Automated Design Program for
Air-Handling Apparatus
3
2
1
M. Nagatomo , S. Tanaka and N. Tohda
Kajima Corporation
Tokyo Japan
This paper describes a computer program that can be used to calculate
the heating and cooling load, the supply air volume, the psychrometric data,
The program is based
and the specifications for an air-handling apparatus.
The program
on equations that express the change in the state of moist air.
can be used to select the appropriate apparatus and calculate the required
air volume for either a non-reheat system or a reheat system. It also can
be used to quickly optimize the design by performing alternative calculations
for various hypothetical conditions,
Key Words: Air-handling apparatus, apparatus dew point,
automated design, cooling and dehumidifying coil, cooling load,
psychrometric chart, reheat system, single-duct air system,
supply air volume,
1.
Introduction
The process of designing single-duct air systems requires the calculation of cooling-heating
load, a psychrometric analysis, the calculation of supply air volume, and the selection of the apparaThe calculation of the cooling and heating loads by computers has been widely studied and many
tus.
programs have been developed. Programs that consistently treat the entire design process have not
Because it is djfficult to treat the psychrometric analysis by computer and toesbeen formulated.
This paper
tablish and systematize a standard for engineering judgement during the design process.
formulas
approximate
up
setting
by
process
design
the
treats
consistently
that
program
a
describes
to express the state of moist air, simplifying the phenomena under several hypothetical conditions,
and establishing the standard for engineering judgment.
2.
Program Outline
This program is to be used after the preliminary design of the air-conditionin g facilities is
completed and the types of systems, the zones, anP the kind and conditions of the energy source are
determined.
1
Dr. Eng., Chief of Environmenrtal Engineering Department, Kajima Institute of Construction
Technology.
2
Chief Engineer, Kajima Computation Center.
3
Mechanical Engineer, Design Department.
579
The input data are as follows:
a.
Data for load calculation: outdoor design conditions, room design conditions,
thermal properties and quantities of the materials constituting the room, internal heat
load, etc.
b.
Data for system-design: type of system, chilled-water temperature, steam
pressure, type of humidifier, type of filter, etc.
The program consists of three blocks.
The first calculates cooling and heating loads, based on
the theory of periodic heat conduction, which assumes the room temperature to be constant. From
the input data of the load calculation, summertime cooling load and wintertime heating load for every
room are calculated by hour and summed up by zones.
The second block takes the results of load
calculation and calculates the states and the volume of supply air by the psychrometric analysis of
system-design data. If no solution can be obtained by that process, the room conditions are automatically changed and the load calculations are repeated.
The third block determines the specifications of air-handling apparatus, calculating the apparatus load as well as the energy source capacity
from the system-design data and psychrometric data, and selects the equipment.
The data showing
the apparatus efficiency required for the apparatus selection are included in the program with the performance value stated in the manufacturer 1 S catalogue converted into formulas.
The data to be printed out are as follows:
• The peak load of each room.
• The supply air volume of the room.
• The hourly load of each zone.
• The specifications of air-handling apparatus,
the psychrometric data, and the capacity and
conditions of the energy source.
3.
Algorithms of Psychrometries
A psychrometric chart is generally used to obtain and analyze the data concerning the state of
moist air.
In order to do the same with a computer, all the characteristics of moist air have to be
expressed by mathematical formulas.
The general psychrometric chart has enthalpy and humidityratio drawn as oblique coordinates, and dry-bulb temperature, wet-bulb temperature, and relative
humidity as constant lines. The data of moist air necessary for the calculations of supply air volume
and the selection of the coil can be expressed by dry-bulb temperature, humidity ratio, and enthalpy.
To simplify the numerical analysis, approximate formulas may be used, so long as no practical problem arises.
In this program, therefore, the state of moist air and its changes are expressed by
using the enthalpy and the humidity ratio.
The dry-bulb temperature of moist air employed in the
following formulas ranges from ooc to 40°C when the atmospheric pressure is 760 mmHg.
Equations for obtaining humidity ratio with dry-bulb temperature and relative humidity, given:
PWS (T)
*
=
735.557
EXP (-7. 90298* (TSIT-1. 0) + 5. 02808*ALOG (TSIT)
-1. 3816E-H (10. 0**(11. 349* (1. 0-TITS))-1. 0)
+8.1328E-3* (10. 0** (-3. 49149•(TSIT-1. 0))-1. 0))
w
= 0. 0062 *RH*PWS (DB+273. 16)
I (760. 0- 0. OhRH*PWS (DB+273. 16))
(1)
(2)
Equation for obtaining enthalpy with dry-bulb temperature and humidity ratio, given:
H = 0. 240*DB + (597. 3 + 0. 44h DB)* W
(3)
Equations for obtaining humidity ratio and relative humidity with dry-bulb temperature and wetbulb temperature, given:
PW
w
PWS (WB+273. 16)
0. 622*PW
I
O.S*(DB- WB)'<760.0I755.0
(760. 0 - PWS (DB+273.16))
580
(4)
(5)
RH
o
( 6)
100, O*PW / PWS (DB+273, 16)
Equation for obtaining humidity ratio w 2 , when the air with dry-bulb temperature DB 1 and
humidity ratio W 1 changes with the given tJ. H/ 6. W constant and dry-bulb temperature becomes DB 2 :
*
0. 24* (DBz+DB1)
C-597. 3-0. 441*DB 2
C+597. 3+0. 441 DB1
C-597. 3-0. 441* DB 2
(7)
Equations for the approximate relation of enthalpy and humidity ratio when relative humidity is
constant:
(Within dry-bulb temperature of
HS(W)
o
ao -
30°C, the error is limited to
:t
D. 4o/o.)
-3.32635 + 1673. 25*W- 49827, 4*W**2 + 1005561. O*W** 3
H95(W)
-3.13977+ 1669.23*W
49134.4*W**2 + 983042.0*W** 3
H85(W)
-2.93914+172 6.00*W
54017.6*W** 2+1128573.0* W**3
( 8)
( 9)
( 1 0)
To obtain enthalpy H 2 and humidity ratio W 2 when the air with enthalpy H 1 and humidity ratio
changes with the given constant Ll H/ t:.. W, and relative humidity becomes 95o/o, solve the following
equation:
w1
(11)
Equation (11) can be solved by applying the Newton-Raphso n Method.
To obtain dew-point temperature of air with humidity ratio
byeq(B) and then use eq(3).
4.
w1,
first obtain dew-point enthalpy
Calculations of Supply Air Volume
4. 1
Fundamental
If the state of supply air and its volume can be set to satisfy eqs (12) and (13), the room temperature and humidity can be maintained under conditions similar to those of the design.
(12)
597. 3
( 13)
1. 0 - SHF
In determining the state of supply air and its volume, however, there are the following limitations:
There is a lower limit of the supply air temperature which prevents
vapor condensation at the outlet.
ability of the chilled0 There are limits of the cooling and dehumidifying
water coil.
• There are upper and lower .limits of air volume for the air distribution within a room and for economic and health reasons,
0
When the air volume within the range of the above limitations is minimized, the equipment will
If such limitations are established and standaridized, it will not be hard to use
be most economical.
The conditions set up in this program for such limitations
the computer for psychrometric analysis.
are given in Figure 1. As to the change of the state of
calculations
air-volume
for
and the procedure
air passing through the cooling-dehumi difying coil, t:. HI A W is assumed to be a constant. It is also
assumed that the change of the state of air makes no change in the air volume.
The state of supply air should be above the dew point temperature of the room, to prevent vapor
condensation at the outlet, and below 85o/o relative humidity, to prevent the state of air leaving the coil
from being too close to the saturation line.
581
The relative humidity of the air leaving the cooling-dehumidifyi ng coil is to be below 95o/'o and the
apparatus dew point temperature is to be above its specified dew point temperature.
Considering the
coil performance, the variation of chilled-water temperature, and the value of D. HI D. W of the air
passing through the coil, the designer must set the spedfied apparatus dew point temperature to be
higher than the chilled-water temperature by 3°C or more.
As to the minimum volume of supply air, choose the larger one from either between outdoor air
volume or exhaust air volume, as is required by the. design.
The maxilnum will be, as a rule, below
15 times of air changes per hour, but this can be ignored if it interferes with other factors.
The heat gain caused by the fan can be determined by the fan efficiency and its total pressure.
Their exact value cannot be estilnated until the duct system is designed.
So they most be assumed.
The centrifugal type is one of the most common types of fan used in the air-handling apparatus; its
efficiency is 0. 5-0. 65.
Thus, lithe efficiency is assumed to be 0. 5, the relation between the total
pressure of the fan and the rise of temperature caused by heat gain is as follows:
FTD
=
( 14)
0. 0162*PT
The total pressure of fan will be assumed by the designer according to the layout of the duct
system and the type of filter.
Since the actual temperature rise is 1. 0-1. soc, it is not necessary to
maintain complete accuracy.
It is assumed that the fan is located in the discharge-side of the airhandling apparatus.
The supply duct heat gain is ignored.
It can, however, be estimated to be about 5 percent of
the sensible heat load of the room and added to the apparatus load.
4. 2
Non-Reheat System
If the total heat load of the room, the sensible heat factor, the required outdoor air volume, and
the room and outdoor conditions are given, the psychrometric data and the supply air volume are calculated by eqs (7), (8), (10), (12), (13), and (14).
In case the solution cannot be obtained or the apparatus dew point falls below the specified apparatus dew point, the room conditions are automatically
modified and the load calculation is repeated.
The dotted line in Figure 2 shows such a case.
As in the basement zone, where the cooling load is small, the supply air volume calculated in
the above way may turn out to be too small.
In this case, the temperature difference between supply
air at the outlet and the room air will be reduced so that the supply air volume can be equal to the required minimum volume.
In the example in Figure 3, the state of supply air changes from 6 1 to 6.
In modifing the room design conditions, the dry-bulb temperature and the humidity of the room
air will be modified to keep the effective temperature of the room constant.
In this program the drybulb temperature is reduced by 0. soc and the relative humidity is increased by 5o/'o.
In the case of
Figure 2, 1 r is moved to 1.
When the room conditions are modified, then the load calculation is repeated under the new conditions. If the apparatus dew point is too low even when the conditions are
modified, reheating calculations should be performed.
4. 3
Reheat System
In the case of a reheat system, the specified apparatus dew point is initially set to be the apparatus dew point, and the relative humidity of the air leaving the coil should be 95% to maximize the
temperature difference between the supply air at the outlet and the room air, and thus to minimize the
supply air volume.
In the case of Figure 4, if the supply air is assigned the room dew point 6 1, the
apparatus dew point cannot be obtained, as indicated by the dotted line, because of the inadequate
selection of the state of supply air.
If the total heat load, the sensible heat factor, the required outdoor air volume, and the room and outdoor conditions are given, the appropriate state of supply air
can be obtained by solving the following simultaneous equations:
1. 2* (H1 - H 6)*0AQ
( 15)
QT
582
w4
Ws
(16)
H4
H95 (W 4)
(1 7)
H3 - H7
w7
w3
w1
w3
w2 - w1
Hs
Ws
-
H1
w1
H4 - H7
w4 - w7
H3
H2
(18)
H1
H1
( 19)
597. 3
1,0- SHF
(20)
If the state of supply air is known, the state of air entering the fan or leaving the reheater
When the volume of outdoor air and the latent heat load of the room are
be obtained by eq (14).
however, the air temperature at the outlet approaches the room air temperature; consequently,
In this case, the
air volume may increase and becomes greater than the specified air volume.
conditions must be modified and the calculations performed as in the non-reheat system.
5.
can
large,
the
room
Example of Computation
This program has been applied to the design of the equipment for a hotel, to be built in Tokyo.
The hotel is 47 stories high, has 3 stories underground, and has a gross floor area of 114, 600m2.
Thirty of the cooling zones are to be serviced
It has 44 cooling zones and about 330 types of rooms.
The other 14 zones will be serviced
by all-air systems, of which 18 will employ the reheat system.
by the primary air fan-coil system.
The input data to the program consist of about 2, 500 punch cards, mostly' for load calculations;
The computer calculathe data cards for the computation of designing the system number about 50.
tions take approximately 15 minutes.
The specifications of the air-handling apparatus and the psychrometric data are shown in Figure
5 as an example of the output. As can be seen from this example, the computation of psychrometric
data was sufficiently accurate as compared to the manual calculations using the psychrometric chart.
The manpower required to prepare the input data was approxim.ately 50 man-hours, or about the same
manpower required for the load calculations.
6.
Conclusion
The formulas and the procedure for supply air volume computation and the psychrometric analysis can be applied to the computer design of not only a single-duct system but also a dual-duct system but also a dual-duct system or a primary air-handling apparatus of the water system,
The advantages of using the Automated Design Program are as follows:
• Great amounts of design labor and time can be saved, and engineers
can promptly follow up on any change in the architectural design.
1
e The discrepancies arising from the designers experience and personality can be eliminated, and even inexp~rienced designers can obtain
the same results with equal safety and accuracy.
• Comparative studies of computations with alternative design factors
are easy, thus an optimum design can be achieved.
We express our deepest gratitude to the staffs of the Kajima Corporation Designing Department
and the Kajima Institute of Construction Technology for their assistance in developing this program.
583
7.
(1)
(2)
References
ASHRAE, The Task Group on Energy
Requirements for Heating and Cooling,
Proposed Procedure for Determining
Heating and Cooling Loads for Energy
Calculations (1968).
(3)
Uchida, H., Moist Air and Cooling Tower,
Syokabo, Tokyo (1965).
(4)
Carrier Air Conditioning Company,
Handbook of Air Conditioning System
Design, McGraw-Hill (1965).
ASHRAE, Handbook of Fundamentals (1967).
8.
Notation
Letter symbols used in this paper are defined as follows:
AQ
c
DB
DP
FTD
H
HS
H95
H85
OAQ
PT
PW
PWS
QT
RH
SHF
T
TS
w
WB
Supply air volume (m 3/hr)
Enthalpy-humidity difference ratio, b. HI t:.. W (kcal/kg)
Dry-bulb temperature (°C)
Dew-point temperature (°C)
Temperature rise caused by fan load (°C)
Enthalpy of moist air (kcal/kg)
Enthalpy of moisture saturated air (kcal/kg)
Enthalpy of 95o/o relative humidity air {l;;;:cal/kg)
Enthalpy of 85o/o relative humidity air (kcal/kg)
Outdoor air volume (m3/hr)
Fan total pressure (mmAq)
Partial pressure of water vaper in moist air (mmHg)
Partial pressure of water vaper in moisture saturated air (mmHg)
Total heat load of room (kcal/hr)
Relative humidity (o/o)
Sensible heat factor (non-dimension)
Absolute temperature (°K)
Absolute temperature, 373. 16 (°K)
Humidity ratio of moist air (kg/kg of dry air)
Wet-bulb temperature (°C)
Subscript symbols are used as follows:
1.
2.
3.
4.
5.
6.
7.
refers
refers
refers
refers
refers
refers
refers
to
to
to
to
to
to
to
room design condition
outdoor design condition
condition of air entering coil
condition of air entering reheater
condition Of air entering fan
condition of supply air
apparatus dewpoint
584
, _________ i __________ l
:
:
RESULTS OBTAINED FROM MAIN
:
PROGRAM
I
~---------------------~
YES
COMPUTE
STATE OF AIR ENTERING COIL,
COMPUTE
REHEAT-COIL, FAN AND ROOM,
STATE OF AIR ENTERING AND
AND SUPPLY AIR VOLUME
LEAVING COIL, APPARATUS
DEW POINT AND SUPPLY AIR
VOLUME
"'
"'"'
NO
YES
MODIFY THE SUPPLY AIR
YES
TEMPERATURE
NO
MODIFY THE ROOM DESIGN
,---------~---------,
CONDITIONS
:
I
I
,----------~----------1
:
RETURN TO MAIN PROGRAM
I
:
AND REPEAT LOAD
:
:
CALCULATION
:
RETURN TO MAIN PROGRAM
:
I
I
L--------------------~
*A. D.P. :APPARATUS DEW POINT
L---------------------~
Fig. 1
Generalized Flow Chart of Supply Air Volume Calculation Subprogram.
1, 1 1
ROOM DESIGN CONDITION
2
OUTDOOR DESIGN CONDITION
3, 3 1
5, 5
1
ENTERING COIL
ENTERING FAN
2
6, 6 1
ENTERING ROOM
7, 7 1
APPARATUS DEW POINT
8
SPECIFIED APPARATUS DEW POINT
9, gt
ROOM DEW POINT
7'
Fig. 2
Psychrometrie s of Non-Reheat System.
1
ROOM DESIGN CONDITION
2
OUTDOOR DESIGN CONDITION
3, 3'
ENTERING COIL
5, 5'
ENTERING FAN
6, 6'
ENTERING ROOM
7, 7'
APPARATUS DEW POINT
2
3'
3
Fig. 3
The Case where the State of Supply Air is Determined under the
Limited Condition of Minimum Air Volume.
586
1
ROOM DESIGN CONDITION
2
OUTDOOR DESIGN CONDITION
3, 3 1
ENTERING COIL
4, 4 1
ENTERING REHEATER
5, 5 1
ENTERING FAN
6, 6 1
ENTERING ROOM
APPARATUS DEW POINT
7
2
3'
1
Fig. 4
Psychrometries of Reheat System.
587
~H~
S_f'_§_CL_F I CAl JON_ Q_F Alk HANDLING UN_IT
.i:!l N_~ _t:J ~'
*
U-Nil
_ . iC
__r,U!;_I RJl.L Hl'.IE_ R____ _
~lZE:
NU.
* _FJ~N
<>
9
. -NO.
*
HEAl lc'G COIL
*
F'Ut-1I DH-fE-K
p,
3· 5_ MM___ <_ 20 TU8ES/ROW
F :p; -:r. U
MM-
SIEAM GRID
"''"
'"
**
-·7oo·o. CM/H
•
tfO. --MM-Ao·--
~~
3~-75-Kw-·
~~
*
CO-dLit-.JG- COIL
F•
l~
_-'~-l~ .!1:~"-~-?. J.NG_L~-- JLV_C. "L_$..~J-~----------- _______ ·- --· ----~ ~--·----··
AIR FILTEH
.. RGLT..
20 TU8ES/ROW
<>
29,
*
tk?Q.~ _M~----- _!<____ --~_8_Q_~_S_(.$__)____ "~-- __1.
1'150·~--
*
-MM . ---~;--
1:Rows
0
i-
KG/h
0 ;9 SM-
<>
* .
o:·2· ·K"w·
*
SYSTEM DESIGN DATA
*
PSYCHR[1M~TRIC
1 Rl,U~ lJFS I GN
2
0L:1 DOUR
3 E-t-.:Tt-Rn;G ·cn-lL
4
E~,--IE.RlNG
~AI'~
-s -uc.:Tu:r· . --. --- . -·*
( COULl NG
UAIA
HEAT Sl.URCE DATA
D8
-HT<
26.0
33.6
O.Q1U4SI
O.Ql/j4Q
30.6
14.5
·-------------1?-:--9--
--CAPAC tTY ·
(KCAL/H}
Cl.'UL TI''!G (;U! L
Ht-AT1NC-· CU-IL,
!---ILMIDIF-IFR
62664.
b4d29.
18Y34,
)
--- Er,r-fl·
12:63
19.33
0.01529
10.09
O.OOY5.:.i
9.23
·-----·--9-::;s-
vor.::
(l/MTI\')
20 n.
zc- :s -
STEAM PRES-s.
<KG[SCM)
--
11.5
125.3
29.1
Fig. 5
24.o
-2.9
2 OUTDOOR
-3 ENTeRING GO]L
4 ENT. HUMIDIFIER
f.7
------5 -oufu'T ____ - ------4b.u ·
WATE-R YEMf;:-·---5-fHM il.
(KG/H)
TNLET
OUTL~-L
-
6.3
- Lli'l ------,Hi- -
i- R66KDEs!GN
-~-o-;--o·rJ953
---wAT~R
< HEATING
--or·- -- --------
Example of the Output.
2. 0 0
0.35
·-
39.0
------
----"
)
ENfH
10.26
0.26
U,0123B9
4.18
0. 0 u 3~__9_ --- 1,1._99
a:uo?40
14.16
O.OU74Q
o.oo16o