei I I t -- - I I. I I I J .-"k -4-11- r ----- -· I, i J 1 Ii · " ..... -v r I I I I i i I1 q .1 -- I t- . t I - - , I i ,, j '! i /I Nx I 'i !I· : %L7~~~ d/ / !~ i 1~- I, 'VI N,' I ·1 I . I x !i I i ti 1NI 11 \ . i .. : \) .. I - M- %J I,%% ',; ZA,,-i -4!4'" -1 '0) i. Li ; r T 7tLZ___221::=,.Z_. : !· - ... 7W k. i .' W/ .~ . I I ·-t I -£ J I i ' 1 I c---- ------ I L- ii I ,I 1 bsI il i -.. ! Ii 4 q Sv F- VI i -- c--. ---I 4 . -!i Ii -+I I ii- i ;· , I I I I* j ----I .II" i I ) k----. I I C----- 1 i . .n i~ i.'. I -- - ----- I c ---*---- I.. C·-- t 1 .- ,--.-i ------ I -·I c i r r r-- -- I I - I I 1 , ... ',Fg _1____ I k. .i hI - ,> % I i ) I i. i I .X I--c--- i ,~ I .r R m!ili I I 11 f ..... I. i 4 i - I _ by 1 I I _.__ I It i\ C ___ I .'H~ ttH---- iI il I .-- .. II·i( L ,V I 1 II ! i-" i ii III i" -.- 114 ' 61 .j, .- I '" -- i I T . _ I ! i --- . I I [ II I I L . -.- L__ . . : · v J r t 1--- _ __ _ J .. - I . - I-J. 'Q. Z- P,ELf rW~A___ I ,. ___ ' ! . , ,! i ~.= i.-f ! ' [ N '~ u f ? 21 , __ ,r1, I i,~ ; · mate solution use a method similar to that in Case VIII. CASE X: Element (dA) and semi-infinite surface, latter generated by line moving parallel to its original position and to plane of (dA). Method of solution:- pass plane through normal to (dA), perpendicuand lar to generating line.of other surface. In this plane (0') (n) are angles made by lines connecting (dA) to edges of surface, with the normal to (dA). A dA FA- (sin '- sin 0")/2 where only plane angles are involved. FE (P)(pe) CASE XI: Two parallel circular disks with centers on same normal to their planes. For solution see reference given in Case VI. CASE XII: Special case of XI, with disks of same diameter. A = That of either surface. FA= See graph on Fig.No.30, FE= 7 ; line 5. approximately, P1P2 1 E( <1 -+-- P3 -1 Pe CASE XIII: Two equal rectangles in parallel planes and directly opposite one another. A = That of Either. FA= /(FA,)(FA,) and p.ps(FE( + P. where,(FA,) - . '1 1 Pa factor obtained for Case XIV, for squares equivalent to smaller side of rectangle. (FAn) = Same factor, for squares equivalent to larger side of rectangle. CASE XIV: Two equal squares in parallel planes and directly opposite % kS Iti llb % 't 4 t .%, 5~ J 'VP'w-S i one another. A Either. FA= See graph on Fig.No.3O,line 4. When areas are small compared to distance apart, FE is nearer to (pl)(ps) ; when areas are large FE is nearer 1 1 to P1 Pe CASE XV:Two rectangles with a common side, in perpendicular planes. A = Either. FA= See graph on Fig.No. 3 1 ; FE= (pl)(Pa) approximately. See note below. CASE XVI: Parallel squares or disks, connected by non-conducting but re-radiating black walls. A = Either FA= See graph on Fig.No.3 ; FE= (1)(P2) approximately. See note below. CASE XVII: Parallel rectangles connected by non-conducting but re- radiating black walls. A = Either. F = Obtained from Case XVI in the same manner as Case XIII is obtained from Case XIV. FE = (Pi)(P8) approximately. See note below. NOTE: In Cases XV,XVI,and XVII, an exact formulation is impossible unless the entire system is completely described. However, where (P.) and (Ps) are 0.8 or higher the approximations given are satisfactory. __ Lr - -' Z0 J< z Iz I d raa I, JLAJ,. :13=;3 >(J.-- i. i' II N zo I 1I I j' 1 8 i -trrb I 0o 1. i -.-I-2 - I~~~~~ t~~~~ iI 1:11I -1 I I ' ... t : i - -t--f8 I. I I i . iI .. --- I I | 1 I I' i V.. I U,) \- . i I I (In I l | \ w '*--r-l----t-tV T-+t -t--V\:t-tt--t----V-t l -- C I t - -2 .. .... '. a 0 ;~~~~~~~~~~~~~~~ 1 1I ZI_ I I II i i;l X z :{.~ IF I I -, 0 I toN i--------I.I I II . ~' 'i' ' \ I1- i; I I I I i- II II I ' 1 a- I II I n-0 I I t1 I I I Il I I I II I I II: i· NZ, t1 '-L I : I- LLI IVL- .l \ I \ I. ) z I- \ 1 _ I\ -- r-·- . -- - +- - - -- - - - v K-' 7 . x-·;-·-· · - ASL - ] | cq-i'\ - - i·------- -L---l . 1 | L I @TY liN iI: : LL 1 .. * _ o0 M0 ' .. - . · Ill t .; W N - C. k _ V - , , * I 7 yy--. CZiZ LI, x K- -ll . '14--l I _ -~--· - - -- \, \ 7 mPC~ I I tr , . . .. N --- -,-..- ; - rr . 'I I 80OijVi 1n o f n (-WI' 0rl u, -7x o 8ti2 N ia -- o CHAPTER VII RAT,'I 'Fl ", Y.~ AT TR-S-f'3ER 'RO IT RAI... TR.. THEIR ? RO PTH '~ C°~T'T AO3:Su : oTSFR PRODUCTS OF COMLUSTIO"T ALONuG OF TRAVEL 'H2,CUGH 7HE EOILER RADIATT HEAT TRANSFER :OI. GSEOUS PRODUCTS OF THEIR PATH OF TRAVEL TROUCH O.SUSTION ALCONG THE BOILER Introduction As was mentioned above, the radiant heat tr-nsfer within the ioiler can be divided into two distinct prts: first, tlat which takes place between the solid shapes and surfaces forming the combustion nd second, thantwhich takes chamber, lace between the gaseous products of combustion and the solid surfaces that they see in the combustion chamber and in the "heating surface" compartment. The fundamentals of radiant heat trpnsfer between solid surfaces hve already been discussed above, nd the subject matter presented here will therefore be limited to the fundamentals of radiant heat transfer from flames faces of the combustion nd products of combustion to the solid space sur- nd the surface of the water-backed gas pnassages . Radiant Heat Transfer From Flames To The Walls And Other Solid Surfaces Within The Combustion Chamber The nture classified for the of flames, in an oil-f4iredheatin urpose of rdiant heat transfer boiler, can be nalysis into three types as follows: (1) The non-luminous flames. (2) The semi-luminous flames. (3) The luminous flames. The non-luminous fla.mesresult when there is _067- a sufficient amount of air available to insure a rapid and complete combustion of the fuel oil. The luminous flames result when the supply of air to the combustion chamber is not sufficient to produce complete combustion. The essential difference between non-luminous and luminous flames is the presence in the letter of molecular incandescent articles, which are usually groups of carbon atoms resulting from break-up of hydrocarbon oil molecules. The semi-luminous flames represent, of' course, the intermediate stages between the non-luminous and luminous types. From the point of view of thermal efficiency it is self evident that the most desirable flame in the combustion chamber of a small heating boiler is that of non-luminous type. It is true, that with a non-luminous flame a greeter extent of heat transferring surface is required than with a luminous flame, since the radiation from non-luminous flames is lower than that from luminous ones; however, this disadvantage is amply offset by a higher thermal efficiency, and by lowering of flame temperature,with consequent lowering of soaking of heat into the walls of the combustion chamber and hence a longer life of refractory lining. Under actual conditions it is of course impossible to obtain an absolutely non-luminous flame; however, the approach to it is so close that for the purpose of prediction it can be assumed to be nonluminous. The error in radiant heat transfer computations introduced by this ssumption will seldom exceed 3 to 5 per cent of the actual values, whereas the emmissivity constants employed in calculation of radiant heat transfer re seldom known within 5 to 10 per cent of the actual values; hence, this assumption ? flly of the flames The principal mss sists is in justifiable. the combustion space con- rimarily of the followlin gnses: (N2), (CO2), (02), (H2 C), and quantity of (S02). Carbon monoxide is of course present in the small flmes 11 cses when combustion is incomplete; however, in sufficient mount of excess bon monoxide is ir is where a supplied the concentrtion of car- negligible. Of the bove mentioned gases, only carbon dioxide nd water vnpor need be concerned in estimption of radiant heat transfer from flames, since nitrogen nd oxygen do not rdinte any ppreci-ble amount of heat at the flame temperature found in combustion chambers of boilers. The mechanism of rdiant ably nd heat transfer from flames is described ully in splendid discussions by H.C.Kottel in Trans. of Amer. Inst. of hem. Engineers, Vol. 19, p.17, ing 'V1hemistry",Vol. 19, p. 338,1927. review the above mentioned works of the theory of limited to the nd in "Industrial and Engineer- As it is not the writer's or to o aim to into an a.bstract exposition rsdiant heat transfer, the discussion given below pplication of L±ndamentalsto rdiant is heat transfer cal- culestions. Briefly, the rdiant area of the of these surfaces bounding it is (P) is 11 pOrts o verage integrated of the g gs to a unit is . roduct.tera the radlatin'ggas in atlength(ft.) of the radiant mass to the bounding -- mss two vri.ables: one and the other the partial pressure o aossDheres nd (L) is the from from a function is the gs te:lperature (tg) (P L) i-n whic beams nergy eitted surfa.ces. At the same time, the radiant energy emitted by the unit 6? rea of the surface nd absorbed by the gas mass which it boundsis lso a of the product term (P L), -- function and of the surface temperature (ts), End surface emissivity (). Thus the net radiant heat interchange between a mass of flames and a unit area of the solid surface which bounds it is a function of the following variables: P = Partial pressures of the radiating constituent of the flames, atmospheres. lames,0°F. t = Temperature of t = Temoerature of surface bounding the flames,0 F. L = Average integrated length of radiant beams from all parts of the flame to the bounding surface. Ps = Total normal missivy of the bounding surface. The signifig-nce of all these terms, except the term (L), is self evident. The value of (L) can be determined mtheuatically for any geometrical shape; however, for all practical purposes, the short table given below will be sufficient for all radiant heat transfer estimates, as the shape of combustion chambers can seldom be built to conform exactly to those of true geometrical figures. Average Lengths Of Radiant Beams In Combustion Chambers Of Various Shapes (L) in ft. Shape Sphere 0.666 (Diameter) Long cylinder 1.0 Short cylinder(height=diamleter) 0.666 (Diameter) Cube 0.666 (Side) - 70- (Diameter) Figs,,Nos.33 and 34 attached here present graphically the relationship between the variables (P L) and (tg), and the radiant energy emitted from carbon dioxide and superheated water vapor present in the flames. The same two figures also give the relationship between the variables (P L) and (ts), and the radiant energy emitted from the solid surfaces which is absorbed by carbon dioxide and water vapor present in the flames. Since carbon dioxide-gas is somewhat opaque to the radiation from water vapor and vice versa, the two together radiate less energy than the sum of their radiations calculated separately would indicate. This discrepancy increases with increasing thickness of the gas mass, with increase in concentration of either of the two radiating constituents, and is particularly pronounced at high temperatures; at temperatures below 6000 F., however, it may be neglected entirely. H.C.Hottel gives a correction for mutual absorption of radiant heat in mixtures of carbon dioxide and water vapor at the radiant wave length of 2.7 u,(See: Ind. and Eng.Chem., Vol. 19, p.888). A chart has also been prepared by Hottel and S.A. Guerrieri, which gives a graphical method for determination of correction for superposed radiation of water vapor and carbon dioxide at infra-red wave length of 2.7 u; Fig. No.35 attached here gives.a reproduction of this chart. Using the basic data given on Figs. Nos.33 ,34 and 35 , the net heat interchange by radiation between the non-luminous flames and the inner surfaces of a combustion chamber can be calculated by means of the following equation: X =(As)(Ps) (C - Kg)-(C + Where: - 7/ _ + W- K) noW' Jad .04 . ,Pd ,oo *' - -J a a W IP6 'n; J.'d N h0 -3 A1b w . _ Y_ 1 v %I J- 7't - n .I I I x N IN .It 'A N \.t N T llu w N 4. I .. I, - 1j 1%, I\ AN Ia II \I \ 'IV IN I . I bI N lA\ . N- I ie T N v. 4 I 1j ¢ . ~, I I k\1 N U 1 N N l* 1tQ _~J w, ~ ~: \ "~~~~ K -4 -t ,_ 1, ~ 0) 4 N ii P:'~ F 999 if 11 - 14 k "a fp I,14Z %11- 11 s 1, 'It II - it P ,4, -jN A N zaIla O ic, * r A I _ _ O " I ZA o· ZY a a Z9 I111 " k1'N` " ,,, " . lN _ _ CS " 1Z, o a0 o uu.c3i=·.,c=;;----CiSS-·· -O 'at o ~, . - ts ev _ _ _ 1 " o _ " _ 1, ..\1 ...s|wna.J ...... _- 'w) m~ -i**------c-C--r` Ir I IM. ,~ _ .' ;..'_,l. , i . , .~ ,_, ,. ' + ._..... ...-.. .. ... t' t( , _,' , . .... , : ' ". ~ ' ,: . i, ,".',.........,h '--,--t:--:ir+-.._-tt ----+ .-. · ~-~ . .· '-.-j__t~~~~~~~~~ -~L -t- ,-!-~-,+..v .~4 .... '--~- -. -4,-.... 1· .-' '~ *;0 "..'- '. ' ' -' - ' ,, -' ,' -.. L" G C. ' 0J . ~. ~' 8~ ?', t .; ''~ i ,i ..~-{ ' t ' ' ' '- ~,-; ,4 .~ ". .: : . .t, . . , . ..ii ...- , ~,-~- . 4- * -~ - 4 - ' t . - : '.. . , _. 8 ~~~~\ ..-; '~ . .,, ~--? t, ,--'--~-rTT* t- '\' ; ->>5+q + ~s t-~, ,., ,.,','~ ' ;,. '-.' -- ;. . · ....... "_ .- : ...-. ^ * ii;F . r ''. ', ; *- i '> ~~ ~ 7.-,! C-L) t- {·I-·· c-·~ · · t··L*1 k : : ' g--t-+ t 'X+ . ' t ;~~.'.~' -' ~'--·-t.· _ti 'ir·cl,~ ' ··--- t-·"'t-t . - * , ' · l-- , , '+- .· ··. ;; ', iI ~·+,{ ' ·~';'. ".;·t-t-tf t -- - ':·-L '5 ! .. L. "I.-L ... ~-4'~i-i ~.. ~ . ,·i: -- · \t'. . ....- LC 3 . ,.-. .i. ..... . .-... ~....+ ,. . · ' '' ,~-.· " .,.· {-.~-·: -~~·~ t -.--- - + t ~ ' ~{Cti-' ·. . +*^4 t ;-~-t.,---4 >. . .~ ·*·---+·- ·+-·+,-- · 1 i ~~~~~~~~~···--·-i ·- C--)-~ ~ ~~~+,a....r ! · J.~ ' . '4-;. .-. -.' . \! .--i. '.-4'- :--.--', : 1 ' -...... . ... - ' i~~ i ' ' i a .. ,' ._. '"'..'..'. ""'..:--..-.*.. . . . . .,-...-,..........--..........-+...4. . . . .. ..... -. .t.T-,-/-r[ ',~ -*J ..; ,-7· -·- '" , , ~ .....:,4~t'{ ~'v,',-"~--· '," '- ' r ~- ' -~--+-*- ' ; t - , ,' L. , ,;; , ¥; 4- ', '.'.. ' ,~ .' 'r ,·' ........ 1.,_... I- r r A i", "'""* °, I'"' 9·.. -;-... 4--.~-- ' - -- r-. ... ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~· . . i ... -,-,,l ~- ? -~ ---,l--~-C - ~- -- + . ~1......---- r - ~,-rc .... *,· ,-,.-'--:~.~r-~ i :~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ I 'r ta i 'J .'t I. t '. . . , I ,~ · ; I ' ; : ''f' .." ' I. ! i .o ,j, -- +.+ I -. --- * ttt, - -, ot .- . '-' . Ir . . '\ 1- i ·-r -t -·t-"·C··-·· !;-I i · ·i;l \,i - ii.I j j I N , t·---t ?j i ! r II O. U1i· :------t?4 i l-·i··j j cu i : ·i 1A. La I ~ > Ly cO L. I " \i i fI i Z H' '~f .~ . Ov. td3 (L .. ,, !\ a Q, <. nl NI II -~~T ' ·: 4i , ` ·Q~~~ A_ olW 2 Li 1 I rD II ItI \i f f 1 \I i ~[h ,, \ It iZ :I\ I ; i· I t · ~ I\ X j!Xj '' I It. i' L a§ U. L- w I-. i i' i' 0, ', I\ r 'ii : t ~. '~' \ \i r IL wJZ, _uw o kI i P w' cr 0z_ ni0 z L 1\ X; I\iiii IX 'Q r i .I Ir 1. ~~~~·E· ,- ' _R I, -. .~ u 1~' ' W < bI i a < inw x. ,il wM " o CL z aZu -CLilc-- j!1" i 1 I iV(\ . V \I\ ' B ., i .I ; ! ' ·\ 1 ') I 1% W ;· ' iI r I _ i- koO t---L-C- . I iv I 'L~ t 1--· \I "Iii ._ ! , i~~~~~~~~~~~~~~~~~~~~~ 4 r i. , ','' -X'| [s;'X.. ,^''X ._ t - - --. .- - r ,* I I . I..i. t-- \i4 ?i ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ · [ i. i I : ;\Y YV 1 *~ o O .U W C7 COf aI CZ .Oy O O M i i a ' o o eV , .. , V o W v O 2 co . . WV O 40 { - . W .0' 0 tr 9S . \i Yhnl\ NNil Al C) V ; > , \n i 1\ x_ \- i . e3 -A.· - Q = Total net radiant heat transfer from flames to solid surfaces, Btu./hr. = The area of solid surface which "sees" the flames, sq.ft. A Ps= Emissivity of the solid surfaces as given on p. . C = Radiant heat emission from the mass of carbon dioxide gas, g. as obtained fromrFig.No. 3 3 at the average temperature of the flames, Btu./(hr.)(sq.ft.) C e surfaces of the com= Radiant heat emission from the innrmer bustion chamber absorbed by carbon dioxide, as obtained from Fig.No.33 at the average temperature of the surfaces, Btu./(hr.)(sq.ft.) W = Radiant heat emission from the mass of water vapor, as ob- g tained from Fig.No.34 at the average temperature of the flames, Btu./(hr.)(sq.ft. ) W 5 - Radiant heat emission from the inner surfaces of the combustion chamber bsorbed by water vapor, as obtained from Fig.No.34 at the average temperature of the surfaces, Btu./(hr. )(sq.ft.) K g = Correction factor allowing for reduction of radiant heat emission from flames due to mixing of carbon dioxide and water vapor, as obtained from Fig.No.3 5at the average temperature of the f1lames,Btu./(hr.)(sq.ft.) s = Correction factor allowing for reduction of radiant heat emission from the inner surfaces of a combustion chamber due to increased opaqueness of flames containing mixed carbon dioxide and water vapor, as obtained from Fig.No 35 at the average temperature of the surfaces,Btu./(hr.)(sq.ft.) 7- - I 3 4 ., . 4.. i . i !;IpI! - ., I '.i ' i I i.: I4 . : .' t: ' '. .. -1: i t; !i.. i .L I . ' t. ''. tk , : .: !,: . i ': -..z:' i' '.77 I - : -. I. -.,,.. .I.rI.. .,..T :: :: r:-ll;;.,'.,,.,: :,.: .-.. -..,,4. :i ::! I I ~ ~~~ ~ ~ ~ ~ ~~~~~~~~4_ LL_ ., . -,,. -. . r.... I -II' 1 t': L,".'.:.".klfr" i:---1:: ;i:; .' I It ; I ,, I : : L - I , 1 . . . . . I , j : ! i i - , : ; f .1 ! : I , , t 1. __~ : : -, ,- I t I.... ,! ' . . .t Ij . .; ; . . . __.. . ... I '. . ....... I.' · ___,__ ... j. i. ... ,... .:..... fees.I "AP rarl-e' . i2I . I '- _ .I ' . T: ., l. . I - == I .I.. ,. !_ i 1t i.: .i: ::'.: }i r. -I ! 1 i ' I 1 It: !..-I ..'.... r.t i-V Cc' ~.. 3r .. I ,_r; arrrre A. . . . . L, .. ... j I,: 1.5 orte I I 1 . I.., s.. . . . -t... L fi . .. ':; 'i- it,--. I i ! . 1 ., i '4 IIfl . .. 'I':;I -! 9 e A4tiit .. i e4. iflf .. -- . -iR . 1- - V. 4 :. i;-fil I 1. a - : UT :-:r . .. I I. : :i ' . .- . I.,.~ it..'l, .z5 t : ' ' .1 1. .1. .1. I - - :" . . : : , ': 4 -;-- : -:'- .- . I I' . 2.'5 ...-.. 1 _ I ...... _ . . --. I t. !.:;:. I.. . t . . .. trtt-t *' l . ' I L1 .1 1:. ... . . IT .. : __ ' .. .. .i '::i. ' . I 44 k'4 .:. . .; .. I . .... -I rrrI. I J 7': -.. - ... .. . . . .- .' -.: -.. I!,-, .I -- 'A ' L: ;. L _ " - J - '. . . .. *1 .- I I ' .. i: ~t: : *I a ri-. .-. -i -1 Iq .I ' I . .. 1 !. 7.- .. ,_ 1 ;' t 1 : 1: 5 I ... :' r: E. :: : '-' I -, rJ tStrtt7t..1' 4:.. . . i. . ~ .... i... . .' . ; . . , ,. __. I . :1 ; '.5 I. . .. . .. ... .. i -.. .... I - .. 1.3 . II . I 2.5 3 2.t ..: 4.5 Z. :..: .......,.~ _;i:d5.".*:;5.. _I.. ; ; :. , '-· SS -'1 I.. . L- .'R: '.. .- I': . :F ,, C' E ' ' ,". ... ..'.... · .5 .. ' '1I 'i . I ... I--- ... I-. . -' ' i , .-. .... I. '.... I I .- I' ' .I --... I-- -:: . ' Ib_R__ ,11" The Average Flame Temperature In order to determine the quantities (C ), (W ) and (K ) given in the above equation it is of course necessary, first of all, to lknow the actual average temperature or the flames (t g ) which is the principal variable controlling the magnitude of (C ),(Wg) and (K). Fig.No./ to , the construction of which is explained on pp. , gives the theoretical flame temperature resulting from complete combustion of a hypothetical average fuel oil with various quantities of excess ir; it of course must be corrected for the radiant and convection heat trnsfler from the flames to the wlls and water-backed surfaces within the combustion chamber. The actual flame temperature is necessarily lower than the theoretical flame temperature by an amount, such that the sum of the radiant and convection heat transfer from the flames will be equal to the heat loss from the flames due to their cooling from the theoretical temperature to the temperature at the exit from the combustion chamber. Or expressing it mathematically: + Qc Qr = M Cp(t~- t2 ) dp Where: Qc = Convection heat loss from flames to inner surfaces of combustion chamber, Btu./(hr.) Q = Radiation heat loss from flames to inner surfaces of combustion chamber, btu./(hr.) - Weight of products of combustion generated in the combus= tion chamber, lbs./(hr.) C = Secific heat of products of combustion between tempera- turee (ti) and (t2 ), Btu./(lb.)(°F.) -73- t = Theoretical flame temperature immediately after combustion, F. t2 - Temperature of the products of combustion at the exit from the combustion chamber,F. This method o course presupposes a linear variation of flame temperature, which is true for all simple combustion chambers. The Average Surface Temperature The average surface temperature (t) is the controlling variable which determines the values of terms (Cs), (WI ) and (K). For all combustion chambers of simple shape, constructed so that all parts of the flames see ali solid surfaces simultaneously, and in which there are no extensive water-backed surfaces which can see the flames, -- the temperature of the inner surfaces of combustion chamber may be taken as the arithmetical average o all surfaces in proportion to their area. For.those combustion chambers, however, in which a considerable amount of water-backed surface can see the flames, determination of average surface temperature involves several heat balances external heat loss due to the boiler room including nd convection heat transfer inside the chamber. Radiant Heat Transfer From Hot Products Of Combustion To WaterBacked Surfaces Of Gas Passages The subject matter presented below deals with the radiant heat transfer from the products o combustion after they have left the comnbustion chamber and are moving' in the gas passages, the walls of which are in contact with water. As the temperature of the products of comnbustion falls, the radiant heat transfer diminishes in importance and convection heat transfer of the boiler cn ssumes the chief role; however, in no part radiant heat transfer from the products of combustion bc neglected if consistency in final heat balances is desired. In general the same principles apply to radiant heat transfer from hot products of combustion to wter-backed surfaces as were outlined above for radiant heat transfer from flames to inner surfaces of a combustion chamber. The bsic = equation still holds true, in which: (As)(Ps)( g )-(C 8 - + K Where: Q - Total net radiant heat(trnsfer from hot products of combustion to solid surfaces, Bu./(hr.) = Area of solid surface bthed A by the hot gases, sq.ft. s given on p. Ps - Emissivity of solid surface C - Radiant heat emission . rom the mass of carbon dioxide gas, g as obtained from Fig.No.33 at the average temperature of the products of combustion, Btu./(hr.)(sq.fLt.) C s = adiant heat emission rom the solid surfrace bsorbed by carbon dioxide, as obtained from Fig.No.33 t the average temperature of the surface, Btu./(hr.)(sq.ft.) W g = Radiant heat emission from the mass of water vapor, as obtained from Fig.No.34 at the verage temperature of the products of combustion, Btu./(hr.)(sq.ft.) W S = Radiant heat emission rom solid surface absorbed by water vapor, as obtained from Fig.No. 34 at the average temperature of the surface, Btu./(hr.)(sq.ft.) = Correction factor allowing for reduction of radiant heat K g emission due to mixed state of carbon dioxide and water vapor, as obtained from Fig.No.3 ture of the K 5 at the average tempera- roducts of (combustion, Btu./(hr.)(sq.ft.) =- Oorrectionfactor ,llowing emission from for reduction of radiant heat he solid surface due to increased opaque-, ness of the products of combustion caused by mixing of carbon dioxide and water vapor, i s obtained from Fig.No. 355st the average temperature of the surface, Btu./(hr.) (sq.ft.) Use of Figs.Nos.33 , 4 and 3- is self evident, with the ex- ception perhaps of the evaluation of the term (L) which appears in all of them. The term (L), known as "the effective thickness of the gas layer", is the verage integrated length of radiant beams from all parts of the radiating mass of gas to the bounding surfaces that it sees. I Values of the term (L) for use in Figs.I!os.3S , 34 and are essentially as follows: (1) When the products of combustion flow in long boiler tube, (L) = 1.0 (Diameter) (2) hen the products of combustion move outside a bank of tubes with centers on equilateral triangles, nd the clearance equals tube diameter, (L) = 2.8 (Clearance). (5) When the clearance in (2) is equal to two diameters, then I I (L) = .8 (Clearance) -74- (4) When the products of combustion move between parallel plates of dimensions considerably larger than the distance between them,(L) 1.8 (Distance between planes) = The Average Temperature Of The Products of Combustion The average temperature of the products of combustion on which determination of terms (C ), (W ) and (K) g wg (g curately by the following expression: t t gav. = + t + (t, - t') - Ct s is based, is given quite ac- - t) B -2~ 2.3 log(tg -t)/(t g~~~ -t") s Where: tav g ~v. = Average temperature of the products of combustion in the gas passages, OF. / tI = Temperature of the surface bathed by the products of s combustion, at the inlet end of he water-backed gas passages,°F. t" s = Temperature of the surface, at the outlet end of the water-bscked gas passages,°F. t ' g = Inlet temperature of the products of combustion, (usually same as that of the gases leaving the combustion chamber),°F. t" = Outlet temperature of the products of combustion, (u- g sually the same as that of gases leaving the boiler and entering the flue), F. -77- The Average Temperature Of .Solid Surfaces The average temperature of the solid surfaces on which deter- ) and (K) is based, is determined,as fol- mination of terms (),(W · lows: (Lt + t) t av. = 22 Where: ts av = Average temperatureof the solid surface bathed by the products of combustion,OF. tI a = Surface temperature at the inlet to the water-backed gas passages,°F. to = Surface temperature at the outlet end of the water- s backed gas pass-ges,0 F. THE NCIAL TOTAL EISSIVITIES OF IIMfNER SURFACES OF VARIOUS COM1BUSTION CHA.iBERWALLS A WATER-BACKED SURFACES Surface Temp.°F. Emissivity (1) Brick, silica, unglazed, rough 1800 0.80 (2) Brick, silica, glazed, rough 2000 0.85 (3) 2000 0.75 500 0.95 Grog brick, glazed (p) (4) Cast iron, rough, strongly oxidized 100- (5) Cast steel plate, rough 100 - 2000 0.82 - 0.89 (6) Iron or steel covered with soot 100 - 2000 0.96 - 0.94 (7) Cast iron, oxidized at 1100°F. 400oo-1100 o.64 - 0.78 (8) Steel oxidized at 1100°F. 400- 1100 0.79 - 0.79 (9) Wrought iron, dull, oxidized 100 - 700 0.94 stee.l,(8% Ni, 18% Cr) 4o0o - loo 0.62 - 0.75 Copper plate, oxidized at 1100°F. 400- 11o00 0.57 - 0.57 (10) Alloy (11) Z FARTIII COTVECTION TRANSFER OF LIBERATED HEAT ENERGY -90- CHAPTERVIII nO,.~,jECMTC!HEAT ToANSo R C'WECTC- N HAT TRAS ,, E-, I.'OjM GASEOUS ~ PRODUCTS 0 ,,,UTO C0,MBUISTIOTN ALONMGTHEIR PATH OF TRAVEL THROU¶H THE BOILER COINVECTIONHEAT TRANSFER FROkMGASEOUS PRODUCTS OF COMBUSTION ALONG THEIR PATH OF TRAVEL THROUGH THE BOILER Introduction The path of the gaseous products of combustion in a small oil burning heating boiler can be divided into two parts in accordance with importance of convection heat transfer along it; these two parts are the combustion chamber and the heating surface compartment. Convection heat transfer in the combustion chamber is comparatively small; this is due, of course, to the small amount of heat transfer surface exposed to the flames, which is necessarily limited in order to maintain a high combustion temperature. Most of the convection heat transfer from the products of combustion therefore occurs during their passage through the heating surface compartment.where they are given the opportunity to come in contact with a considerable amount of "water-backed" wall surface. In the discussion presented below,it is intended to outline and develop the available methods for calculation of convection heat transfer from the products of combustion to solid surfaces with which they come in contact during their passage through the boiler. Heat Transfer From The Products Of Combustion To Solid Surfaces Within The Combustion Chamber Heat transfer by convection from flames and products of combustion to the walls of a combustion chamber can be estimated only approximately, since it is impossible to determine with accuracy the -82Z- true average velocity of gases circulating within he combustion pace. The only criterion available for quantitative comparison of flame turbulence within two different combustion chambers is weight velocity of gas flow; which, though being an important cause, is not the total index o turbulence. Fortunately, the controlling resistance to heat flow from a combustion chamber is that offered by the walls themselves and not by the gaseous film separating them from the flames; therefore, an error in estimated convection coefficient 's large as 25 per cent of the actual value will not introduce n error greater than about 2-5 per cent into the overall coefficient of heat transfer through the wall. In general, estimation of convection heat transfer from the flames to inner surfaces of a combustion chamber can be made with fair degree of accuracy by means of the fundamental equation: (h D/k) = 0.025 (D Gx) 0 '85 (c yk).4 Where: h Convection (or film) coefficient of heat transfer, Btu./(hr.)(sq.ft.)(°F.) D Inside diameter of the combustion chamber, ft.(If the chamber has cross section other than circular, the term (D) becomes the "equivalent diameter" which is equal to four times the hydraulic radius of the given cross section.) k = Thermal conductivity of the products of combustion, Btu./(-hr.)(sq.ft.)(°F./ft.) G = Weight velocity of the products of combustion, lb./(hr.)(sq. -83- ft. of chamber cross section). U = Absolute viscosity of products of combustion, lb./(hr.)(ft.) = centipoises times 2.42) Note:( c Specific heat of products of combustion at constant pres- = sure, Btu./(lb.)(°F.) Note: All physical properties of products of combustion given above should be evaluated at the average temperature of the gas film separating the surfaces from the main body of gases. Heat Transfer From The Products Of Combustion Moving With Turbulent Flow Inside Straight Boiler Tubes And Similar Passages Turbulent flow of the products of combustion in straight passages is accompanied by heat transfer which obeys the general equation of the form: (h D/k) = 0.0225(D G/) 0 8 (c/k) ' 4 This equation correlates the data of numerous investigators whose works are listed below. It is applicable to all instances of gaseous flow where the Reynolds number exceeds 2000, and where the concept of equivalent diameter is applicable. The terms in this equation have the following meaning: h = Film coefficient of heat transfer, Btu./(hr.)(sq.ft.)(0 F.) D = Inside diameter of conduit, ft. S k = Thermal conductivity of the geous Btu./(hr.)(sq.ft.)(°F./ft.) mixture, G Weight velocity of gas flow,lb./(hr.)(sq.ft. of cross sec- = tion); also, G = (V)( t ), where (V) = linear velocity in (ft./hr.), and ( ) = gas density in (lb./cu.ft.) Absolute viscosity of gaseous mixture,lb./(hr.(ft.); also = o = viscosity in centipoises times 2.42. c = Specific heat of gaseous mixture at constant pressure, Btu./(lb.)(°F.) Note: All physical properties of the gaseous mixture used in the above equation should be evaluated at the mean or average temperature of the main body of gas flowing through the conduit. Graphical solution of this equation is given on Fig.No.36 ; which, of course, is applicable to other instances of heat transfer accompanying turbulent flow of a gas inside hollow cylinders and other similar conduits. Heat Transfer From The Products Of Combustion Moving ith Turbulent Flow Inside Coiled Tubes Or Pipes This case of heat transfer is met comparatively seldom in practice, and the main value of the calculation method given below is in determining heat transfer from products of combustion flowing in bent tubes or bent portions of straight tubes. Heat transfer in coiled tubes was studied quite thoroughly by Jeschke(See: Zeit. Ver. deut. Eng., Vol. 69, p.1526, 1925).Based on his experimental data Jeschke recommends a correction factor by which heat transfer in straight tubes should be multiplied to obtain heat transfer for the same conditions of gas flow in tubes bent in a curve zs~al 1oalu 1 .- it Z 6 z ;11 1), 0 tI 1.1 I I MOO t3 \A ,. ., :1--: 11-- !- ; 1. I i . . e .. f .- , . . . : I .1. .- ,i - 1-! . i - I :: ;- ;.:--1 i i . ! . I I . - i.-. ; . I . I : ; i I; .i I/,I -~~~i~-,-r=--=~~L--. -.. ---. 1111kolm References To Data On Heat Transfer From A Gas Moving With TurbuilentFlow Inside Hollow Cylinders See following references: 'Experiments on the Rate of Heat Transfer from a Hot Gas to a Cooler 'vIetalic Surface", by Babcock and Wilcox Co., 1916; "Der Warmeubergang in Rohrleitungen" by W. Nusselt, Zeit.Ver. deut. Ing., Vol. 5, 190; "Der Warmeubergang von stromender Luft an Rohrwandungene, by H. Oroeber, Mitt. Forsch. Arb. Ingenieurwes, Heft 150, 1912;"Versuche uber Oberflachenkondensatoren, inbesondere Dampfturbinen", by Josse, Zeit.Ver. deut. Ing., Vol. 5, the Rate of Heat Transmission between Fluids and 1909; " On etal Surfaces" by H.Jordan, Proc. Inst. Mech. Eng., Vol. 4, p. 1317, 1909; " Uber die Warmeubertragung von Stromenden uberhitztem Wasserdampf an Rohrwandungen und von Heizgasen an Wasserdampf", by R. Poensgen, Zeit. Ver. deut. Ing.,Vol. 60, p. 27, 1916; and paper by Fessenden in Univ. Missouri Bulletin, Vol. 17, No. 26, 1916. of radius ,(R). This fctor is given by the.following expression: F = 1 + (1.77 D/R) Where: F = Multiplying correction factor, no dimensions. D= Inside diameter of the tube, ft. R Radius of the curve into which the tube is bent, ft. Heat Transfer From The Products Of Combustion Moving With Turbulent Flow Perpendicular To A Single Cylinder Or Tube Products of combustion moving with turbulent flow perpendicular to a single cylinder such as a boiler tube or a boiler roof, transmit heat to the solid surface at a rate which is given by the following equation developed by Reiher: (h D/k) 56 0.35(D G/) Where: h = Film coefficient of heat transfer from the gas to solid surface, Btu./(hr.)(sq.ft.)(0°F.) D = Outside diameter of cylinder, ft. k = Thermal conductivity of the gas film clinging to the solid surface, Btu./(hr.)(sq.ft.)(°F./ft.) y = Absolute viscosity of the gas film, lb./(hr.)(ft.); also = centipoises times 2.42. G = Weight velocity of gas, lb~(hr.)(sq.ft. of cross section) also G - ()( ),where ()= gas velocity ft./hr. nd (:) = gas density lb./cu.ft. Note: The physical properties of a gas given in this equation - 87- should be evaluated at the mean temperature of the laminar gas film separating the solid surface from the main body of moving gas. Fig.No.37 attached here gives semi-graphical solution of this equation; also, it gives the plot of the curve correlating the data on which the equation is based. As can be seen from Fig.No.31, there is a slight discrepancy between the equation plot and the data plot. For usual computations when the physical properties of the gas stream are not known with a great degree of accuracy, the equation and its plot are fully satisfactory. When a greater degree of accuracy is desired, however, the data plot on Fig.No.3 is recommended in pre- 1 ference to the equation. The data on which this equation is based has been obtained by the following investigators: Reiher,Mitt. Forschungsarb., Vol. 269, p 20, 1925; Paltz and Starr, Thesis in Chem. Eng., Hughes, Phil.Mag., Vol. 1, .I.T., 1951; J. A. 118, 1916; and Kennelly and Wright, Trans. Amer. Inst. Elect. Eng., Vol. 28, p 363, 1901. Heat Transfer From The Products Of Combustion Moving With Streamline Flow Perpendicular To A Single Cylinder Products of combustion moving with streamline flow perpendicular to a single cylinder such as a boiler tube or a cast-iron compartment, transfer heat to the solid surface at a rate which can be estimated by means of a simple equation of the following general form: (h Where: /k) = f(D C/)n _ ____ 1 4 23 /dOA// ~ ~; .: -. 1 14. . - I -,. ;i I, L' .. -'a---"".. ; ;. :!-.: 7 '1I I' i- j:'' . G '' ' - :;.'.~~ . I rL :'i. i ,.. -i i .. i a , ,F_; . - 0 T !I-' I ,I: t; .I:: -, ;' . ;. . l. 23 , I p, . . . ' . . . 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L , - :-I ill.6 6i - 1-4936. - il , ~'I- ..'_ ! - L +A%_ -_ 4. _4- +_ 0 i.,..4..~.-h..,~.-..~-.~-. . . u,..44.~u,.4.~,. , a'; Z 1·fi -.-... .%] I- - f) . .... .......-. . -·-····· 4 8 ~T '._L___~.: :ii.:~' ':-,-!+.-'~4.-.'=.-'-L,.!L..,.i.4-,:.!~&::i~L..'"';~L~i? jCa ' ' ''·-·-· ·· --· · 6 I 9 -~~ ~~~~~~~~~~~~~~pq ,.-:-4J ~ 4,.~4 ~.4.~JL~'. ;~'~-,--$.~~;o;. ~-~..,,~ "--4-4...-....' 9 8 6 5 3 2 9 /o,,0o Iw · I i' ' i T I, h = Film coefficient of convection heat transfer, Btu./(hr.)(sq.ft.)(°F.) D = Outside diameter, ft. k = Thermal conductivity of the given gas, Btu./(hr.)(sqft.)(°F./ft.) = Absolute viscosity of the given gas, lb./(hr.)(ft.) G = Weight gs velocity , lb./(hr.)(sq.ft. of cross section area) f = Proportionality constant, no dimensions. Based on data of Kennelly and Sanborn (See: Proc. Amer. Phil. Soc., Vol. 55, p. 55, 1914), that of L.V.King (See: Trans. Roy. Soc., London, Vol. 214, p. 575, 1914), and that of J.A. Hughes (See: Phil. Mlag.,Vol. 51, p. lla, 1916), the constants in the above general equation can be evaluated and it assumes the following forms: (h D/k) for (D GA) 3.45 + O.A5(D G) range from 0.10 to 10 and (h D/k) = 0.38 + for (D G/u) range from .455(D G/) 56 10 to 1000. Note: All physical properties of gas given in this equation should be evaluated at the mean or average temperature of the gas film separating the solid surface from the main body of gas. The data on which the above equations are based is correlated by the solid curves given on Fig.No.38 attached here. The equations themselves are represented by straight dotted lines, which as can be seen do not coincide with the data curves. For usual computations, when the physical properties of the gas stream are not known with a great degree of accuracy, the equations ,.. - 3 2 . l.) - '- .. T - : 11 , · 8 : F'i: . ._7. -: , IL ''. Jvv I .:_ _. . ' :,-s ioJ. _ ;-r An--;,_' - --- -- I . . .~ _ C'. IL' *.W!A . . . .. i .. 7 _.- 7. ;'! 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''t '.i!,IM-"l !r |:. . 1..1.0 f1 A ':_ I 1 44, rJ ,,-': !L F-: ' ':: - s ~~~~~~·...... '.l;!l 't;, . |,..... '~ ·-- t--tt;r.. · ,- ': t ·.,.l= ..--t-: ::-,.!:" i : ..:.;.... I.."---. ! 1 ,M-, ,::,>}. i~H :,i., >,: .: , ... + : i Sij-.-i. i ''-'L..... 4 tt! !.e i. ,;:4..t...t~~ it,.-t ,._T: i ¢; 'T'i' -f.'.- !.,.. . .... ..... .il.|'t~L, I1. , -,!,1. i t-;-. ; ..,.l - 1 -'~. |i ';F;; ., I ': .. ':::' $ . 11 ",,,'.'..Ji't '!,., '"'""r 'l4;' :,ht':-! -, ! i:,." r.,.Lr .r .. 5 I ! F :.1.''' 1_ 5 , ,: . ;_ _' _ I) T. iS 1- 'ItE t __. i. 1 il I !!|,j' :,'i . 1 VIF I-AFA !.' i r_ .: !l:!.':-. . ---. Zi=.';'.,-'a:t:,.'-l:~1f';i' : .. . tu i| li~ ii .t. ;-_. ....--1|.r.; . ,. .. ,::;...,::,. .. '~r[ i.5..l.&t.. #v'-· '1 i..,--t .j. ,:_.i ' ,'-~,: ; -. ,. ~.i-.-. ~-i.~ i j!.l~,.: ... I ,Ii.:~ .,,,- ·i-;i--.-' -.,.,-L-,..-,, --.. _j ' :* ; b.!.. f i'!lii |re W 1- -It !! .;_'' ;' Ali ! _' ' __i_ _. . . .i - l>b E --- 'L It!!! ".i._ fI- : ,, i . -; ... -. .I_ - :. :..i-~. 1i 6 .: L .. , tf..-t ,1.; I !:..Lj, -:. ._j!_ -. -1.7- r=.j ___ - -. .._.. _.. .I . _--- i- - . - -_ I I _- - : ~' - ,. !..--. ! .:li i.':; ; !.j:ti: L..;I. '.J.F.... . ,,,_, ;_-.--- t .......... m 'lj i.-I' ! - a _. . ; T ! i h- :t.r t I-.t-- .LL...4.-, Ir * '_ i , J.0 T7 j - -.-' tt[-pl- :-i ~ [- ;'' 9 , _ii~ffgllrtlU2ji,,B, i- 3 --. ' : . i- ' -- F ,! M:::l.Mllli;:f 11 'tWslli-i .- E; 1..---, T.'' :'1 r -' -= -~ ' Li T'q-r -1 . i l: i i- _.....- _.. Haiti I' 2 '"I i:!i'J!:.l.'..:. -: ! ..-c:; .d:.:i-: ! ! .--.Z.!-.., ,' ! · . Ir .':.-i'~ :, t.'. 1 ·: . , . . |. ,-|!!; !· it i,... ,~, Il . :... ,, . .. j.:: ,. ....-.. .. I j >, ... '.. -piiA, . .::I:. :: ...,.. F ~:'__.j& J:.t 9 8 '", 1 -~4 ; i -1. *I r _. 1 A _ .. 7 6 -t' I.'. v--&, ' 4.:~ - eI .= I.. .'- ..- J_i- - 5 A '..: ' ,,...~.,.:.. '. .. /W :. 1; .-::ttL j ! i i1-.I I. I I. .' . . . _: i ..L'¢;-i=LS'-i!'.:4=~ili:'-,L,~'~-t.-.-. i., l.i f.. : .,' !:i iii, i I: ': I 4 F1'-,iW '. .i I: tl,'l',ll i:,,, ',! I _ li;!i' ii;W..,i 11 j!?" ,1.,.,,:,.~ l. il l '~ M and their plots are fully satisfactory. When a greater degree of accuracy is desired, however, the data curves are recommended in preference to the equations. Heat Transfer From The Products Of Combustion Moving With Turbulent Flow Perpendicular To A Bundle Of Cylinders Or Tubes The most outstanding set of data on heat transfer from the outside surface of bundles of cylinders has been gathered by H. Reiher and was presented in his paper" Warmeubergang von stromender Luft an Rohre und Rohrenbundel im Kreuzstrom" (Heat Transfer to Pipes and P4e Bundles from cross Flow Air Streams), Forsch. Arb. Ingenieurwes, 1925. Based on this data he was able to formulate a general equation for calculation of heat transfer from a bundle of cylinders to a stream of gas moving with turbulent flow perpendicular to the bundle. This equation can be written simply as follows: h = a(k/D)(D V e /) n Where: h = Film coefficient o heat transfer,Btu./(hr.)(sq.ft.)(°F.) a = An experimental constant, depending upon the design of the tube bundle, i.e. its depth and tube arrangement. k = Thermal conductivity of the gaseous mixture, Btu./(hr.)(sq.ft. )(F./ft.) D = Outside diameter of cylinders, ft. V = Linear velocity of gases as at the narrowest free cross section, ft./hr. -90- V Al = Density of the gaseous mixture, lb./cu.ft. = Absolute viscosity of the gaseous mixture, lb./(hr.)(ft.) n= Exponent depending upon cylinder arrangement. Note: All physical properties of a gas used in the above equation should be evaluated at the average temperature of the film separating the surface from the main stream of gas. For specific bundle designs the constants (a) and (n) in the above given equation assume the following values: For cylinders arranged evenly: n = .654 For cylinders staggered: n = 0.69 Value of Constant (a) Arrangement Rows of Cylinders in Even -Depth Staggered 2 0.122 0.100 5 0.126 0.113 4 0.129 0.125 5 0.151 0.151 It is easily seen from this equation and the corresponding constants that the effect of velocity on heat transfer is greater for the staggered cylinders than for those arranged in even rows. It is also evident that the value of constant (a) increases more rapidly for the staggered than for the even arrangement. This is due to the fact that in an even arrangement the first row is the only one which receives a -9/- complete direct impingement of the stream, and therefore has the highest value of (h); the subsequent rows are progressively less effective since they are scrubbed only by the minor eddy currents. The staggered arrangement, of course, has the advantage that the gas stream upon leaving ny row, strikes the next following squarelywhich augments the eddy currents considerably. Heat Transfer From The Products Of Combustion Moving With Streamline Flow Perpendicular To A Bundle Of Cylinders Or ubes This case of heat transfer may be estimated by means of the same equation as given for streamline flow perpendicular to a single cylinder on p. 9, since streamline flow is not ffected by tube arrangement. It is important to note, however, that the turbulent flow commences at lower values of Reynolds nmber for streams flowing perpendicular to the outside of cylinders than for streams flowing inside tubes or pipes. Thus, turbulent.flow for streams flowing perpendicular to pipe bundles begins at Remynoldsnumber of about 1000, whereas inside tubes it begins at Re= 2000. PART IV TRAII\SFER OF HEAT EERGY TO VATER TRANS,ISSIOiNOF HEAT FROI HOT SURFACES TO WATER Introduction Heat flow from hot surfaces to water, as encountered in heating boilers, can be divided into two distinct classes according to the mechanism of heat transfer, namely: (a) Heat transfer to non-boiling water, and (b) Heat transfer to boiling water. Both mechanisms of heat transfer have much in common; yet they differ sufficiently to necessitate separate treatment of each. The treatment of heat transfer to non-boiling water differs from that to boiling water in that the former is entered upon directly with demonstration of applications, while the latter is discussed in considerable detail. Heat transfer to boiling water necessarily includes extensive discussion of the bsic phenomenon involved, since it differs mechanics underlying the ppreciably from that encountered in all other phases of heat transfer in a heating boiler, or for that matter in any biler. -9_ CHAPTER IX HEAT TRAISFER TO NON-BOILINI - 95S- VATER HEAT TRANSFER TO NOR-'BOILING WATER Introduction Heat transmission from hot surfaces to non-boiling water, as met with in a hot water heating boiler can be divided into three broad types, according to the hydrodynamic nature of water circulation. (A) The most prevalent mode or mechanism of heat transfer from hot surfaces to non-boiling water in a heating boiler is that which is due to natural circulation or free convection induced by difference in density between connected columns of water; the difference in density, of course, being caused by variation in thermal expansion between two or more columns of water at different temperatures. (B) The second common mode, is that which accompanies the forced streamline water flow with Reynolds Number not exceeding 1100. This mechanism is found in those hot water heating boilers in which a positive circulation is induced by means of a small pump. (C) The third mode is that which accompanies turbulent flow of water with Reynolds Number over 1100. This mechanism of heat transfer has been employed to date in only a few isolated instances, and that in comparatively large hot water heating boilers. The discussion presented below aims to cover the basic theories underlying the three modes of heat transfer to non-boiling water, and the quantitative relationship mong the variables affecting them. -9- HEAT TRANSFER BY FREE COINVECTION FROM HOT SURFACES TO NON-SOILING W¥ATER Due to the fact that heat transfer by free convection depends considerably on the shape of the boiler passages in which water is being heated, the subject matter presented here is divided into several parts, each treating free convection heat transfer from an elementary surface. hen a complex passage is encountered, heat transfer from its walls can be estimated by using a composite film coefficient based upon the proportion of various elementary surfaces from which the walls are formed. Heat Transfer By Free Convection From A Vertical Plane to Non-Boiling ater The treatment of the subject of free convection heat transfer to non-boiling water is begun with heat absorption from a vertical plane because such a surface is simple to construct, and also because the analysis of heat transfer from it is applicable to other shapes as well. The first equation for calculation of heat transfer by free convection from a vertical plane was developed by Lorenz (See: Paper by L.Lorentz in Wied. Ann., Vol.13 p 582, 1881). This equation is formed of three dimensionless groups and is written as follows: (hNT/k)0.548 (c/k) -97- (e2.Bgt/JX 25 Where: h = Free convection film coefficient of heat transfer, Btu/(hr. )(sq.ft.)(°F.) N = Height of plane, ft. k = Thermal conductivity of water film, Btu./(hr)(sq.ft.)(°F./ft.) c = Specific heat of water, Btu./(lb.)(°F.) = Absolute viscosity of water, lbs./(hr.)(ft.) = Density of water, lbs./cu.ft. B = Thermal coefficient of water expansion, as a fractional change in original volume per F. rise in temperature; units, reciprocal of temperature. g Acceleration of gravity, 4.18 108 ft./(hr.)2 At = Temperature difference between the plane surface of the solid and the ambient mass of water, F. Note: All physical properties of water given above should be evaluated at the mean temperature of the water film separating the surface of the solid from the ambient body of water. Heat Transfer By Free Convection From Horizontal Planes to Non-Boiling Water Heat transfer rom horizontal planes, whether the water is heated by the plane surface from above or below, can be estimated by means of practically the same equation as proposed for calculation of heat transfer from vertical planes. In fact an adjustment in the value of the constant factor is all that is necessary. In accordance with data of Griffiths and Davis (Spec. Rept. No.9, Dept. Sc. and Ind. Research, H.M.Stationery Office, London,1951) and that of King ("Free Convection",Mech.Eng., Vol. 54, p 47,1952), the constant factor in the equation mentioned above becomes o.566 for horizontal planes heating water below them, and 0.695 for horizontal planes heating water above them. Heat Transfer By Free Convection From Outside Of Long Vertical Cylinders To Non-Boiling Water The outside surface of a long vertical cylinder with a comparatively large diameter transfers heat by free convection in much the same manner as a vertical plane. Therefore, it is quite natural to expect that equations representing free convection heat transfer from either should be similar. The most authoritative equation for calculation of free convection heat transfer from long vertical cylinders is based on the following data: Paper by C.W. Rice, Trans. Amer. Inst. Electr. Engineers, Vol. 42, p 655,1925; Paper by G.Ackerman, Forsh.-Gebiete Ingenieurw, Soc. Vol.5, p 42, 1932; and, Paper by Heilman, Trans. Amer. ech. Eng., FSP.51. p 257,1929. The recommended form of this equation is as follows: (h D/k) - o.57{(c /k) (D . t *B.g .t/Y) 0,25 Where: h = Free convection coefficient of heat transfer, Btu./(hr.)(sq.ft.)(°F.) D Outside diameter of cylinder, ft. k = Thermal conductivity of water film, Btu./(hr.)(sq.ft.)(F./ft.) c = Specific heat of water, Btu./(lb.)(°F.) y = Absolute viscosity of wter, lbs./(hr.)(ft.) = Density of water, lb./cu.ft. B = Thermal coefficient of water expansion, as a fractional change in original volume per F. rise in temperature; units, reciprocal of temperature. g = Acceleration of gravity, 418 at 108 ft./(hr.) 2 Temperature difference between the outside surface of the cylinder and ambient mass of water. Note: All physical properties of water given above should be evaluated at the mean temperature of the water film separating the surface of the cylinder from the ambient body of water. Heat Transfet By Free Convection Inside Of Vertical Cylinders To Non-Boiling Water Free convection heat transfer from inside surface of vertical pipes to non-boiling water was investigated quite thoroughly by Colburn and Hougen (See: Ind. Eng. Chem., Vol.22, p 522, 1950), and based on their own data and that other investigators they recommend the following equation for calculation of the free convection coefficient of heat transfer: (h /k) = 0.128 t(ci/k)(Do. h B. t/a)ng sit2 3 All terms in this equation have the same meaning as in the -oo00- equation for calculation of heat transfer from outside of vertical cylinders to non-boiling water given on p , with the following exceptions: For instances of heat transfer inside vertical cylinders, D = Inside diameter of cylinder, ft. at = Temerature difference between the inside surface of the cylinder, and the main body of water inside the cylinder. Heat Transfer By Free Convection From Outside Of Horizontal Cylinders To Non-Boiling Water Heat transfer by free convection from horizontal cylinders has been investigated and studied considerably by many experimentors. The most outstanding work on the subject is to be found in the following ppers: by A.H.Davis in Phil.Ylag.,Vol.44, p 920, 1922; by G. Ackerman in Forshung.-Gebiete Ingenieurw., Vol. , p 42, 1952; by 1915-16; and by Petavel in Trans. .Innchester Assoc. Eng., p 3355, Wamsler in itt. Forshungsarb., Vol. 98 and 99, 1911. The data gathered by these investigators can be correlated by means of the following general equation: (h D/k) = A(c .j/k) (D3 e2-B'g-. t/, 2 More specifically, for single horizontal cylinders with outside diameter less than 10 inches, the constant (A) in the above equation becomes 0.525; while for cylinders with diameter over 10 inches, A=0.47. The other terms in the equation have the following meaning: -/0/- h Free convection coefficient of heat transfer, Btu./(hr.)(sq.ft.)(°F.) D = Outside diameter of cylinder, ft. k = Thermal conductivity of water film, Btu./(hr.)(sq.ft. )(F./ft.) c = Specific heat of water, Btu./(lb.)(°F.) J = Absolute viscosity of water, lbs./(hr.)(ft.) = Density of water, lb./cu.ft. B = Thermal coefficient of water expansion, as a fractional change in original volume per °F. rise in temperature; units, reciprocal of temperature. g At 8 Acceleration of gravity, 4.18 10 ft./(hr.)2 Temperature difference between the outside surface of the cylinder and ambient mass of water. Note: All physical properties of water given above should be evaluated at the mean temperature of the water film separating the surface of the cylinder rom main body of water surrounding it. The principal limitations of the above equation is that it is applicable directly for calculation of heat transfer only from single horizontal cylinders or rows of parallel cylinders located in a horizontal plane. For calculation of heat transfer from a vertical bank of horizontal cylinders it is applicable only when it is possible to obtain the true mean value of (At) between the surface of all tubes and the water that surrounds them. -/02- Heat Transfer By Free Convection From Inside Surface Of Horizontal Cylinders To Non-Boiling Water Heat transfer from inside surface of horizontal pipes to fluids circulating within'them has been studied extensively by Dittus (See: Univ. of California Pub. in Eng., Vol. 2, p 71, 1929), and by Colburn and Hougen (See: Ind. Eng. Chem., Vol. 22, p 522, 1930). On the basis of much experimental data Colburn and Hougen proposed an equation for calculation of free convection coefficient of heat transfer from inside surface of horizontal cylinders-:towater flowing within them at very low velocities. The equation has the following form: (h D/k) $b64 (c u/A)(DI. tig B At/u2)} 0.25 All terms in this equation have the same meaning as in equation for calculation of heat transfer from outside of horizontal cylinders to non-boiling water given on pDD , with the following exceptions: For instances of heat transfer inside horizontal cylinders, D = Inside diameter of cylinder, ft. t = Temperature difference between the inside surface of the cylinder and the main body of water inside the cylinder. Heat Transfer By Free Convection From Miscellaneous Surfaces to Non-Boiling Water The several instances of free convection heat transfer to nonboiling water described above, of course, cover only a few of the -/03- possible practical shapes that might be given to heating surfaces of a small heating boiler. However, this will not affect the accuracy of heat transfer estimates; since the resistance to heat flow presented by the laminar film on the water side is only a fraction of that presented by the laminar film on the gas side. Therefore, an error, say of 10% n the estimated film coefficient on the water side will seldom result in an error of over 2-3% in the estimated overall coefficient of heat transfer from the hot products of combustion to the circulating water. It is recommended that the free convection coefficients of heat transfer to non-boiling water from surfaces not given here should be estimated by means of composite formulas based on the equations given above for elementary surfaces. To illustrate: heat transfer by free convection from inside surfaces of a rectangular water-passage can be estimated by means of the equation given on page 103if the term (D), internaldiameter, is replaced by its equivalent "hydraulic diameter" which is equal to four times the hydraulic radius. Mathematically: Hydraulic Diameter = 4R = 4(A/P) Where: R = Hydraulic radius, ft. A = Area of conduit cross section, sq.ft. P = Inside perimeter of the conduit, ft. Other approximations readily suggest themselves when actual problems are confronted. -/04O- I HEAT TRANSFER ACCOMPANYING STREAMLINE FLOW OF NON-BOILING WATER PAST HOT SURFACES Introduction Heat transfer from hot surfaces to non-boiling water, which accompanies streamline flow of water, has not been investigated as thoroughly as heat transfer by natural convection for two reasons: first of these is that pure streamline flow is seldom encountered in design of industrial equipment; and the second is the fact that in many instances of streamline flow, heat transfer due to free convection of water overshadows the heat transfer due to forced convection. Due to lack of extensive data few generalizations are possible, as most available methods for solution of problems involving heat transfer accompanying streamline water flow are of semi-empirical nature. Heat Transfer Inside Horizontal Cylinders To Non-Boiling Water Moving With Streamline Flow Data on heat transfer from inside surfaces of horizontal cylinders or pipes to non-boiling water moving within them with streamline (laminar) flow has been gathered by several outstanding investigators. The most authoritative information on the subject is presented in the following works:"Heat Transfer to Liquids in Viscous Flow", by C.G. Kirkbride and W.L.McCabe, Ind. Eng. Chem., Vol. 25, 1931; "Heat Transfer in Streamline Flow", by Drew, Hogan, and McAdams, Ind. Eng. Chem., Vol.23,1951; "Studies in Heat Transmission.-Flow of Fluids at Low Velocities", by Colburn and Hougen, Ind. Eng. Chem., Vol. 22,1950; and Kiley and Heat Transmission to Oil Flowing in Pipes," by Sherwood, angsen, Ind.Eng. Chem., Vol. 24, 1952. Fig.No.3 9 attached here gives the correlation of the data gathered by the above mentioned investigators, and also shows graphically the relationship among the several variables which affect heat transfer from inside surface of hollow horizontal cylinders to non-boiling water moving within them at low velocities. It is easily seen from the curve plotted on Fig.No.S3 that relationship among the variables affecting streamline flow heat transfer inside horizontal cylinders can be given algebraically in the form of two equations: one of these representing the portion of curve A-E, and the other representing the ortion E-D. The equation representing the portion of the curve A-E upon analysis can be seen to have the following general form: ham (D/k) = (P)(W c/k N) Where, (P) is a constant. Upon substituting corresponding values of ha m(D/k) and (W c/k N) from Fig.No.39 into this equation, the constant (P) is found to be equal to 0.637; therefore the portion of the curve A-E can be represented by the following equation: ha m(D/k) = 0.637(W c/k N) This equation, of course, should not be used when the value of the term (W c/k N) is greater than 18, nor should it be applied when -/06- .. I 1-A! . IC/U .' . .. ..... . 'q :'' . ; . :-.:. ;_: -- :.;.. : ; I ·!:. : - : . .: . . I- '-L. : : , I. ..: ," ~ .: ; 7 -- -. . - ~ ~'·--- ---- :-:i4 , -:-- r'' ..... .: .~~~~~~ : · -'T=.--" .... ; .. '~. _ ,, . .. .:..., ,mlzl::!J.'?.~~ ?E I , ----·----':.. . , .:.- ::-! -- ...-4:- - ··--·- '" ...i ::-' t-~-'?'?-'?::-= ;- ...:: 4I- . .. i . . . .: ... .A ...: - 3.5 i . : =' - ... -. .. I .. "~ "'. LL . "I -l--- liim I....I:'. i:-... . -.- '"-- l, ;i'.-i i ,_ . : : - t';' ~'.i! i!-... ...... II -. -.1 . Il. . 1. .- .. .......... -. :. . :. r] c - ' i '*I .I . I . I .. 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Similarly, the portion of the curve E-D can be represented by the following equation: ha m(D/k) = 6.2(W c/k N) ° 2 0 This equation should not be used when the value of the term (W c/k N) is less than 18, nor should it be used when the Reynolds Number exceeds 2100; in the first instance it would give values above the actual and in the second values below the actual. The terms used in these two equations have the following meanings: h am = Coefficient of heat transfer from inside surface of cylinder to non-boiling water flowing inside, based on arithmetic mean of terminal differences in temperature, Btu/(hr.)(sq.ft.)(°F.) D = Inside diameter of cylinder, ft. k - Thermal conductivity of water, Btu/(hr.)(sq.ft.)(°F./ft.) W = c = Specific heat of water, Btu/(lb.)(°F.) N = Heated length of cylinder or tube, ft. Rate of water flow, inside the cylinder, lb./(hr.)(tube) The mean overall temperature difference to be used in conjunction with the coefficient (h ) as determined frpm the above equations is defined as follows: (T-t)a m = (T'-t') + (T"-t")}/2 Where: -/0 7- T = Average or mean temperature of the surface on inner side of the cylinder wall,°F. T'= Temperature of inside wall-surface at water inlet end,OF. T"= Temperature of inside wall-surface at water outlet end,°F. t = Average or mean temperature of water traveling along the heated portion of the cylinder,°F. t'- Temperature of water entering the cylinder,°F. t"= Temperature of wter leaving the heated portion of the cylinder,°F., after mixing. Note: All physical properties of water given above should be evaluated at the everage or mean temperature (t). Heat Transfer Inside Vertical Cylinders To Non-Boiling Water Moving With Streamline Flow Heat transfer inside vertical cylinders differs from that inside horizontal cylinders in that the vertical position of cylinders permits considerable natural convection heat transfer which even overshadowsthat caused by the forced water flow at low velocities. Considerable data on such flow was gathered by Colburn and Hougen (See: Ind.Eng.Chem., Vol.22, p 522, 1930). Based on their data the following equations can be formulated for calculation of heat transfer inside vertical cylinders to non-boiling water moving with low velocities: (1) For upward flow, h= 0.128(g. (2) For downward c .B.k. t/) ° -333 c .B.k .4t/)) 0 33 flow: h = o.149(g. e /0 9- Where: h = Individual convection coefficient of heat transfer, Btu/(hr.)(sq.ft.)(°F.) g = Acceleration of gravity, 4 18 108 ft./(hr.)2 = Density of water, lb./cu.ft. c = Specific heat of water, Btu/(lb.)(°F.) B = Thermal coefficient of water expansion, as a fractional change in original volume per F. rise in temperature; units, reciprocal of temperature. k = Thermal conductivity of water film, $tu/(hr.)(sq.ft.)(°F./ft.) At = Temperature difference between the solid surface and the ambient mass of water, J= F. Absolute viscosity, lbs./(hr.)(ft.) Note: All physical properties of water given above should be evaluated at the temperature of the water film separating the solid surface from the main body of circulating water. The upper limits of these two equations, of course, are met at water velocities which result in heat transfer by forced convection equal or higher than that induced by natural convection currents. Heat Transfer From Outside Surface of Cylinders To Non-Boiling Water Flowing Parallel to Their Axes This case of heat transfer accompanying streamline flow of water can be solved by means of the same equation as given for calculation of heat transfer to non-boiling water inside horizontal cylinders on page /06, and to non-boiling water inside vertical cylinders -/09- r on page lb. All that has to be done to make the above mentioned equations applicable in the present instance is to substitute for the term (D), actual tube diameter, an equivalent diameter. Considerable amount of experimental data and nalytical study have shown that the equivalent diameter is given with sufficient accuracy by what may be called the "hydraulic diameter" which is equal to four times the hydraulic radius; the hydraulic radius, of course, being equal to the cross section area of the wter stream divided by the wetted perimeter. Heat Transfer From Outside Surface f Cylinders To TNon-BoilingWater Flowing At Right Angles To The Cylinders The phenomenon of heat transfer which accompanies streamline flow of water at right angles to heated cylinders can be differentiated in accordance whether it takes place from single cylinders or bundles of cylinders. As most of the reliable data on the subject matter has been obtained from investigations of heat transfer from single cylinders, it is presented first. (A). Heat Transfer From Single Cylinders Heat transfer from outside surface of single cylinders to nonboiling water flowing at right angles to the cylinders has been studied by several investigators, and the most reliable data on the subject can be found in the following papers: Nat.Phys. Lab. Papers, Vol. 19, p 245, 1926,England(by A.H.Davis); Franklin Institute Journal, Vol. 184, p 115, 1917,(by Worthington and Malone); Forshung.-Gebiete Ingenieurw., Vol. p 94, 1932,(by Ulsamer). -//0- 5, Fig.No. 4D gives the correlation of the data gathered by these investigators, and also shows graphically the relationship among the several variables which affect heat transfer from single cylinders to non-boiling water. It is easily seen from the curve on Fig.No. 40 that the relationship mong the variables involved in the problem at hand can also be given in the form of an equation as follows: (hDA) << .)" 0.86(D-;)°44 The terms employed in this equation (or in Fig.No.4O ) have the following meaning: h = Individual coefficient of heat transfer from outside surface of the cylinder, Btu/(hr.)(sq.ft.)(°F.) D Outside diameter of cylinder, ft. k = Thermal conductivity of water, Btu/(hr.)(sq.ft.)(°F./ft.) c = Specific heat of water, Btu/(lb.)(°F.) -= Absolute viscosity of water, lbs./(hr.)(ft.) = Density of water, Ib./cu.ft. V = Linear water velocity, ft./hr. Note: All physical properties of water among these variables should be evaluated at the temperature of the film separating the solid surface from the main body of water flowing by the cylinder. (B) Heat Transfer From Banks of Cylinders or Pipe Bundles Heat transfer from outside surface of a bank of cylinders to non-boiling water flowing past them at right angles is considerably -/I- . _ . :. . .. .. _. .. . 1.:... rI' · ......··--·----- I /0 i . ... I |.: -- .: : t '`"''-"I" ::. * 11-1111 .::M I . . :-;._ ____, --I.. .: .: .T-.:: : . -T- 1' ,. - i F r ,, .. .,,y, _ J. : 1 .. -, I .: 1. .:'T- .. · ·::· :-:' ,. : : :ii-..- I i - . : . 7 __- - __ _ I ..... .- r'- ! . -. F-- . .: .. .. : -. . ;; :·;T -. : . j .i F; ,... . !"'Z.. 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S...!j: I I.J -. . . . i . : . : L r - . 1 . .L. . .: ! :, S i - ', : j, j *;:|, ' _ _5' ·-- 1:-e .... . (5 . t_' ' - , II L r*---- 5 t) R t ,I.sr F . I .r L :.i a&1 .i :!i r- LN __ z ' _ -...I :. :'.i. :· 8 , .,., _,. X. I . :I I . I1 ' - 1 . :.:,. ' '._ 1 .r : 1-: I I .' .__ ) 1 : _W --. _' i,+ :ti . _1 Jl .. e I-. . :'I.. : , ,1:I"81 .le _ .. 1 I' ! ..4t .. - I . .-W -. . V. ... . .i .' ..1* En;I.: it 1- lB 1;'" Ii ill11 s p - 5 .'..'o'~ _ ..... _ ... ' ............ :' _c :.~2 . EL rl :h '1: ! I ,4 : .t ' I' :' !,1 .:7I i: I1. _J _ . . I, ',I'il- ' I.,_.. .4- 4 'l :' L._. .. __ "; 5- . t I C 1040 more difficult to estimate than heat transfer from single cylinders. The principal difficulty is due to the fact that the influence of cylinder arrangement upon turbulence of flow is not subject to accurate mathematical calculation. Another difficulty is due to lack of authoritative published data which could be used to develop a general equation. The most satisfactory procedure developed so far is given by McAdams (See: p 132,"Heat Transmission" by W.H. cAdams, McGraw Hill Book Co.). He recommends an equation based on unpublished dta , which has essentially the following form: (h D/k) (o.*/k) ° ' = .5(D V /o6 Where: h = Individual or film coefficient of heat transfer from outside surface of the bank of cylinders to water flowing past them at right angles, Btu/(hr.)(sq.ft.)(°F.) D = Outside diameter of cylinders, ft. k = Thermal conductivity of water, Btu/(hr.)(sq.ft.)(°F./ft.) c = Specific heat of water, Btu/(lb.)(°F.) j = Absolute viscosity of water, lbs./(hr.)(ft.) t =-Density of water. lb./cu.ft. V = Apparent water velocity past the tubes, ft/hr. This velocity is obtained by dividing the volume of water flowing by the net area between the cylinders or tubes. 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' d~je@............ O 00S--, ,,, -..... I , ' F-- _ - ' _ .. f' · ·' ~ - . . ......2t'0'SO 1a-'":V/A~ :Ftli :-[ 0 '' 'ra .F W~gol .: HEAT TRANSFER FROM HEATE~ SURFACES TO NION-BOILING WATER CIRCULATING NITH TURBULZENTFLOW IN HEATING BOILER PASSAGES Heat Transfer to Non-Boiling Water oving With Turbulent Flow In Boiler Tubes Heat transfer to non-boiling water moving with turbulent flow in straight conduits has been studied by many outstanding investigators; in fact, uthoritative references are too numerous to be presented here, and are therefore given at the end of this section. Briefly, heat transfer from inne-:wall surface of clean boiler tubes to non-boiling water moving within them with turbulent flow, i.e. at Reynolds number over 2000, can be estimated by means of the following equation: (h D/k) = 0 0.0225(D G/) '8 (c /k) 4 Where: h = Film coefficient of heat transfer from inner wall surface to the main body of moving water,Btu./(hr.)(sq.ft.)(°F.) D = Inside tube diameter, ft. k = Thermal conductivity o water, Btu./(hr.)(sq.ft.)(°F./ft.) G = Weight velocity of water flow, lb./(hr.)(sq.ft. of cross section); also G = (V)(e), ft/hr, and ( ) = where (V) = linear velocity in water density in(lb./cu.ft.) = Absolute viscosity, lb./(hr.)(ft.); also centipoises times 2.42. c = Specific heat of water, Btu./(lb.)(°F.) -1/ - = viscosity in Note: All physical properties of water given above should be evaluated at the arithmetic mean of the terminal temperatures of water. Under special circumstances, when the temperature of the water film clinging to the wall surface is considerably higher than the temperature of the main body of flowing water, the physical properties of water should be evaluated at the mean temperature of the film.This can be done by means of the following relationship: (t - t) (t - t) 0.5 (tw - tb (tw - tb ) ) Where: t w t f = Temperature of wall surface, = Temperature of the film, tb t. 1 °F. F. Temperature of the main body of water, °F. = Temperature of the interface between the laminar film and the main body of turbulent water,°F. The equation given above for calculation of heat transfer accompanying turbulent flow of water has the following limitations; (A) It is applicable rimarily to horizontal tubes with length exceeding 50 diameters. For horizontal tubes shorter than 50 diameters it will give values a few per cent lower than the actual value; also, for vertical tubes in which the low proceeds at Reynolds Number less than 5000, it will give values a few per cent lower than the actual. Increase of heat transfer, over that indicated by the above mentioned equation, when the flow takes place in short tubes is due to -//-- additional turbulence created by 1 end effects' ; whereas, the increase in heat transfer when the flow takes place in vertical tubes at low water velocities is due to vigorous free convection currents which arise near the vertical wall surface. The Simplified Equat on If in the equation, ' 0.0225(D G/j)0 (h D/k) 8 (c /k) the physical properties of water, k,p, 4 and c, are expressed as functions of temperature then it can be simplified into the following form: (h D) = (0.00486 + o.ooo486t) (G D)0 8 Where: t = The arithmetical mean of the water terminal temperatures,OF. All other terms have the same meaning s given for the original equation. Fig.No.43 gives the graphical solution of this equation, and also shows the lower limit below which it is not applicablej.since ti calculated values will be considerably less than the actual. References On Heat Transfer Data To Water Moving With Turbulent Flow Inside Conduits (a) S.M. Thesis in Chem.Eng., M.I.T., 1924, by Baldwin and Sherwood. (b) Paper in Ind. Eng. Chem., Vol. 23, p.30 1, 1931, by Lawrence and Sherwood. -116- , ... i r rc= ... N - - 9CC'ON 0 !sw;lr 134jnX9 T tD . ! __ . .x 'i .. i; : .L .: , 1 . 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' I 1 _ .A= rl_ -1 a- {- z "QD blSS] I - ID : ; 'A'N t:.r --- ! ---- . +^ t- t -- - t- 1-- l :t ~·-!' -- - ,. 1 : C,i -- :t-- 4.- ;Tw F .... ,.....| ilrXiiil _,, ,,4-t; t l:4 -I1 , t ; I . ... .1I 1-:;--?-, f1'l-i 4-- -1 Z r-'. t--L ~~~~~~~r-- 'f ) --- I- Fiji , ) I L-:- ii IN a ((T. q O t a (c) Paper in Ind. Eng. Chem., Vol. 20, p. 234, 1928, by Morris (d) Der nd Whitman. armenbergang and stromendes Wasser in Vertikalen Rohren"',by Stender, Julius Springer, Berlin, 1924. Heat Transfer To on-Boiling Water Moving With Turbulent Flow Inside Passages Other Than Round Boiler Tubes Whenever water passages in a water 1eating boiler hve other than round cross section, the methods for estimating heat transfer given on pages //Y and / still hold if the term (D), actual diameter, is substituted by an equivalent diameter. The equivalent diameter for a conduit of any cross section, also known as"hydraulic diameter" is equal to four times the hydraulic radius which is defined as the quotient of (A/P); where A= cross section walls, rea of conduit, sq.ft. nd P = erimeter of the bounding ft. Thus an equivalent diameter of a rectangular conduit can be obtained simply as follows: (1) Sides X ft. of rectangle, end Y t. (2) Area =(X Y) s.ft. (5) Perimeter = 2(X (4) Hydraulic rdius + Y) ft. xy =( +Y (5) Hydraulic diameter = 4 X Y 2(X+Y) = 2X Y X+Y Hydrnulic diameters for other cross sections are obtained in a similar manner. - P 7- Heat Transfer To Non-Boiling Water Moving With Turbulent Flow Perpendicular to Bundles of Boiler Tubes This case of heat transfer to non-boiling water has not been much investigated to date, and there is practically no published authoritative data which could be used as a basis for a general equation applicable under widely varying conditions. For the purpose of this paper, however, the equation developed by Prof. McAdams (See: "Heat Transmission", by W.H. McAdams, McGraw Hill Publ.Co., p 232) is sufficiently accurate and will result in estimates that will seldom be in error more than20%o. A modified form of this equation is given below: (h D/k) = .4(D G/a) (c k Where: h = Film coefficient of heat transfer rom the outside surface of tubes to the main body of moving water, Btu./(hr.)(sq.ft.)(°F.) D = Outside diameter of tube, ft. k = Thermal conductivity of wter, Btu./(hr.)(sq.ft.)(°F./ft.) G = Apparent weight velocity of flowing water, lb./(hr.)(sq.ft. of net cross section between the tubes) = Absolute viscosity of wter, lb./(hr.)(ft.)-; also, u = centipoises times 2.42 c = Specific heat of water, Btu./(lb.)(°F.) Note: Physical properties of water in the above given equation should be evaluated at the average of the terminal temperatures. -/18- Heat Transfer To Non-Boiling ater Moving With Velocity Near Critical in Vertical Boiler Passages When the flow of water in vertical heating boiler passages takes place with Reynolds number below 3000, heat transfer which accompanies forced water turbulence is augmented by heat transfer induced by natural convection. Under certain physical conditions the heat transfer induced by natural convection overshadows that which results from turbulent water flow; in such cases heat tr.nsfer should be calculated by means of the free-convection equation given on page of this thesis, under Heat Transfer By Free Convection Inside Of Vertical Cylinders to Non Boiling Water". -;I?- CHPTER X HEAT TRANSFER TO BOILING -/20- XVATER HEAT TRANSFER TO BOILING WATER Introduction As far as the problem of heat transfer is concerned, boiling of water (or any liquid for that matter) is the formation of bubbles of vapor within the body of water nd their escape to the space above the bounding surface between the liquid and the gaseous phases. The phenomenon of boiling as observed under ordinary laboratory conditions or in commercial practice, is usually that of water containing various dissolved impurities: as salts, such as aOls, MgCl2, NaCl, etc.; and gases, such as Oxygen,Nitrogen, and others. When a highly purified distilled water is heated up,however, ! there is no boiling in the ordinary sense of the word; there is present only a very high rate of evaporation when the temperature of the body of water is raised to the proper point, which depends on the pressure and distance between the free water surface and the solid surface from which the heat is being transferred. Most conclusive experiments of such evaporation at a rate equal to that of ordinary boiling and yet without any ebullition were made by Heidrich (See:'Verdunstung von uberhitztem Waseru V.D.I.,No.37, 1952). By carefully heating distilled water Heidrich obtained an evaporation rate as high as 6.15 lb./(hr.)(sq.ft. of free surface) with hardly a sign of any bubble formation below the free surface. It may be noted, at this time, that the temperature of the water during Heidrich's experiments was as much as 16°F. higher than that of the steam above it. - I2a- As far as the purpose of this pper is concerned, the discussion will be confined to heating, evaporation, nd boiling of water of usual purity such as supplied in a city for everyday uses. In particular, the writer aims to investigate in this chapter the effects of various factors on the individual or film coefficient of heat transfer from a hot solid surface to a body of boiling water in contact with that surface, and to summarize the available scientific data so that it may be applied to design of steam and water heating boilers. FACTORS AFFECTING TE BOILING OF WATER .JD THE INDIVIDUAL COEFFICIENT OF HEAT TRANSFER FROM A METAL SURFACE TO A BODY OF BOILING WATER Observation and study by several experimenters have established definitely that the rate of evaporation during boiling, and hence the rate of heat transmission from the solid surface in contact with the water, are dependent pon the following factors: (1) Surface tension. (2) Convection currents. (3) Temperature level of the boiling water. / (4) Condition of the heating §Srface. (5) Height of free water surface or the hydrostatic head above the solid surface from which the heat is being absorbed. (6) Shape and arrangement of the heating surfaces. (7) Viscosity and conductivity of water. -_ia- MECHANISM OF BOILING As wasmentioned above, for all ordinary purposes boiling consists of formation of bubbles of steam within the body of water and their rapid escape causing the familiar picture of turbulence or ebullition. The latest investigations show that the bubbles of vapor do not form at all points of the boiling water, but that they originate at favored points on the hot solid surface from which heat is being transferred, and about the gaseous nuclei within the body of water. The initial formation of bubbles represents the principal resistance to evaporation of water during boiling, and as will be shown below, surface tension of water is the force behind that resistance. Effects of Surface Tension Upon Heat Transfer to Boiling Water Due to surface tension (B) in the outer walls of a small bubble, the vapor pressure (P ) within the bubble is less than the saturation vapor pressure of the liquid (Pliq) at given temperature (t), and the relation is expressed by the equation in .G.S. system of units as follows: / ( P- Pl kg/ Pliq. p0 kq. qm k w"k/cu.m. _2B 81dynes/cm. x Rmm. kg/cu.m. Where: P 0 = Vapor pressure within the bubble of water vapor. Pliq = Saturation vapor pressure of water corresponding to temperature (tliq. )°O. -/23- B = Surface tension of water at temperature of (tliq)°C. R = Radius of the bubble. w = Density of vapor. w' = Density of water. When F.P.S. system units are used the equation assumes the following form: P lb/sqein. - P lb/sq.in. B dynes/cm. )( lbu.ft. o Pliq. -87,500 Rin )(w' lb/cu.ft. - w lb/cu.ft. where symbols have the same meaning as in the C.G.S. form given above. Thus, it is easily seen from the above given equation that in order to form a bubble of water vapor with internal pressure P, the liquid surrounding a bubble nucleus must be superheated to a temperature (tliq.) corresponding to vapor pressure of water (Pliq.);(tliq.) is of course greater than (to), depending upon the relation between (PO) and (Pliq.) The above given equation also points to the fact that boiling, as we use the term every day, is impossible for a single homogeneous liquid, as a very high superheat would be required for the initial formation of infinitely small bubbles. A pure, homogeneous, singlP liquid when heated to the proper point, depending upon the pressure, would begin to evaporate at the free surface at a rate substantially equal to that of ordinary ebullition. Under ordinary conditions of boiling, however, there is an ample opportunity for bubble formation in the body of water as well as on the solid surface from which the heat is being transferred. In the body of water itself the principal nuclei for bubble formation are small bubbles of dissolved air. They are very small of course but of finite radius, nd therefore it requires only a definite superheat to fulfill the requirement of the equation, -' 0liq.-9.81 Pliq (B R w )( w ) this being in C.G.S. system units. On the solid surface, from which the heat is being transferred, the small depressions are the principal nuclei for bubble formation. The superheat to which the water must be raised to initiate the formation of a bubble around the nucleus is primarily a function of the radius of the nucleus. However, as water approaches its critical state the increase in vapor density has an ever increasing effect upon the superheat required to produce boiling. In all cases with which this paper is concerned, the equation discussed above, of course, includes the density factor practically as a constant, since the temperature to 2500 F. and 14 to nd pressure vary only between 190 0 ln./sq.in.Abs. respectively. After formation of a vapor bubble of finite radius R,the difference between (tliq.) the temperature of water on its inner surface, and (to) the temperature of the vapor within the bubble, gradually diminishes as the bubble grows in size; but (tliq) always remains greater than (to), which enables the bubble to grow at the expense of evaporation of water from the boundary of the bubble into its nterior. Eventually the vapor bubbles reach sufficient size, and due to their buoyancy, rise to the free water surface. Besides being a resistance to bubble formation in the body of water, surface tension also plays an important role in heat transfer and bubble formation at the solid surface from which heat is being transferred. If, for example, the solid surface is oily and the water does not wet it, the bubbles grow at the surface to large proportions and form spots of high resistance to heat flow.(Jakob,V.D.I,NIo.48,1932,observed as a usual occurrence, bell-shaped bubbles with base 0.25 in. diameter). On a rough, clean surface, that is wetted by water, the bubbles assume an elongated form with a small base at the solid surface from which heat is being transferred. Due to their small base the bubbles are torn off easily from the surface by convection currents; thus a greater portion of the surface is in contact with the water at any one time, which results in better heat transfer than that which exists when the surface is not wetted. Another effect of surface tension upon heat transfer during boiling is that it creates around the bubble of water vapor a stationary film which moves together with the bubble during its rise to the surface. Heat transfer through this film is due mostly to conduction, which explains the slowness of bubble growth in the body of water when the temperature difference between (tliq. ),the temperature of water, and (to), the temperature of vapor, is small.(Jakob,V.D.I.,No.48,1952, estimated by means of rapid photographic study of the growth of vapor bubbles, the average coefficient of heat transfer through the film surrounding the water vapor bubble to be about 2500 B.t.u./hr.)(sq.ft.)°F). Fig.No.43 shows the shape and nature of bubble formation-at three surfaces: surface (1) easily wetted, surface (2) partially wetted, and surface (3j5) oily and not wetted at all. 7-"/es -HCI/e - 4-o,--*a Z,/b Pt - /0 6'efrface " of //g , (i, J fa* r,ac-I (22 -- 4, 41w'd - I,, ,, ,,/ Bus,,.,,/ ! I 71,--.,:740-7.r (3, ,00/Y -Mo.4 , 9 3 Effect of Convection Currents on the Individual or Film Coefficient of Heat Transfer from a Solid Surface to Boiling water The present state of knowledge about effects of convection currents upon the film coefficient of heat transfer from a solid surface to water warrants a positive statement of at least three qualitative effects: (1) Increased velocity of water over the solid surface supplying the heat decreases the film resistance in two ways: first, by sweeping away the vapor bubbles from the surface, and second, by decreasing the thickness of the laminar water film at the surface. (2) Natural convection currents increase with increase of temperature difference between the solid heat transferring surface and the body of water, which explains the increase of film coefficient (h) with increase of temperature difference. (3) When a vigorous mechanical circulation or forced convection is present the film coefficient (h) is not affected by the increase of temperature difference. This condition exists, of course, only when the mechanical circulation is sufficiently strong to overshadow the effects of the maximum natural convection that can be obtained with the particular type of apparatus in question and with the highest practicable temperature difference (t) between the solid surface and the body of water. THe most conclusive experiments showing the eff4 cts of forced circulation on the film coefficient during boiling were made by L.Austin.(See:"Uebe den Warmedurchgang durch Heizflachen' V.D.I.,Heft 7,Berlin,1903).Austin's data on heat transfer from a vertical iron - /27- -c f.." plate to water is represented on Fig.No.4.4by three curves. Curve I shows definitely that film coefficient (h) is increased with increase of temperature difference between the surface of the plate and the body of boiling water. This is due, of course, to increase in natural circulation. Curves II and III show that rise in temperature difference and therefore the natural convection had practically no effect upon the film coefficient of heat transfer either when the water was boiling or when it was being heated at 1220°F. The effect of natural convection currents on the film coefficient of heat transfer was studied qite carefully by K.Cleve.(Bee: "Modellversuche uber den Wasserumlauf in Steilund Schagrohrkesseln" V.D.I.Heft 22,Berlin, 1929). Cleve boiled water in electrically heated vertical tubes, and his data shows a definite relationship between the film coefficient (h), temperature difference from pipe surface to water, rate of heat input, and water velocity entering the pipe.Fig.No. 4 5 ,Curve(h), shows a rapid initial rise in value of the film coefficient which continues until the temperature difference rises to about 95°F.; after that the rate of increase in value of film coefficient (h) drops off rapidly. The rapid initial rise of (h) is due to quick removal of the vapor bubbles from the walls of the tube by convection currents. All through the rise of temperature difference (t) the volume of vapor bubbles increases with increase in velocity of convection currents. At about (t)- 9.5°F. a point is reached at which the volume and number of bubbles increase more rapidly than the velocity of comvection currents which sweeps them a- -/2 - way; hence, the surface becomes covered with vapor bubbles a greater rll ___ 13 MEMEMERN-WW~··_~_~·.rr .4 I 3 1'- l II L I_·-· 1 ·- 1 · · ·-CRt$5 L0Q1;AfIR-FMImC¢CA3e N' 34b. EUGENE. 2 5 NCN .L.Zi SEEG'IIcN ASE :C EN -C '-·-CI·r7rr-----l--- . ,- , . "1 , '. 'i-- - _L I_ ': __ · C ~~~~~ .~~~ 14.4'' -T -:I-1 - L--- ----- ~ - --- I ·- '61 '074 ;we I --- C--'-··----"·"---·L i . --- r---··T--- - · ·· ·· ·- ·- I . 'I I I·lr I: I.'' !09g~ -- ·--· · TII-·--- -- ·--r·-· /4 I -4- -- · ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~a -i---------- S4 .6+v/. 1#1 -·- .;h - 4 ! i . FY···-II-- ,,'.. - ·-- ·--- .5 40/O ---- -· ------ IIIf 0! : ·-- .r- -1··1 I-· .1 I . i eA ..... ..... :.. j j --I '· I-_--I a I ' " '~'~~~~~~~~~~0"', ,, f . : . .- xowvwt ; j, IF%.: .. - . --- '"':I'i %-i ~4 46 %f 4wo i . i : 4i 'i i" . 7 ! , · L I j I I , ! i...._] I -. - _...- .. ----II 4 I- ._-_ I . .--- _ . F~ ~ . .. ...... .-. :14 i ,i M~-- i I -- - . ·-- - : i3po iF- .. 1001 C------··--·-- ... : .I-- . I . - L - q. . . I i 4 ! .. . C- i - ~ --. _ a . . I - - , . I! p._.___ J i .-I,-10, . --- -:AIV ",'I' 1 'i .. ·. i - 0 i. 4m . . . . - j i "t' i , I __ t. ,A , 'i ~ ' ' ~ .!_ .,, I i"",7-AA . f -7,Vr Ii .I ' .. _ 12 -- L ..... i iI --- (, i i_..!~ .... rI- . . -Roa . . 'i · . i , , . .i.i.:.._ i . -.I m I ....- I . .. -- I--..-~-..,!-.-..-.. ~ . 4 iI .I , I i~. I . i qiC .- ! ! I i .1 ....... t ....... I ·----- 4Ao ;CAVG A*54 , .. -----i F' /w...........'.... I, ~ . , ~ .- -.-- I i ' I. ... I'~ .. .. .. 1 i· I.. ' ' . . -._.. i.'i: ~' i i :-'~ .';,,'i'- ~..i... ...' :............:...- e% I ,. i ~i~ ! Q1 ...--7 '- fI -~ r ,,, · · I ·. ,'~ ~ ~~~~~ II...-,.-.".: ..... i-t...... · 1 ' ~~~~~~~~~~~~~.......... . ' . ,.. t l.JC..' ' I~~~~~~~~~~~~~~~oI -~~~~~~~~~i .J ... .. ~J.. , ....... .~I:1~: , ..., IN., I , ,.,.,.!....i:.I.,.:._}.o j. ' , .j=_ -t...~.. ,--I '"-- ''-·~-9~..- .. - - ~ ... .-- i ........ ?... .. ~,...- .... .... .. ~...-....1 .!~~~~~~~~~4 'F-+ .i c , . f~ ~~ 'I _. r- ..- .{ ~ a.~ i ~ ~~~~ // 1 i L r ... ." : // -I ! A, ' - - I VA,- A I~I ! I ""%~~-O/ '-r---: ',-' 'I I"'-: :-'. i'I "W~'' /4,,,~- - /.. -'-. A' ~ccl /al - . - ----- /r ~ percentage of time and the rate of increase of heat transfer to the water diminishes. Curve (q), plot of total heat transfer through the tube, of course shows the same relationship to the temperature difference(At) as the film coefficient (h). Curve (v) shows the variation in velocity of water entering the tube with rise of temperature difference (t). is seen at once that up to about (t) - From its shape it 9.0°F., the buoyant force of the steam bubbles was increasing at a greater rate than the resistance to fluid flow; however, after (t) reached 9.5°F., the volume of steam and water mixture increased to such an extent that the corresponding increase in pressure drop through the tube caused a lowering in inflowing water velocity. The increase in total heat input even when the quantity of water entering the tube fell off, is explained by the fact that the steam leaving the tube at the lower rates of heat transfer contained more entrained moisture than that leaving the tube at higher rates of heat transfer. Effect of Temperature Level on the Film Coefficient of Heat Transfer From a Solid Surface to Boiling Water It is an accepted fact that the individual or film coefficient of heat transfer from a solid surface to boiling water increases in value with the rise of temperature level at which the boiling takes place. In general, the effect of rise of temperature level on heat / -/2 9- transfer has been observed and studied considerably in many fields in which data were required for design of some special apparatus.Most of the collected data, however, deals with the overall coefficients of heat ransfer, and is not suitable at all for determination of the film coefficient. As far as qualitative effect of rise of temperature level on the film coefficient is concerned, such outstanding investigators as Badger, Van Marle, and Claassen and others have definitely arrived at the conclusion that the film coefficient increases with the rise of temperature level of boiling. The most suitable set of data that can be used within the range required for small heating boilers, was obtained by Linden and Montillon,(See: Trans.Amer.Inst.Chem.Eng.,1930,Vol.24,p 120). Their data is the result of study of heat transfer to boiling water through the walls of a single inclined pipe heated by steam on the outside. The pipe was 4 ft. long and 1 in. in diameter. Curves 1,2 and 3 on Fig. No.46 summarize Linden and ontillon's data on film coefficients and show at a glance the increase in film coefficient with the rise of temperature level of boiling. The values or rlm coerricient on F3g.Ro. '-t can e also represented by means of an equation: h =C(nt)25 Where: h B.t.u./(hr.)(sq.ft.)(°F.). C = Constant depending on temperature level. 4t = Temperature difference between surface and body of water. Fig.No.47 shows constant (C) plotted against the corresponding N~ ~~ ~ ~~~-S ~i~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ,L~~~~~~~~~~~~ 30m I 9 ? 4.5 i I., 3 3 1I2 I 2 1. .2 1,~ ti I 9 p . ;.. ;*ijs E s;_!. . ....... . . _z. L .. .. 4.5 4.5 ;T....... *.i;12;---X .....~....................... -i.... ! i I- - r ..I--, ii' - a. .. i - .-.. ... : 1 . - . . ... 2 . - - - i"-: · '-':' :::- __f__l ·· __ ;...... F--.4 : . I _.__-- .- _-·--- _ . __ _.v ·--- ;·· · r .Is . .... .... ~'""'"--"r. :,'l:-f-..:. . . I ~.- : I . .-1-" . . : --. :.. .i ... . --# --------- : JI- : -; -. I -, ;: :i I4- j'. , 1'!: - -4 : .: ! . ; . T ; . , - ,I, . ;.:.:r.. : . '. - ; - , I-i~ 4 - 1, I - ; :- -- 6-J ,- .;-.; !- . ...... I: .:. . ..' " .: .. .... I. . ... :. ..- ... I - :. 2 !5 :- -- ! *. i.5 . . :- . .: . i. - . ,- ,;.. ...... e ;|~~~~~~ _II e 1i 45 . j:i....r - : ':CNE flIE ' : - 1SCA:ECCOS _.):ARn'- rZ " . --.. .'.. ....... . . A ..... *4!~. .ECTiLl ''' , . . . ~ ' ..... .... ...... _r*''' '$;@ '... ....................... ~~-- :- j j'i !: ,.,, . ... ,I.,..1:I;,i - -'|~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ :!" ": .'|.... !, ....... _ : 5 EN .LJ .,- . ,zrcr~~/ .. .. , e.a: UL _ .?:1 I- 8 9 i F: ._-_:.'_ . rsr ....--! -:" -'- - .: ---~: i 'f 1 i 3 35 . , ! : R ...I;:Li.t :!'!-: -'.i-r-t:-':r''.'--'' -:?. .... 1j.j;+ ''''''' .-. ...!.m ..... L.. .... :z. :.. 1 --t=-::- - ,- .. ..... ...'!..-.-'' Lti+8 - ' .. i.-Hit og~~~~~~~~ :·Ij. .. ,, * A> ........... t W &,,,z0X1J >sZA 4 { th j :--- ,.,.~~~ -: .-. :: '' '-' i· . - ,.......................,... ---- . -= -'-.... . --- ::'-- .. ..- ..... .. .11**...................:..... . ... . ...'.............. ...; ":::I=:'";.'- :: .- i ::::;. . .:L .. d :_, ,, '4_,t........ rL.:' o-A'g*f ' ': wiwr_4_4 ,........ -!4 n , : TI4 I -: U, I- ~: --. !-I- : .2,f--, .. -. 1 .,!o. ',:: ; .......... il : % :! . . ! . . . ....... :":-t- '.*,:..... ........................I.... . ::::'l':: 8 *S='~ ',,: ':· ;' '-.'q.::-:" ___.,.::.- -1 : ...- ;' ,-!" L........... i e-.. 2 ' .0 . O .. 3 ' . _ .... -. ......... 't 1 4:-. =, _~~~~~~--- ? e ·_ 9 . .. ._. i J__ _ __ 1 0. 1Z41 0/7 0o8alaft7 of Z ;'t,,:eeo w · I f 4. IF f v- %I w f ; /,3o I .-20. . 24: 1o:I2PO. k$oAZ4, 0 ( AAA 9'vu 4300 I I I 111 i', oI 0 300° IOO~ N 250 C . R0b°a - Soc 2so - I- I -0& -- I a- .4 .5 .6 .7 .8.910 a . / Costarot-C etoaqszvqR ' h, c (~~) ' . 0 7' 60//My N IO, Zo e G / ed 3.0 ?,v e? a zhr em/o~or'o tye of7 79/, -Z * f4z%~ .- ,g B. tu./d() (-.4)(g..j f He'az' rr OZ ntsf1tr he Surf ace 7&'mP Sj4)olF-etw e e an, f/e od/ of£Pb'y. 1YLx ter. sM7 IP3+ temperatures of boiling. The points through which the smooth curve is drawn were obtained from equations of Linden and Montillon. Fig.No.4 8 represents Linden and Montillon's data as a plot of Temperature of Boiling vs. Per Cent of Nominal Film Coefficient. The nominal coefficient is the value of water film coefficient at 210°F. Another set of data that is applicable to estimation of effect of temperature level of boiling on the film coefficient is given by Cryder and Gilliland,(See: Refr.Eng.,No.2,1933).Fig.No. 49 shows their data as a plot of Temperature of Boiling vs.Per Cent of Nominal Film Coefficient, where the nominal coefficient is the value of water film coefficient at 212°F. Although Figures Nos.46,4I,49, show the effect of temperature level on film coefficient only for various tubes, the correction due to effect of temperature level on heat transfer can be applied approximately to film coefficients obtained with other surfaces, since the water film coefficient is not the controlling factor in heat transfer from gases to boiling water. Effect of Condition of Surface Upon Rate of Heat Transfer to Boiling Water in Contact With That Surface .orksof all recent investigators of heat transmission to boiling water bring out the following conclusions: (1) A rough,clean, metallic surface gives a higher film coefficient of heat transfer to boiling water than a smooth metallic surface; and the rate of heat transfer is in general approximately pro- - portional to the roughness of the surface. -/3 his phenomenon is explained l , ] ... i i '~~~~ p~~~ Q U - ... ii: *t: c~~~~" c~~~~ I I - : $I a-. .1; -. -- - -- - : r- : l | _ ''' "''' '' t-· · : ·- :--· ·-· 4& . e . ' 'l ^ _ -:' ' r .. ., _. . '' I i - - - - 4-: . | . ft; -':. 1.' - f S l ! pI p X> i'5 b_ \ _.j,._ . . :,,,k :: 4 ........ _ .1 f -- }_ . I : . ^ . ' ' -E - - 'I : ' . + .4sto ''.; L --1>k ,. . . -, . . l..s !i,.. ,.... .. i :. .1:t: .- 1,< . I- E- 1.-.1; 1 ' I x,..;-t. - -N' '- 4 1<X rc 1- 1:h11 rs W: -<-- XELT-- I 1- - mlt-v''''' § 1->M; l R 1.-l- i ,. \ i t- T:! i-) it:-l -r- 1 - r S ... W -t F a l l t- l 1. 1 :'-1 I .1 1 I I j 1..vs : . I . t 1--'.'!:-.'1 t1, ,, :l'':-: .. t 1- i -tj :'; -1 :i1-:;.|-.- . . r-' | l t ;-[ t 1'. ''-:-1.... I' ' t :1-: -X- :{- t: fFS4tA iw 1- 1 wWil ll-rx r-a I 1.\1... 1-.:-;1'.:5 :5-s : l | s! 4 ,.... .. ..e .. . .. ..-. ... ' |.% 1- I 1: ' i -- HE\ I . 1'- sI 1-:1sN1T-- ii...j a s. b . 1----- 1'': 1 X. 1:tS . I Qs il . .. . F..'''1 g Ms.-n, 1 . I. : 1: rl , tNT 4 t t ..> tF h..6 -, I I , x 4 t« N W-:1.; .1§\t _ ' ' I ... I; I-;1-.',[t-f::. i ' . ^ t -st. 1 t1' -1.t 1 1 .,. ,,.- - . .. ........... -1 ;t- ,> ., t ;:-- 1 . I , . 1 ': ' l': ' '' - '''" - | 1: ........... .. _..... ..' i CJ :: ' - ' ' _ 1 -tH ]t :1 L ! IL.1'ti0-f i'' .,,.. _*. ', '._ ' : _._.. .. .! ' .' - ;' _ . _ ................................ rl_ L -L@- t! ;-t.:.1: . .. t. . , .. li 1- ::1 I . [,..,. *E q 3. 'I . , ,s, . . . .. .. Wi IN l-.\--,'a '<.i l t*<z -F-.F --,,;-1 -_| ;' ' :'I';I ' ' ) - -t- 1 nl _i._'_ .'-.''. w -- - t-+,. . . .__ . 3a -;X: ';n:: -;1 - t: -1n .!s4-- 1: 1 -: 8: _ g i}LL _, t 1' :1 --=%-1' 1:--:8\ i'M L .. 1to 1 t-:: *+*Wit ts %2 q:.s __. '....' :.'. -- ' 'tu:' 'ou i- i. -I-o i - I t II. ,. |' ' 1 1,;- '1't ' I Q k _ i't ri } - , - I A-J .4 [. . i.:, 1:-,.,' ;.: t 't ,i i'7.-ti0/ 1:.f. . I..._ - .] i . . . I;i r } -r: :J ! . | --t-- ---e '. . I - -. !- :;I: -'I:: , 1 , It , 1;:'' .: t- i.. . Tr: .. ...:' , - I, I; , .~~~. . . . : i 1 '; I - - It i, :t I t; l"% ll'F'' i OF- A: ' .1 .w 1-t ''' --. ·-I ., : ..· · ·· .. ·· , te-t t .-...... ;.F (-i '-t '1fe:w. Ww ·- 1; Q S9w-};R? - , . . . i. . I i .. . : , .I. . , . . , I i :. . eo . - ... ' -I I t . ; . tt' !, I .; i ..... . . . l-.: .. I:. t- , I I r : 11'. .: I f. .. . . -, ' , . I - .: . I , , -.. I -, - - - . -1. -. -.- . -- -- I '-I 1- I l lNi~ 1144w 11 I· ;~~~ I i ~~ f~~~~~~~~~~~~~~~~1 | ~ ~~~~~~II 1s i1 ! I iX -~~~~~~~~ ~~ i I I !- ~1 ~ :l 1 ;1i I ~l _ !IM 1 -~ I I ~~~ -0 ~ llb l ! \ -F I~A ~ .~ i ~ 1 l llll1 ~lr; la I t TI i 1 ?t ! ' ! ~ ?- - L! 1 in l I ai ~ f'z~9 ! ~~ ili ! i~ t< - ~t -1t t by the fact that a rough surface presents more nuclei for initial formation of water vapor bubbles. However, it must be remembered that in any boiler the surface in contact with the water becomes coated with a scale after a shorter or a longer period of time,depending on the purity and quantity of make-up water, and the initial roughnesses are soon obliterated and their effect on the rate of heat transfer lost. Therefore, when selecting the film coefficient for design purposes, the surface should be assumed to be smooth and the lowest value of the coefficient (h) must be used. (2) Any deposit on the metallic surface that tends to reduce the wetability or adhesion between the water and the surface reduces the film or individual coefficient of heat transfer from that surface to boiling water. Under normal conditions this difficulty is not likely to occur. As far as calculation of heat transmission is concerned, it is not necessary to take into account the reduction of water film coefficient due to poor wetability of the surface, as the resistance offered by the water film during boiling is equal at the most only to 2 to 5 per cent of the total resistance to heat flow from hot gases to water. (3) Presence of scale on the water side of the surface causes a considerable reduction in rate of heat transfer from the surface to the body of boiling water. The resistance to heat flow caused by formation of scale is twofold: the first thin layer of scale covers the metallic surface in contact with the boiling water and reduces the film coefficient of - /32- heat transfer by obliterating the nuclei of bubble formation; subsequently the resistance to heat flow increases with increase in thickness of scale and is primarily a function of conductivity of the scale and its thickness. / The first effect, as was mentioned above, is taken care of in design by selection of a film coefficient for a smooth surface. The second effect can be calculated without much difficulty once the conductivity of the particular type of scale is known. In general, one must bear in mind the fact that a layer of scale in a small steam or water heating boiler presents a resistance to heat flow seldom greater than 5% of the total resistance to heat flow from hot gases to boiling water. With steam heating boilers in which the condensate normally returns to the boiler, and with water heating boilers the problem of scale formation is negligible. As long as there is not any appreciable steam loss and but little make-up water is required, a heating boiler can operate for several years before the scale will become sufficiently thick to affect appreciably the rate of heat transfer. Below are given some average values for conductivity of boiler scale: Eberle and Holzhauer,(See: Arch.Warmewirt.,1928,Vol.9,p 171 4 and 1929,Vol.lO,p 3355 )give for conductivity of boiler scale the range between 1.5 to 1.8 B.t.u./(hr.)(sq.ft.)(OF./ft.). Partridge recommends for average value of boiler scale about 1.3 B.t.u./(hr.)(sq.ft.)(°F./ft.).(See Formation and Properties of Boiler Scale,Univ.of Michigan Engineering Research Bulletin No.15,1950). -/3 3- Temperature Gradient Through Water Film at Surfaces of Different Roughness In connection with the studies of the effect of roughness of surface on heat transfer to boiling water, Jakob and Fritz also made some interesting studies of temperature gradients from the heat transferring surfaces through boiling water and to the vapor above it. Fig.No.SO shows definitely that the greatest temperature drop occurs in the water film near the heat transferring surface ,and that the temperature drop through the main body of boiling water is very small at high rates of heat transfer. In general, this figure also shows that regardless of the condition of the heating surface, the main body of boiling water can be assumed to be practically at the same temperature throughout. (Total temperature difference (t) for any curve on Fig. No. 50 represents the temperature drop from the heat transferring surface to the vapor above the boiling water). Effect of Height of Free Surface or Hydrostatic Head on Heat Transfer to Boiling Water The hydrostatic head, or the level of free water surface above the solid surface from which the heat is being transferred, has no appreciable effect upon the film coefficient of heat transfer,except in a few instances. The water layer at the bottom of the boiler is subject to steam pressure plus the hydrostatic pressure, and therefore in order to boil, it must be superheated to a greater degree than the water layer near ' -.... ' ....... ~ :i' ' : '--. -'.i i. ...............:. ....: ........... :_i..... · .............. - 1 ..... · ~ t .......--~~~~~~~~~e.... rc~-'"'e ......... ~-' . . . . j · :·' .~.._..~ _.L-%_:~_.; ..... :_.j ' - e Z ' J '.'7 ' . ..... .:t . ~~'...! w ..... ~-/ - - ... j ' x~s j' :..T.TTTT-7i-_7.;Z;;.-;:i-:_: '.' :;.:. 7''.L':_ .7::7--'.~'L~;:7-~7L;._F:~;j::. .... .'__~_ ........ ~-,---,-'~..... - --- ~- ...=-.,-q-~........ ~.... ~....... 7 ........ .... : ........... ..... : ... 7 .--........~........- -i.. .,-... .--.-.. -. ..... ''..--- ........,-- .. ~": ', - 7": i~"7'"~-7''- t7-----:-~":t~'-'qt';L .,.',-:-';;' -: ......-- ;'.' d?...:':.. --'':-: - . ' "' .;_ T ~_.'''.-.~-~,'~--7-:t:',-''- : ; : l ~.r,;''~'~ 'r.... ---r-/' --.T}2~' :7 [ ... .."~,.... / :7T !,, . '~,. et I: ', ...........---,,-..-~T, 'i.,:4 ~-----...... ................ =-'--; ..... ¢.~, __. ..- _....~-L-,4,.; .. ;--' ,.!.;~--,-.... ,w, .... .'.,..... :-~ '"~-;~'-?-~l'-+I --4...,,.''. .. .~.c~...I ........ -.... r-.-~-4.......-.. +_, rZ '-- --'-,';''~ ~~~~~~~~~~~~~~~~~~l ............. iI Z i tI 4.1I 2 "'s ..... '" > :1~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ f~~~~~~~~~~~~~~~~~~~~~~~~ ; , --.. ..-... ~....~,....~~.. Above the free surface. This difference in temperature between the upper and the lower layers of water in a boiler has a twofold effect upon the film coefficient of heat transfer. First of all, the rate of heat transfer at the lower levels drops due to decrease in overall temperature difference between the gases and the boiling water. But this is only a partial effect: since with increase in temperature, the volume of the lower layers increases while the density decreases, and thus the velocity of convection currents is increased, and the increase in convection currents is of course accompanied by increase in water film coefficient of heat transfer. The total initial effect of rise in water level above the heat transferring surface is that the water film coefficient increases with the rise in water level; however this increase in rate of heat transfer does not continue indefinitely, but passes through a maximum at some water height which depends upon the physical design and construction of the particular boiler. Quantitative studies of the effect of hydrostatic head and water level on the rate of heat transfer were made by several investigators; however,their data is not directly applicable to estimation of film coefficient of heat transfer in boiler design.(See: articles by W.L.Badger,Trans.A.I.Ch.Eng.,1920,Vol.13,Part II, p 139, and Badger and Shepard,Trans.A.I.Ch.Eng.,1920,Vol.13,Part I, p 101). The best thing that one can do when setting out to design a boiler is to lay out the heat transferring surfaces so as to insure the maximum possible natural convection in water passages. Once good circulation of water is secured, the negative effect of hydrostatic - 35- head on the film coefficient of heat transfer will be at its minimum; and considering the practical limitations in form and shape of small heating boilers, this is all that can be done at present to eliminate the lowering of the film coefficient due to hydrostatic head. The accuracy of boiler design will not suffer greatly due to lack of definite experimental quantitative data concerning the effect of water level and hydrostatic head on the water film coefficient of heat transfer; for it should be remembered that-the resistance presented to heat flow by the water film is only about 2 to 5% of the total resistance to heat flow from hot gases to the body of boiling water. The analysis of the effect of hydrostatic head or water level on the water film coefficient of heat transfer is extended further in the chapter.on-"Rational Basis for Design of Water Circulation in Heating Boilers. Effect of Shape and Arrangement of Heating Surface on the Film Coefficient of Heat Transfer to Boiling Water The relationship between the shape of the heat transferring surface and the film coefficient of heat transfer is best shown on Figures Nos.J/,46J2,5S, which are based on the data of several investigators well known in the field of heat transmission. 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': . ..- _~_ __ _ r ----------.:.:': . nJ Curve (2) Vertical Plate. Curve (3) Horizontal Plate (Water Above). Curve (4) Horizontal Plate (Water Above). Fig.No. 4 6 gives the relationship between temperature difference and the film coefficient of heat transfer for the following surfaces: Curves (),(2),(5),(4), and (5) Inclined Tubes (Water Inside), and Curve (A) Vertical Tube (Water Inside). Fig.No. 52 shows the relationship between the film coefficient of heat transfer (h) and the rate of heat flow,B.t.u./(hr.)(sq.ft.), for the following surfaces: Curve (1) Horizontal Pipe (Water Outside). Curve (2) Vertical Plate. Curve () Horizontal Plate (Water Above). Curve (4) Horizontal Plate (Water Above). Fig.No. 53 shows the relationship between the film coefficient of heat transfer (h) and the rate of heat flow for the following surfrces: Curves (1) to (5)Inclined Tubes (Water Inside), Curve(A) Vertical Tube (Water Inside), and Curve (II) Vertical Plate. Effect of Viscosity and Conductivity on the Film Coefficient of Heat Transfer From a Heated Solid Surface to Boiling Water The best attempt to evaluate the effect of viscosity and conductivity was made by Cryder and Gilliland, who formulated a general equation for calculation of the film coefficient of heat transfer from a solid surface to boiling liquids, which is given below in its simplest -/3 7- V I o - . - - c I . -1 ------ , .,.. I i -"--- I .t \1N S- . ' 14 -1 1) k ~on o -, ~ : -- 4 -- 4-- () N Z t - -1-- - N I % A -I 4 i 1 ',,3 ~ ~ ~ E ~ q:zl ,;:4 ,Zt No 11:4 IC4 'the Cs , , %4i I i 4.1'. ... . ,: . -...--. ... e I~ -i' . -V . , 2 S,:..2 .5 2 : 5 ~~~~~~~~~~. 4 .;?&'--,-.' ~~~~~~~~. ''-:*.....: ........................ .. 4I' ... .~ j:..: ! .2. · .m... -.. ,J2.2 . . . . . . _ . . 4 .5h,' . 7 .'',"-5 _ '~ ....... ~~~~~~~~~~~~~~~~~~~~~~ 1.~~~~~~~~~~~~~~~~~~~~~ :. 7~~ - '.-"'-: -' ''-- . ,'I ''... .- .... . . ...' "'.,. '.: r . . : ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~....... ..- - . -. 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I.:' Mw 6A E.,:. /0a. is AL 2.5 3 36' 5- 6 7 a 9 /O .,.-m .. . . 16- A .24F.30 40 r,-g /ov ,-o 'go i. form: 0.38(CZ/K)a t8D2K/Z)b(Z2/SDy)c hD/K Where: h = Film coefficient of heat transfer,B.t.u./(hr.)(sq.ft.)(°F.) K = Thermal conductivity of the liquid,B.t.u./(hr.)(ft.)(*F.) 0 Specific heat,B.t.u./(lb.)(°F.) S = Specific gravity At = Temperature difference y Surface tension, poundals/ft. D Outside diamter of tube, inches Z Viscosity, centipoises a,b, and c are exponents which have the following values for liquid boiling outside the tubes: a = 0.425; b = 2.239; c 1.65 This equation represents one of the nearest approaches to determination of influence of viscosity and conductivity on the film coefficient of heat transfer to boiling liquids. It has, however, only a narrow range of application, since most of the data upon which it is based was determined in a small evaporator heated by a single horizontal brass pipe 4 inches long and with outside diameter of 1.15 in. What is more, it does not take into account several important factors which have been shown to have a definite effect on rate of heat transfer to bllng wter: these are, the latent heat of vaporization, density of the water vapor, surface tension between the liquid and the metal surface, shape of the heating surfaces, and last but not least, the nature and velocity of liquid circulation. The lack of definite quantitative relationship between the rate of heat transfer and viscosity-conductivity properties,however, is not a deterrent in so far as the work of this paper is concerned; since the data on water film coefficient of heat transfer as presented here are based on extensive experimentation nd include at least in emperical manner the factors that are not present in the theoretical equation given above. Thus, estimation of the water film coefficient can be done with considerable accuracy even though the exact theoretical calculation of it is not possible at present. Basis for Calculation of the Film Coefficient of Heat Transfer From a Solid Surface to Boiling Water It is recommended that for design purposes the selection of film coefficient of heat transfer from solid surfaces to boiling water should be based on data from curves given in Figures Nos.4 XA, , 46, 4, 3. 2, The film coefficients estimated from these graphs will probably be in error from 10 to 20%; however, since the resistance to heat flow caused by the water film is equal only to about 2 to 5% of the total resistance to heat flow from the hot gases to boiling water; the error introduced into the overall coefficient of heat transfer will seldom exceed 3%. When using Figures Nos. 46, 7a ,2, ed that the abscissa of the graphs (At) J3, it should be remember- is the temperature difference between the solid surface supplying the heat and the main body of boiling water. In other words, the film coefficient as given in these graphs includes the thermal resistances of the laminar film, the buffer layer between the film and the core. Method of Estimating the Film Coefficients of Heat Transfer The estimate of the film coefficient of heat transfer to boiling water can be made with comparatively high degree of accuracy in 7 steps. (1) Obtain the thermal resistances of the metal wall, the probable scale deposit on the water side, the soot and carbon deposit on the gas side. (2) Obtain the film coefficient of heat transfer from hot gases to the wall. Its reciprocal, of course, represents the resistance to heat flow offered by the gas film. (3) Compute the sum of resistances to heat flow offered by the gas film, the carbon deposit, the metal wall, and the scale on the water side. (4) Divide the sum of thermal resistances as obtained in step (5) by 0.95; the result will be what an be called the"probable overall thermal resistance from hot gases to boiling water' (5) Calculate the approximate rate of heat transfer from hot gases to boiling water by using the "probable overall thermal resistance" as determined in step (4) and the overall temperature difference between the gases nd boiling water. (6) Corresponding to the approximate rate of heat transfer as obtained in step (5),Figures Nos.'Z and 3, will give the value of the film coefficient of heat transfer from a solid surface to boiling water, which will be within 3 to 5% of the expected value. (7) After determining the film coefficient (h) as directed in step (6), it should be corrected to allow for the temperature at which the boiling takes place; since Figures Nos.ll 3 give the film co- and efficients for boiling at atmospheric pressure only. | Figures Nos.47, 6,and 4 , attached here, give an approximate method for adjusting the nominal film coefficients corresponding to boiling at 212°F. to their proper value at other temperatures.The use of these figures is self evident from the notes they contain. (Note: For illustrative example on determination of the film coefficient of heat transfer from a solid surface to boiling water see appendix for Sample Calculations). PART V SPECIAL PROBLEMS CiAPTER XI HEAT LOSS BY ADIArICO FROCLOUTSIDE SURFACE OF A BOILER JACKET HEAT LOSS BY RADIATION FROM OUTSIDE SURFACE OF A BOILER JACKET Estimation of radiant heat loss from the outside surface of a boiler to its surroundings in the boiler room is comparatively simple since it does not involve high temperature or complex surface relationships. All cases of radiant heat transfer encountered here can be calculated by means of the basic equation in the form, q = 0.172 (A) (T. / 4 O100) - (T2 / 100)45 (FA)(FE) Where: q = Net rate of radiant heat transfer, Btu./hr. A = Surface area of the boiler jacket, sq.ft. FA Factor which allows for the average angle through which the boiler jacket surface sees" the boiler room. FE = Factor which depends on emissivity of the boiler jacket surface, and emissivities of the boiler room walls, ceiling and floor. T = Absolute average temperature of the boiler jacket surface, 0 T F. = Absolute average temperature of the boiler room walls, ceiling nd floor, OF. The only terms in the above given equation which require some explanation are the two actors (FA) and (FE); however, their evaluation is simple. -4#- Since a boiler and the boiler room might be considered as an enclosed body nd enclosing body respectively, the enclosure being complete and the enclosed body being lrgs compared to the enclosing; then, as unity for practically all locations the factor (FA) might be tken of a boiler in the boiler room. Again, considering the boiler and the boiler room as enclosed end enclosing bodies, the factor (FE) is evaluated simply by means of the following equation: 1 F- 1 FEl Px 1 P2 Where: P = Average emissivity of the boiler surface. P2 = Average emissivity of the boiler room walls, ceiling and floor. Note: A table of various common emissivities applicable in this equation is given on pso; also, Fig.No.54 attached here gives a graphical method for determination of factor (FE) Calculation Procedure The calculation rocedure for estimation of radiant heat loss from the outside surface of a boiler jacket is best outlined and described in the form of a concrete example; therefore, from now on the discussion will consist of application of the above given equations and study of practical considerations involved in the attempt to fit actual conditions into theoretical equation. Assumed:(See Fig.No. s55) a rectangular heating boiler of the following outside nThat ____ _ __11_1_ 1__1_ 1__11_ _____ i i 4 ___ I--1 . j ---C-----~---4---- 1 -----C---L----- I 4! IN __l--·----·C--- I i ___ _._I 1471, __, I I Ii [ 1\ -----L--, .... "I N; I L~ i I - !t-- - -i _.i L_1-__ I-_I_ _ Ir T , ------------ ----------- ----t- i I _ - - -- II - 4 i . 41! 4, 14% I Ii V ,- I.-- - A I I f i ---7 14 - --- i I - N44 i$, % i I ----- ---- ---------- rr-l-l-M; · ------ ~~~~J A V, NA .YC_-LY i I -I,, ,"N z:k -- 10) I , - . -- " % !I -- 1,1t\1 ! I k, -- . Ij i-- ---\J-t I-- - ' " ll y ; 91 I I iU~ ' I. -- , i Y I i -- k I -Ì i --i k- \ \ I.,--- i .I I I I I - 3 !tq II -- --- i 1 Ir Aev-- X k k TtI t I · k _Q; "I-4f. ii: Vj T-- I I I I 1- i,-- rl -- , 1~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ i . LI \ , I IN- ! hu 0 ; " IQ.4 AiIII - %x\ Z-I 4 a, ) I in ;-, --'11)-! --- 1 'J . i -4 \," ik V, N I- L I : I i I L I I _ VV l. i\ r4-N-N-i % --- i 11 FJ1 ii-.I ---·-------XC--t---h3- i i i s t - I Cm '" 1 -.F Iii , ~--- -- I i -- l, --- ---- - i i II, , A... . I i~ ' -_1_-c·___-_-e--------- L --- 1-a II; It-l- ---% II -\- ,, % 'I. \ ,Al, - ' IN, I iq --LL .. II ,-- -1 .\f ---rllc " i N V\ I I i _ I ... I - II ,, ' I I i' i ---- 1' " J) ! i i ----------- L - --A v, -\ILV - V -% i ----- ------Ni I j I '%& -M. \ A, -, ·---- i t I i - I i I", ~~~---~-F~~-----:~~~~~~~~~~~~~~+ & k - 1'4, I..- .. ii i \ i ANc--- i -ft c-rr---c, \ v -- yi --I-- -1 i iI (,I ,? '\ i Ii .... \ , -- A I%,(O ; I i 1 t --, ----- ------ AN-- _Y-YI_ I-- ---V I \i \x : \ L-. I I I_-I -%41 , LI_~ I -1- .--1. IN -, 4 -5. · _t U - -.z.\ --i i I 1 - t I I I-I c----- I\ \I I. Is II; i I i - ------ - : %- i- -- %I; it i ii -I -- -f ¥--T-?- -r--q- \\ i Ii. tI I w I--- - ; I (Ij Nj i I : I\ . \ - --- A I , -- -- 1\ - - -i \ "q 1 . IN --- . v, V, ___z, --· __ · ----I 4--- ..- I \ :__~J. __;_ .-N k,. --1i --- i. 7-I.. -.T) 1-1 i ; r \4 11 1k i --- - N" LI) -,: lll (11 n 4 i t I I i I I--- ] '\, -4 - ,\1 I -I k-.". 11- -----;q~ . ', i- \ i....... ,~-~ , ... b, i S 10 -" , i f I i 'S, ,I 11 I j A- -NN" V\- Kl I Q I VA\ ki ! :i - - A- l !,q i..-- i . ;r) -k , I -m-+-t .....- J_ NJ Ii . ; -- -------- i 11N-L I'\ if i -f 1,.---- i I i ,· i , V 1, 6I-L .I-N, I zk -- t -- 4~~~1 - I t - t - l i I Is I I -1 I "I -I · -"··L · I I~~~~~~~ I --- A·; N-3 loK 47/S SI W j - fxesm/kva /V-f , 7 / I J / / / / / '1O74' 7/ / / / / / / / / / kal 0 14& //1as insh ed // In roaq,h k1 o/a4fer / / / / / / L1 I- / / / 7 I kw / Id 7/1 / / 40 1V r, z 7/ / / / . / / / / / / / / / - / ,/ 60 / 7 / z / -Plan -Problhm· Cac u/a l'on / / ~~~~~~~~~~ I s s/55 of ;ad'cn z //e6 Zo osses to Srroanat/lys /, /2aseen&r dimensions, 3 ft. deep, 5 t. wide, nd 5 ft. high, is located in the center of.a basement 8 ft. highn,20 ft. wide, and 40 ft. long. Basement walls are finished in rough plaster. Air temperature in the basement is 70°F. The temperature of the walls and the floor is 60°F. The temperature of the ceiling is 700°F. The boiler is finished with black shiny lacquer, sprayed on iron. The outside temperature of the boiler jacket is 140°F. Required: It is required to find the radiant heat loss from the outside surface of the boiler to the boiler room surroundings. Discussion of Data: The assumption of 60°F. temperature for the walls and the floor is in agreement with the average values as determined by field tests and experiments. The temperature of the ceiling is approximately the same as that of the air in the basement s there is no heat loss to the first floor. A temperature of 140°F. for the outside surface of the boiler jacket is an assumed value. In practice the temperature may vary from 105 to 1150°F. for well insulated units to 130-160 for poorly insulated types. Procedure Details: The exact solution of this problem as it stands would involve two separate computations of heat transfer; from the boiler to the ceiling. to the walls one and the floor, and another from the boiler Such procedure would involve highlycomplicated shape relations and is not justifiable because of the values of constants involved. uncertainty of the A much simpler method is to treat the inside surfaces of the basement as being at one average temperature, the average being based on the arithmetical ratio of the surfaces. Area at 70°F. = 20 40 = 800 sq.ft. Area at 60°F. = 800 + (120)(8) = 1760 sq.ft. Then, t= 70(800) + 60°(1760) = 63F. 800 + 1760 tav This assumption of 63°F.- for the average surface temperature of surroundings in the basement, permits consideration of the problem at hand as a case where . comparatively large body (the boiler) is completely enclosed within another body (the basement), and thereby simplifies considerably the whole problem. Setting down the fundamental equation, q = 0.172 (A){(Tx. / 100)4 - (T2 / 100)4'(FA)(FE ) in which the terms on the right side have the following meaning: (a) (A) (b) .(FA)~ (c) (F ) Outside boiler surface = = 4(5)(5) + = 60 + 9 = 69 sq.ft. 1 (also see Fig. No.66) 1 Pi P2 Since from table of emissivities on p./iq',emissivity of.black shiny lacquer,(p.) = 0.875, and emissivity of pl-ster surfacep.50) (P2) = 0.91; 4o°F. therefore, + 460°F. (d) (T1 ) = (e) (T2 ) = 630°F. + 460°F. (FE) = 0.805 = 6000°F. 523°F. Hence: q = 0.172(69) f (600/100)4 - (523/100)4) (1l)(0.805) x/2 8 CV I N i ° 20 t, 40 60 or /00 / 7emerctareT Curl/e6 , --- ete..#-.ni~2 eia for Coeff/cient j 9 elernin a/ Ijecr a tio, /10 /60 /80 200 S1arjazce I o"" Ra&1al,-a-ool f ad/a7ok' jVeatser Wh e E,ow1,5,s;, V~Y =/a (t 2 -J-46-0) 4 - t., -Iel0),- - . A, X/%2 /0. 1 2 -t Irrl Coae/iciet of dza/a? E9 Ileat Z--aorser 'o Y6 s.A.( 1934 M. I. T. q = 5210 Btu./hr. Considerable saving in time required for computation may be effected by use of Fig.N0o.56attached here, which gives the coefficients of radiant heat transfer defined s follows: (t1 + 460)4 (h) (t + 460)4 - (17.2)(10 (t Thus, for the problem (h) ) - t2 ) iven above, = 7.1 (108) (17.2) (10 q = (hr)(A)(FA)(FE)(t - t2) 10 ) = 1.222 but, Hence, q = 1.222 (69) (1) (0.805) (140-65) q = 5220 Btu./hr. Use of Fig.No.5 6 s particularly helpful when there are many computations involving different temperatures. Effect Of Boiler Jacket Finish On Radiant Heat Losses Considering the emissivities of various surface finishes as given on p./l?, it is seen that little can be done to reduce radiant heat loss from the boiler jacket by selection of a shiny surface, unless it is mirror-like, literally speaking. Expense considerations, of course, make ue of a polished nickel or chromium plated boiler jacket highly questionable. A fair'reduction of radiant heat loss may be accomplished by use of good quality aluminum paint; but, here again, a finish of good quality is expensive -- nd the poorer finishes darken with time and their emissivity increases until it approaches that of an ordinary paint. THE IN0ORL&AL TL'OTALEISSIVITY OF VARIOUS BOILER JACKET FINISHES Temp., F. Surface (1) Snow white enamel varnish on Emissivity,(p) 70 - 100 0.906 o. 9o6 70 - 100 0.875 iron plate. (2) Black shiny lacquer sprayed on iron plate. (3) Flat black lacquer. 100 - 200 0.970 (4) Oil paints, all common colors. 150 - 250 0.92 - 150 - 200 0.52 (5) Aluminum pint, 10 A, 22% lacquer body, on smooth or rough 0. Fi0 surface. (6) A. paint, 26~.Al, 27% lacquer 150 - 200 o.30 body, on smooth or rough surface. (7) Porcelain, glazed. 70 - 100 0.924 (8) Nickel, electroplated on polished 70 - 150 0o.o45 70 - 100 0.11 iron, then polished. (9) ickel, electroplated on pickled iron, not polished. -/Y9- .96 THE YTO MAkL TOTAL CEILINTG, E:IJSSI1ITY OF VARIOUS 1;;ALL, BOILER ROOMI AMID FLOOR FIITISHES I Temp. ,OF. Surface i>iVilty, 50 - 200 0.91 (2) Asbestos bonrd. 70 - lOO o.96 (5) Brick, red, smooth. 70 - 0.95 (4) Oil paints, all colors. (1) Plester, rough, lime. o100 100 - 200 (5) Paper. 70 0.92 - (p) .96 0.94 References Both tables given above are based on data presented in, "Industrial Heat Transfer", by A. Schack,(John Wiley and Sons.) "Heat Transmission", by W.H. McAdams,(c.raw -/50- Hill Book Co.) CHAPTER XII HEAT LOSS BY NATURAL CONVECTIONT FROMl OUTSIDE JACKET TO ATMOSPHERIC AIR -IAS-- SURFACE OF A BOILER HEAT LOSS BY NATURAL CONVECTION FROM OUTSIDE SURFACE OF A BOILER JACKET TO ATMOSPHFERIC AIR Since boiler jacket design is varied and is subject to style demand it naturally has no standard shape; therefore analysis of heat loss given here is devoted primarily to development of methods for estimation of heat loss from elementary surfaces of which any boiler jacket may be composed. In general, boiler jacket may be considered as constructed of the following elementary geometrical shapes: (1) Vertical Planes. (2) Horizontal Planes. (3) Vortical Cylinders. (4) Horizontal Cylinders. When these elementary shapes are not actually present, the existing shapes can be approximated with sufficient accuracy by considering them as a combination of the four shapes given above. Heat Transfer By Natural Convection PFromPlane Vertical Surfaces To Atmospheric Air The most authoritative data on this subject has been obtained by Griffiths and Davis (See: Food Inspection Board, Spec. Report No.9, Dept. Scientific and Industrial Research, H.M. Stationery Office, London, 1932), who made an extensive study of heat transfer by natural convection to air from solids of various shapes. Other valuable studies have been conducted by I.Langmuir (See: Trans.Amer. Electrochem. Soc., -152- Vol. 2, p 299, 1915). On the basis of their dta, heat transfer from plane vertical surfaces such as plates or walls can be calculated by means of two simple equations of the following form: (1) h = (2) h 0.25 25 .( t)0 0.275( At/H) 0 , and 25 Where: h = Natural convection coefficient of heat transfer from the solid surface to the ambient air, Btu./(hr.)(sq.ft.)(°F.) At = Temperature difference between the solid surface and the ambient air. F. H = Height of the vertical plane, t. The first equation is applicable to calculation of heat transfer from high plates or wlls over 2 feet high. The second equation is applicable to calculations of heat transfer from lates or walls less than 2 feet high. The repson that the first equation does not include height of plane as a variable is thet the velocity of convection currents produced by thermal expansion of air remains constant at a height over 2 feet from the bottom of the plane. Fig.No. 1r7attached here gives graphical solutions of the two equations given above. Heat Transfer From Plane Horizontal Surfaces To Atmospheric Air Heat transfer from horizontal plane surfaces has been investi- - ~~ ~ ~ ~ ~ --I 5-{:-.i ~ ~ ~ ~ ____U _ I :?,5 .f ._., L: _I i --iI' , ,_i.., i:-4 : , i :1I , .: -, , i . i-- - . -.- . j*. ' : -r.. _·_··_ii b'i! ." i .t'' 9 I1. ..:...' .C:.i u ;r25 1 l,2 i :__,__1_ T ....':i. i., *.! . hi -:::.!:..|. :: :- : ,. . . ' qf i- .__ 6 :'': ... :,'il.,-'l, : .:W:: ' '":--1''' i ; :1:::: __ : :,: !':':i: i:H:._, _,,";,Hs. :1 I.'*:'.i: ' . : ! t h~'l: -;.:--: @*? ' H"ll49 i;-...... _,'!::l,-f- ..,_..-:: . +. ' ~ *:''riF? .... - *-'.-,,~. ' '' ' .'..-.-."'., !;^_ _ ':; '::.:1.:. ... il.? . i ,, .. I .. § .. , .. , .;r Ll ... ;... . . 4. | . .: :.. I ... '''''' I . . & .. . 0,.. ._. . .1:__... _:._. I*: .: I .Parlw at, ! ...... i.:::::. .,.: .1. t ''! a ,.T.,....! 1'; ... "TU;1,'-<'~ I~ &' ;W e -. , ....... 81 -':'- ... ... . . ., ', : 1-, .. j .. . ' 'I -r.rr i.t'.|tr4 ! l ' ! .-ii: I- X I !::: : -:;'1i! ... * _: L _ l .~.w.-,~?-~ - .t -?*[-,~t _,.,t= -. ,.:~qr . . :.[>- -t - i-'F~'?.- _. 7. 2 _ . -' - .;.D , .... . ''.' .j 3 ''. "'i" -!-!i,_ >..... ''1.. '' ''1. i r: l :.l , .. ,4t"F .t; " L.,. .. ;:;;;:7 "'- .^ .ii: i! !i'~!¢i --"I .,'j.. .1., .. ., j;_, j ci .. ......- ..t- !.': ".- . . ._,*-- -. I.I · i.. -i|,I '- -' ..Le 7 .H i ' -; , -. t !. ,--41 '!: i ., ... :. i , · w r :I 1. f4s .... :... . *' ;. - - - i - -.- : 1 . . . . . : l , t_ . . - , II!. I ____ f 4 ."..' it, k....: . .. - l ' * -:--'I -' ' i .. , Er ~r | . .: ... r... t .;. ..... . :! I 1: ::, !'1'' , . r; ·- . -- ^ i --.- '@ I-et tH ,.... I r ... ;ffis . I - ! -: ;- : .Xu ! I-. c .: I :. 45 .!.... __ :5¢:i.t -.1-.' .. ' .. l . . . ...... .. :....1._:,1.. .... .. Y~CB~ o |,:,! r,:jr.,tZ .."!.. ii T' :. :.--: : :! : -:' a I i . '.t | - t!, L aO: ' _ . 'i 1 t ~"I' ·~'tt,~'" i.F'." ~~ -i :: -;..i.r.i . i ~: . 1. ::t'. - I' .i i____Y j r.a.f. ~7 . :.- i 17% i__ ~ ; .: EX' 9 -.-. 'Ri7. -- ' -p ~- M.--1T ' - ! TtF, 2-0, · 4':;~ .,x. 7 . .. 4-i 4"' : 6 . AA. I-! .1,pjw1-. 4 i :!" : ; 71-A"R i-.g .'4_. . -1:+O....... .1. 'F li....::::':!:,'l i: ::. I,... .'-'i: .H:I-i1 -- J;.. .4...li-lliiw~ P..,, , . , :. ..-2::--, .... : .-- m it:.. t i ., . Ž4W _'~- -: ':.:i4 .~ :i . ' _- .. .. _. . .23. . ccc--c- ::,: :: .:' .:;;,'-I...: I J . ,: t .... .: :,.... · ··-·· .. ;; · · ,..· :·I·I . ....... --I-1.... -. .1,.. . i.::.'"'t,.',1.: '~'.. :i:', ::.'1'" -i ! 7 a 3 -, AO St!AlT5I CA E .RC'-; Sr "r .. ! · - ...-. ;! - ·-- · · ·· :·-·· ;r !· :·l·i!el:··· ·· ·· 1 7 .3 /0 gated by Griffiths and Davis, and also by W.J.King(See:"Free Convection" Mech. Engg., Vol. 54, p. 410o, 1932). Data gathered by these experimenters shows that heat transfer by free convection from plane horizontal surfaces to ambient air can be computed by means of a simple general equation of the following form: h = A( 4 t) 0 25 For plane surfaces facing upward this equation becomes: (1) 0 0.38(t) 25 h = While for plane surfaces facing downward it becomes: (2) h 02(At)o 25 In these equations: h = Natural convection coefficient of heat transfer from the solid surface to the ambient air, Btu./(hr.)(sq.ft.)(°F.) t 3 lemperature difference between the solid surface and the ambient air, °F. Fig. No. $a gives graphical solutions of these two equations. Heat Transfer From Vertical Cylindrical Surfaces To Atmospheric Air Data on heat transfer from vertical cylindrical surfaces to air has been gathered by Griffiths and Davis, by W.J.King, and by Koch (See: Gesundh.-Ing., Vol. 22, p. 1, 1927). The accumulated information indicates that heat transfer from vertical cylindrical surfaces can be calculated with a fair degree of accuracy by means of two simple equations of the following form: -/5Y- ~~ ~ ~ :;- - . i-.-- . T-i<.""17 .- . -i L '_ . ;i.L;.·.: AE I . t .:-; . ,;-. -: a:. ---. ::.; .. :. _ , . .; , : :, ; r, I . , : -:'.: I :.I.;1 . . in, : .,.l . . . ; .......I, § . -. i *_- ' .:, FIT t r I i I. I ..-.... . :: I !, i; . J . . ., i; .t '. . * ..r |. I . i i! | . T. .. - -f- .' t r_ - : :_F ' :.:3; . . i , ·. ; '.;1' . :.. ;. -: . : '. .! --- r---- Sr .x ' *i'' .:!'. . i! ,n, ;:.'1' ;1 ........ . I! ^t : ._.?~.'' .- 1. :1:: ._'.:j .. , '..... i '~::'5: ;_. r~ . .. ; . : :.;.i' .z;. __~'-'?. __i B_ B ,777 i 't.ai .7. Li... - i :, ,.. . . ! .1:7:7,,-..; L:-- 1- ,t:t;:. ':1v !:t:". ::F I : .: ; ' I- . I . .: . ; ; ' : ,- . . . . :. I ;:ti .. - '; ''' :'i:; :l: 1 ----. : itT- .,.1. ,.,...__... . -i ..'' !'j F 3.5 __ I : : - r , : ;-: , ,. : . 3 I . r- i : i i , , I , I ....... :...:: i *! '!! 2 5 . ;g ! ... _ xI . ....I. i __ - _ . ;'. .;. !... ,: . -' : ~Z 1.4 · . 44... :-..- -II-'-ti. 5 . II ! f\ , T JT., II i '- ' A., I. , V. - ! *i, .r . !.1 . - .. I I.. I . . ..'1 FCF'. I . I .. ;-'Ir ,, l: A'7.IFFL: . .1 I I . . T-, 77r f ;.;, .. I .;!, - . .1:. .. :" :......: 1: .1 4 - LI- J.i-.' w t::::. ::-'F:"'.-?..,.F,'C i ':. * r-=! :I 3 ! _- A ..... .·· · ·. . . : . ; 1 ,t _ _--- ., . . A . , .. ... II . "I. 7 . . . ·--- -· -- r----;-- - - . ", : i : L . t-! .1t. t:,; l. I : :I : - .'I'' .- ,,f ..... ' -- : ·- :' :e...:. . '. t!~:" : I . "1.i' .,,.::;, -- _; i___ '' J:.:-'t:2;:"' ..i. , . . - . -, : i-i.-~.-.:i]...~ : : T' :..:-- :, :.;-..: .0 I - .47 ..... : 1 . -| · r | | | I, z - C:: ;'. .... :" '~-· ·-- : I.H ':' . .4 1--'- -. ~ - c if c--· I 4. .4.. -- I I4 .4 '4 . I 4- I... . I P - I I ., .. .. , . 7_ .': ... . L ° bran i . . .. .4 I .5 . /0 .4,- . 4'o (1) h = (2) h .4( t/D)' 2 0.4(1/H)057 ( At/D)025 The first equation is suitable for calculation of heat transfer from cylinders over one foot high; while the second equation is to be used for computation of heat transfer from cylinders less than one foot high. - The terms in these equations have the following meaning: h = Natural convection coefficient of heat trnnsfer from the solid surface to the ambient air, Btu./(hr.)(sq.ft.)(°F.) at Temperature difference between the solid surface and the ambient H = Height air, F. of the cylinder, when less than one foot high, ft. D = Outside diameter of cylinder, inches. Fig.No.E attached here gives the graphical solution of these two equations. Heat Transfer From Horizontal Cylindrical Surfaces to Atmospheric Air Data on heat transfer from horizontal cylindrical surfaces is probably the most abundant in the literature on heat transfer by free convection.The most authoritative information is to be found in the following works: Paper by McMillan, Trans. Amer. So. Mech. Eng., Vol. 48, p. 1269, 1925; Paper by Heilman, Trans. Amer. So. .ech. p. 257, 1929; and that of Langmuir, Phys.Rev., Vol. Based on their dta, ng., FSP 51, 4, p.401, 1912. the following equation can be formulated for calculation of heat transfer by free convection from horizontal cylindrical surfaces: 4. 5 4 7 6 9 3 -: 4-4- L- 7 _ _-I . ' -:- _ . - ' . . - _!-, '. ::: ,7i* I I3:. _ : : . - % I : : - -.-, ' , I 7I - _I '1 1 . ._ - ' . i - m . - i: ; .:i ." 11 - 1 , -7 . - I . : i :i!it :I - , r, ..,. . -r I I i - - -..+, -I t ' I- ' ' --- ' 7' -I I, -: ; !:; . . I 1 I ,_j I ., ; .. I; .. '! I _. - . i - - . I . -- -I-I-i I I . qif Yi' 4 I I ,I-, I- I. ,; II . 1 .- ; - , ,,, I. I I I i I I - I A.S . : . i , . . - - , I I - , . ;- - i I ll i, .. - ' * , t . I.j,.,,,,7 4.; .4 i4 . -1 7L 7 7 ft flit J--,-i -i1 :.!t ,+. 1f14 i, ti :i I1...,.. 1 "fl : - I !1 . , . ..i I '7 . 1 -1 - . _t ! , : i -1 . " . i - , . i , . 1- ,1 .- Q. :: -i , , - , - 1.:''' In . '~~~~~ .4t . -.|.;. 4 IIii 15 II -- I - . , .. . - - "1 ' , r- -- t - I . : t -t II : ,t . I. 7I 1... -, -1. 3 L :_; 1 1.t ,- - ,I ,..1 L ,4._ '- - -- i :- - I: iz I 5 - . -7 ; I ': ... -... 1 _. -|. . -:i 4 'D .=._ I z 51 - . : -1 ,i . | . t-, , ........ - ' - - - js z . - . i i I I -' I I , ; t i I . 1: aL . 'J - , ~ . -) :/-i.g.r e - 2 .. . i . --- _ ,,.T, _ > 't'; ,' * .e r ,, tt ,. - r 1^;;1; 1' s..:. ,__ ' 4_ ! t , q_, , ' ,__ ' ,. . ;: t-; . * r .- . !-i''. 4 .i -.1,,,,t . ., .; + - L;--, -i:4 *- _ 1__-p :- , _ __ t t 4 , ' ' . f * I * - ' I . .............................. _. . _, _, _ _ _ ;- P f 1 - r j J '' ' '' ' ' __--l ' ' i -- I . : . / ,;:t*:j. .vt- iX /. 4t{'2 '} | ' | | - r - t - -- , . - ,_, -. _, Chile! . ,.- e ; ' ': [ -- j - ' ' I AT_* I -, )) z 1 r I 1111.I , 9 - - I ·/ 0 . , r ' I ., . g : . . . I , I I r ., ' ' 7"1.4 1 '' L -1-_ ! i'/; ! . i -+ '' | ' i , F. :. Z,; , . - i,t; ' , , : I' : -; , ' i ' i :-- . .t ..! _.L-: f-i/ .I;' . et--I * e 1 t T - - -- S | e , ;- , ,, 1::: : t ' - ' .- '-1 - ': * . 1r .1'1 1 '. - g L .,,, ,. ; S * e ................ 1- t | t35 __ t::!b.Rel#-*-Ec--./§. .. ht>4 , E * > ; ,; ' ' I : '. ' l' + 1':' ! -:: 1'::;':1::: i I i, t j, -l :::, -t : 1;!--:l - l . .. I ..................... If Z ~~1- 1 -b ; _- _ _s_ -, I -t ( -: 0 . i 2*1 I ... _v.*. !- - .j j;"'-':-!:.: >,;: !'.* ' " ' -t4iPa | - , t---t-ti- __ - -s /0 | , } -;_ ._>- ' -t-- I r, *,1t _- _, :_, I K s _.-.e I i __ . 7 :. .1 4 ,, _. . 7 h = 0.42( At/Dl) 0.25 Where: h Natural convection coefficient of heat transfer, Btu./(hr.) so.ft.)(°F.) t Temperature difference between the solid surface a.ndthe ambient air, °F. D = Outside diameter of cylinder, inches. The use of this equation is somewhat limited by the fact that it is based on experimental dta 25 and 700°F., where (t) nd diameters vried was varied only between only from 1/2 to 10 inches; however, for purposes of estimation intended in this thesis it is sufficiently accurate. -/5' - CHAPTERXIII I2ER.ITTEi.TT OPERATICO OF SALL ITS EFFECT IL-FIRED HEATING BOILE ON DES IGN FEATURES age INTERiITTENT OPERATION OF SALL OIL-FIRED HEATING BOILERS D ITS EFFECT ON DESIGN FEATURES Introduction In the great majority of smaller oil burning boilers the amount of heat generated in the combustion chamber is regulated by means of a thermostatically controlled shut-off valve. When the temperature in the building rises above the desired point, the thermostat activates the shut-off valve and the flow of fuel is stopped. After the temperature in the building has fallen below the desired point the burner is set into operation once more. It is highly desirable when the burner ceases to operate, that the interior of the combustion chamber as well as the gas passages should remain at as high a temperature as possible; frst, because lowering of the temperature within the combustion chamber means delay in starting up, and second, because cooling of the boiler interior is usually a direct loss of heat. Another objection to frequent and wide variation of the interior boiler temperature is that it causes severe reversals in expansion and contraction of refractory materials, with consequent rapid deterioration of combustion chamber lining. Cooling of the combustion chamber, with its accompanying harms, is particularly marked in those units which do not have an automatic flue damper which could close the flue when combustion is interrupted temporarily by the thermostat. Heating And Cooling Of Boiler Structure During Intermittent Operation Heat loss or heat gain by the boiler structure can be estimated Adab easily by means of a simple equation written as follows: Q = (w)(l)(t'- t ) + ......(Wn)(on)(t + )(t - t) + (3)(C3)(t' - t") )( - t") Where: Q - Heat loss or gain by the whole structure of the boiler during the time when the temperatures of its parts changed from (t') to (t"), Btu. (w1 ),(w 2 ) etc. = Weights of various prts comprising the boiler structure. (C ),(o ) 1 2 etc. = Average specific heats of the materials from which the boiler parts are made, Btu./(lb.)(°F.) (t'),(t') etc. = Initial mean temperatures of each boiler part, °F. 1.. 2 (t"),(t") etc. = Final mean temperatures of each boiler part, F. The apparent simplicity of the above given equation, however, holds true only for steady conditions of heat trnnsfer, when the mean temperatures of boiler parts are tken as arithmetic averages of boundary temperatures. In usual intermittent boiler operation the time of complete cycle is too short for establishment of a steady state of heat transfer, end the temperature of the boiler structure varies in a most complex manner. Therefore, determination of heat loss or heat gain by the boiler structure during intermittent operation resolves itself primarily into calculations of the true mean temperature of its various perts. -'5?- Temperature Distribution In Boiler Structure During Intermittent Operation Based on studies and research of many investigators in various fields of heat transfer, it is possible to state definitely that temperature distribution in the structure of a small heating boiler operating intermittently depends o the following variables: (1) Frequency of periods. (2) Length of inactive periods. (3) Ratio of actual operating time to total heating time. (4) Amount of air permitted to flow through the combustion chamber during inactive periods. (5) Physical properties of materials from which the combustion chamber nd the boiler setting are built. (6) Rate of heat transfer for the inside surfaces of the boiler to ir passing through it during inactive periods. (7) Extent of insulation on the outside of the boiler setting. The mthematical are so complicated that relations mong the variables enumerated above nalytical solution of problems involving them usually requires the use of complex partial differential equations and much arithmetical computation; -- as a matter of fct, some cases are so complex that no mathematical solution has yet been obtained for them. However, by application of graphical analysis of unsteady heat flow as made by OGurnie and Lurie (See: Ind. Eng. 1923) the hem., Vol. 15, p 1173, pproximate solution of intermittent heating problems can be made comparatively simple. Gurnie and Lurie showed that the analytically derived equations of unsteady heat flow for various simple bodies, such as the shere, -/60- cylinder, flat slab, and others, can be plotted in terms of four dimensionless groups sas follows: x / R (1) A relative position ratio = N there: x = Normal distance from.mid-pl(ne to point in body, ft. R = Normal distance from mid-plane to surface, ft. (2) A temperature difference ratio T- t = T T t. 'here: T Temperature of surroundings, °F. = t Temperature at position (N) within solid at time (e), tl Initial temperature of the body, °F. (3) A thermal resistance ratio = M = / 0 F. k Rk / (hT)R 'here: k = hcr Tnerm.l conductivity of the solid, Btu./(hr.)(sq.ft.)(°F./ft) cer. h T = Combined coefficient of heat transfer by radiation T and convection between the surroundings t temperature (T) and surf-ce of the solid at (ts), Btu./(hr.)(sq.ft.)(°F.) R = As defined bove. k (4) A relative time rtio = X 3 ~c Where: = Time from start of heating or cooling, hrs. = Density of solid, lb./cu.ft. c = Specific heat of solid, Btu./(lb.)(°F.) -/6/- K and R = As defined tle charts above. lotted by Gurnie and Lurie give te among the dimensionless rtios (), (Y), (, relationship and (X)"re assumption that during any one run (T), (2), (K), (), bsed on the and (c) remain constant. This assumption, however, does not introduce any grave errors, and the predicted results are usually within 5 - 8% of the true values or better, depending on how closely the actual conditions pproximate the assumptions. The fundmmental charts made by Gurnie and Lurie are reproduced here on Figs.Nos.6 0,6 1 , 62, ject to the following (a) Fig.:o.60 for the ? and 63 . The use of these charts is sub- liL:itations: was designed primrily for an infinite slab, i.e. slab with two dimensions much larger than the third. 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Z': !:!: 1...; - .. ' : ;.. . - '. I IG' 4r. '. - -· --: ;-.:;. T -- . -. .I , ~.. I1-I*. ---- -- -, YkK7 . -. __. I - .. i . -. ''i -. .--.. T--,-: .- ;';,..; ..-.. .ITTPV7Tj 1\ · L i IC_______I_·_ . L''-_ 4 -- r. -, - I , j-. : ..: i i .- . -.. X--4 il_ I .";-rt I ; t~~~ I r~-~~~-+·-r~t-------- ! . 1 . I .-- . " ' .ft 1 mw~ 0v -- · I - · Application Procedure Application of graphical methods outlined above is best made by means of an illustrative problem, as the number of variables involved is too cumbersome for verbal description. Given: (1) A cubical combustion chamber constructed as shown in Fig. No.64 . (2) The initial temperature of the brick is 50°F. (3)Surface coefficient of heat transfer from the flames to the inside brick surfasceis = h 2 Btu./(hr.)(sq.ft.)(°F.) = core (4) Thermal conductivity of the brick lining at 1000 and 2000 °F. is respectively 0.60 and 0.65 Btu./(hr.)(sq.ft.)(°F./ft.) Density of brick = 115 lb./cu.ft. Specific heat of brick = 0.250 Btu/(lb.)(°F.), between 70 and 2000°F. () Thermal conductivity of asbestos covering is 0.10 Btu./(hr) (sq.ft.)(*F./ft.) Required: It is required to determine how long it will take for the brick surface in contact with the steel casing to reach a temperature of 500 after the burner is set in operation. The flame temperature is assumed to be 2500°F. immediately upon starting up. Solution Procedure (a) The presence of the steel shell between brick and magnesite - 3- F. = G0 fC / to= 6-oo 0/- 4 3 -,m0 F/Y. No.64 may be neglected due to its small thermal resistance. (b) As the total heat flow through the asbestos covering even F. is equal to only : at 500 (500- 50)(0.1)(2) = 155 Btu./(hr.)(sq.ft.); rom the brick surface in contact with the steel shell the heat loss may be neglected. T£hisgives an opportunity to treat thnebrick lining as one rom both sides ( neglecting the helf of a slab which is being heated end effects). Neglecting the heat loss from the outside wall and the heat loss due to end effect, is perfectly justifiable since the properties of materials involved are seldom known closer than within 5% of the true value. (c) Then substituting in the above given dimensionless equations : N = x/R = o/R = 0 R) = k/(h Y= (2500- - 50) = 0.817 500)/(2500 (0.60) X = k A c R2 ~~~~~~~~= Corresponding = 0.188 6 hrs. -0.1880~ (115)(0.250)(4/12)2 (d) From Fig.No; X is obtained 0.60/(2 4y) = 0.90 0: to N = 0, MI= 0.9, and Y = 0.817, the value of to be equal to 0.42 (e) But, X = 0.188 6 (g) Therefore, e = 08 0.42/ 0.188 -/6& - 2.25 hours APPROXI4ATE GPRAPHICALÌETHOD 0F FINTIG DISTRIBUTIOT HE TEIPERATURE IN UTNSTEADY EAT FLOW nOUH HAMBER WALLS AND OTHER SIIiILAR CASES There COMBUSTION are many instances of heat flow and temperature distribution where exact mathematical solutions require a considerable amount of labor, and are not justifiable since the physical properties of the materials used in furnace and boiler construction are usually known only within 10 to 20% of the true values. In other cases the shapes of bodies involved in calculation are irregular and do not lend themselves readily to mathematical analysis. A very practical and simple semi-graphical method for solution of the above mentioned roblem was developed by E.A.Schmidt in "Foppls Festschrift" 1924, p 179-187(Berlin,J.Springer). The writer here presents his modification of Schmidt's method, since there is further possibility of simplification without sacrifice of accuracy. The writer combines the method of Gurnie and Lurie charts with that of Schmidt, which results essentially in an almost pure graphical solution. The developed method is applicable to most problems of plane heat flow, and also to some cases where the heat travel does not deviate very much from plane flow. The method is essentially as follows: starting with a given temperature distribution in conducting body, the corresponding distribution after a known short interval of time is obtained by means of -/6 - the Gurnie and Lurie chart; after that, by repeating the process in Schmidt's manner, the successive distributions after any number of equal time intervals can be found. The Principle of Schmidt's Method Let t, t, and t, denote the temperatures at any moment in a conducting body at three equidistant points,(P),(Q), and (R),(See Fig.No.65) lying on a straight line parallel to the direction of heat flow: then the temperature at the point (Q) is equal to(t + t)/2 after an interval of time given by e = (cpX2 )/2K where X=PQ=QRand (K/cp) is the thermal diffusivity". Where: Conductivity of material. X c = Specific heat of material. p = Density of material. That (t + ts)/2 is the temperature after time 9 (cpX2 )/2K = can be proved as follows: consider the rate at which heat flows into the slab of material between the lanes represented by (AB)and (CD); let the temperature gradient at the plane (AB) be represented by a straight line through points (S) and (T), that is, by (t - t 2 )/X as a first approximation. Therefore the rate of heat flow across the unit area of lane (AB) is approximately equal to K(tx - t 2 )/X. In the same manner the rate of heat flow across the unit area of plane (CD) is approximately equal to K(t8 - t)/X. Hence, the net rate at which the heat is stored up in the slab between planes (AB) and (CD)is equal to: -/66- NV. T-T= = a/ - 3 _ 2 tZ L) t I' ;z7/Y.j 31) 'b , U - -, J7'o L-" j'_P ;4;/ -eX- - d "~~^~~"e"""t4~~- (z -~CL T57W i"aY·;*·c·/za-t;M.e Ve -LL-DLLt --2 57- III lez- <9- Cpc;2 ) /= /- /, /Pdet 6ox Catduct/>i -zlk;-y" It~ -664ee of m)zep//. / If / 65 ,F . Mo. 9. K(t - t2 )/ - K(t2 - t)/ = K/X(t + t - 2t2 ). The volume of the (DC) is equal to (AC) 1 lab ABCD per unit surface area at (AB) or X. Therefore, if (cp) represents its specific heat per unit volume the rate at which temperature rises at the center of slab ABDC is equal to: Ktt + t - 2t2 )/(cpX) = K(t - 2t2)/(cpX2 ) + t 'nere (K/cp is the thermal diffusivity. Hence in time e = (pX to 2 )/2K the temperature rise will be equal : K(t + t - 2t2 )/(cpX') (cpX2 )/2K - t + t - 2t2) - (t + t)/2 - (to) which gives degrees rise per unit time. Therefore the temperature at point (Q) after time 6 = (cpX2 )/21 is equal to: to + (t In Fig.No. + t)/2 - t = (t2 + t)/2 65 the resultant temperature after a period of time is represented by point (T') at intersection of ordinate at point (Q) with the straight line through points (S)and (U). Application of Graphical ethod for Determination of Temperature Distribution in Unsteady Heat Flow Assume that we are given a wall of a combustion chamber (See -/67- Fig.No. 66 ) which is initially at a uniform temperature (to) throughout, and that the inside face (AF) is suddenly raised to a temperature (to) and subsequently maintained at that temperature for some given period of time. Since (t2 ). the inside surface temperature, is considerably higher than that of the outside surface during operation, we can assume safely that during the operation the outside surface of the wall remains approximately at its initial temperature (to). Actually, of course, the outside surface of the combustion chamber may be from 30 to 100°F. higher than its initial wall temperature which at the beginning was equal to that of the surrounding air. The initial temperature distribution in the wall may be taken as given by the line AFGHKL where (AF)= (t - t); that is to say, the surface (AF) is at temperature (tj), but no heat has yet penetrated into the slab. Now, let us divide the walls into a number of equal thin slabs by division lines (BG),(OH),and(DK).In general, the accuracy of the solution is greater with a greater number of subdivisions; however, for the purpose of illustration four sections will be sufficient. Let us assume that for the particular material and given wall thickness it is found from Gurnie and Lurie Chart that for a semi-infinite solid, at time - (cpX2)/2K from the commencement of heating, the temperature at a distance (1) from its initial vlue from the heated surface increased (to) by an amount equal to 0.5O(t. - t); while the temperature at a distance (2X) from the surface has increased by O.4(t- to). The temperature distribution after (cpX2/2K) hours is there- -/ a S- *- Aha/ 4-/s/a A -- C 1 I j I Graoh/c/ 7w )eferm/ri/n4t/on 07-o' J2'strie>fbon in Z/%steolay /Mea .g' Ale g 66 yA fore approximately represented by the line AOKL, and OH = 0.04 AF, and X = FG = GH Hk = = where IG = 0.50 AF, K. The advantage of beginning with values as obtained from Gurnie nd Lurie charts, instead of Schmidt's first step of graphical construction, is that smoother distribution curves are obtained. The steps of graphical construction Draw line A, re now as follows: intersecting BG at P. Draw line MK, intersecting CH at Q. Draw line L, intersecting DK at R. Then APQRL represents approximately the temperature distribution after a time period equal to 20 (cpX2 )/K. Now, starting with distribution APQRL: Draw line AQ, intersecting BG at S. Draw line PR, intersecting CH at T. Draw line QL, intersecting DK at U. The broken line ASTUL represents the approximate distribution after a time period equal to 50 = (cpX2)/2K. This process can be continued as far as desired giving us the temperature distribution in the wall after any multiple of units of time. It is easily seen that the temperature distribution approaches the straight line AL as time increases, AL of course representing the steady state of heat flow. IK -/69- PART VI FLUID FLOW APPLICATION, OF FUNDAMENTALS OF FLUID FLOW TO DESIGN OF SMALL HEATING BOILERS Introduction The discussion presented below is intended to furnish a scientific basis for the solution of all principal problems of fluid flow that might confront the boiler designer. In particular, the methods of calculation given below should be useful in design calculations of experimental models. When used with a proper mixture of judgement they cans effect . considerable saving of time, money and effort that must otherwise be necessarily expended on an extensive so-called research by cut and try" method. Every heating boiler, or any boiler for that matter, is primarily a heat exchanger in which heat is transferred from a hot fluid flowing on one side of a separating wall to a colder fluid flowing on the other side of the wall. The flow of either of these fluids is accompanied by friction, and consequently it requires a source of energy for its very existence. The energy supplying the motive power necessary to create and maintain the circulation of fluids within any heat exchanger usually comes from two sources: (a) the forces of gravity which originate due to difference in density between connected columns of the fluid, and (b) the fLorcesof pressure which is originated by mechanical means.In many instances both modes of creating circulation can be used simultaneously. In general, the gravity circulation (also called natural convection) is less expensive to maintain than the mechanical circulation -/ 7/ 1 1 \, (also called forced convection); however, use of mechanical circulation often results in indirect economies which more than offset the higher direct cost o circulation. Also in many instances mechanical circulation offers the only solution of the problem at hand. In considering the design of any oil-fired heating boiler we are usually concerned with two separate circulation systems,namely: (a) that of fuel oil, air, and gaseous products of combustion on he high temperature side of separating wall, and (b) that of water or steam, or a mixture of both on the low temperature side of the separating wall. In both of these circulation systems, the analysis of fluid flow can be made from two points of view: the first of these being fluid distribution, and the second , fluid pressure loss. In keeping with the above mentioned twin point of view, the discussion presented here is divided into two principal parts: the first, entitled "Orifice Flow of Fluids in Sall Heating Boilers", and which deals with fluid distribution; and the second, which is entitled "Fluid Friction and Its Effect on Fluid Flow' and is concerned primarily with fluid pressure loss and maintenance of fluid flow against frictional resistance. CHAPTER XIV ORIFIC FLOWI OF FLUIDS 7 I'i,Si:,'ALL HEATITNG BOILERS ! ORIFICE FLOW OF FLUIDS IN SALL HEATING BOILERS Introduction The fluid flow in a small heating boiler, or for that matter in any heat exchanger, is one of continuous encountering of restrictions, many of which may be considered as orifices. Thorough understanding of fluid flow across these orifices is essential in design for proper fluid distribution as well as for accurate calculation of pressure losses. The discussion presented below is applicable to flow of liaquids,and to all instances of gaseous flow met with in heating boiler design. The theory and analytical methods given here are not applicable to those cases of gaseous flow in which the pressure drop is greater than ten per cent of downstream absolute pressure. However, since the gaseous flow in boilers practically never ndergoes a pressure drop over one per cent of the .downstream pressure, this limitation is of little concern in the work presented below. Efficiency of Orifice Flow A jet of liquid issuing from an orifice is one of the simplest illustrations of the principle of conservation of energy. Knowing that the orifice receives its energy in the potential form (Qth) charges it in the kinetic form -2g and dis- and assuming the energy discharged to be equal to the energy received, one finds the theoretical velocity across the orifice, which is given by the expression VT Where: /7Y V = Fluid velocity across the orifice, ft./sec. g = Acceleration due to gravity, 32.2 ft./(sec)(sec.). h Unit pressure at the upstream side of the orifice, in ! terms of feet head of the fluid in question. The transformation of potential to kinetic energy in practice is accompanied by a loss due to eddy currents which transform some of the available mechanical energy into heat. However, when preperly designed the orifices need not cause a large energy loss. In many instances the orifices can be designed so that their efficiency of energy transformation is over 95%. In general, the orifice efficiency may be defined as the ratio of energy output to energy input. ORIFICE COEFFICIENTS Coefficient of Velocity Due to fluid friction the actual velocity of a fluid stream or jet issuing from any orifice is always less than indicated by the equation V = /2~-. The velocity obtained by means of this equation, which is applicable only to frictionless hypothetical fluids, may be termed the ideal velocity. The ratio of the actual velocity to the ideal velocity is called the"coefficient of velocity". Coefficient of Contraction The area of the opening through which the stream or jet issues is something that is readily determined, but in many cases the area of the jet cannot so readily be measured without special equipment. Hence it is desirable to know the relation between the area of a jet and the area of the opening through which it came. Exact knowledge of this relation is valuable not only for purposes of prediction, but it is equally useful in laboratory or model testing, especially in those instances where the jet or stream is not subject to direct measurement. In a great number of instances an orifice performs the duty of a Gate between two chambers which are filled with relatively motionless fluid. In such cases the fluid jet or stream contracts as it passes across the orifice from one chamber into the other. This contraction occurs on the downstream side after the fluid leaves the orifice, and is cused by the converging stream lines which originate in the upstream chamber. Since the tendency of each particle of fluid is to continue in its original direction of motion, the stream lines continue to converge after they pass the orifice. However, they cannot cross each other so they eventually become parallel and produce a section of minimum area called the vena contractan. The fact that the contraction of a fluid jet issuing from an orifice i due to the converging of the approaching stream lines, suggests at once that it may be prevented altogether by causing the particles of the fluid to approach the orifice in an axial direction. (The elimination of contraction in the fluid jet issuing from an orifice is discussed under specific orifice designs.) The jet contraction discussed above is one of the most important characteristics of any orifice, and the ratio of the area of the jet at the vena contracta to the area of the orifice opening is commonly known as the coefficient of contraction". Orifice Discharge and the Discharge Coefficient The volume of fluid discharged by an orifice in unit time is the product of the sectional area of the fluid jet leaving the orifice and the velocity at that section. Normally, in all hydrokinetic calculations the sectional area of the fluid jet and the corresponding fluid velocity are taken at the point where vena contracta occurs. The rate of fluid flow can therefore be expressed by a simple equation of the following form: Q (cA) (c n ) Where: Q = Rate of fluid flow,cu.ft./sec. A = Area of the orifice, sq.ft. 2 = Ideal velocity of the given fluid jet due to pressure at the orifice caused by (h) feet of fluid head,ft./sec. c' = Contraction coefficient for the particular orifice(no dimensions). c - Velocity coefficient for the particular orifice(no dimensions). Sometimes, for convenience only, the coefficient of contraction and the coefficient of velocity are combined in a single factor called the "coefficient of discharge'. Thus: (c')(c") = C and Q = CAgh -/77- 1% Where: C = The coefficient of discharge, and the other terms have the same meanings as explained immediately above. THE PLANE ORIFICE-CONTRACTION AND DISCHARGE The sectional area of a jet of fluid issuing from an orifice in a thin metal plate, or from any plane orifice with sharp edges, is approximately sixty-one per cent of the area of the opening. This contraction is due to inertia mainly of that portion of fluid which approaches. the orifice along the plate. These particular particles reach the orifice opening while still moving at right angles to the final direction of the jet, and their inertia requires a space and time to complete the change in direction. The boundary surface of the fluid jet leaves the opening in a direction tangent to the inside face of the plate as shown in Fig.No.61. The influence of this cause is not too complex for mathematical analysis. The size of the stream at vena contracta as derived by purely analytical method is found to be smaller than the orifice opening by the ratio Tr/(7+2).The numerical value of the"coefficient of contraction" for a plane orifice is accordingly 0.61. This figure is met closely in practice. Only minor disagreements occur, and the larger of these are found only in those instances where the velocity of fluid approach to the orifice is high and where the fluid viscosity is a controlling factor, as in very small orifices such as used in oil burner nozzles. Calculations of flow in jets of small diameter require a slightly increased coefficient because of the relatively larger influence of cohesion and friction in slow- 1 i ·: re ; 1 I'' !,/x / J l - I / N J - -· i- / / #68 /i ;e-entrrt.)7 Orifice 67 '-'ye A Typcal/ P/ane Orifice .. (NM1 7in MW,/ r -7 - - --- -- -- I ,-1 1 ,I- I - -- - - -- p' ---£ r __ - I I I I I h I I O · gO · 4 I I -- | - - A :: - _F, V & ,, - s' 0 *e* 8'y _--- - - i I -- N IN N JJ Or/g'/n of Disre Or/ie eS5W ing the stream lines adjacent to the plate and thus removing some cause of contraction. For the average orifice, the rate of discharge conforms closely to the product o the ideal contracted area and the ideal velocity at the vena contracta. Thus for a plane square-edged orifice, Q = 0.61(A)2gh Where: Q = Rate of fluid flow, cu.ft./sec. A = Area of the orifice, sq.ft. =g' Ideal velocity of the fluid jet due to the pressure at the orifice caused by (h) feet of fluid heat,ft./sec. Fluid discharge obtained by this equation is as nearly correct as can be expected without reference to actual calibration of the given type of orifice. Systematic errors resulting from use of this equation will range from 0 to 5 per cent. RE-ENTRANT ORIFICE - CONTRACTION AND DISCHARGE Fig.No. 6 8 shows a typical re-entrant orifice also called "Borda's Mouthpiece".Here the contraction is greater than in a plane orifice due to the fact that some of the fluid articles approach the opening along the outer surface of the tube from a direction exactly opposed to that of the fluid jet finally issuing from the orifice.The analysis of this case, however, is even simpler than that for the plane orifice. Referring again to Fig.No.68 1 we see that in order to maintain the equilibrium of forces involved in creation of the fluid jet, the jet must be of such size that, with its known velocity, the inertia reaction will be equal to the unbalanced static force on the upstream or high pressure side of the orifice. The fluid jet reacts with a sustained dynamic force capable of providing the velocity of a weight of fluid (Q ) each second and accelerating it from zero to the full velocity (V) during that second. The acceleration of the fluid mass in the et is caused by a force which produces a reaction in the fluid chamber on the upstream side of the orifice equal to F' = Qe. g The inertia reaction reaches the walls of the chamber through the internal pressure of the static fluid, the unit pressure of which is the same in all directions.The unbalancing of the static force (F") is therefore entirely due to the absence of a portion of the chamber or container wall having an aren equal to the area of orifice (A) and on which there is a pressure head (h). The static force can accordingly be expressed thus: F" A h. Knowing that (F") and (F') are equal and remembering that V = /2- and that Q = c'A , it is self evident that the following relationship holds true: (C A2gh))( from which c g) = Aeh ' 2 2 This means of course that the completed fluid jet occupies only one-half the area of the orifice opening. 1 The coefficient of contraction,(c'), is equal to 2 however, only in those cases when the re-entrant tube has comparatively thin walls. Caution must be exercised when dealing with tubes of appreciable thickness. The fluid stream is controlled by the outside of the tube, not the inside. A small thickness added to the outside of the - /0- tube, will accordingly make an appreciable difference in size of the jet. The coefficient of contraction for any special case may be easily found when the ratio of thickness to internal tube diameter is known. The contracted stream is one half the sectional area of the outside shell. If the thickness is increased Dast a certain limit the condition of a plane orifice is approached (See Fig.No.74) and the contraction factor of 0.61 prevails. For tubes which are cut off square at the end, this limit is reached abruptly when the thickness of the wall is increased to approximately one-twentieth of the diameter; that being the condition when one-half the outside section-area is sixtyone per cent of the inside section-area. INFLUENCE OF SHAPE,SIZE,LOCATION AND FLUID HEAD ON ORIFICE DISCHARGE Influence of Shape of Opening on Orifice Discharge Extensive'investigations and experimentation have shown that it matters little what shape the opening of an orifice is made. There are only minor differences in the coefficients of contraction for the orifices in the form of a square, a circle, a triangle, and an elongated rectangle. The quantity discharged through an equal area of opening is the same within the rnge of accuracy of ordinary measure- ments. The maximum variation due to extreme shape of orifice rarely exceeds two or three per cent. One might expect a measurable reduction from the standard coefficient of 0.61 for a plane circular orifice, to that for a long narrow slit; however, experimental and test proce- -/8/- dure must be made with precision if any difference is to be discovered. For all estimating and prediction purposes it is safe to accept the theoretical figure of 0.61 for the base coefficient of contraction for all shapes of plane orifices. Influence of Size and Head on Coefficient of Discharge Size is not a factor influencing the coefficients of an orifice except in a minor degree due to friction or viscous drag on the orifice plate. The effect of this small influence is to cause the orifice to discharge a greater quantity of fluid than it otherwise would, because of a partial relief of the cause of contraction. The failure to contract fully is not accompanied by a proportional reduction in velocity of the stream except on the contact surface. The average velocity of the stream is therefore practically normal and the area greater than mormal: hence the slight increase in discharge. For all practical purposes this variation is negligible except in the case of small orifices and low heads, and here a special calibration is easily accomplished if greater accuracy is needed. Either a comparatively large orifice or a large head will furnish sufficient dynamic force to render the frictional nnd discharge influence negligible. Fig.No. 69 attached here shows hopwis the influence of physical dimensions on coefficient of discharge of square-edged round orifices. A change of several hundred per cent in the ratio of fluid head to orifice diameter results in less than 5 per cent variation in the value of the discharge coefficient for a wide range of orifice sizes. /a?2- _ __- · __·__ - - - - - - - _ w -------- -- : L_ Ii i------ i I I I I-I r I i-' II| I it *If i __ X. i- InI -- --- 1- : Q4 ... -!- -- iT-- I . .-' WtI - -I I _v Id Wd W- 1 I . 4 Sj '14 1 - 1 - . f/ - ._.i _ -i F _ - t l - ._ ii i 51 i L74 S. 0A lex __ i- _. ''i ?nIf ?l~T I/? i- . -- ! - l i ------ --- - - .1 t IT ~__II iI ,.+_ 1a- _____ | |-- i 1 I L--- __ _I .1 if 4-1 i __ · ____··__ -- RF08 P2 _. .-14-i 44t li/i : -- );Oll tw rAdre :_ vL !i I 7& ! I r 0'00';06 c I t-v i r - -- _ _ l . _ _ *'8 -''i 1. - I l L, , h cl -- I -- 1 -- i-!. r i-c I 7: 'i : -ii ' .- ... : - -. 1 .. 'I --s *I ! i_ I I ~l t I - [ _. LL1 Iil .. '.II . 71 1__ .cI1.-1: . Pe i. ----- : .' . ' i) i: . . I a7 1- _.. 1 s r----r- . I I i r I . 1 I- -- I i I' ' ... . t--+-_. __ i -t 1 i · l- : ;2 I--4. I_.': -- r- -, I E, i i i -7 i I . ,I ---- t . r I I --i i -- t-- e. ,e. * I III -- - -- p---, -r ti- . d74- I i- . _1_. --- _ I i. in ----·---1 I ... j I F; s " i I. Ii t L-I - iP I-" -I-~~~~ !:: 1- -1 t e. 1:. I- 1 i----- i .:I ' I'I i l' I 1 _ --- _ - ;.__, _ . . __ _ L --. !! I- 7F2? -& 1-2- ia ! : 1- t-r--I i F Ii te I· 1. . = S-ia _ 1 _,_ I _ |-C . t_ _ I_ ___ 4 . . · -_ _ . _ --- I .1._ .. L~~~~~~~~~~~~~~~~~~~~ __. --- -- ' _ . A %7#7 ! .1c" --- ---------- Influence of Orifice Location on Coefficient of Discharge In general the plane or the re-entrant orifice is not sensitive to location with respect to the side, bottom or top of the chamber or container from which the fluid issues-- unless the walls or other surfaces are located in such a manner as to cause a smaller channel of approach to the fluid jet. As long as the edge of the orifice is located not nearer than its full width or diameter from any guiding plane at angle with the plane in which the orifice is located, the error introduced into discharge calculations will not exceed 5 per cent. SUPPRESSION OF JET CONTRACTION Suppression of Jet Contraction By IMeansof Bell Intake to the Orifice The only effective means of materially changing the contraction ea factor of an orifice is to direct the pproaching stream lines in such a manner that they will arrive at the opening in a direction as nearly as possible perpendicular to the plane in which the orifice is located. A noticeable influence results from a slight rounding of the edges of the orifice as shown in Fig.No. 70. If the edges are well rounded-so that the curved surface followed by the enveloping stream lineslas opportunity to shape itself in a manner similar to that of a normal jet issuing from a larger sharp-edged orifice, the jet proceeds from the outer face of the orifice plate into the downstream space or chamber without further contraction. Fig.No. 7 illustrates a fluid jet issuing from an orifice with well rounded edges on the upstream side. The exact shape of the curve on the upstream edge of the orifice is, of course, not circular, but the circular curve does not depart sufficiently from the ideal curve to prevent its use in most practical cases. Assuming a circular rounding of the edge, it is comparatively simple to compute the radius necessary to prevent further contraction of the jet. The procedure for computation of this rounding is described elsewhere in this thesis. Suppression of Jet Contraction by Restricting the Approach to the Orifice 'Whena plane orifice is located at the end of a channel or a passage with a comparatively small cross-section, it will discharge a jet with a larger sectional area than a similar orifice places in the wall of a large chamber or container. This is a perfectly explainable result and the amount of increase in sectional area is subject to calculation although a simple solution is not yet available. Fig.No. 7illustrates such an orifice. The theoretical figure of 0.61 for the coefficient of discharge is still applicable in most practical cases to an orifice thus located; however, when the approach is greatly restricted or there is some special reason for need of greater accuracy, a correction must be applied to the above given theoretical coefficient of discharge. Fig.No. 73 attached here shows the influence of restricted channel of approach on coefficient of discharge of a plane orifice. The curve plotted in this figure.is based on experimental data col- - /t.~- t -~ - ~ vm- - ~ ~ ~ - / Fi- - - - -- >/ - - A" I -- - -~ . "I - X // ./3q _0 J 079 ' F. 74 ! A Re-enfrant Orifice With 7hAm W/lla//s /P/arne re trifh aOri Restricted Approach /I/ rn-. e m W-01 . ,- - g -- _ - --_ -w - 7/ ////Y "91#7 -,6.1 Ora'ce O.A7.ltlr- W/ifhBe// P,, oy ZtcaKe , ,, oaundee tagfes) with e// zita<e (Fl//y oundOAd& Edges sAW I i i - i -- _4__-- j , ~L .t 'i i .._2-- L_ t I4 B eIl Al ez~caitol aw _ ! 'i iq J;4 -4--. I- . . . . _ .............. _ .. . -r I 1^ kr e I ; s I If W'lF ! . I : I !j - i i _ I I 107 ; i7~ __ _ i I -- i l__i I_ i I t- 1- tr I- i II . I I-or L _ - i------- . II t er,I . S - .!tl 71 -Ii . i ., - f tl I II _. --- I Ih .. ? -. A 20_,O· AF' ~%aI F! Y - -i-t--- _-----· -- 1 ---- I_ i - - j ,i- ___ : l - l CPI"eOACtlk fir , ...-·-----·-- - | !_··_·___ __·__· j · _____ - - - ii I I _ t-- . i1 i----C-C - --- ---- 4! +--- i ---- * IL.Fl -"- i--i i I- 1 I -4- ; i i II- I _ -r- iii C -1----- -L--- - -_L = rr1 -r [-I . rl----- . I . ,'A , I I I# __. , I _· _ . --- I,---~ M 0 rt- r -- -;. 9 t-- 5. ,W a I~ 6r LCr- --I-- I. I _ -7-- Tt- . . t·-·- t~--- Ij 04Orli r--c i - _r L i I t---- i a: ll I It 014 rr rr r- ,j j r----. I i 1. '------- i-- i I 13 --- t----r-rr-----· II; ' --.. I-I ti i - Ii n-- _, -1 - -i 1 ·--- c---- I! i I 1 p-- ! I i ---- i-.---' ·- . I. : - 1.... r- A - -c-- 1 i_ I 1~f t----- -----c - I _I on, Aj __j te 0 -0- mI ! b 4 i--- 0_ I-----_T __ ,L4 i If ---- ! -- t l r - - ~-...--.._~ rl r'- H. 27/ I ;:F l C---- - l L! .Al. I- l ---. q:-- _ F e |- -- t-- . I l ------I ·- 1 -7 r- __ I_ 'i i - i -l -· -· I __i--- --- - I i I I-- _1 i - -i1 I - ! l ! I f ! l l l- s - . -_= F..... 1 . | l l-- - row - - A. .- F rI . . ____ r- i_ I . - Z 4~ -- -1 l l 1 1 --] - - nL I_ W.9W ._ A_ _. lected at the Experimental Station of the University of Illinois,Bulletin No. 96. The head of fluid at the orifice is, of course, made up of two parts, the static head and the velocity head. The sum of these two parts is commonly called the total effective head and is expressed thus mathematically: = Ph 2g Where: h Total effective head of fluid at the orifice, feet. P = Static unit pressure in the channel before the orifice, pounds per sq.ft. e= Density of the fluid, pounds per cu.ft. V Velocity of fluid in channel before it reaches the orifice, ft. per second. g = Acceleration due to gravity,ft/(sec.)(sec.). CHAPTER XV FLUID FRICTIOIT, AILDITS EFFECT Oi, FLUID FLOW -/ 8 - FLUID FRIiTION AD ITS EFFECT ON FLUID FLOW Introduction Fluid friction has two principal effects on flow and circulation of fluids as encountered in heating boiler design. First of all, its presence demandsa source of energy in order to maintain circulation; and secondly, its existence determines the design of the fluid passages in so far as it affects fluid distribution among the several paths. Determination of magnitude and nature of these effects can be made either experimentally or analytically. The experimental methods, at the present state of our knowledge, yield more precise information than the analytical methods; however, as was already mentioned above, the experimental methods involve a great expenditure of time, money, and effort before the approximate solution is found. And since it is only after the approximate information has been gathered and studied carefully that the final design and performance testing can be done, a considerable saving in cost of development can be made if the preliminary studies are limited to analytical considerations. The approximate solution and the first design based on it,of course, will not yield a product with characteristics and performance in absolute agreement with theoretical calculations; however, the overall discrepancies will constitute an error not greater than a few per cent of the expected theoretical quantities and magnitudes. What is more, with definite knowledge of the fundamental behavior of the variables involved in the problem, the corrective steps to attain a final product are certain and definite in their direction. Careful and -/, 7- Y thorough analtical preparation should require not more than three models beforB the idea could become a reality-- a finished product of high quality. The first model would be built on the basis of theoretical calculations alone. The second model would incorporate all major changes that tests would reveal desirable in the first model. The third model would include all detail improvements nd can be used as a sample of the product for rating purposes as well as for tests of the physical qualities. FLUID PRESSURE LOSSES DUE TO FLUID FRICTION The most noticeable phenomenon that accompanies flow of fluids within a heating boiler (or any heat exchanger for that matter) is the loss of pressure which they undergo along their path of travel. This lost pressure represents the conversion of potential energy into kinetic energy and thence into heat energy. Pressure losses due to fluid friction may be divided into two groups: (1) Surface friction losses, and (2) Turbulence or eddy losses. Surface friction losses may be further divided into two groups: (a) Surface losses due to wall friction in the passages where the fluid is traveling, and (b) Surface friction against the various shapes that may be located within these passages in the path of the fluid flow. Likewise, turbulence o groups: eddy losses may be divided into two (a) Fluid pressure losses due to change in stream cross section, and (b) Fluid pressure losses due to change in stream direction. VISCOSITY The principal cause of pressure loss in fluid streams, as was mentioned above, is fluid friction which is due to viscosity. The viscosity of a fluid may be defined simply as a measure of its strength in shear. Absolute viscosity may be defined as equal to (F)(b)/(V), where (F) is the force per unit area of a small plate necesfsary to move it with a velocity (V) parallel to a large plate at a small distance (b) from it, the intervening space being filled with the fluid in question. Viscosity therefore involves dimensions of force, space and time. Thus in absolute English units, absolue viscosity is given as second poundals per square foot, which equals pounds per second foot. In metric units absolute viscosity is given as second dynes per square centimeter, which equals grams per second centimeter. The unit of viscosity in the metric system, that is, one dyne second per square centimeter, is called a"poise A more convenient unit for engineering purposes is the "centipoise"( which is naturally = 0.01 poise); since the use of poise results in fractional values for viscosities of most common fluids met with in engineering work. Viscosity of Liquids Viscosity of liquids is primarily the function of their temperature, and it always decreases as the temperature increases. The -/ 9- pressure has a very small effect on viscosity of liquids and for all practical purposes, especially within the ranges encountered in small heating boiler design, its effect is negligible. The principal liquids with which this paper is concerned, are, of course, water and fuel oils. Fig.No. 1 gives the relation between temperature and water viscosity; while Fig.No. 5 gives the relation between temperature and viscosity for several common fuel oils. Viscosity of Gases and Vapors Viscosity of gases and vapors is fundamentally different from viscosity of liquids in that the viscosity of gases and vapors increases with increase in temperature, while that of liquids is lowered with increase in temperature. Pressure has but a slight effect on viscosity of gases and vapors; this is especially true for the low pressures encountered in the work with which this paper is concerned. Fig.No. 76 gives the relationship between temperatures and viscosity for oxygen, carbon dioxide, ir, nitrogen, sulphur dioxide,water vapor, hydrogen and carbon monoxide. Conversion of Viscosity Units In metric system, the units for absolute viscosity are: dynes/(cm)? (cm./sec.)/cm (second)(dynes) (m) But, 1 iynels:(gram)(..)/(sec.) 2 , therefore absolute viscosity can also be expressed as (grams)/(sec.)(cm.) -/90- rr :.m __ .... . : '-r- T_ .. -- -T , ii 7 -- _Y 5 --- · i -i-! 3 3.5 4- 45 . ..:i . .. .-: . ... : . ::' ..: ::a a, :: ~'h !4 !',:!! r i i::f: 4-i.!5 '' ·-.- · _ :- , i: .-L i : t7 , [ : .' r· .i'r.. . l-v : . : :: -:', ' :'i ::~.I 1 -- -7, , ..i :'-7-17 'h I - 7!.. · ; ·-·--I,-··-!---·.........r~ · -~-::.:J.. !: .:,"ii¢: -... .. ::' i --- - -+t l. . ., ..... , · - q ·.. 4-- . ~4: , hiI : : t -7__ .- -_. : i-. L14f --. . z . . ... I i L .-. '' '' ' ' · ·' ' [. -- .: -i i ..... ;:.. . . p__ : : .: . r,: I :: ;__ Ii.i, ) - - i .. ,... · ·. i .:- - :'.:.':~'::':':: ·"'' -- .-'-:n... . 'N -I-"" "1' _ - : _.. ; .... - "..' -, J .. ,-·,r· .-.i~ ljX' ;`.-V-:: .... . Q-: - . . . . "II III'I I'.:.':.. I .. . i d:;:=ff ... .. ..T :3:J ' :::.., -:. ..... ,:..: ,.... =;., ;-,-l.,.-~.-i I::. r:t~',:: .. 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L _ P.. - 9~-i . z ''' ,,- I- -- 4' __ -e -I - 7 .... ~. ~~~.i , ,~:.; ~ ~z,, Jz ~!~.i.,: ·: '.. i,:,i ~ !.: ......·,,,' '!. -- :.':"~:.-?.;7 .:t...~ ';:'!':J.-'::-~ 't... ;]i i';.' :..: ":.~- . r. . - I' --- .. :._... ..I.......:.1....-- '' - - '. ~ T'~~~~~~~~~~. ]7i 1; I-` . 7 .4:-z (- t·-L+.!-i-:":,!:-:': .....1: : ~ . . " · . :? ... ,. L'~;~:.i ' ;· .r i ·-- :L:~. .. ;..... ...... i:tNll I;.. -- :-- t-- ·-· · 1 4 :-t-' i I ..... --i: 4 ..i4. ! ....... 1'1 s. :~.-;.%h" : : . ·---- L ...';-,.~!,..:.. .'.:-..~.. "".,::i::t.. ... I,.,. '.:· ;iT ---- -- -t..:. .. i''~:. :: -- '-·, · --· -- · · ·---· :; - 2.7 -, .. 7 .. . . ·- · · -·- i '''' '' +··· · ·· · · ---· t -- -.-...-. ::?-::'r: :-:':1. :':'::::l:::F~·::l:I:i: :~li-L: P .- 2 d-,' :- ~P';~i : - -~i·!z - :.... .:'¢ ~~~~i.:--I...:--.' ~'--'. ..... .: .. :: :~,4, 'I::'':-rL-A . :' -:-,;It2 ~' !-i-!... ' : ::;~ i;] - -l---- "' ' --- . .... ' ~ :-:; :~ '1: .:=~..x-.-:- =i.m; 1: _ ---. ... .._.. tr::r. _. ~- ': ; T.,41,ft : : r ·· · 3 1.5 -- '.;.:: :j; : I -_ _f " 7a .6 7 8 9 ----rr-.._.-----ar.r rl-r 5 -. _. ..... 'L'... .... fi ;.,.. , _- i!. 'j.· . :'T; :: =: ' .7¢'~:~ '.': '. .'. - 11m -· :~~~~~~~~: F ': .-; 1 ',.~ ::::;:i ' .... j. ;' - , :, , ". I000 Gas and Va/oor kscos//els - I 3,5'00- Z. 3,000 %Voo-2,500 0 . 3 0 2,000 - I -0 06 0.05 - o -o.oa-s /00oo qj .6 5 . 0.04 0.03 /6 .7 0.02 ii /00 I00 J. *9 0. 0/ *12 . a -/00- 0.006 0- Mo. 0 .004 0. 003 I Abso/ule ixsrosi/ , ,= / =ic~S -%y1 o= .e n si4, 77 / °2 0 3 COz s A/r = 0.0006 72 xZ (se C)(t.} Z= C"n ,7o/ises I s zx 2.42 .5/ f$e eCsiv.? # e/, /4/z 7 SO2 9 /270 /2 //2 /6 CO Abs. L$/Se. 7 M. /. T7 /6O.701 AfCar 6 .Based 0"7 ;Va., 1r , Zif f . Chem. ,34, G~Ae'reaux kol 22, . 13e2 " ~19301 U' In the English system, the units for absolute viscosity are: ) (sec.)(poundals)/(ft. But, 1 poundal = (pound)(ft.)/(sec.)2 ; therefore, absolute viscosity can lso be expressed as (pounds)/(sec.)(ft.). For simplicity of calculation, below are given four fundamental conversion factors for transformation of viscosity data from one system of units into another. (a) Viscosity in centipoises/100 = viscosity in poises = (Gm.)/(sec.)(cm.) (b) Viscosity in centipoises x 0.000672 = viscosity in (pounds)/(sec.)(ft.) (c) Viscosity in centipoises x 2.42 = viscosity in (pounds)/(hr.)(ft.) (d) Viscosity in centipoises x 360 = viscosity in (kg.)/(hr. )(m.) VISCOSITY O FLUID AiIXTURES The viscosity of fluids encountered in considerations of heating boiler designs is often not that of a pure compound but that of a mixture of two or more compounds. Thus the products of combustion are a mixture of several different gases; and the water is actually a mixture of water and steam. Viscosity of Gaseous Mixtures The problem of expressing the viscosity of a mixture of gases or vapors in terms of the properties of the pure substances is comparatively simple, and can be solved with good accuracy by means of the following equation: 1/2 = a/Z' + b/Z" + etc. Where: Z = The viscosity of the mixture. a,b,etc. - Volume concentrations of gases present. ZZ",etc. Viscosities of pure gases of which the mixture is made up. Viscosity of a gaseous mixture determined in this manner will seldom be in error more than 5 to 6 per cent, provided of course that the viscosity of constituents is known within the same accuracy limits. Viscosity of Liquid Mixtures Viscosity of liquid mixtures, or mixtures of liquids and vapors is at present not possible to determine theoretically with a high degree of accuracy. The best known simple method is offered by Egner, and it often results in error from 5 to 15 per cent.(See: Meddel. Vetenskapsakad. Nobelinst.; 3, 22, 1918). According to Egner, the viscosity of a mixture of liquids,or liquids and vapors soluble within each other, is given by the following mathematical relationship: log Z = X'log Z2 +.X"log Z" +etc. Where: Z = The viscosity of the mixture. X',Xt etc.= Mol fraction of pure constituents of the mixture. Z',ZP etc.= Viscosities of pure substances of which the mixture is made up. FLUID FRICTION INSIDE THE VARIOUS PASSAGES AND CONDUITS COMPRISING A HEATING BOILER Fluid friction inside conduits of various shapes has been the subject of a good deal of study and investigation during the past fifty years, and the available data and methods have been developed to a considerable degree of perfection. The discussion presented immediately below is a brief resume of the fundamentals on which the subject is based throughout this chapter. Nature of Fluid Flow - Two Types of Flow Much experimentation and study by many capable investigators has shown definitely that the flow of any fluid may be divided into two distinct types, as follows: (a) The straight line flow (also called streamline flow),and (b) The turbulent flow. Streamline Flow In the straight line flow every particle of fluid flows in a direction parallel to the walls of the conduit, and there are no transverse or mixing currents. There is no axial motion whatever near the walls of the conduit but as the hydraulic radius of the conduit is approached the axial velocity increases. The frictional losses of any fluid moving with streamline flow along a circular conduit or passage has been proved experimentally as well as analytically to follow Poiseuille's Law which is stated thus mathematically: dp/dN - 32pV/gD2 there the symbols have the following meaning: dp = Differential pressure due to friction,lb./sq.ft. = Absolute viscosity,lb./(sec)(ft.) = 0.000672 x centipoises. V = Average velocity over entire cross section; i.e. volumetric rate of flow divided by area of cross section perpendicular to direction of flow,ft./sec. g = Acceleration due to gravity, 32.2 ft./(sec.)(sec.) D = Internal diameter of the conduit or passage, ft. dN = Differential length of pipe, ft. The application of the above equation is comparatively easy in all practical cases. The only difficulty in its use is the evaluation of average viscosity of the fluid in those cases when it is being heated or cooled. Heating or cooling of a fluid as it travels in a conduit results in a variable viscosity and consequently in variable friction at different points along the conduit. For the sake of simplicity, instead of integrating the variable pressure drop along the whole length of the conduit, it is recommended to obtain the average viscosity of the fluid along its path of travel by graphical integration. In many cases, when the change in viscosity is comparatively small or approximately linear, an arithmetic average of viscosity at the entrance and the outlet of the conduit will be sufficiently accurate for all practical purposes. A vast amount of experimental data definitely shows and proves that the streamline flow described above can exist only under certain conditions which are determined primarily by five variables, namely: (1) Velocity of flow. (2) Hydraulic diameter of the conduit. (3) Density of the fluid. (4) Viscosity of the fluid. (5) Roughness of the conduit surface. The relationship among the first four of these variables and their behavior are such that when grouped into a certain term known as the "Reynolds number" they reveal much concerning the nature of the fluid flow which they represent. Reynolds number, named after the scientist who contributed to its understanding and application, is commonly written thus: Re = DVA/u Where: Re = Reynolds number ( no dimensions). D = Diameter of circular conduit, or hydraulic diameter of an irregularly shaped conduit, ft. V = Average velocity over entire cross section of the conduit, ft./sec. = Density of the fluid, lb./cu.ft. = Absolute viscosity of the fluid, lb/(sec,)(ft.) = 0.000672 x centipoises. Experimental data shows that normally as long as the value of Reynolds number is below about 1100, the flow of any fluid possesses the above mentioned characteristics of streamline motion. When the Reynolds number is greater than 1100, however, then the fluid particles no longer flow in a straight line parallel to the walls of the conduit; they swirl and bounce in vortex line motion at -/?s- the same time as they move onward in the conduit. In distinction from the streamline flow, the flow which is characterized by such eddy currents is the main stream is known as "turbulent flow". Numerous experiments show that nature of fluid flow also depends to a large extent on the relative roughness of the conduit surface. The actual Reynolds number at which streamline flow changes into turbulent varies between 1100 and 3000 depending on the "relative roughness" of the conduit surfaces. The term "relative roughness", mathematically speaking, is the ratio of average protrusion inside the conduit to its diameter. Turbulent Flow The frictional losses of any fluid moving with turbulent motion along a circular conduit or passage has been proved experimentally as well as analytically to follow the Fanning equation which is given below. The most common form-of Fanning equation is written as follows: dp/dN f V2 /2gm Where the symbols have the following meaning: dp = Differential pressure drop due to friction, lb./sq.ft. dN = Differential pipe length, ft. f = Friction factor, no units (dimensionless). - Density of the fluid, lb./cu.ft. Average velocity over the entire section of conduit,ft./sec. V g = Acceleration of gravity, 32.2 ft./(sec.)(sec.). m = Hydraulic radius of the conduit, cross section divided by wetted perimeter, ft. -/ 6- For circular conduits, such as pipes and round ducts, the Fanning equation can be rewritten thus: dp/dN = 2f 7 2/gD Where: D = Internal diameter of the conduit, ft. and all other terms have the same meaning as above. Another useful form of the Fanning equation is written thua: dp/dN = 6.49fW2 /2gtD Where: W = Weight rate of flow of fluid, lb./(sec.)(pipe) and all other terms have the same meaning as given above. The friction factor (f) given in the Fanning equation is based on test data. Investigations of numerous experimenters have shown that this friction factor depends primarily upon the Reynolds number, and slightly on the relative roughness" of the conduit. Figures Nos.77, 78, 79, 80, show graphicallythe relationship between the Reynolds number and the friction factor (f) to be used in the Fanning equation. The family of curves on Fig. No. 77 gives the relation between the friction factor (f) and Reynolds Number for conduits and pipes of different diameter with relative roughness similar to that found on steel, wrought iron, and galvanized surfaces. The family of curves on Fig. No. 7 gives the relation between friction factor (f) and (Re) for conduits with relative roughness similar to that found on cement surfaces, light riveted plate walls, sheet ducts, and best cast iron surfaces. The group of curves on Fig.No. 7gives -/97- the same relationship , ... rqO .- M 'ON ' (D p- N " U3SS3 S 3Ajn13. -!l: (D to ' -:'' 3''-t :: ........... t''-- :· ) CD F ",- CN L. -I --', - .._-: ='-- -· " _ C% <~i.E9~i@-B!Y^: -lt, r .::Lt li.i;u·-1: .t. . i--j: -I.: :31; I :- :! --'.'1!- -- :,.1_mk-l-A - '_: C : -:,: ',''-: /-. I | ,/-st t i.. 5z-. .....---. -t--------..--.. ..... : :: -! wi~l l:: : r.: !.:,::-! _ '!:~ ·:.: ..' .: _,_ :._t. _.. -L-_:-Xi t-----::-:-!:' .__ _ .'j '_ _.;.. _ 1_1_ - .... "' T·-i'T' LJ; · · : ··' 7-': : ': , , ' ......... * I -__-i - 1;l-li- *,_ --; -1 |--- t:"· I:..., 1 1. :.-'-:.---:--,--i-" o + --i- i'r_ _ :.. -~- .i.,.... ... ... 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F:....,.,.:'""''!:>~ i;-i..~ ~........:_?:.s..: -7..::'.. ... ....:.-.-'.......:....:................:.:+:'.::: .... 1~.... T? :.TT-, tr-~-' . .. T7i:7-:''7'.'. i-~..----.~: ... .-.--,........."';-.,~ .~. ... ~ I. ..~ ::::::.::::.::.t-:,::::--7~tl:: :::==:::= -'.--~ --':::.:.'~'. ' -~:~ i.".-..-:--.--.-= F':F? ~-.-~:! '"-:.[.:l-:, " :r' . .',: . '-:. ~...---,' . - --. '-- ·-,:..:'-:-*-,-:t== ,;:~': - : :_~~-7.,7;-.. .... ....":"': .............. ,............. ........ ........... i. ........ l.. .... :. . ... . ... : ...-... ...... l... . ,-·.+_~ ·-i~~~~~~~~~~~~~~~~~~~~~~~~~~i~~~~~~ r..,._ I....: .. f · ~, , i" 1- ,...';' :':--i : ..~ ... 1 . 1 . '~ : ... . , ... .... ... : ....iit - . : ... :·. ;. · ....-.... ... , ~,...., .. 'x '~~·~~ ~ ~ ~ ~ ~~·~ .,i-·-..- ,li .1iltil'li'i'! Ii t'r~rT~-rTJ-'~'~J-r il': J"i t:1''.-' ,~'J11 1 Li1[1 .',' . ~'."]·b'.~ .~i~'ht q ']']~1i~. .'' '/..!.it I ~~ ~I., 117~ 'l hlj~ilN . ... ·_ .- ...................... I!']-l'lrt]-:[F-- ;- [: ..- 1 .. F"" T-!' 1 o N . t o D tg O ° D g ° O v O " Q Z 0 c9CE 'ON , '. ;U-I l,.Iy ',.,i.J "13Jin3 'A 'N "030 :3SB1 Iq o i CD 1-- 0 ~1 ~.. : - '. N Ii . :...... .. a, X.-LEI I .. i--l E, !. 4 -= - t; _ Ni l i- - - t - - - X9:: - ' -k:kf,''i 1..,..t .'· .. .. . S1 G 1-AJ · 14 ~~ -_ W - - :. i:-:|...T ::.-:-. i...... ii.. t _ vi J I ! 'F7 ~ Ff 'i }= -4i.- Ff ' | t- ; L - .X *7-1±-b' . 'I -. f I -,---1- r - 2 l # W f -% .F -" i: - i 'm:-. -.. I X 1 rl-l-Jv-i--I----h I--· 1 _ <g t . ...-.................................... -_ I: - :...'4 . 1X-i-: !--¢ -- t i---:co .. L .. . .. . .. .7... ±.. : 7717--- , .-- i- :: :: i | :, .:.: ::lhiii 1Q_ 0) t0 D O 0 - i _ ',. ni_ L-' !I __';:''_'l' .. I--i-t,::i-- 17- -i -: .~..I ... : . _ c . I I ... . .... . . i. :, ."-':-'-'· :::::::::::::: ........ ::.::: .u::..':. ' .... .... 'l.;----:"--::' :'--:':1......-:._:..,._:..-=.:.:-:--:...-::-_.: i.'.'r::::..: -:-.-.. "'.:P. l-:i:i~.:"E.:-.::~.::::::::::::::::::::::: ".'-~.. ::-.:-.-.... : ....................... ~....:-~-:-:........:~-,"~~....--,~ .. .... :...-. ...tl ~"......--..... :_:::<,.:i..:::_:-:::._.:;.'':" ~--.--:..,-;...~....::u.....,....-.i....I.. .... ,~~~~ ~ ~ _: ...................... -~ ...-'- ... ±.. C) % lc m c~. 10 U! qs 0) s CD , ro. O ID N o o , o; for conduits having a relative roughness similar to that found on average cast iron, rough formed, and concrete surfaces; while, Fig. No. 80 applies to conduits constructed of first-class brick or heavy riveted plate. Uso of curve (C) on Figures Nos. 11. 18.19, or 80 is explained immediately below. Relationship Between Fanning Equation and Poiseuille's Law If the right side of Fanning equation is equated to the right side of Poiseuillets law as given above, and the resulting equation is solved for the friction factor (f), then the value of factor (f) for streamline flow is obtained. Thus: dp/dN = 2pV/gD 2 and f = 16/DVt = 16(/DV )= = 2feVe/gD 16/Re f = 16/Re where Re = Reynolds number. This relationship makes it possible to apply the Fanning equation to both the turbulent and the streamline flow. Curve(C) on Figures Nos. ¶, 18, 1q, 80, represent graphically the relationship between Reynolds number and the friction factor (f) for streamline flow. .. . .N . N ' 3S s3 V 13.jin3) 00 -- 0- U C) CO CD m C - z In I 0 '·' .·11·: o Ir ::: -.-.- ;.L.... ....: -------- I :..i -- 1 ---- It fn ..i.. --- -fT-r·--;----circ.-.-l-..- 3·--1 -r-_ i-·1 ·J: i --ii- 1 ?-r·-+.I.._.i.. L:. r1.. .I_.ii I _-I ..L.__. -T--I .-j-..-. I-------- ·-- I': '· '·'·---. -i ! · __. . .;_.,. i _.I . · : _ · I -1 -- - .... ----C·-:l-·-i-- ..j /. :. i. 1.-- .i.... 1 i· ,... !-··---1--·- I ... ---;-·-·-·---·-·--···· , · , · · ·t : -· --- ·-· I ·--i·-·· I -··--- -·· ·· --- f -i. 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' ' .:' . _. . 1: . . . 1 1·4- :: :-:I I· L.1: :-)..-.---;-·r-·-·-· i I__:---L(-·-·-1 ·I .i .- _.__C_... ._j__L.I_. i. :.... _ ' ........ -Yr: i .I 1 . ;. ... l .:_ .- - - .- .- t-.i | 2. Ll 1L. r Iw I-~'"!--t-.I, 'I...- · ; I , · · ; · N o · -- · - r o In APPLICATION OF FAMTING EQUATIONIAND ITS LINtITATIONS The Fanning equation for calculation of frictional'losses occuring during low of a fluid is strictly applicable only to straight conduits of a regular geometrical cross section, and whose length exceeds the hydraulic diameter bout 50 times or more. Flow in Circular Conduits The basic form of Fanning equation which is written thus: dp/dN = 2fTV2/gD is applicable primarily to straight circular conduits. The meaning of the symbols in this basic form was explained elsewhere above; however, terms (D) and (f) and their use require additional clarification and discussion at this point. The term (D) stands for internal diameter of the conduit measured in feet, and applies only to conduits having uniform circular cross section along the entire length. A conduit consisting of several sectionsSeach of different diameter,cannot be considered as a conduit of some fictitious average diameter but must be divided into its component prts, and the frictional losses be determined separately for each part. The Friction Factor (f) While the proper substitution for term (D) is important, on accurate determination of the term (f) depends the whole usefulness of the Fanning equation. r j # CUryt C , which was already mentioned above, gives the values of the term (f) to be used in the Fanning equation.However the frictiol *r factor (f) in itself depends on the variables which make up the Rey- nolds number, and it is the proper selection of the latter which determines the accuracy of factor (f) and hence the accuracy of the Fanning equation. Of the.four variables comprising the Reynolds number, viscosity is usually the most difficult to determine for use in actual problem dealing with flow of a fluid in a heat exchanger. This is due to the fact that the viscosity does'nt remain constant but varies with change in temperature of the fluid as it is being heated or cooled.The exact mathematical prediction of the average viscosity of a fluid flowing in a heat exchanger is a problem which cannot be solved at present due to a large number of independent variables. However, trial and error methods when applied with graphical integration can yield results sufficiently accurate for design purposes or laboratory work. These pproximate methods for determination of fluid viscosity in heat exchangers can be used safely in those cases where the temperature of the fluid undergoes a comparatively small change between the inlet and the outlet of a given conduit. Two such methods are outlined below. In cases of streamline flow, i.e. flow at Reynolds number of less than 1100, satisfactory results will be obtr.ined when the average viscosity in a conduit is taken at an effective average temperature (t') which is obtained in the following mnner: t' =t + (t t) -2 oo - 2 Where: t' = Effective average temperature of fluid in the conduit. t - The average temperature of the fluid when thoroughly mixed at the outlet from the conduit. tW = The average temperature of the conduit walls in contact with the moving fluid. In cases of turbulent flow, i.e. when Reynolds number is greater than 1100, satisfactory results can be obtained when the average viscosity in a conduit is taken at an effective average temperature (t") which is determined as follows: t" = t + ( t 2 ) Where: t" = The effective average temperature of fluid in the conduit. t = The average temperature of the fluid when thoroughly mixed at the outlet from the conduit t w = The average temperature of the conduit walls in contact with the moving fluid. Flow in Rectangular Conduits Streamline Flow The equations for calculation of fluid friction losses for streamline flow in rectangular conduits or passages have been derived by several investigators. The principal limitations of these equations is that they have been derived for isothermal conditions of fluid flow-that is flow at -aol- constant fluid temperature and therefore constant fluid velocity. Such equations , of course, cannot give even approximately accurate results when applied to flow where the temperature of the fluid might change as much as 500 per cent. The most useful equations concerning the flow of fluids in rectangular conduits (as well as other geometrical shapes) are given in Lamb's "Hydrodynamics",(Cambridge University Press,Cambridge,England). The simplest expression for determining the pressure loss of an isothermal fluid flow in a straight rectangular conduit is given by the following equation: dp/dN = 4V/ABgn = 4Gy/ABtn Where: A and B re sides of he rectangular duct. V = Average velocity- Volume rate of fluid flow divided by the area of cross section perpendicular to direction of flow, in ft./sec. = Absolute viscosity, lbs./(sec.)(ft.)= centipoises x 0.000672 G = Mass velocity= Weight rate of fluid flow divided by the area of cross section perpendicular to direction of flow, lb./(sec.)(sq.ft.) = Fluid density, lb./cu.ft. n = Factor depending on the ratio of the length of sides of the rectangular duct. dp = Differential loss of pressure caused by friction, lb./sq.ft. dN = Differential length of pipe,ft. But in the Fanning equation: -2- 2- dp/dN = f 2 /2gm where m is the hydraulic radius of a given conduit. For a rectangle m = AB (A + B) Therefore the Fanning equation applied to a rectangular conduit becomes: 'dp/d 2g(AB)/2(A+B) = V 2 (A+B)/g(AB) Upon equating the right hand term of the modified Fanning equation to the second term of Lamb's equation iven above we obtain the following relationship: f V(A+B)/gAB = 4V./ABgn which, when solved for (f) yields: f = k4/V (A+B)n Where: = Absolute viscosity, lb./(sec.)(ft.)= centipoises x 0.000672 V = Average fluid velocity over entire cross section, ft./sec. A and B = Sides of the rectangular conduit, ft. = Density of the fluid, lb./cu.ft. n = Dimensionless function of B/A NOTE: Function (n) is given on Fig.No. of this thesis. Then the modified friction factor just derived is used in the general form of the Fanning equation the theoretical calculations of pressure droD in streamline flow agree closely with experimental data. ,' .,. . ... : '--C- . -.' |; i.,i ' 7 . I I cL- ' --- .I . I;.i' .. 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I,..-.- t,..ij_. 1·· cl-----I 1 -.--r- -T- i I : i. : : - r-i-_ !! -_t-' · -·-- I . T .. '' i . , I . . i . 1- .I, . .. .I _i-. _i- . - . ' I , I--j-- .. I I I ,t 1.1 ... ... -i-111-1 -~..,... ..... ! i I··: ·i · ·. f .... i . ' Lt t lt . |t-----s. , , -.-% -,= l t* I 1 1 r. --i I; I .---.c-I I i i --- ?· : .1 ..I l T ..1 · · ·· . _ I. f C----- . _1 r · ,GPi.... I ·; :: I ·· · 1 ._i .. 1 : : ?---- - - '--' --- ,. 17-- :.. . ,iill ;-L- · i _ .--.---... ' r t---r ;--- i · : -· L_._ - I i .. i . :... - :: ! : ---- i - -· .I !-- -- ..- b...I I _r - "-- -- - --- t -- ,- i· ,:1 .- -"-i - .-I ·-U.._ ... ._.j.L.,. I T- :t-:- : . I ' !. I ' ; *' I I II -' ' '. +_. -i..... I 1--- I, ,:. :14-- _ il_ l . , 1· -· ' I. . ' ' ..'i !-! - - .- L ·--l·--·-c·l ___ .4___ !:,,: . -- . ... · -- _ ._ _L.-- . i--·l--i- ; : --- I i... t.. I I · 5., -. . . - , t -.-- .- ... .. . i -*--·I-- :-- 1-- I` -*"' - .' - t -__,._ - .i - ! | .. I. '--'T I- . . i .... ~.. . :-i . 'ji ' i i ., __-I - t- : ·I ' : i 1.'; !: I , i .' i+-I-c -I ·· I 1.. i . I . . i -t""-' . !;---·---I·----' I' . 1 1 --. Li I -J-- - ._ ';-.- i ?!-- - i .. i ']; I . r ..-. . I _ _ ___ F · ---*--- I I-t·l I I '--C1 _ ___ . 1t-'i -- - ..... L---V.17$ l[. . --. .--. - .... r,. -. .--, _~ . . i -L i. I . r- - -i I .I .. ' i.... ' ' ' ' l:n I L ij . qr, . . a 7--r wt:t-r-. _,. . . . .: .. . .-. _ : !:I _. :. (See S.M. Thesis in Chemical Engineering,M.I.T.,1930, by Trahey and Smith; and article by Cornish in Proc.Roy.Soc.,London,1928, p 691). The available dta also points to the fact that the transition from streamline to turbulent flow in rectangular conduits occurs at a Reynolds number of 1100 to 3000, depending on relative roughness. The Reynolds number in this case being, of course, written thus: Re = 4mV/A = 4mG/u Where: m The hydraulic radius of the rectangular conduit, ft. = V = Average fluid velocity over entire cross section,ft./sec. Density of the fluid, lb./cu.ft. = G Weight velocity, lb./(sec.)(sq.ft.) 5 Absolute viscosity, lb./(sec.)(ft.)= centipoises x 0.000672 ~= Turbulent Flow in Rectangular Conduits Frictional losses or the pressure drop which occurs during the turbulent fluid flow in a rectangular conduit can be calculated by means of the Fanning equation, using the "equivalent diameter" also called the hydraulic diameter, which is equal to 4 times the hydraulic radius. The available data supports this procedure fully. (ee: article p 145 ; and paper by by Atherton, Trans.Amer.Soc.LMiech.Engrs.,1926, Lea, Phil.ag., !~~~~~~~ ~ ~~ . K 1951, p 1235). FLUID PRESSURE LOSSES DUE TO TURBULENCE A FLUID FLOW AS ENCOUNTERED IN HATING EDDY CURRNTS IN BOILER DESIGNS Introduction For all practical purposes the flow of fluids encountered in heating boiler designs can be assumed to follow the laws of hydrodynamics for noncompressible fluids. This assumption will seldom if ever result in an error measurable in practice, or even under ordinary laboratory conditions. That this assumption is basically sound is apparent at once when one considers the fact that the flow of air and products of combustion in a heating boiler takes place at practically constant absolute ressure- the variations being seldom over 0.5 per cent. Incom- pressibility of water is, of course, an established fact, and the flow of steam from the point of origin in the boiler to the steam outlet normally takes place with a pressure drop of less than 5 per cent of the absolute pressure. The importance of fluid pressure loss due to turbulence and eddy currents is often underestimated in mechanical designs, and undue importance is attached to fluid pressure loss caused by surface and fluid friction in conduits. In a typical or even any hypothetical heating boiler, for example, the products of combustion suffer not so much pressure loss due to friction in the passages as they d due to sudden changes in the cross-sectional area of the path and consequent turbulence. Bearing in mind this unique importance of fluid pressure losses in heating boilers due to turbulence and eddy currents, the discussion 20.S- presented below is developed in considerable detail, and each importnnt case is identified ccording to the cause -2 06- nd its nature analyzed. FLUID PRESSURE LOSS DUE TO TURBULENCE AD EDDY CURRENTS Loss of Fluid Pressure Due to Abrupt Expansion of Stream Cross Section The simplest and the most frequently occurring fluid pressure loss due to eddy currents is found in the abrupt expansion of the stream section as shown in Fig.No.8 2 . Here the stream is moving through the smaller conduit with a velocity V'. A moment later its inertia has carried it into a larger space where the velocity is greatly reduced. Eddy currents are therefore produced with violent agitation. Small masses of fluid moving with the higher velocity combine with masses moving with the lower velocity until the entire mass is set in rotational motion with a relative velocity equal to the difference between V' and V" velocity in the expanded section. The amount of energy thrown into rotation per second is therefore equal : Qt(v'-V" )2 /2g These eddy currents cannot be reclaimed but continue to spin until brought to rest by fluid friction.(The internal heat is increased, but the cooling due to heat capacity of the fluid is usually so effective that the rise in temperature is scarcely measurable unless the same fluid be recirculated by pumping). This loss of kinetic energy of rotation can best be evaluated as lost fluid pressure in terms of linear fluid head, the amount of which can be found easily as follows: If the lost kinetic energy of the fluid be expressed as (Qje) -2 07- foot lbs. per second, then since Q = (Q)(V'-V") 2 /2g the head lost is equal to h = (V'V")2/2g Where: h = Loss of fluid pressure in terms of fluid head, feet. conduit of small cross V'= Fluid velocity in the ustream section area, ft./sec. V"= Fluid velocity in the downstrem conduit of large cross section area, ft./sec. g = Acceleration due to gravity, ft./(sec.)(sec.) The preceding explanation of eddy current loss is based on physical analysis without extended mathematical deduction. One interested in the mathematical derivation on of the static hich involves considerati- nd dynamic forces is referred to the original work of Borda. Loss of Fluid Pressure at Square-Edged Intakes A common occurrence of loss of fluid pressure due to abrupt contraction of the fluid stream is found in many instances of intake to a conduit fronma chamber or plenum space. Fig.No. cal flush intake to the 3 shows a typi- round conduit. The edge of the conduit being in lane of the upstrearm face of the head-wall, the contraction factor will be that of the plane orifice or 0.061. The stream lines although submerged within the conduit will form in the usual manner and all the fluid taken into the ipe will pass through the constricted area as shownin Fig.No.83. The velocity through the contracted section is, of course, greater than at the normal section of the conduit, -2 - P/ Id I Kl II I i I a3 . A r,pt8 expansion of Stream Cross Secrfo 5ware- dqe .Zntaxe II / F . 6 " teeentrcanfZntae i/vith Thin wa//s of Abrupt Contrractorn Strea, Cross tSeeflon velocities being inversely proportional to their respective areas. The portion of the cross section of conduit outside the contracted stresm will be filled with violent eddy currents and the amount of lost energy because of these currents can be obtained through the same analysis as employed in the case of any abrupt expansion. All intakes of this type, large or small, are accompanied by the same ratio of stream.line contraction since, within the practical limits of accuracy, the contraction factor of a plane orifice is the same for all sizes as well as for all velocities of flow. The lost fluid pressure can accordingly be expressed as a constant percentage of the velocity head in the conduit and the amount of this loss can be derived simply as follows: If the velocity through the contracted section is assumed to be V nd the velocity through the full section of conduit is taken as V", then the fluid head lost is equal to: (v'-V"1 ) 2 /2g Also, V'= Therefore,h .6 .V V( I -V11)/2g or for the square-edged intake in general, h - o.4 1(V")2/2g Where: h = Loss of fluid pressure at the square-edged intake, in terms of fluid head,feet. V"= Fluid velocity in the full section of the conduit, feet/sec. g = Acceleration due to gravity, ft./(sec.)(sec.) The multiplying factor 0.41 my be called the "coefficient of fluid pressure loss" for a square-edged intake. Verbally it states that -2 0 l9- the fluid square-edged intake is equal to forty-one ressure loss at ressure had per cent of the velocity in the conduit. Loss of Fluid Pressure at Re-Entrant Intakes The fluid pressure lost in a re-entrant intake formed by a thin walled conduit extending into the intake chamber as shown in Fig. No.84, can be obtained easily by means of the equation derived for expansion losses in general. The size of the fluid stream, before it breaks up, is but one-half the area of the conduit, and accordingly the velocity at the contracted section is double the normal velocity in.the conduit. The difference between these two velocities is therefore equal to the velocity in the conduit itself, and the loss of fluid pressure because of eddy currents is therefore equivalent to one entire velocity head. Stated mathematically: h = (V'-Vn)2/2g and since V'= 2v", the head loss h (V") 2 /2g It may be therefore said that the "coefficient of fluid pressure loss of a thin-walled re-entrant intake is unity. Influence of Wall Thickness on Loss of Fluid Pressure at Re-Entrant Intakes If a re-entrant conduit has walls of appreciable thickness the intake loss will of course be less than that for a thin-walled one. The stream lines are directed by the plane end of the conduit nd the ii~o n+. + A n rla r+ i 1 l '1 T T- i' -_,11? 711 r~~n +-r, ~ ~ I ~ds therefore, the coefficient of pressure loss is less than unity, inasmuch as all conduits must have some thickness. Wall thickness is an important factor, and even a small thickness will occasion an appreciable reduction of lost head. Re-entrant conduits with walls thicker than the specific critical thickness cause the stream lines to be directed along the end' face of the conduit and, therefore, they perform according to the conditions o flush-entrance with coefficient of fluid pressure loss equal to 0.41 as for other square-edged intakes. Critical Wall Thickness of Re-Entrant Intakes hnenthe walls of the re-entrant intake are thick and present a face approximately perpendicular to the axis of the conduit, there are two surfaces tending to direct the streamlines,-the outside surface of the conduit and that of the end face. One or the other of these surfaces must control the nature of the flow, since the formation of either set of eddy currents prevents the formation of the other set. For example, if the streamlines were directed by the outside of the conduit, and on return could strike squarely into the mouth of the intake, there could be no additional eddy currents formed by the flow around the inside edge. It is, therefore, clearly evident that the total loss cannot be the sum of the two known losses. But since the same water cannot follow two paths at once, a critical point will be found for some articular thickness ratio, (t/D) 'lhere: t = Thickness of wall, and D = Inside diameter of a circular conduit or the hydraulic diameter of a rectangular conduit. A conduit with wall thiclknessless than the critical will have the stream lines directed by the outside surface of the conduit with the resultant contraction factor of 0.5 and with a loss of fluid head from consequent expansion. This loss will, of course, vary with some inverse function of the thickness-ratio and tend to become zero when (t/D) = 0.206, since this thickness results in the outer sectional area becoming double the inner. The influence of the end face area however prevails with tle stronger currents when (t) is greater than (0.05D), that being the thickness which makes 61 per cent of the inside sectional area equal 50 per cent of the outside sectional area. Experiments verify the above analysis and indicate a loss of head consistent with the assumption that the stream lines are directed by the outer surface of the conduit, for all thicknesses of wall less than 1/20 of the conduit diameter. For conduits hving walls thicker than 1/20 of inside diameter, the coefficient of head loss is equal to 0.41, indicating the correctness of the assumption that the stream lines in such cases are directed by the intake end face. Fig.No. 86 attached here shows the influence of wall thickness on the fluid head loss, at the re-entrant intake. Loss of Fluid Pressure at Rounded intakes A well-rounded bell-mouth entrance to either a square-edged or a re-entrant intake permits the fluid to enter the conduit with practically no loss of head. As explained under description of "Suppression 1K -· .*'-;........... ......: ... ~ .7 IIN ~........ ,,-; ....I __* ~ ........ -~~~~~~~~~~~~~~~~·· l:~.++~.L .... .,,~J...... .... :itI.. ......~~ .... ........... t ........ i~ ....... i- .: r - __ - r-.- l .... 1 · l~ l .... ¶V~': !' .. ....... ----- I-i- ~~~~~~~~~~~~~~~~~~~i::L'::, I·· __ - :l _?Li; :'-tl~~~ i.L. .iI-· ,1. =.,. : ~.~ r ?.~ ... ,,~.t , ~ ~ ", , ~ ' .... :.:.....,,_:, ..~: ' ~ ~-, r :,~~r . j.:..,-:::~:..:.:~. .l:: .,:.... ;. ·I· .....~.,,~.:~ ... i..... 'F.': ,h .'~-.:4 r":.~ .-. ',J. :i... . '' ,~" , e:...·...;.~-,=,'...': i/~?_::-~~:'........ -- ti.,'~..''.. .·~ ~ ' ...': -.~. ! :...,:. ... , :~.:~:: l'..... . ; i. :t:-!,L,'-i.; ~:~,e~~, J;~.:.' .:: .!:~ :'.i :r. .... TT ,......,.-'Z,~e. -.;,- ., .-. -~,, K·: ./.... :.!::i~-: ' 1--:' "''':~: : I. . :~.:~-..:_..u . ...·:..,._'.!. . :"k ,'::.... .. ':.-:' -1 -~-~-:::"t:,'1:.';":: ~'~. '", II' L.~. .'.:'-t: ' l : ..." :t .... I':' 1. . . . ;·-..t"',.'::-:.~. -! -tII -'- · ':: '' " "'F--£?. '--;' .'T"::''. i.-.-, I:-,,--.:::-, :r. :.=' ' ,;'...... '... 1-.. .-.'-..t..-!::` .:· .~I 1_::.:,.'. . . 1.:~ . . ": :. ~-,~...,........ ... L.....i. .. ,i '~":... . :!-..,. . . '- .. . .-. I .... J: . !........ ., . t.· .... , . .. I .. '.. .... ','' I'' ~~~~~~~~~~~~~~~~~~~~~~~~~~~ .I.: ~~~~~~~~~~~~~~~~~~~~~~~~ '': i.'"~ .... ",:...' :':~.-. -' ". '-:.-: ,'' :'l' ','-''. ,.:...·~'i.':'-[-u.. Iii . :~, :..-·.·.~ I... :. ... .. ,. . -i.-1-.- i-:-.~-,--: .: .. r.-; 'i-. ............. ... :~?.--:..~~ i ::':- ... ... :j . ! ..... ' . -, '-,. 1.,.1..... ..::... \,·~ .t-. .:1:::.1. ·.-,.:.. ~~,....:J~.I-.:::. - ..... . .. "":-:..: ".-.~i ... "'.:-!' 't"` ) ,"-.. :.:i'l ''-- ~'.'......, "-.~~~~ ii:!:1i ::~."::;:::l:' : ~" :i.",--'I '.:::-'4------~ ~--.-I"' .--·::.-..-..:Trq'~+'~--.-~~~ ;:'::.".~~~~~~~~~~ .. "-' ,,. ...1.. .:-.,t,-:"~ '- -.. ~~~'i'~ ''"-'---. .. t..:-...-. .~- _ ~ . v.. ":-j::.... - ...,)...... : ~ '.. :,'F:.!-..:-::! . '-. - . . .l-. ,... . .;: ~. '. . . . ...,.....1: "' ~ - ' ' :-i:.~ !Z -f. r ::· r-~ ::"-i' :" 'I~ -:: : ': !t ~'\;..'· ... - .. 'i-,t4.]i'. ii": "I".i,-' -... '-- ,--r-.' .. j'j' i ' -.... i.:'.. .. . !- !~ ', '~.'-: i. :-' -i ' , ft( (-I ..1 i ·' :i' I... ... .... -··.(-'-?. ,-., i-.. ...· '-, - ... . -.·. · ·1 ' I· .. .:. · :·- ---. tI-II ·- *.. . I I · r--- -I- .-.. :.... ."'. . - I - ..: : 1t....... ;,, ;.t., ·'-~-~ -:--.!... . ............. ........ ... ..::-L'i,:'.':';-::'.."_:, :...;T; . . .......: ·... : 1-- ·- I, .1 -r~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ I . tei ~.....~~~~~~ .... ::t.l..t:..: !:.· !-..! . -,.-:-. :·I~--··i , -'::-,~·-~.,i·.... -:·',.: __ --- · ·r -· ·i · rI .. i n , :~..,,-,~.::~.,:::--,,.:..~ r .. .....;. : .. . ·-- I- ·-- · ·· · · · I·~~~··-- I- ,......r-. r·~-.:\ . ..· ,::.: . .- .- .~.~~. -; ,.~.-,- i~L -; ~ ~ i _ ... 1 - - .''I:'.-t ... ;,...~ I - .., _ T t , . ' : '' '. :..j......-~ :t. 1. . . . , "~' I . - _ J. i ,, II~~ -'- . K~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~·..... .~~,..... -.I....... ~..-[ -. -....... ·- · · ...... 1I "* ?',+'t', -+~-,~..-·: :..: ..... '... ":.... '-... '"·-................. . . · · ...··· I ·.. --·--· ~.'~~~~~~~~~~~~~~~~~~~~~~~~~~~ ' ..... I· .:...:j.... · ~-1 "· I-: SI : l · :·-t·,I-,· I~· . . .+~ .. l--; .---·- ·.- · -.... ! -"'; " .."' .1..'-"' C·-l··l~~~~~~ c .:c·~ ?::!:-L· IC· L·-i?:?;'-;-::?:i!! ~:'~':!:: "~~~~~~~~~~~. .'; ' ·4-~~~ I ~~~ ~ ~ '; ' ~ ~; ~ ~)I'~ ~ .:,I-.-' ._-~ ~ ~~~~~~~~~[.~-..~·)' dl'" i' ' '·f j ' ' I I .-'I' ' t: I z I -. i I· [ : .... --I~-- of Jet Contraction By means of Bell Intake to the Orifice", this is due to the fact that the entering stream does not contract, therefore it has no opportunity to expand and produce eddy currents. Since,. as previously mentioned, contraction is almost completely suppressed by a correct circular arc of rounding, there is little or no advantage in using other curves. Critical Radius of Intake Rounding By critical radius of rounding is meant the smallest possible radius that will result in the elimination of contraction of the fluid stream and thereby prevent any abrupt stream line expansion and consequent loss of fluid head. If an intake is provided with a mouth just equal to the area of a plane orifice of such size that it will discharge 3. stream with cross section equal to that of the conduit, there will be no expansion within the conduit; and consequently there will be no pronounced fluid head loss. In order that the bell-mouth may have this required area,equal to the conduit area divided by 0.61, the diameter of a bellmouth must be greater than the inside diameter of the circular conduit in proportion to the square root of this ratio. In other words the diameter of the bell-mouth must be equal to 1.28 D. From this it is self-evident that the radius of the rounding must equal 1/2(1.28 D-D) = 0.14D R = 0.14D ' hlere: R = Radius of the rounding of the bell-mouth approach to an intake. L. -243 - D = Inside diameter of the conduit. Similar reasoning can be applied to selection of bell-mouth intakes to conduit sections other than circular. Loss of Fluid Pressure at Partially Rounded Intakes The above analysis may be applied also to any radius of rounding less than 0.14D. In this case the coefficient of fluid pressure loss will be greater than zero and less than 0.41. The pressure loss for any special case of intake rounding may be easily computed, however, by considering it as loss due to abrupt expansion. The section area of the contracted stream in such cases is equal to 61 per cent of the bell-mouth area, and is smaller than the conduit section area; consequently the stream upon entering the conduit re-expands to the full section of the conduit. Fig.No. 81 shows graphically the influence of intake rounding on the coefficient of pressure loss. The curve shown on this graph was computed from the analytical method described above. Experimental data agrees well with this theoretical analysis and it may be used without reservation for all practical calculations and estimates of pressure loss due to partial rounding of the intake edges. Loss of Fluid Pressure Due to Abrupt Contraction of Stream Cross Section Fluid pressure loss due to a sudden contraction in conduit cross section results from the ultimate re-expansion of the contracted stream within the narrow portion of the conduit. Fig.No. 8shows -- ~.; .; .:i-.. ,-~ 'i ;...'......';~F .. .:~· "· · ;·;-·f--!+ ;-,...... ----- ; -· 1·-;I · ·:1 i , ·- 'I ;;t - ~l-(~·:;_j J " ·1;... · '···- I- . l i* -. 1- I ; , · ) -·- ' -- ,~·- ' ~' - i-: . .. ;,t~',''...$.............. ..... ... . ...:. . . ..... ~. . .. ~.; ,~~~~~~~~:;..;:... ,~'.... .. -...I... . . ...... .:...'. ....I..,.. t...... ~-.~~~ ~ ~~~'**' ': i~'i~:.-!~:=f,~ !' :..1:::. ... ,....: k~,. ..!.,t .!-!: . ;, ' - - ..L-C. ;. '' . '"'1 '_.· ' . ''......... " ...... ' ,_ ' I ... 1 I i ~ .... ,., ' ' i 't ... ......... i t- I I _ ":;:.'.. - ::I"'.''. ":....":.-.'.:....."'.-'' -", ... ~':.',.t:'-,:.. L:::: -:t...· ;:!J '.' I : ; ..~ ~" i' -. ;' .. :- ~ ~ ~ ~ ~~ '-. .. J.; ; . ... !:,.... -'--" .' I . .-......~,~,'.--. -:~ '~,/,~ -· ''1 : .- :---· I-' ... " -':... · .....:,. · · ·~-·r-r)! ..' ' '· · ' . t' I' ' :-i." .. ; . i----I ... ... :··· . · I ;' . -I·: . ; ... !, _ ,...,, I- -I :· . ; :. ... · .- ~!. .i.4 - ... . ....-.- .- ' - ''I.. I ' . .I. #". .' .. ;·- .·· ~ .... ' ' ','" I ... . ..-. i ; ... ' ....-..-...... .... i.~1.,....l.. ~. , .... ,4...I,~...~.:... ·.· ~. .,.-... ,. I ,...,. " ·~~~~~~~~~~~~~~~~~~~ ~' .. . t. ....:' I ~.X///~I,.... '~/iI"::t."-·f: '" t ·I : ~'.'1;:;': -:'!--.~i.':... i: .,.: :';,'-· .-'· .I'.- :i:.. I': I Z:''I -'...'".f . . t }' ~~~~ ' ....... ,~~~~~_:.... _,i;' ::f.: .i -.:- ........t ?'.............. -- ....... ·. . .. ;·Q~~~~~~~~~ :I : ;. 4-1 ~~~~~~~~~~~~~~~'...::.. . t.'' ~ l, '':.<,--~:'..~'",::~'..:':':--",.-~ ......... ~ ~'"t ~i"'"1'~':'.~'~-:~ ~ , .:............ , ......... t'-."}: ""''~:..!'_ ~".''.. · i :'.:.-l~".t . ..:..::::.. .: ._.. ':.:.. ..::.'I _ : - ..... , - '-..! -'~ i':.:--:;': ~i: i . . L !:''., t. "i:;. "- :::'-~",i':::'; :~-:,;:"-''.''::" :t;.... . : .'. '... :. : . : . ~~~~~~~~~~~~~~~~~~~~~~~:' ...... .:i . . :''... . : ~ ':-:... -:.. : ~"... ': ; ~. ''1: .... ,:.,~ ...., ... ,.-. ~ ... '.~,.-', - I ' 1-; "- " ....... j~ I ......' '~"t' . '1' ,:-':. ;I-':: .......... L ." i·........- :·('-.I 1 . .I . ". . . ---- ..t- · F.....· I" -.-- ...;--'-· ' "-, r· ,r' '-~~l .'·-:~: ~,'. ~t,- ·. .:~£·'t . . . . .~ .~, r . .;~, ~:~. i· . .. .t- '~, ........ ,t-:, ·: : ....... r,-~ ~~,.I.. : , 'F· ::: . ... ,. . ·I . ;,'!l'.... + ! .. i . . ].J. '., ... -. 1/. .. ... . :- .;-i ; I · ' & ;-- -·' Iiii .. .-' i''-:" . i.... /i IC · ,, I .-. .. ;.-i . -... .:.1.... :.) - r:-,.l . :-.. .... ~.? - :! !~;;· :''?'.: :~:;~~:. . :- ,~.... .:-j:..:.-i,~" I ~ .... -' :-::~ ... tI '.I.-:. !-.~ .... t ; . ' t' , : '~ , ,u , · ' ' :I.~: ',I.. r f: . ... . ! " ~: ¢' graphically the manner in which this loss occurs. The pressure loss caused in tis mnner may be computed by means of a simple equation in the following form: v2 2g ¥he re: h = Loss of fluid pressure in terms of fluid head, feet. v = Fluid velocity in the narrowed downstream section, ft./sec. Acceleration due to gravity, ft./(sec.)(sec.) g K = Factor depending on the rtio (a/A); in which a = inside section area of downstream conduit, nd A = inside area of upstream conduit, both in terms of sme Fig.To. 88 units. gives the relationship between the factor (K) and the ratio of areas (a/A). Loss of Fluid Pressure Due to Turbulence and Eddy Set Up by Change of Stream Direction Whenever a fluid stream undergoes sudden change of direction, a certain portion of the initial kinetic energy is lost due to turbulence nd eddy currents. If the cross section area of the fluid stream remains the same after the change of stream direction, then the stream velocity must necessarily be the same as before the change in stream direction, and the kinetic energy loss which occurred during the change of direction is replenished at the expense of the fluid static pressure. Bel'oware described several common instances of change in stream direction nd the methods for computing the fluid they occasion. pressure loss which .1i. _ _ _ _ c-c -. i ---- i I - . _ . II -- _..c* j.. i 1 ! I ·· · ·'' '-e -----i t·t'; I FXIii' . i,t- Y<. i i · -!-7 C-Ia//C _ ! _i i 7-- uce 7 .- 1-· ; i i : i I : -- r r---I --' ... 1,.. - i-· i ;-- _ I 1. iL I. I -- , :- ·---·- I ·--- i I .1 .. ----f ,i II. I ... - -c·-·-- .. i . .- ---- _ .. - i. I 'I' II i .,--! i· i - .t .i . i I-· ;i (· --*-- - r iIUPA~S '' .i 1 :· I , i I- _ i I ', I - i i i _.i .- --I i -,I i · 1. I i -- !Ii I: ' >- r i- I r- I · I ·· 1' I !--h . t · -n Is. i -· ; I -- -i' I .+ kt .I ._ · ·--- -r-- y- ·i i j ..I ·' I[ ; I I ·i c If ,I-- --- D tI : . 't < i l - . i t 4-- L_ I ! · ! ' ' ! i ! i ' t L- --------- L As M . IZ~ A i I I i 1. t- ----------- i - I i !! . - - ii; ! I ._ L ) _ 1 i1 1, ir t . -.IL-A" I Ii l tt --- i i II1 i-C i----- I i L, F---- r I I _..... I -t 1: ! I' '.F. _e - I I i i. - .. .i_ I ·i i I 1 il. I--- I I · 1 ·-- Ir ---- _ L I · I t t U- 1.. i I 1 iI ---- M I ii1. . 1 : · 1 1 i i -· I ·--- t T.-7 I i ®, --- ·---- i i i, i .,,, i I ! 1· · · · ·--- -i---1 - I $.. --- !· ..---- I 1. -z _ t .L--- r I I A5eo -FI _· iC 1 1 . . .L---I ! i :t i I .1 ·. II --g a- r r-· ,.--I -..- Ii- t - I - c ·- i I i i 1. i I- .-LI --- r-- c I ' i · 1 I - .-- --i 1 i t * I · t. ---- ':' -- -- 1 - ----- -t- - - - - ! T *--1 II I -- !i . . .. - . -kaA4/ . A.l-I-r '" Loss of Fluid Pressure Due to 90° Change in Stream Direction Occurring at an Intersection of Two Conduits Figures Nos.89, 90, illustrate four common instances of fluid pressure loss which occurs in 90 degree turns formed at the intersection of two conduits. In all four cases the fluid pressure loss is given by a simple equation in the form: v2 2g here: h = Loss of fluid pressure in terms of fluid head, feet. v = Fluid velocity in the conduit, ft./sec. g = Acceleration due to gravity, ft./(sec.)(sec.) K = Coefficient of pressure loss, which depends on the nature of the change in stream direction as illustrated on Figures os.89, and 90. Loss of Fluid Pressure Due to 90° Changes in Fluid Stream Direction Occurring in Gradual Turns of Circular and Rectangular Conduits Fluid pressure losses occurring due to a gradual change in direction of fluid stream are not subject to simple clculations. Their computation involves complex hydrodynamic equations which unfortunately are derived for ideal fluids, thus making the accuracy of their application wrhollydependent on experimental coefficients. A simpler solution, yet yielding as accurate results as the of PressureLoss 90 O Chaoe: Streom Direc eon 6ccUrn~ -9 iO Crcu/ar an'ed Coef/clients /P O ,crriny ;erfagZ rX Cona4eit Itnersections i 1 /r = .40 K= 26 1 2R i, ·: Who " L o L D, =/.o L >4.D,H= 0.88 h=K/2f 2y 7*'4s~; 19, 91 I I most complicated procedure known today, is obtained by assuming that the fluid pressure loss due to gradual change in stream direction constitutes a certain portion of the kinetic energy present in the stream traveling at a constant average velocity. Mthematically this is stated simply as follows: v2 h= K 2g Where: h = Loss of fluid pressure in terms of fluid head, feet. v = Fluid velocity in the conduit, ft./sec. g = Acceleration due to gravity, ft./(sec.)(sec.) K = Coefficient of pressure loss depending on the radius of the turn in the fluid stream, nd the form of the conduit cross section. Fig.No. 91 attached here shows the relationship between the coefficient of pressure loss (K) nd the ratio of the turn radius to the width (or diameter) of the conduit. The data on which this figure is based has been obtained as a result of extensive experimentation and can be made with assurance of satisfactory results in all instances of fluid flow as encountered in design of small heating boilers. - 21 7- I i·t L:' ,i,·'].! ~'I! I' !I ti'1 1 0i 4_La -i 1i i : t ,: _t ' tC - I 0 - -f i >-;4I Oi s 1· I · ~ i I' 1 i I! I t .z : ·J· !i ij-!- 'i * I i im ! ! i . '' " ' I- t ' I -~ : t [ I ! ,.E! -rs->sa ,ti I,*/r , it.... I I1: !I " i o§ _ |I _ 1Sl ! fg j f : i < I' 1 i>A -- t! _ It i , I! ' t - t'' . · c~ ob a ml * . Imi rce-,i i 5, | i1 I i · rt/Lo, 6f~j7C ~ ffjpiciv r -L~,-t X~~I· I L~~bU P~s '- i l : -- 5' . I ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~I t',-i' i ' ; 'i i--I ! i t ~' ~ I-----... T., .-T--~.-- ' i .' " I ·! 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I i I 'qi I I' ' t HiiAPTER XVI :I ~r RzATIC.hYIJ EBLIS FOR-S jIs:: CF idA^Zn BOiLERS 4.. -218- RCULA:ION Il 3LALL £ATINTG RATIONAL BASIS OR DESIGJ OF WATER CIRCULATION IN SIALL HEATING BOILERS Introduction Circulation of water in any heating boiler is quite a simple phenomenon if analyzed from the hydraulic point of view; yet one can see time and again designs in which circulation is so poor that sections of the heating surface burn out repeatedly, and in which heat transfer is considerably lower than that possible with a given temperature difference between the hot gases and water at about 200 to 230 OF. Based on the cause of convection currents, the circulation in heating boilers can be put into two classes, the hot water boiler circulation and the steam boiler circulation. Fundamentally water circulation in a steam boiler and water circulation in the hot water boiler are based on the same laws of hydraulics; however, the phenomenon of natural convection in the steam boiler is complicated somewhat by the presence of steam in the currents of water. In order to simplify the study of circulation roblem nd bring forth the fundamental principles underlying the natural convection in heated water, the discussion is begun with analysis of circulation in hot water heating boilers. -2 9- ANTALYSIS OF ?'ATERCIRCULATION IN HOT WrATER HAAPlING BOILERS In a hot water heating boiler, or for that matter in any boiler, the water is her.tedusually in a row of parallel compartments. These compartments may -be formed by no more than two or three partitions, or they may be individual tubes in a bunch of several hundred. By proper arrangement and interconnection of the several compartments in which the water is being heated, it is possible to secure the maximum circulation of water that can be attained with a given size boiler. A vigorous and correct circulation in the boiler is absolutely necessary to insure the following: (A) First, r pid starting, i.e. short heating-up period. (B) Second, prevention of overheating of the sections exposed to high temperature radiant flames. (C) Third, a high rate of heat transfer. Natural Convection in The Single Compartment Or Single Cell Hot Water -IeatingBoiler When water is heated in a single compartment the convection currents usually tke the forms shown on Fig.No. It is easily seen that in a single lrge 92. water compartment the velocity of convection currents cannot reach the possible maximum, since it is imoossible to utilize completely the available head created by the difference in densities between the rising and the falling currents of water. The principal deterrents to forceful cir- -2zo0 - ;e 1 t -0 #0 I Jzteer 4, 'on I ,I I 'errz9 etar ~?:.;,,~.-4 culation are the local convection currents at the various points on the heated surface and the resulting disturbance of the main convection streams. :i. .... A single compartment boiler presents no danger as far as burn- ,~.~. ing out is concerned; however, it is very slow in starting-up. Circulation can be increased considerably in this type of boiler by the simple expedient of breaking up the water space into two compartments by means of a plate partition as shown in Fig.jNo.93. In the boiler of design shown in Fig.No.93, circulation goes on at the same rate around its circumference. Natural Convection In a Hot Water Heating Boiler With An Extensive Heating Surface Any heating boiler of a design incorporating a considerable amount of heating surface as compared to its volume is usually constructed so that an appreciable portion of te surface is formed in- to compartments which heat the water in parallel, i.e. at same con=-~,,.;:,..,:., ditions of heat transfer. ater circulation in such boilers presents an entirely different picture from that found in a simple single compartment type. In a complex hot water boiler design, and for that matter in steam boiler design, the first problem that one encounters is the sub~division of water circulation currents among the parallel passages in '.1,-::--,.. which the water.is being heated. Assume that a hot water boiler design is proposed similar to X:':'"~"~`· that shown on Fig.No. 4 ; then, study and nalysis of circulation in this hypothetical boiler is best accomplished in the following manner: Si.P _ ..k;d Figures Nos.94-Aand 94boiler channels show water circulating through the aving walls heated by flames and hot gases; Fig.No. 94-4shows downward nd Fig.No.4-Bupward flow. (A) Assume that the stream of comparatively cold water bing heated has been divided equally among the downcoming channels,ql, q, q3 , q4 having initially equal temperature t t2 , tt t4 . Now, if of these smaller streams, say q2 , takes up heat a little faster than the other three; then, t2 becomes greater than t t , , or t4 . , q The columns of water q and q4 become, therefore, slight, q ly heavier than the column q2 ; the currents q , 'and q4 commence , ts to flow with greater energy, and their velocity increases; t and t4 commence to become sensibly less than t , ( this assumes a conconti- stant water film coefficient of heat transfer) while current q nues on the contrary to take up more heat and its density decreases with rise of temperature. In the end, the entire flow of water takes place through the branches q , q , and q4 , while in the branch q2 at the same time a reverse current which circuthereis established lates as indicated by the dotted arrows on Fig.No.94-A. Therefore, based on the above demonstration we can state in a general way that a current of water which is being heated carnnotbe subdivided equally among descending channels. (B) However, when subdivision of the stream of circulating water is.made through ascending channels, the results will be as desired. Assume that a hot water boiler design is that shown on Fig.No.'L, roposed similar to and that the stream of water being heated has been divided among the ascendingchannels q , q , and q4 , has Co/d /Wafer co/a 6ases .Z.#7,falatla -/ot .14later Fil I -t f= oft dot 14/1.er aso/es Gases o/ad lafter 79. igp(-- ing initially eual t ter-'perlturs aad 4 Now, if one of the smaller currents, say q2 , should suddenly become stronger than the other three, q ts , or t4 would be greater than t ts , of q , or q4 , then, t , . But, if t 2 were less than t, or t 4 , the weight of column q q3 q3 , or q4 ,-- would be greater than either that and the flow in the column q2 would decrease by an amount proportional to the difference in weight between the column q2 and columns q , q3 , or q4 . With gradual decrease in velocity of q2 , t2 would rise, and gradually approach the temperature in the three other channels; thus, the flow in all channels would tend to balance itself automatically. Based on the above demonstrations, a rule can be formulated stating: That if it is desired to heat several streams of water flowing in parallel, then the streams must be heated in ascending channels or passages in order to insure uniformity of heating and a vigorous circulation. a i :,j I;, :·, ,a Forced Circulation of Water in a Hot :r :· --i .. L: ;i r ,· ·-. ater Heating Boiler The simplest way to insure correct water circulation in a small heating boiler and all its accompanying advantages is to install a small water pump and thus insure a positive flow in any de- c-5 i sired direction. r Fig.No. 9 shows a simple diagrammatic arrangement of a small hot water heating boiler with forced circulation of water. vWhendesigning the water passages in a hot water boiler with i forced convection, the most important things to keep in mind are: i·I .i.; r"l: ·ti a I -.2 z 3 I 4 n . I-u f 4t, 6jOac f4 -l ! i m- -- _ - o r m _m - I- 7 :1 H H I-H t H H .0.- W HoftGs Passaes- 4 .I . k 04ver Pu ,m/, /-,, Irro _I A Am as - w"A A . _ A I- A m -. "i , Sfa -%--kyaer 4& /es - Cross Fr' do 6s ka wallere Choa-'1r37her ros Slla'n a Ga's AZsg 99e 7h-,*lo&,q i -?#: I io. WI (a) Equal distribution of water among the several parallel passages, and (b) Desirability of a low water pressure drop across the boiler. Equal distribution of water among the parallel passages is insured by laying out the aths of water flow so as to offer an equal resistance to.water flow in all channels. The simplest way to accomplish this is by providing small plenum chambers before and after the passages in which the bulk of the water is to be heated, and by making the cross section and length of water path the same for all parallel passages; Fig.o. 9 shows a diagrammatic sketch of such a boiler. In order to obtain a low water pressure drop through the boiler, all fittings must be ample in size, all changes in direction of water currents must be gradual, all water passages should be of sufficient cross section to permit low velocities, and streamlining of entrances and outlets should be resorted to. A small increase in cost of fittings and patterns will result in a design that will require a smaller water pump motor, and will have correspondingly lower operating cost than a similar design without these refinements. For methods and details of calculation of water pressure drop and selection of a water pump for a hot water heating boiler, the reader is referred to the chapter on "Application of Fundamentals of Fluid Flow to Design of Small Heating Boilers". - .-L ANALYSIS OF WATER CIRCULATION IN A SMALL STEAM HEATING BOILER Introduction Circulation in a steam heating boiler has usually a twofold origin. First of all, generation of steam bubbles at the metal surfaces and within the body of water creates local circulation and turbulences regardless of the design of the boiler; second, properly designed water passages or channels induce long, vigorous convection currents throughout the boiler. The force behind ll circulation in the steam boiler is, of course, the difference in density between two connected water columns, which is caused mostly by the presence of steam bubbles in one of the columns. Difference, in density of columns due to difference in water temperature is a comparatively negligible factor in production of circulation in a steam heating boiler. }Mechanismof Circulation When boiling takes place in any section of the body of heated water, the generated vapor bubbles rise and on their way upward displace and carry along a certain amount of water from the lower to the upper portions of the boiler. The velocity of water carried along in the stream of rising bubbles depends on three factors as follows: (a) The rate of steam generation. (b) The velocity of vapor bubbles. (c) The shape of the vessel. I Velocity of a spherical vpor bubble in a body of a comparatively still water is primarily a function of -threevariables: namely, (1) Density of water. (2) Viscosity of water. (3) The size of the steam bubble. Qualitatively the nature of this function is easily determined, since the buoyant force lifting the bubble of vpor is directly proportional to its volume, while the frictional resistance between the surface of the bubble nd the water boundary is proportional to the surface of the bubble. However, under actual conditions thia relationship does not hold completely. The low rate of bubble rise follows the theoretical formula quite closely; but, as the upward bubble velocity increases the acceleration decreases, nd at a certain rate of rise acceleration of bubbles ceases, resulting in their rise through the remainder of the path at a practically constant velocity. This loss of acceleration in rate of bubble rise is explained by the fact that with increase of bubble velocity their shape is changed from spherical to a spheroidal form with consequent increase of the hydrodynamic resistance or drag factor. The rate of evaporation divides the phenomenon of bubble rise in the body of any liquid into two types: first, that of bubble rise in a quiet body of that liquid; and second, that of bubble rise at a rate sufficient to cause an appreciable turbulence. The data which applies to the first type is not applicable at all to the second type; since in the latter, due to a large proportion of vapor bubbles in the body of liquid, viscosity of the mi:ture is lowered considerably, and the velocity of bubbles relative to the liquid becomes many times greater than that of bubbles rising in a quiet body of liquid. This paper deals primarily with a comparatively high rate of bubble generation which is always accompanied by a considerable turbulence. The rise of vapor bubbles in a quiet body of water is found usually only at the start of ebullition and does not last any appreciable length of time. Induction of circulation in water columns by means of air and vapor bubbles was investigated quite thoroughly by Hofer,(See: V.D.I. Forshungsheft 138); by Behringer and Pickert,(See: V.D.I.- Forshung. No. 6, 1932); by Schmidt,(See: V.D.I.-Forshung. No. 55,1929); and by Cleve,(See: V.D.I.-Forshung. 322). These studies point definitely to the following conclusions: (1) Relative velocity of vapor bubbles rising through a column of water increases with increase in volume rate of bubble formation. As was explained above, this is caused by decrease in viscosity of the water column due to enrichment with vapor. (2) Circulation of water also increases with increase of quantity and volume of rising vapor bubbles. This effect is due primarily to increase in number of rising bubbles,and partly to decrease in viscosity of water-vapor mixture. nd Circulation of water, considered as a function of quantity volume of rising bubbles, passes through a maximum at a definite or velocity in the column or tube in which circulation tkes vap- place. 'Thismaximum coincides with what may be called the limiting velocity of vapor through the water column, which depends on the cross section of the tube or the passage in which circulation is considered. At this limiting velocity vapor does not rise through the water column in the j.2 2. form of individual bubbles, but flows upward as a continuous stream which pushes its way throuEh the whole height o the column. Natural- ly, the amount of water circulated by such a continuous stream of vapor is very small. According to Behringer,(See: Forschung No. 6, V.D.I. 1952), up to this limiting or "cri-tical"vpor velocity the circulation of water in a given tank or column-like passage can be determined by means of the following empirical equation: Where: - (The' symbols have the following meaning when the British tem of units sys- is used..) W = Volume of water circulated, cu.ft./min. W g .," b = Volume of vpor = / ; where rising, cu.ft./min. = density of a column of water without vapor bubbies in it, lb./cu.ft.; m = mean density of andem a column of water containing the vapor bubbles, lb./cu.ft. A = An experiu-ental term showing the loss in water circulation dependent on the diameter of the tube or passage within rinichcirculation takresplace, in cu.ft./min.(See Fig. No. 6 B for a plot of the constant (A) vs. tube diameter.) = An experimental term which shows the loss in water circu- l1tion dependent on the volume velocity of vrpor through the water column, in cu.ft./min. 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Assume that the iven vertical column of water is in a boiler tube which is heated along its full length, and that the overall heat I transfer coefficient is the same at all points of the surface. The . ·: steam generated will, of course, make up most of the mixture flowing - upward, since the specific volume of steam at 2120 F. is about 1600 times greater than that of equal weight of .t j. qwater at te same temperature. Now, if we neglect the comparatively minute amount of water k - carried long by the stenm bubbles, the average density of the column of water-vapor m:ixture is exresed s follows: :-' m= m : 1/L fLt(dL) 0 ~Where: m = Zean or = Density average density of water colman, lb./cu.ft. at any height (L), lb./cu.ft. The higher the considered cross section of the boiler tube the more stepm must flow through it, since it must pass all of the steam that is generated below it. The volume any cross section of the tube, of sleam that ss'uing tat L)vg / -22 12 (36oo00 hfg) - through heat tr-nsfer rate is con- stnnt at all point3 of the surface, is equal to: Wg = (q D passes :Where: w = Volume flow of vw or, cu.ft./sec. = Rate of heat inflow, Btu./(hIlr.)(sa. q ft.) D = Internal diameter of tube, inches. L = Ieight of tube, ft. v = Specific volume of generated vapor, cu.ft./lb. g = Latent heat of v.porization for water, Btu./lb. , corresponding to pressure in the tube. The volume flow given by this equation corresponds to nominal velocity equal to: Vg g wrea I I L)vg/4 3200 h =(q D P~~~~ 2/4(144 i' Simplifying: V = (q L)v /(75 Dh This velocity of steam,(V ), is of course treqonly for a 0_ ,, cross section o' te tube absolutely the steam rises not at velocity (V ), ree o' iwater. but in the n the actual case orm of bubbles at some velocity (Vb) proportional to the volume of generated steam. t the uniform condition of steam generation we have the following relation: R = VJ/b Thlen, density :'here: = (q L)V rr / (75 D h Ig V) b t any height (L) can be expressed (l-R)t 1 + = Density of water-steamn mix-ure j as follows: -230 _ t a given height, lb./cu.ft. = Density Q of wnter withou steam at the same height, lb./cu.ft. - Density of stenam t sme rherefore, =/L oint, lb./cu.ft. at the mean height of water colurin: -(q L vv/75 D V m=d-1/2( L v/75 D hg Vb) bg IHencethe ratio of men b = mean/' (q L v D hfg Vb) + 1/2(q fg L v/7 D f \bTJ b is to o = 1-1/2(q ++ ) eual (dL) to: L v /75 D h V)(l-/ is very smallin comnarison to unity, For ,a;ter(pl/t) and therefore can be neglected; which results in the following form of equation for (b): b 3y rmeans of 1l-(q L v Cr)/(150 Dh 0 'V,) his equation the value of (b) can be found for any given vapor bubble velocity through the water column. The terms in this equation hve the following meaning: b = Ratio, no dimensions. a = Rate of heat inflow, Btu./(hr.)(sq.ft.) T. _ .-. c -h f .llh ni wi,.ier rvlv' nn ian r l r vire. i 4 + place,ft. v '= Specific volume of generated vapor, cu.ft./lb. - Diameter of tube inches. hf, = Latent heat of vaporization for waer, Btu./lb. V. i -~23 = Bubble velocity relnive to vwat-er in the tube, ft.sec. I- Qcvr--' Fig.No.88 shows the relation between this relative vapor-bubble velocity and the density of water-steam mixture in boiler tubes of variour diameters. No extrapolation should be mde on the Fig.No. 98 outside the area covered by the given curves, since the nature of the phenomenon chances completely at the boundary conditions. These boundary conditions include, density of water at 212 0 F., density of saturated water vapor at 2120 F., pipe diameters below 1/2 inches, and pipe diamneters above five inches. The nature of the phenomena has not yet been studied outside these boundary conditions; however, this will not prove to be an obstacle to practical application, since all ordinary problems fall ]j-:: within the area covered by the curves on Fig.No. 9 8 . One boundary condition that may be met occasionally is boiling in compartments of larger cross section than that of a five inch tube. In this case the relative velocity of water vapor bubbles should be taken as given for the steam mixture; sinceall 5 inch tube at corresponding density of waterexperimental evidence points to the fact that for tube or column cross sections greater than that of a 6 inch pipe, there is no appreciable increase in relative bubble velocity with increase in diameter or cross section area. Thus it is easily seen that the ratio (b) can be determined simply by use of the equation: b = l-(q L vg)/ (150 D hfg Vb) in conjunction with the curves on Fig.No. 9 8 in the following manner: Assume known: (1) 1 inch diameter tube t 'Z3Z- F .1 - 8 ': 31 - 4 cT j, L .... 4 T, .. ,i: __,.. ! i.L . : ~ - U- -z- -, .! + 1 l2i ' __; . . -.. - T144f· I . I I lo :-- T:"... .': ':-L iL. '- -. '- ·-, '"'~4'_-..r' ;. .. -42--"--: . .:~ ,:- ' ,.':F. -=jr ,- \{.:_~' .. .-.. - ·-- .i tt2¾7L77 -·-·- -;·l--· !-t - * i\: ~ |, · · -^ * b o e1 '.._' ,'- ,.- '- L - -:44 I- ' -t ,] 1 - I ..- - _ . ....i .,; '' .--r 4.'-.' . | t_ r-' --- h._'_ I . .,,t- - 7' CI-i-rc1 . 'i --LPI JlI .... t s'- I · ·' 1 :---I ; . I - i~i ··-LT -- -t-' ' '-- U-- t--- --- ,-._..__4 .i...;.... __··. _' - I 4i ; ·i - - · . : d_.; .J.I _ . L- · '·· -4^__ _ .X _ _-..... _ -T-T; -'-.L.,. _.: ..L-t-: -. -,---~.I-·-t' .. '- . I J.O , . ! _ @ _ 25 - I i - -_ A 4' - - . l X · .-- . · 1._i_ r- ..... ··· .!_ i |.. . _i;_- : ...... 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' i.I : -._ | -r~ \ _, : '-: ' - 7 ... 1-,j :IA, ' :......r:....'-;.. __ A _ ' ' I I rC.. = - I (2) Tube height, 4 feet. (5) ater boiling at 2120 F. (4) Heat inflow into the tube, 4000 Btu.r)(sq.ft.) Required to determine the ratio (b), which may be called the specific gravity of the water-steam mixture circulating in iletube. Solution: (1) From above ssumptions hfg = 970 Btu./lb. v g = 26.8 cu.ft./lb. (2) Assume a reasonable vapor bubble velocity in the tube, say 5 ft./sec. (3) Then, i b = 1 -(40004-26.8)/(150o1970o5) b = 1 - o.59 = 0.41 (specific gravity) (4) Since density of water at 2120 F. is pproximately 60 lb./cu.ft.; therefore, density of water-steam mixture in the tube is equal to ·· 60 0.41 = 24.6 lb./cu.ft. (5) From Fig.No.9 8 , note that bubble velocity of 5 ft./sec. corresponds to water-steam mixture density of 25.8 lb./cu.ft. (6) Try another vapor babble velocity, say of 5.5 ft./sec. Following the same procedure as given in steps (5) and (4) will give watersteam mixture density of 27.8 lb./cu.ft. At the same time, on Fig.No. 9 8 vapor bubble velocity of 5.5 ft./sec. corresponds to water-steam mixture density of 24.5 lb./cu.ft. (7) Plot the assumed values of vapor bubble velocity against density of water-steam mixture as calculated above in steps (3)and(4) and as obtained from Fig.No.98 . Draw two curves, one through the calculated ,·· i ,: points and the other through the points taken from Fig.No.S9 . The in- i - 2 33- tersection of these two curves will give the relative bubble velocity of generated steam and the density of the water-steam mixture in the tube; thus, Fig.No. 9 gives 25.45 lb./cu.ft. or density of water- steam mixture and 5.14 ft./sec. for vapor bubble velocity in the hypothetical problem given above. Once density of water-steam mixture is known the ratio (b) is determined simply by substitution in the equation, b = em/ qi Where: e = Mean or average density of the water-steam mixture in the tube, and = Density of water without steam bubbles and at the same temperature as the water-steam mixture. Now, \ the circulation of water in the tube is found by substituting the known values of term (W ),(b),(A), and (B) in the equation: g , · b Wg( Lb 1 - A - B Thus: (1) Wg = (q D Where the following is q D = L)vg/12 60 hfg given.: 4000 Btu./(hr.)(sq.ft.) 1 inch =5.14 = L 1. v =4Pt. g = 26.8 cu.ft./lb. hfe = 970 Btu./lb. fg Therefore: Wg = 4000 1 .14 4 26.8/12 60 970 i = 1.925 cu.ft./min. : L-". . o 3do-z~~~~~~~~~~~' , :44. F: -::tI- .i--1 r . -. ~t-~~ ~ ~ i i'[ -.------M , ~ ... _-.. l'.._.. ---- " T'!-:' j . I-- -- -.; .-:. -I : 1. l + .- T I . .. $ '..''-· · . I~' -. t.... 1 4 .~--:--" -- : r f - ;; " . : --4-..-. i ' !; ' ' i. ' : .. .- i ---. ---- + 1 '. --. i - . 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':": . . 4- ~ ", ~" [ ';~~ L- - ' ., it'- I . ~· t . , . ~, -. . . -t - . . ,- -- i . i - ;f ,,~ g . . . i .1 . .... i -:..:: -+ --i ;t; I·,_J. . _._. _< . *. -j .... 1. ... , , it. ...,. . ,... . . m. .-..''':[ ".''..''.".','".."'.["'"":: ' , . , ·... , I ... -r. !-- .' .....-.. ... ........... .- ' _ ! - : ~t '"- ~ I. · , - i , -- -I ~·;" '' · - ',, i'I· [ r :---'. t . . I . . . . l m = 25.45 lb./cu. lt., 99, (2)Sincefromii ' = 60 lb./cu.ft.; terefore, (5) From Fi.ITo.96-find b = 25.45 / 60 nd at 2120 F. C.425 for tube lit-h i; ternl dinmieter of one inch, A = 0.17 (4) Also diameter FiE o.9 8f.d from or-:oponding to internal tube of 1 inCl', rAdstemiviocity J - / f6 i D2 / (4 144)J= 1.925 / 0.527 = 5.5 ft./sec.; that B = 0.96 cu.ft./min. (5) Therefore: 'l - 1. 925 0.425 ) - 0.17 - .96 i, = 1 .425 - 0.17 - 0.96 = 0.295 cu.ft. The volue of ( 1 ) ltou.h rob bly in rror as m'uch rs 5 tO 15:j, is an indication of te probable circulktion in design nd is proposed boiler rticularly useful for roportionin he circult'on amon-the several pths whic. it m ight tke. L /in. APPETDIX CURVES FOR S.PtIFICATICN L OF CO.PUTATICON oif 6ases- Spec/fbc /Hefs - - 1'7,'- zased on (/9 11l o-aa' 6e,-JI,Ž ? / 92 vr. 3ey.F CP /1 a. Press.=/4.7 -00 n / LX - 0.70 - 0,60 20 3 - 050 a I- I 000 6 - 030 -2,500 11 QJ 12'9-13 * 13 - 3,000 --o./1 0./0 -3,500 LI 2 W/ader ca6ove/34/°F ,3 6 he/ow134F , Crbon iox;de Keo 7 // 8 /V/to e 9 Air . /2 Su/fur 1/3 ,, /" or /34/ 0 oboe /34/ FCor 16orz A/roviae. oxJo/e be/oWa /3l4 /- -', bowve /38/ 4° ,.ov Af4.r /7 Ther7 Conc4rfill W/t er 0 0. O- 0./a 0. /5 0.20 300 k 0.25- 200 0.30 4%. /o0 t //O-.- ZNI xa 0 - 50 0.#o O. 4-- 0.5 -0 From 'tIrn 1/o/ Year - /929 X /# A1. . 77 '34. -- i.- -- ''' '-'.. · -- -·r:-l · II ".- :'I......- ; ... -- t --·- -- .. t--- --- "` t I - . 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