Refrigerant Distribution Model Development
by
Sheit Sheng Chen
B. S. in Mechanical Engineering
University of Texas at Austin, 1993
Submitted to the Department of Mechanical Engineering
in partial fulfillment of the requirements for the degree of
Master of Science in Mechanical Engineering
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
June 1995
© Massachusetts Institute of Technology, 1995. All Rights Reserved.
Author..................................
'Dpr'eio
"ehnca"niern
a.......1 .................................................
ent of Mechanical Engineering
AtoDea
May 12, 1995
Certified by .............................
1...;'.
....
'.....-/./
Professor Peter Griffith
Department of Mechanical Engineering
Thesis Supervisor
. ................... ...
Professor Ain A. Sonin
Chairman, Departmental Committee on Graduate Students
Department of Mechanical Engineering
Accepted by ..........................................
;ASSACHUSETTS INSTITUTE
OF TECHNOLOGY
AUG 311995
LIBRARIES
k 'tCEft
Refrigerant Distribution Model Development
by
Sheit Sheng Chen
Submitted to the Department of Mechanical Engineering on May
12, 1995, in partial fulfillment of the requirements for the degree of
Master of Science in Mechanical Engineering
Abstract
The objectives of this research were to evaluate the performance of the evaporator distributors and to construct an analytical model to predict the flow distribution. An experimental
apparatus that provided design and off-design conditions for the refrigerant was used to
test the distributors. The factors examined included distributor mounting orientation, load
conditions, refrigerant degree subcooling, and feeder tube lengths. A refrigerant flow
model was constructed based on Baroczy two-phase flow model and fundamental fluid
mechanics theory. Algorithms were developed to implement the model. A series of experiments were run to measure the distributors' performance and to validate the model.
The distributors tested were found to give rather uniform distribution with deviation from
the mean less than 10%. The model developed successfully predicted the flow distribution
when the distributors were subject to a variety of conditions. The model is valid as long as
the flow does not choke in the feeder tubes. The feeder tube length was found to be an
effective parameter to control the flow distribution. The distributor mounting orientation,
load conditions, and refrigerant degree subcooling did not affect the flow distribution for
the range of conditions tested.
Thesis Supervisor: Professor Peter Griffith
Title: Professor, Department of Mechanical Engineering
Acknowledgments
I would like to thank my advisor, Professor Peter Griffith, for his guidance, support,
kindness, and enthusiasm throughout the course of this research. Without his help and
patience, this thesis would not have been possible. I must say I have gained a tremendous
amount of knowledge from his teachings, especially in his simple, yet effective, empirical
approach, and great engineering intuition and insight. It has been a truly rewarding learning experience.
I would also like to thank the Carrier Corporation for funding this research. My special
thanks go to Professor Gerald Wilson for bringing this research to MIT and to the rest of
the faculty and staff members in the MIT-Carrier research group.
I am indebted to some of the finest technical people in the department: Mr. Anthony
(Tiny) Caloggero, Mr. Norman Berube, Mr. Robert Nuttall, Mr. Norman MacAskill, and
Dr. Wayne Bidstrup. Their invaluable technical assistance, friendliness, willingness to
help, and warm spirits have helped me to complete apparatus modification, debugging,
and experiments. Thanks also go to Mike Demaree for his advice and help in dealing with
the refrigerant.
I would also like to extend my appreciation to all my teachers at the University of
Texas at Austin and at the Massachusetts Institute of Technology. I am grateful for their
teaching.
Many thanks to the gang in the Heat Transfer Lab: Aaron Flores, Marc Hodes, James
Moran, Dominic Napolitano, Peter Noymer, Andreas Pfahnl, Tolga Ozgen, and Tad Snow
for the laughter, support, and friendship.
I must offer my gratitude to Professor Thomas Sheridan for funding my first research
project in MIT. My appreciation also goes to the gang in the Human-Machine System Lab.
I would also like to thank Ms. Leslie Regan for her friendliness and administrative help.
Finally, I want to thank my parents -- Yew Yang Chen and Chiou Fang Cheong for
years of unconditional love and support. This thesis is dedicated to them.
3
To my parents.
4
Table of Contents
1 Introduction ...............................................................................................................
10
1.1 Problem statement.............................................................................................10
1.2 Background ....................................................................................................... 10
1.3 Objectives ......................................................................................................... 12
1.4 Approaches ....................................................................................................... 13
2 Experimental Apparatus and Testing Procedures ..................................................... 17
2.1 Reservoir........................................................................................................... 17
2.2 Main vessel ....................................................................................................... 21
2.3 Data acquisition system and pressure transducers............................................25
3 Mounting Orientation Test........................................................................................ 26
3.1 Test (set 1) ........................................................................................................ 27
3.2 Test (set 2) ........................................................................................................ 29
3.3 Test conclusion ................................................................................................. 29
4 Flow Regime Map Analysis ..................................................................................... 31
4.1 Critical flow ...................................................................................................... 31
4.2 Taitel-Dukler flow regime maps ....................................................................... 32
5 Model Development ................................................................................................. 37
5.1 Formulation....................................................................................................... 37
5.2 Lim itations ........................................................................................................ 41
6 Experiments and Results ........................................................................................... 44
6.1 Test m atrix........................................................................................................44
6.2 Data and results.................................................................................................47
7 Analysis .................................................................................................................... 50
7.1 Flow distribution...............................................................................................50
7.2 Mass flow rate ................................................................................................... 64
7.3 Pressure drops across the throttle and feeder tubes ......................................... 65
8 Conclusions............................................................................................................... 68
References .................................................................................................................. 70
Appendix A................................................................................................................... 71
Appendix B................................................................................................................... 73
Appendix C ................................................................................................................... 79
Appendix D................................................................................................................... 81
Appendix E ................................................................................................................... 83
Appendix F ................................................................................................................... 86
Appendix G................................................................................................................... 134
Appendix H................................................................................................................... 135
Appendix I ....................................................................................................................
Appendix J ....................................................................................................................
137
138
Appendix K................................................................................................................... 151
5
List of Figures
Figure 1.1: Air conditioner system based on vapor compression cycle schematic ....... 10
Figure 1.2: Thermal expansion valve, distributor, throttle, and feeder tubes ................ 11
Figure 1.3: Type I distributor.........................................................................................15
Figure 1.4: A cut-out view of a Type I distributor......................................................... 15
Figure 1.5: Type II distributor.......................................................................................16
Figure 1.6: A cut-out view of a Type II distributor ....................................................... 16
Figure 2.1: Schematic of the experimental apparatus.................................................... 18
Figure 2.2: Apparatus picture; The meter ruler placed on top of the main vessel
is to show the scale of the apparutus. The vessel with a gage pressure meter
on is the reservoir. To the left of the reservoir is the condensing tower. Two
compressed nitrogen cylinders can also be seen...................................................... 19
Figure 2.3: Apparatus picture; Two sight windows can be seen on the cover of the
main vessel. The key below the windows is used to drain the refrigerant from
the measurement glasses after flow distribution measurement. The wire leading
out from the cover provides the electricity to the light bulb in the main vessel.....20
Figure 2.4: The amount of liquid refrigerant collected in the glass containers indicate
the performance of the distributor..........................................................................22
Figure 2.5: Measurement glasses, turn-table and a verticallly mounted type II
distributor.................................................................................................................23
Figure 2.6: Measurement glasses, turn-table and a verticallly mounted type I
distributor. Only 5 of the measurement glasses on this turn-table were used ......... 23
Figure 2.7: Pressure transducer no. 3 (center) and no. 4................................................ 24
Figure 3.1: Schematic of experiment setup with distributor mounted horizontally
(feeder tubes coming out from the distributor are not shown) ................................ 26
Figure 3.2: Distributor hole orientation (with the direction of gravity indicated)
for 1st set of experimental runs................................................................................ 27
Figure 3.3: Schematic of experiment setup with distributor mounted horizontally
after 90 degree turn (feeder tubes coming out from the distributor are not shown). 28
Figure 3.4: Schematic of experiment setup with distributor mounted horizontally after
180 degree turn (feeder tubes coming out from the distributor are not shown) .... 28
Figure 3.5: Normalized refrigerant distribution with distributor hole orientation shown
in Figure 3.2 .............................................................................................................
29
Figure 3.6: Distributor hole orientation (with the direction of gravity indicated) for
2nd set of experimental runs.................................................................................... 30
Figure 3.7: Normalized refrigerant distribution with distributor hole orientation
shown in Figure 3.6 .................................................................................................
30
Figure 4.1: Flow regime map for horizontal flow with P= 140.37 psia, T=72 °F, and
D=0.00549 m (stagnation conditions: T o = 95 °F, Po = 240 psia); The
crossed-out area indicates the flow operating region............................................... 33
Figure 4.2: Flow regime map for vertically downward flow with P=140.37 psia,
T=72 °F, and D=0.00549 m (stagnation conditions: To = 95 °F, Po = 240 psia);
The crossed-out area indicates the flow operating region....................................... 33
Figure 4.3: Flow regime map for vertically downward flow with P=129.94 psia,
6
T=67 OF,and D=0.00549 m (stagnation conditions: T o = 85 F, Po = 240 psia);
The crossed-out area indicates the flow operating region ....................................... 35
Figure 4.4: Flow regime map for vertically downward flow with P=140.37 psia,
T=72 F, and D=0.00248 m (stagnation conditions: T o = 95 F, Po = 240 psia);
The crossed-out area indicates the flow operating region ....................................... 36
Figure 4.5: Flow regime map for horizontal flow with P=140.37 psia, T=72 OF,and
D=0.00248 m (stagnation conditions: To = 95 OF,Po = 240 psia); The crossed-out
area indicates the flow operating region..................................................................36
Figure 5.1: Cross-sectional view of a distributor (Type II) assembly........................... 37
Figure 5.2: Feeder tube inlet plenum and the sector division........................................ 38
Figure 5.3: A feeder tube inlet plenum with a set of feeder tubes................................. 42
Figure 5.4: A feeder tube inlet plenum with the same set of feeder tubes as shown
in Figure 5.3, but with different arrangement......................................................... 43
Figure 7.1: Experimental and model flow distribution results for E4-1........................ 50
Figure 7.2: Experimental and model flow distribution results for E4-2 ........................ 51
Figure 7.3: Experimental and model flow distribution results for E4-3........................ 51
Figure 7.4: Experimental and model flow distribution results for E4-4 ........................ 52
Figure 7.5: Experimental and model flow distribution results for E4-5........................ 52
Figure 7.6: Experimental and model flow distribution results for E4-6 ........................ 53
Figure 7.7: Experimental and model flow distribution results for E5-2 ........................ 53
Figure 7.8: Experimental and model flow distribution results for ES-4........................ 54
Figure 7.9: Experimental and model flow distribution results for E6-1........................ 54
Figure 7.10: Experimental and model flow distribution results for E6-5 ...................... 55
Figure 7.11: Experimental and model flow distribution results for E7-1...................... 55
Figure 7.12: Experimental and model flow distribution results for E7-4...................... 56
Figure 7.13: Experimental flow distribution results with the same throttle size
(Dt = 0.080 in) but different stagnation conditions ................................................. 57
Figure 7.14: Experimental flow distribution results with the same throttle size
(Dt = 0.052 in) but different stagnation conditions ................................................. 58
Figure 7.15: Model flow distribution results with the same throttle size (Dt = 0.080 in)
but different stagnation conditions.......................................................................... 58
Figure 7.16: Model flow distribution results with the same throttle size (Dt = 0.052 in)
but different stagnation conditions..........................................................................59
Figure 7.17: The experimental flow distribution results for two runs with similar
stagnation conditions but different mass flow rates................................................. 60
Figure 7.18: The model flow distribution results for two runs with similar stagnation
conditions but different mass flow rates..................................................................60
Figure 7.19: The experimental flow distribution results for E5-2 and ES-4 .................. 61
Figure 7.20: The experimental flow distribution results for E6-1 and E6-5 .................. 61
Figure 7.21: The experimental flow distribution results for E7-1 and E7-4 .................. 62
Figure 7.22: The model flow distribution results for ES-2 and E5-4 ............................ 62
Figure 7.23: The model flow distribution results for E6-1 and E6-5 ............................ 63
Figure 7.24: The model flow distribution results for E7-1 and E7-4 ............................ 63
Figure 7.25: Mass flow rates determined by stop watch measurement vs. mass flow
rates from reservoir hydrostatic pressure change measurement .............................. 64
Figure 7.26: Mass flow rates predicted by Henry-Fauske's model vs. mass flow rate
7
determined by stop watch measurement..................................................................65
Figure 7.27: Model predicted and measured pressure drop across the throttle............. 66
Figure 7.28: Model predicted and measured pressure drop across the feeder tubes...... 66
8
List of Tables
Table 6.1: Test matrix....................................................................................................45
Table 6.2: Feeder tube configuration.............................................................................46
Table 6.3: Mass flow rates in experiments .................................................................... 49
9
Chapter 1
Introduction
1.1 Problem statement
Carrier Corporation, a leading manufacturer of air conditioners, sponsored my
research project for the study of refrigerant flow distribution in air conditioners. The
research was motivated when Carrier found that the air that flowed through the evaporator
was not uniform in temperature when exiting the evaporator surface. The non-uniformity
of temperature indicated that the refrigerants in some of the evaporator circuits did not
remove the heat from the air effectively, resulting in a loss of efficiency in air conditioners.
The refrigerant flow distribution upstream to the evaporator was suspected to be the cause.
1.2 Background
The most common method of refrigeration in domestic air conditioner systems is a
vapor compression cycle (Howell, 1987). As shown in Figure 1.1, such a system consists
of four major components: evaporator, compressor, condensor, and throttling valve. The
throttling
valve
compressor
Figure 1.1: Air conditioner system based on vapor compression cycle schematic.
10
refrigerant, which is the fluid flowing throughout the system, serves as the heat transfer
medium. The refrigerant enters the evaporator circuits at a temperature below room temperature. The heat of the air passing through the evaporator circuits is transferred to the
refrigerant. The compressor then compresses the refrigerant to a high temperature and
pressure. At the condensor, heat is transferred from the refrigerant to the outdoor air that
flows past the condensor circuits. The refrigerant then flows through the throttling valve.
The refrigerant undergoes a sharp drop in pressure at the throttling process and its temperature drops back below room temperature. The refrigerant enters the evaporator again and
this completes the cycle. Heat generated by humans, lights, and other equipment inside a
building is thus continuously transferred to the refrigerant at the evaporator and carried by
the refrigerant to the condensor where the heat is transferred outdoors.
As shown in Figure 1.2, the throttling valve consists of some or all of the following
devices: thermal expansion valve (TXV), distributor, throttle, and feeder tubes. The TXV
_
ofl
to evaporator
circuits
from condensor
expansion
valve
Figure 1.2: Thermal expansion valve, distributor, throttle, and feeder tubes.
modulates the flow rate of the refrigerant. The distributor houses the throttle and distributes the refrigerant into the feeder tubes. Each feeder tube is connected to the corresponding circuit in evaporator.
11
At the exit of the condensor, the refrigerant is in a subcooled state. After flowing
through the throttle at the distributor, the refrigerant flashes and forms a two-phase flow.
Because heat is mainly picked up by the refrigerant in liquid form at the evaporator, it is
important that the two phases are distributed in the same ratio in each feeder tube that is
subsequently connected to the evaporator circuit. If an evaporator circuit contains mostly
the vapor refrigerant, only a small amount of heat is transferred from the air to this particular circuit. On the other hand, those circuits that carry more liquid refrigerant will have
some of the refrigerant leaving the circuits still in liquid form, without making full use of
its heat-absorbing capacity. This results in low efficiency at the evaporator. It was believed
that bad refrigerant flow distribution was the cause for the problem in Carrier.
1.3 Objectives
The focus of this research is on how the distributor, throttle, and feeder tubes affect the
refrigerant flow distribution. The objectives are to determine the performance of the distributor under real operating environments and to develop an analytical model that can be
used to evaluate the performance of a distributor system under a variety of conditions or to
give a non-uniform distribution by choice. In addition, this research intends to provide
some guidelines to the design engineers what to watch out for in the distributor system
design.
Two versions of distributors were provided by Carrier for study. The first type (part
number: 314947-315) shown in Figure 1.3 and 1.4, as is called type I in this thesis, is a
distributor with nozzle orifice at the inlet. The outlets are five drilled holes that receive
capillary tubes (feeder tubes) connected to the evaporator circuits. Figure 1.5 and 1.6 show
Type II distributors (part number: 319072-404). It has a movable piston (throttle) and the
distributor can function both in refrigeration and heat pump cycle. The refrigerant flows
12
through the throttle and makes a 90° turn into the plenum before exiting the distributor
through the feeder tubes.
1.4 Approaches
To test the distributors under real operating conditions, an experimental apparatus was
designed and built. The apparatus provides the design and off-design conditions at the
condensor exit and evaporator inlet of an air conditioner. In addition to refrigerant conditions, other variables such as the distributor mounting orientations, load conditions (i.e.
refrigerant flow rate), and feeder tube's length to diameter ratios (L/D) were looked into.
Since the heat is mainly carried away by liquid phase refrigerant, a flow measurement
technique to determine the amount of liquid phase distributed to each feeder tube was
developed. Sets of experiments were run to evaluate the distributor performance. As specified by the sponsor, R-22 was selected as the working refrigerant for this research.
The analytical model development began with a two-phase flow regime analysis. The
model was constructed on an existing two-phase flow model and fundamental fluid
mechanics theory. Although the model was developed based on the geometry of Type II
distributor, the methodology and concept of the model development was applicable to distributors of other designs.
Chapter 2 gives a discussion of the testing procedures and experimental apparatus
used in this research. In Chapter 3, I present the findings of the effects of mounting orientation on the distributor performance. Chapter 4 covers the flow regime map analysis. The
development and formulation of the flow distribution model are described in Chapter 5.
Chapter 6 discusses the test matrix to study the variables believed to affect the distributor
performance and to evaluate the flow distribution model. Chapter 7 gives an in-depth analysis of the results of the experiments and makes comparison between the measured and
13
model predicted values. Chapter 8 gives conclusions and recommendations resulting from
the research. Appendix A explains the nomenclature in this thesis. The contents of Appendices B through K are referred from the text in the chapters.
14
I
I
,'-- -:-II F-":"
el
I,-'N
a
.. -,-",f
I .1t, " W-4"
Figure 1.3.- Type I Distributor
-
1-I-LIL-Qul
vew of a Type l distributor.
15
Figure 1.5: Type II distributor.
Figure 1.6: A cut-out view of a Type II distributor.
16
Chapter 2
Experimental Apparatus and Testing Procedures
Heather Smith, who previously worked on this project, designed and built the apparatus (1993). Since then, I have modified the set-up and added instrumentation. Figure 3.1
shows the apparatus's schematic. Two pictures of the apparatus are shown in Figure 3.2
and 3.3. There are three major elements in the apparatus.
2.1 Reservoir
The purpose of the reservoir is to store the refrigerant and to provide the refrigerant
with conditions that are at the condensor outlet in air conditioners. Once the refrigerant
has been charged into the reservoir through valves number (no.) 1, 11, and 13 from a
refrigerant supply, the temperature of the refrigerant can be controlled by adjusting the
mixing of cold water and steam into the coils inside the reservoir. A thermocouple is
mounted in the reservoir to show its temperature.
To create a subcooled state in the reservoir, compressed nitrogen is fed through a pressure regulator into the reservoir to exert extra pressure on the refrigerant. The reservoir
remains connected to the nitrogen supply during the experiment. If the reservoir is overpressurized, the nitrogen can be bled off by opening valve no. 3. In nominal operating conditions, the temperature and pressure of the reservoir is 95°F and 240 psia, respectively.
Pressure transducer no. 1 measures the gage pressure of the reservoir. Pressure transducer no. 2 is a differential pressure transducer. It measures the hydrostatic pressure
change of the liquid refrigerant in the reservoir. The measurement can be used to calculate
the refrigerant mass flow rate when the refrigerant is flowing out of the reservoir. The
17
-v
0
0
0
0
'A0
As
0
0
Abb~0
C4
-a~~~~~~~~~~~~~ t-o
:z
0C
1
0Q
**)
t
e_
0~~
C.
0
tb
.0
d0
0
18
Figure 2.2: Apparatus picture; The meter ruler placed on top of the main vessel is to show
the scale of the apparutus. The vessel with a gage pressure meter on is the reservoir. To
the left of the reservoir is the condensing tower. Two compressed nitrogen cylinders can
atlsob)c Sccl,
l(
Figure 2.3: Apparatus picture; Two sight windows can be seen on the cover of the main
vessel. The key below the windows is used to drain the refrigerant from the measur-emcnt
glasses after flow distribution measu-rementC. Thecwire leading out from the cover provides
the electricity to the light hulh in the main vessel.
copper tube which comes out from the top of reservoir and, on the other end, connected to
pressure transducer no. 2 is wrapped with heating tape. The heating tape is turned on during the experiment so that the refrigerant vapor in this tube segment will not condense and
make the pressure transducer no. 2 measurement ambiguous.
In addition, there is a sight glass on the side of the reservoir to indicate the liquid
refrigerant level. The average of the mass flow rate can be obtained by timing the liquid
level drop at the sight glass.
2.2 Main vessel
During experiments, the main vessel is filled with refrigerant vapor or a mixture of
nitrogen and refrigerant vapor to simulate the inlet conditions of the evaporators. When
valve no. 8 is opened (with valve no. 9 closed), the subcooled refrigerant from the reservoir flows into the main vessel and through the approach pipe and distributor. As shown in
Figure 2.4, each feeder tube coming out from the distributor is channeled into a measurement glass, respectively. By comparing the amount of liquid phase refrigerant flown
through each feeder tube, how well the distributor system distributes the refrigerant can be
determined. This is the technique used in this research to evaluate the performance of the
distributors. If the liquid levels in the measurement glasses are uniform, it indicates a good
flow distribution because the liquid to vapor ratio in all the feeder tubes are about the
same. By turning horizontally the turn-table that supports the measurement glasses, each
measurement glass can be observed and the liquid level recorded through the sight windows on the cover of the main vessel. Figure 2.5 and 2.6 show two pictures of the measurement glasses and turn-table.
If valves no. 9 and 10 are open (with valve no. 8 closed), the subcooled refrigerant
flows through the distributor and feeder tubes which are outside before entering the main
21
vessel. The pressure transducer no. 3 measures the pressure drop across the throttle while
the no. 4 reads the pressure drop across the feeder tubes (see Figure 2.7). These
pressure drop test measurements are used to help evaluate the flow distribution model
developed later in this thesis.
refrigerant
glass
container
JU J ^vIUl~~I~
Figure 2.4: The amount of liquid refrigerant collected in the glass containers indicate the
performance of the distributor.
A condensing tower is connected to the main vessel. Ice water circulating inside the
condensing tower condenses the refrigerant vapor in the tower and the liquid refrigerant
flows back to the main vessel. However, R-22 vapor requires much lower temperature to
be effectively condensed and retrieved, the condensing tower was therefore not used in the
experiments in this project. After each run of experiments, a refrigerant recovery and recycle unit was used instead to recover the refrigerant from the main vessel and charge it back
22
Figure 2.5: Measuremlent glasses, turnL-table and a verticallly
mounted
type II distributor.
Figure 2.6: MeasuLrement glasses, turnsable and at verticallly mIounLtedtype I distributor.
ilasses on his turLn-table were used.
Only 5 of te measurenit
Figure 2.7: Pressure transdlulcer no. 3 (center) and no. 4
2.I
to the reservoir.
The distributor can be mounted with different orientations in the main vessel to study
the effect of orientation on flow distribution. The distributor (Type II) can house various
sizes of throttles. The throttle size can be used to control the total refrigerant flow rate
through the throttle to provide different load conditions. In addition, the feeder tubes can
be cut into different lengths in order to get the desired L/D ratios.
2.3 Data acquisition system and pressure transducers
The pressure transducers no. 1 and 5 are strain-gage pressure transducers each with a
range of 300 psig. The no. 2, 3, and 4 are variable-reluctance
differential pressure trans-
ducers with ranges of 0.5, 200, and 32 psi, respectively. All of the five pressure transduc-
ers along with the K-typed thermocouple in the reservoir are connected to a Dash-16 data
acquisition board. In addition, a cold junction temperature is measured as a reference to
the thermocouple. There are a total of 7 measurements taken and 7 channels used.
Throughout
all the experiments in this research when the data acquisition system was
used, the scanning sampling rate was set to 250Hz. Therefore, the interval between readings was 0.028 seconds for each channel.
25
Chapter 3
Mounting Orientation Test
Before evaluating the distributors for mounting orientation effects, some preliminary
tests with a Type I distributor were performed to determine if the flow measurement technique concept was capable of indicating the distributor's distribution performance. As
described in Appendix B, the apparatus gave consistent and reliable measurements on the
flow distribution. The preliminary tests also showed that the type I distributor gave rather
uniform distribution with deviation less than 10% from the mean.
To study the effects of mounting orientation, I mounted a type II distributor horizontally (see Figure 3.1). This is the orientation for which I would expect to see the worst
maldistribution if it were due to the formation of stratified flow in the distributor. Each of
the feeder tubes was 20.5 in. (0.5207 m) long and the R-22 was conditioned to 95°F and
240 psia in the reservoir before the experiments began. Two sets of experiments were run.
refrigerant
,.
s
onnector
distributor
a1zuzt apIUaW-
p,
Figure 3.1: Schematic of experiment setup with distributor mounted horizontally (feeder
tubes coming out from the distributor are not shown).
26
3.1 Test (set 1)
Figure 3.2 shows the relative locations of the distributor holes with respect to ground.
For the first two runs, the two approach pipes were arranged as that shown in Figure 3.1.
Figure 3.2: Distributor hole orientation (with the direction of gravity indicated) for 1st set
of experimental runs.
In the 3rd run, I turned the short approach pipe 90° in the horizontal plane to see if there
was bias by the approach pipe arrangement (see Figure 3.3). For the 4th run, as shown in
Figure 3.4, the short approach pipe was rotated 90° more so that it was right underneath
the long one. As shown in Figure 3.5, the flow distribution in all runs were consistent. The
flow distribution did not seem to be biased in any way by the approach pipe arrangement.
Feeder tubes "a" and "d" consistently received more liquid. The distribution pattern did
not indicate the formation of a stratified flow. If it had developed, the feeder tubes coming
out from the holes located lower down would have had passed more liquid.
27
refrigerant
f
1
2
connector
short approach pipe
UIStI IUUtLUI
Figure 3.3: Schematic of experiment setup with distributor mounted horizontally after 90
degree turn (feeder tubes coming out from the distributor are not shown).
refrigerant
$
,
.
.
g
connector
Ut1JIUUVI
--
,nt
i..,
.l.ulz
oh nn~.
Figure 3.4: Schematic of experiment setup with distributor mounted horizontally after
180 degree turn (feeder tubes coming out from the distributor are not shown).
28
I .Z
1.1
, 1.0
_
-
~
Ii
.-
7 0.9
H0.8
-0-
0.7
t0.6
d
st run
- - 2nd run
-&- 3rd run
0.5
< - 4th run
S 0.4
N
~0.3
0.2
Z0.1
I ITI
0.0
a
b
I
c
d
T
e
feeder tube
Figure 3.5: Normalized refrigerant distribution with distributor hole orientation shown in
Figure 3.2.
3.2 Test (set 2)
With the same experimental set-up, the same distributor and feeder tubes, but with the
distributor rotated (Figure 3.6 shows the new hole locations with respect to ground), I did
another 3 runs. The results are shown in Figure 3.7. Feeder tubes "a" and "d" once again
received the most liquid. The variation of liquid level for this set of runs was smaller but
the flow distribution pattern was essentially the same as that of 1st set of runs.
3.3 Test conclusion
Although the flow deviations among the feeder tubes for the distributor tested were as
high as 10% from the mean, the flow distribution was consistent between runs regardless
of the distributor hole orientation. The results indicate that the distributor non-uniformity,
rather than the mounting orientation, plays a role in flow distribution. A flow regime map
analysis, which is discussed in Chapter 4, can explain why a stratified flow was not formed
in the distributor for these 2 sets of test. In addition, a flow regime map can predict under
29
what operating conditions that the mounting orientation can be a significant factor for the
flow distribution.
a
g
Figure 3.6: Distributor hole orientation (with the direction of gravity indicated) for 2nd
set of experimental runs.
1.2
1.1
1.0
R0.9
30.8
-.-
0.7
&0.6
1st run
-0- 2nd run
0.5
--
'0.4
3rd run
N
' 0.3
00.2
Z0.1
0.0
I
a
I
b
I
d
I
c
I
e
feeder tube
Figure 3.7: Normalized refrigerant distribution with distributor hole orientation shown in
Figure 3.6.
30
Chapter 4
Flow Regime Map Analysis
In addition to predicting the effects of mounting orientation on flow distribution, a
flow regime map analysis can help select a suitable two-phase flow model for the basis of
the flow distribution model developed later in this thesis. The values of the mass flow rate,
quality, and thermal properties at the flow segment of interest need to be predicted in order
to construct and interpret the flow regime maps.
4.1 Critical flow
For the nominal operating conditions of air conditioners, when the pressures at the
condensor and evaporator are 240 psia and 90 psia, respectively, it is expected that the
flow through the throttle will be choked (critical flow). The mass flow rate will reach a
maximum value which depends on the fixed inlet conditions. The mass flux is called the
critical mass flux and the ratio of the throat pressure to the stagnation pressure is called the
critical pressure ratio (Whalley, 1987).
The best model for predicting the critical mass flux is Henry and Fauske's two-phase
critical flow model (Henry, 1971) (see Appendix C). The model can be applied to nozzle,
orifice, and short tube choked flow. To get the mass flow rate, I used the conditions at the
condensor exit as the stagnation conditions for the Henry and Fauske's model. Therefore,
To was 95 °F and Po was 240 psia. The iteration result showed that the critical mass flux
was 46.14 lbm/s/in2 , and it corresponded to a mass flow rate of 0.232 lbm/s for the distributor with throttle size of 0.08 inches. The critical pressure ratio was 0.72.
The next step was to iterate the refrigerant quality. Since I was mainly interested in the
flow regime after the throttle, I iterated the quality at the throttle discharge. Appendix D
31
shows the formulation for the quality iteration. The calculation also involves Baroczy's
model for two-phase flow pressure drop across a tube. The details of Baroczy's model is
discussed in Appendix E. For the quality calculation, I knew that the enthalpy did not
change during a throttling process. Therefore, I made a guess of the pressure at the throttle
discharge, and iterated the value until the guessed pressure drop across the feeder tubes
matched the one predicted by Baroczy's model. For mass flow rate of 0.232 lbm/s, the
quality at the throttle discharge was 8.76%. The saturated temperature and pressure were
72 °F and 140.37 psia.
4.2 Taitel-Dukler Flow Regime Maps
I used Marc Hodes' algorithm, which is based on the Taitel-Dukler model, to generate
the flow regime maps (Hodes, 1994; Taitel, 1990). Four flow regimes are defined in the
model. They are bubble, annular, intermittent, and stratified.
Figure 4.1 shows the flow regime map for the flow in a horizontally mounted type II
distributor for nominal operating conditions. The input diameter is 0.00549m (0.216 in),
which is the diameter of the throttle discharge. The 0 degree input for the angle of inclination indicates that it is a horizontal flow. The thermal property inputs correspond to the
conditions in the throttle discharge where the predicted saturated temperature and pressure
are 72 F and 140.37 psia. Figure 4.2 shows the flow regime map for a vertically downward flow of the same thermal conditions.
Once the mass flow rate,
, and the quality, x, at the throttle discharge were known, I
could calculate the gas superficial velocity, j,, and liquid superficial velocity, j, at the
throttle discharge. First, the mass flux, G, gas mass flux, Gg, and liquid mass flux, Gl, were
calculated by
32
Psat= 140.37psia,T = 72F
104
.
103 *
010
++
++
U
o
.
.
I
+
+
+
+
+
+
+
+ + +++
+ + ++-+
++ + +
++ ++
+
+ ++++
++++
X X XlX
000000
10
X
._,10
0o°
+ E
NE
. . . . . ..
.
. ..
.
.
. . . . .....,..
liquiddensity= 1204.6kg/m^3,liquidviscosity= 0.0002042N*s/m^2
vapordensity= 40.93 kg/mA3,
vaporviscosity= 0.0000132N*s/m^2
surfacetension= 0.00838N/m
+ bubble
diameter= 0.00549m
annular
o intermittent
angleof inclination= 0 degree
x
stratified
lo'
p
. . ..
X
++
++++ +
+ X.X..X,
+ +
+
+
+
+
+
+
+
+
.4 + + + +
+ + + + +
+ + + + +
+ + + + +
+ + + + +
+ + + + +
+ +++
+ + +
+ +N+00
+ + + + + + +.
+ + + + + + o
+ + + + + o o:
+ + + t 0 0 .
+ + + 0 0
+ + 0 0 WEN WE(
+ A+EANE+NEN
/
N
21
N
+ + + + + + + + + + +
+ + + + + + +00000
+
+ +
+
+000000+
+ + + + + + + + + + ~~~~+~~
~
+ + + +
W+
WW):
+000000
+ + + + + 000000
0 0 0 0 +~~~~~~
+ +O
+O
+NE
W+
WWW
O
(AM
ONE NEth<XX
xNEN.
O O O O O O 000000
NE
0 0 0 0 o o NE
NE
NE NE,NE NE
NEN )Kx
0000
x
v
X
X
XX X XXXX
6,
x,
O
O
O
O
O
X
~'10-
O
O
O
O
O
X
O
O
O
O
O
X
O
O
O
O
O
O
O
O
O
O
O
O
X X X X X
XXXXXX
X X X X X
'XXXXXX
XXXXXX
10-2
-3
A
iv
v
0 0 0 0 oX
00000
x x 0 x
00000
x x x x
x x x x
'XXXXXX XXXOXX
x x x x
X X X O X X
XXXXXX XXXXX
a
1l
3
10
0
x
x
x
x
O
O
O
O
O
O
w
w*v
NE 0NE NE NE
0
0NE 0X
_+~~~~~~
+ X
+ + NE
+ + NE
X
w
w
w*v
w
NE iNENE NE NE )K
NE )NE
K
X NE NE N NE WWW
NE N
N),K
w
NE N N N N N N
X X X
XXXXX
X X X
X
X
X
X
W NE
WK
WK
3W W
x)K O.3
X X X)KNE
X X X XX.XXX.,XENE..N.NENENN_
NENEN
XXXXX
X X
X W
X W
X
X NE
X NEN
X WK
)KXNE
)K
K
X
W W zW
W * W W xx
W x * )K:
X X X X1 X X
XXXXXNNEENNNEENN
N
X
NE N
X X X
X X X
X X
x
10-2
,6 )K
,& I
ME
W
10-'
100
Gas superficialvelocity[m/s]
)KW
W
o10'
W
102
Figure 4.1: Flow regime map for horizontal flow with P=140.37 psia, T=72 F, and
D=0.00549 m (stagnation conditions: To = 95 °F, Po= 240 psia); The crossed-out area indicates the flow operating region.
Psat= 140.37psia,T = 72F
q'
4 A
IlU
liquiddensity= 1204.6kg/mA3,liquidviscosity= 0.0002042N*s/m^2
vapordensity= 40.93kg/mA3,vaporviscosity= 0.0000132N*s/m^2
surfacetension= 0.00838N/m
+ bubble
diameter= 0.00549m
x annular
0
intermittent
angleof inclination= -90 degree
x stratified
103
r+ +
:_lo, + +
+ +
+ +
+ +
.?
1
+ +
0o 101
+ +
0
+
.0
75 102
+ + +
+ + +
+ + +
+ + +
+ + +
+ + +
+ + +
++ +
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
-++
+ +
+ +
+ +
+ +
+ +
+ +
+ +
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+++++++0+++
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+ +
+ +
+ +
+ +
+ +
+ +
+ +
+ YX
0 +N+E+EN
:O+++++++++o++++NE
+ + ~~~~
O+o o+ o+ + +
+0
;100
0
+
+
+
X00
x x 0..
NEEEENNNN
+
+
+
+
+
+
W,~
x
x
00x0
NEEN
+
+
+
+
+
0
W
W
+
+
+
+
+
+
+
+
+
+
+
+
+
0
+
+
+
+
+
0
0
+ + + +
+ + + 0
+ + 0 0
+ 0 0
0 0 E NE
0 K K K
E NENENE
NENX
EN
x
+ { NENENEN
!3
vx
W
x
x
xx,,
~
,
...x.,K
, NENENENENEx
XXX
0
xxx
N W
NEENN
xXx . ..
NENENENENENENENENENENENENENEx
Xx x
x
X
NE NE NE NE NE NE NE NE NE NE NE NE NE NE NE NE NE NE NE NE NE NE NE NE
NEEENN
NEEENNN NEEN
xXx
NEEEENNNN
xxX NENENEx
NENENENENENENENENENENENENENENENENENENENENENENENENE X
NE NE NE NE NE NE NE NE NE NE NE NE NE NE NE NE NE NE NE NE NE NE NE NE
10-2 *NE
NENENENENENENENENENENENENENE
NENE NENENENENENENENEN
NE NE NE NE NE NE NE NE NE NE NE NE NE NE NE NE NE NE NE NE NE NE NE NE NE
NENENENENENENENENENENENENENENENENENENENENENENENENE,,x
-3
1 2
-3
10
10-2
10-1
100
Gas superficialvelocity[m/s]
10o
102
Figure 4.2: Flow regime map for vertically downward flow with P= 140.37 psia, T=72 °F,
and D=0.00549 m (stagnation conditions: To = 95 °F,Po = 240 psia); The crossed-out area
indicates the flow operating region.
33
G
m
(4.1)
AT'
G = G.x
(4.2)
and G l = G' (1-x)
(4.3)
g
where AT is the cross-sectional area of the throttle discharge.
Next, the superficial velocities were obtained by
G
Jg
g
,
(4.4)
Pg
Gl
Pl
and
(4.5)
where p is the density.
The gas and liquid superficial velocities were 9.49 m/s and 3.36 m/s, respectively. An
operating region based on the flow rate and quality range of the experiments described in
Chapter 6 is shown in each flow regime map. As shown in Figure 4.1 and 4.2, the velocity
values indicate that the flow is in the high velocity intermittent flow regime. This flow
regime explains why the stratified flow was not formed in the orientation tests described in
Chapter 3. If the flow rate were substantially reduced and both the gas and liquid superfi-
cial velocities decreased, it would be possible for the flow regime to fall into the stratified
flow which would possibly cause non-uniform distribution if the distributor were oriented
horizontally.
34
To study if the flow regime maps are highly sensitive to the input parameters, I generated flow regime maps with different thermal properties, tube diameters, and angles of
inclination. Figure 4.3 shows the flow regime map with different thermal property inputs.
Figure 4.4 shows the flow regime map where the diameter is that of the feeder tube. In
Figure 4.5, the tube is horizontal with the feeder tube diameter. The maps show that the
flow regime boundaries vary negligibly as the input parameters change. Also note that
there is no stratified flow regime if the flow is vertical. For the operating conditions considered, Figure 4.2 and 4.4 show that there is no significant difference in the flow regime
maps for either the flow is in the throttle discharge or feeder tubes. It can be concluded that
the flow regime maps can indicate a flow's regime quite well given the flow's gas and liquid superficial velocities.
Psat= 129.94psia, T = 67F
i , ........ i........i...........
liquid density= 1217.3kg/mA^3,
liquidviscosity= 0.0002072N*s/m^2
vapordensity= 37.86kg/m^3,vaporviscosity= 0.0000130N*s/mA2
surfacetension= 0.00870N/m
++ bubble
bubble
diameter= 0.00549m
x annular
angle of inclination= -90 degree
0 intermittent
x stratified
103
+ + + + + + + + + +
++ ++ ++
++ +
+
+ ++
+ +
+ ++
+ ++
+ + ++ +
+ +
+++ +
+
+ + + + ++ + ++ ++
o 102
._Z
+ + +
++ ++ ++
++ +
++ +
+ + + + + + + + ++
+
++ ++
+ +++ + +00o
++
+
+ +
+ +
++ + +
+ +++OOO
++ ++ + +0+m00
'+ +++++++++++++++++ +000
'23101
oooo
la
.0
~
-~~~~4
........ i........
A^4
10
+
3W/
{
+W +W +W +W +W +W +W +W +W +W +W +W +W3W
+W
mW
1(3XW
3W13W
>5
mW3
3W(X
31E
+W +W +W +W +W +W +W OW OW OW OW OW OWOW O 3 3f X3( 3W2mW *1
OW.W
OW.W
OW.W
OW.W
OW.W
OW .W
OW.W
OW.W
OW.W
OW.W
OW.W
O .W
O .W
O .W
O .O 3. .X .m .X .m .3W2
. mW.XWX
- 1 -3
Z: 10
XW.3XW
X .X
X
. X3
XX 3.
W 3. 3.
.X .X 3.
. 3. .XW ..XW.ac
.XW X
X
_XW XW XWXW XW XWXW X X X 3
-3W
! ac
10- 2
* mK
4 1-3
X
I
X
X
3W X X
K X
I 3KKX,,X )K
-
l10
X
X
3.
.X
3X
.X
7W 3K m
X
X
W X
X
*,a,,as
10-2i
.X
.X
.X
B1X
W
W
X
X
),.,,X,1,)W
m
X. ..XW..XW.XW .mW.XW
3. ..X .X X
W
..3W(..3S
X 3W( X 32 3W mWXW 3W XW
.XM .
)X
X
X
X
X
X
)K
.
.
3..
XXXzX
1K K
3W
X
X
X
K
X
K
0
100
Gas superficialvelocity[m/s]
X
X
m
3W(WcWmWX
W
X
X
X
W X X
X
X
W .,*W|
m
X:
X 3W(
3.
3W
XW XW
3W1(5
K
lo1
m
mK 3K
X
XK
X
3
W
K W
X
9,*,,W,
X
102
Figure 4.3: Flow regime map for vertically downward flow with P=129.94 psia, T=67 °F,
and D=0.00549 m (stagnation conditions: To= 85 F, Po= 240 psia); The crossed-out area
indicates the flow operating region.
35
Psat= 140.37psia,T = 72F
0'
liquiddensity= 1204.6kg/mA3,
liquidviscosity= 0.0002042Ns/m^2
vapordensity= 40.93kg/m^3,vaporviscosity= 0.0000132N*s/m^2
surfacetension= 0.0083EKl./n
'"'
~ ~~"
+ bubble
diameter= 0.00248m
annular
o intermittent
angleof inclination= -90 degree
x stratified
10
m
++++
.+
++++
101
:+
+
o"
0
,01
++
+++
++++
++
+
+
+
+
+
.
.
.
+
.
.
.
+
+
+
+
+
+
+
.
.
+
+
+
+
+
.
.
+ + + + + + + + + + + + + + + +
+
++++++++
+++ +
++++
+ +++++++
+++ ++0 0
0
+ + + + + + + + + + + + 0 0
+++++++++++003k
+ +
+
+
+
+
', 10
+ j/
0
'~
z
3km
Yt~tA>
+++
+ + +/r 4vzrx#]a
*m m m
+ +++++
+ 3k
+ 3k
+, +
+ + ++
+ ++
+ .,.
+ + +
3kr3kr3gl
. ++
, .
.. ~ 3kzm
).,k
+ + 3k 3k 3k +
+ +
000
3k +k +k + +
0 3k
0 +k
0 +0 0+
3k
3k
Ok Ok
k Ok
k Ok
k Ok
k mk
k mk m
kXkXkWkXkXkXkXkX
3k mk mk mk mk m m
+ +k
+ +k
+ +k
+ ++ ++
3k k k k k kWkX k k kXkWkWkXkX
3k 3k + 3k +
++++
:_+
+3
.+
0
+3
+3
:_+
000000 000
o-'
+++++
4
A•A&&
m
Xs
m
-2
10
3k 3k W m mW
m
m
m
X
m
)K
YA
mK
0 0
3k wkk
_..._
-.....
...---
-.
-2
10
O
O
O
m
m
m
m
)KX
mktkXm
m
m
0
s
m
m
m
m
m
m
m
m
Xm
w
m
X
m
m
m
X
m
m
w
X
m
mmmmks m zc
m
mk
wk
w m
_ mk
w 3k
w 3_w
m
mk
m
w w w w w
m m m m m
wk
k w
w
3k m mw
kmkwkm
kwm m
^ mk
X mk
Wmkc
3k
mk
w mk
w ;s
w 3k
w mk
w m
w m
w m
w
m
m
m
m
m
w w w w w w w w
m m m m m m _ m
wk3 w k
w k 3k
w k3 w 3k
w
._._.-.--._...._..
-
3kWmk
m Kk
10- 3 - 3
10
O
3kmk~k
m
m
Xw
m
m km
ko
3C 3m
w
m
w
m
w
wk
m
wk
m
......................................
-
10
100
Gas superficialvelocity[m/s]
mw
w
m
w
102
o10
Figure 4.4: Flow regime map for vertically downward flow with P=140.37 psia, T=72 F,
and D=0.00248 m (stagnation conditions: T = 95 F, Po = 240 psia); The crossed-out area
indicates the flow operating region.
Psat= 140.37psia,T = 72F
4
10
........
......
3
...... ,..
++ +++
+++
+++++
++ +
+ + + + + ++ + + + + + + + + + ++
+
++
+
+++++
+
+ +
+ + + +++ +++++003'
+++ +++++
+ +
+
+
+
+
+
+
+
++
+ + 00+
+
+
++++
+
++++
+
+
+
+ +
+
+ +
+
+
+ .
.
+++ + + ++++ +
0+O+ o
+ .
.
+ + ++ ++ +
+00
)(XA'+*o3k
3k 3kK:
o~rlrir43k
++
++
+
+
+
+
+
+
D
0 3k 3k 3K W
+
+
+ .
.
.+ + + + + + + + + +
+ + 3k ,3k3k k 3
3k 3k 3k 38
p
-°
0 10
t:: 1o
.0i
000
o0o
000
00
000
000 00
00
oo
.U
aco
M
'CXXXXXXOO
X X X X X X
10
X X
X X
X X
X
X X
X
X
X
0 0
0X 0
0X X0 X0 0X
X
10-
XXXXXXXX
-xx
I n1-3
10
10
.
liquid density= 1204.6kg/m^3,
liquid viscosity= 0.0002042Ns/m^2
vapordensity= 40.93kg/m^3,
vaporviscosity= 0.0000132 N*s/m^2
surfacetension= 0.00838N/m
+ bubble
diameter= 0.00248m
3 annular
o
intermittent
angle of inclination= 0 degree
x stratified
o10 _
0102
........
xx
xx
xx
xx
x
X
xx
x
X
xx
x
x xx xx.X..x.,x.Xx
x
-3
Xx
x
x
..
-10-2
X
xx
x
Xx
x
x
x X Xx
X
o
X
o
X
o
++ F/460/X X)K:;1
k
+
O
+O JO.,/ y
O
O O
X X
X )K X
0
W
W
k3
o
0
o
o
X
o
X
o
X
o
o
0 3k 3 3k 3 3 3kX
3kX
3W
3k 3K 3k 3k 3K 3k 3K 3k 3K 3K 3K 3k
)K )KX 3k 3k X
3 X X X3 X
x X XX
X
o
X
3k 3
V
3K 3k
Wx
X )K
o
o
W
X
X
o
o
W
k XK
)k KX
3K
3k
W
W
Y yc K
X
W
K:
X
X
X
x
X
x
X
X
x
X
x
x
x
x
x
x
X-
X.,
X X
X X3
X X 3k )K X
X
3k
X
x X3
x XK
)X KX Xk
X
X
X X
X X
X X
X
xxx
x
xxx
x
xx
-
10 1
X..X. X X
3k
3k
X X
X
X X
X
.
K K KX 3k 3k
KX
k 3k X
k 3k
3
X 3k
X
W X
X
X X
)K K)K _
)K
X
. . X
X
X
W
)K
X W
... .... ......... ... - - . -_--
100
101
102
Gas superficialvelocity[m/s]
Figure 4.5: Flow regime map for horizontal flow with P= 140.37 psia, T=72 F, and
D=0.00248 m (stagnation conditions: To = 95 F, P = 240 psia); The crossed-out area indicates the flow operating region.
36
Chapter 5
Model Development
Since the predictions of the flow regimes in the throttle discharge indicate that they are
in a high velocity intermittent flow regime, a separated flow model like the Baroczy's
model is therefore appropriate.
5.1 Formulation
Figure 5.1 shows a cross-sectional view of the type II distributor assembly. The total
pressure drop from the discharge of the throttle to the discharge of the feeder tubes is the
same for each feeder tube path. The flow rates in the feeder tubes depend on the tube
section 2
n*
·_
I
·
.ction 4
LI
section 1
th
I
h
,.
-
~~w
-J
--
m
'lIP
f
II
1
L
'I
Figure 5.1: Cross-sectional view of a distributor (Type II) assembly.
37
lengths. If they are all of the same length, it can be expected, from symmetry, the same
flow rate in each tube and thus the same sector angle, Os', in the feeder tube inlet plenum
(The sector angles are shown in Figure 5.2 where a, b, c, d, and e denote each of the five
feeder tubes). A shorter feeder tube generates smaller back pressure at the feeder tube inlet
plenum sector and therefore tends to get higher flow rate as a result of the additional flow
from the adjoining tubes which have higher back pressure.
nl
t
__
a_
_
a
feeder tube b
feeder tube e
ler tube d
talo
inven
ILUV;L
LUU
t;
--
Figure 5.2: Feeder tube inlet plenum and the sector division.
The mass flow rate at section 1 of the sector is described as
rh = pV 1 0Rh,
(5.1)
and at section 2, the mass flow rate is
m = 2RfhpV
Equating (5.1) and (5.2),
38
2
(5.2)
VIORT
(5.3)
2iRf
v2-
The Bernoulli equation between sections 1 and 2 is
P - P2= 2P(2
- 1l)
2
(5.4)
Substitute (5.3) into (5.4),
P.P2
-2v
-Pp
{42142TV2)
(5.5)
At section 3, the mass flow rate is
m =
(5.6)
V3irR
equating (5.1) and (5.6),
VI ORTh
V3 =-
(5.7)
,xRf
The entrance loss equation at section 3 is
P2 - P3
=
KLlpiV 31 V3
(5.8)
Substituting (5.7) into (5.8),
Klv
P2 -P3
=
V 2Rh 2
2 4
KLP
R
R f2
39
(5.9)
Note that in equation (5.8) and (5.9), I use I1
V2
V instead of
in order to retain the sign
which indicates the flow direction and how the pressure changes. Applying Baroczy correlation to the feeder tubes,
P 3 -P 4 = f (R
) pI
2f2
(5.10)
V3i ' V3
Again, substitute (5.7) into (5.10),
P3
=P3 B
IV4I V 1 O2 R 2
~_R 1~P2
IC2Rf4
(5.11)
2
Combining (5.5), (5.9), and (5.11), I get a general equation:
V22
(Vl2R2
1
Pi- P4 =
P, 4
2
V2) + KL
2
R
p IV
V
2
R)
+fB(
R
2f
1
Vi I V1 02R Th2
2
2Rf4
(5.12)
Applying equation (5.12) to all the feeder tubes,
for tube "a",
Pi - P4
1
V2 02aR 2T
~PL
f
gI.t.
I VllVlO2R2h2
-Vj+K~~~~p
~lp
~2R
f
~La L
1
f
I VlI V, O2R2Th2
-P 2
(5.13)
2Rf4
for tube "b",
PV2 2l R 2
PP4 = 2PL4 nR2
f
v2
I
IVIIV- 02
VIKL
+ R
+
K
2h
bI'
T,-r
4
I2 Rf
2
for tube "c",
40
~
2
2
L
1
+f~b(Tgb) P
IV IVIo2R2h
bR
'
2
(5.14)
2c 2X2
P1P4
2
IVIO
2P. 4c 2R2
f
)+KL 2 P
2
1
IVIV, 1 2 2h 2
r2 R4
24+Bc
f
(5.15)
for tube "d",
P-P4 =
2L
_
R2
1
2 +KLP
1
2K+VC2
LP
h
Ld
1 ,1,h
d(v)
P IViId. 2 R4
~2R
+f4
(~f
~
'/)~
f ~~~~f rR
(5.16)
for tube "e",
V2I
P~,P4:
p[, 4-.V204
P.
+
02R IV
2
)+
2P4,2R
--Ke~
T2R
+ f
1 JV 1
2h 2
+fBe(
KKL-
T~f?~
VIOV2R 2h2
L
)2P
I 2R
(5.17)
The angles of sectors add up to 360 degrees, so
0
a+Ob+oc+od+Oe
=
2
.
(5.18)
There are 6 equations and 6 unknowns in this set of simultaneous equations. Unknowns
are
Oa' Ob' Oc' Od' Oe' (P 1 - P 4 )
5.2 Limitations
There are a few assumptions involved in this model. Although Henry and Fauske's
model and quality iteration show that the predicted pressure at the throttle discharge is
about 140 psia, and the pressure drop across feeder tubes is about 50 psi, I assume that the
refrigerant mixture density is constant throughout the throttle discharge and feeder tubes.
In addition, to simplify the model, I assume that the Baroczy correlation factor is constant
in each feeder tube.
41
The model does not account for the bend losses which occur in the refrigerant stream
when it turns into or out of the feeder tube inlet plenum. In addition, this model does not
consider the friction pressure drop in the feeder tube inlet plenum. Figure 5.3 shows an
arrangement of a set of feeder tubes where tube "a", "b", and "e" are of the same length
and are shorter than tube "c", and "d" which are of identical length. The model predicts
that tube "a", "b", and "e" would all have the same higher flow rate whereas tube "c" and
"d" would both have the same, lower flow rate. It can be argued, however, that tube "a",
"b", and "e" might not actually have the same flow rate because tube "b" and "e" might
get more refrigerant flow than tube "a" due to their closer locations to tube "c" and "d". If
this same set of feeder tubes are arranged differently around the circle of the feeder tube
inlet plenum as shown in Figure 5.4, the feeder tube "d" might get the highest flow rate
this time whereas the model will predict the flow rates only based on the feeder tube
length but not the feeder tube arrangement.
a
feedertubeb
feedertubee
er tubed
,FPP.A.
zg~.,glgl
... U.
tUoG
i~
high flow tube,L/Dsmall
I0
lowflow tube,L/Dbig
Figure 5.3: A feeder tube inlet plenum with a set of feeder tubes.
42
asa -%k
a
feedertubeb
feedertubee
ler tubed
feeder
-h.
high flow tube,L/Dsmall
lowflow tube,L/Dbig
Figure 5.4: A feeder tube inlet plenum with the same set of feeder tubes as shown in Figure 5.3, but with different arrangement.
It is not clear how important the bend losses and the friction are in the inlet plenum
until experimental data are taken. For the friction factor, it might turn out to be negligible
because the length/hydraulic diameter in the plenum is small. Section 7.1.1 in Chapter 7
will address this question based on the experimental results.
43
Chapter 6
Experiments and Results
6.1 Test matrix
A test matrix was designed to evaluate a Type II distributor and to examine the flow
distribution model (see Table 6.1). In order to keep the number of experiments manageable, the range for the variables of interest were selected.
refrigerant: R-22
distributor mounting orientation: vertical direction
Since mounting orientation was not important (as discussed in Chapter 3) for conditions of interest, only vertical orientation was used.
piston (throttle) size: 0.052 in. and 0.080 in. (diameter)
These two sizes provided two distinct flow rates through the distributor.
measurement type:
Two types of measurement were performed with the apparatus.
(1) refrigerant flow distribution
(2) pressure drops across throttle and feeder tubes
feeder tube configuration:
Table 6.2 shows the four configurations selected. The slight difference between the
feeder tube sets for distribution and pressure drop measurement was due to the discrepancy in cutting the tubes at the early preparation stage of the experiments.
44
'-' -
Table 6.1: Test matrix.
feeder
tube
feedertube
piston size
(inch)
0.049
i
ii
2-20
/
/V
=
3-1
/
,/
3-2
v/
/
3-6
,/
3-7
/
4-1
_
//
4-5
/
iv
*
c
measurement
.0
U
.4
208.6
1.1
99.8
/
96.6
243.0
13.9
103.8
/
96.6
235.6
11.7
105.2
/
97.9
244.9
13.1
103.1
/
95.8
194.8
-1.2
96.9
/
85.6
251.9
27.4
98.0
/
94.0
184.9
-3.4
102.8
/
94.8
227.0
10.6
99.1
/
80.2
240.5
29.5
101.4
/
97.6
201.4
-1.0
89.2
$r
v/
84.1
254.3
29.8
91.2
$
//
98.3
207.7
0.6
90.4
v
/
/
4-6
=
98.1
/
,/
4-4
iii
/
/
.
>
/
4-2
4-3
.
configuration
0.080
3-5
.
I
/
5-1
/
/
98.2
237.8
10.7
88.6
5-2
/
/
97.2
241.5
12.8
93.9
/
$
5-3
/
/
94.2
217.1
7.9
94.9
5-4
/
/
98.8
215.9
2.9
95.5
6-1
/
/
95.8
215.5
5.9
95.2
6-3
v/
/
95.5
222.5
8.4
93.2
/
/
94.5
251.8
18.7
79.6
$
/
97.2
250.2
15.5
94.8
93.5
216.0
8.3
101.6
/
/
4
6-4
/
6-5
7-1
/
/
.
7-2
/
7-3
7-4
/
/
m_
-
-_
..
_
/
_.
.-
,/
96.2
245.8
15.2
96.9
/
95.7
225.5
9.2
94.0
/
-_
97.0
245.3
14.3
91.7
.
45
.
.
91..
/
,
..
/
-__
/
(i) original package as sent from Carrier1 . The purpose of this set of experiments was
to see if the effect of tube length on distribution could be predicted for an as-provided distributor.
(ii) three adjacent, same-length, long tubes and two adjacent, same-length, short tubes.
The purpose of this set of experiments was to see if the distribution could be predicted for
large variations in tube length.
(iii) two same-length, long tubes and three same-length, short tubes, with one short
tube located between the long tubes. This set of experiments was to examine if the tube
layout had an effect.
(iv) One long tube, one short tube, and three same-length, intermediate length tubes.
This set of experiments would test whether the effect of an extreme variation in tube
length could be predicted.
The comparison between configuration (ii) and (iii) runs can show the effects of friction pressure drop in the feeder tube inlet plenum.
Table 6.2: Feeder tube configuration
configuration
feee
ftube 1.,,,t
lnh
distribution measurement
pressure drop measurement
(i)
(ii)
(iii)
(iv)
(i)
(ii)
(iii)
(iv)
"a"
29.0
22.1
22.1
11.0
25.9
22.5
22.5
11.0
"b"
29.0
22.1
11.0
11.0
25.9
22.5
11.0
11.0
("c"
25.1
22.1
22.1
22.1
22.5
22.5
22.5
22.5
"23.0
11.0
11.0
11.0
19.8
11.0
11.0
11.0
23.0
11.0
11.0
5.0
19.8
11.0
11.0
5.0
""
1. The lengths of feeder tubes indicated in this thesis are the total lengths that include the 3-inch
long, same-diameter copper tube connected to the end of feeder tubes that channel the flow into the
measurement glass containers.
46
stagnation (reservoir) conditions:
The stagnation conditions of R-22 were set approximately around the nominal operating conditions with intended range of subcooling to be from 0° to 30° F. The reservoir temperature, pressure, and degree of subcooling are average values over the full period or
partial period during which the refrigerant was flowing in the distributor. Each value was
obtained based on the data plots (details discussed in Data and results section). Some negative subcooling values in Table 6.1 gives indication about the thermocouple's measurement accuracy and possible R-22 property variation. For the flow model calculation, zero
subcooling values were used instead.
receiving (main vessel) pressure:
The nominal receiving pressure is 90 psia. Similarly, the values of the main vessel
pressure on Table 6.1 were average values calculated from the data plots.
6.2 Data and results
During the experiment, the data acquisition system was started one or two seconds
before the refrigerant began running through the throttle. Thus, the initial, transient, and
steady state conditions could be recorded. Appendix F contains all the data graphs plotted
for each experiment.
In the reservoir hydrostatic pressure vs. time plots, the liquid refrigerant hydrostatic
pressure in the reservoir drops during the experiment. Although there is small amplitude,
high frequency noise in the measurements, each plot, however, is a straight line overall. In
appendix G, I discuss the methods of determining the mass flow rate by using either the
hydrostatic pressure change or stop watch measurement. The methodology of getting the
hydrostatic pressure change rate from the experimental data is shown in Appendix H. In
addition, Appendix I presents the calculation of the effective cross-sectional area of the
47
reservoir, which is required as well to determine the mass flow rate. The measured mass
flow rates are listed in Table 6.3.
The reservoir temperature vs. time plots show the temperature variation of the liquid
refrigerant in the reservoir. In pressure drops across the throttle and feeder tubes vs. time
plots, the sharp rise in the pressure drops can be noted when the valve was opened. In
some plots, when the pressure drop across the feeder tubes is over the range (32 psi) of the
pressure transducer, a horizontal line can be seen.
The reservoir and main vessel pressure vs. time plots show that the reservoir pressure
did not hold at the initial pressure during the experiment even though the reservoir was
connected to the compressed nitrogen supply. Therefore, average values were taken for the
reservoir pressure, temperature, and main vessel pressure. Also note that the initial nonequilibrium transient state shown in the main vessel pressure measurements. The pressure
fluctuated a few seconds after the valve was opened and then steadily increased to achieve
equilibrium.
To obtain the average values for the reservoir temperature and pressure, main vessel
pressure, pressure drop across the throttle and the feeder tubes, I summed up the values in
a range and divided it by the total number of data points taken in this range. For example,
in experiment E2-20, I selected the range to be from time = 10 seconds to time = 42 seconds to determine the average values of the variables.
48
Table 6.3: Mass flow rates in experiments
mass flow rate from stop watch
(bm/s)
experintmeasurement
mass flow rate from reservoir
hydrostatic pressure plot (bm/s)
2-20
0.0863
0.0806
3-1
0.1576
0.1304
3-2
0.1113
0.1006
3-5
0.0767
0.0675
3-6
0.0603
0.0639
3-7
0.0898
0.0882
4-1
0.1135
0.0916
4-2
0.1721
0.1128
4-3
0.1971
0.1497
4-4
0.0591
0.0633
4-5
0.0914
0.0854
4-6
0.0646
0.0643
5-1
0.0677
0.0662
5-2
0.0821
0.0788
5-3
0.1817
0.1732
5-4
0.1409
0.1106
6-1
0.1879
0.1213
6-3
0.1814
0.1586
6-4
0.0982
0.0891
6-5
0.0963
0.0925
7-1
0.2600
0.228
7-2
0.0957
0.0890
7-3
0.1987
0.1874
7-4
0.0911
0.0846
49
Chapter 7
Analysis
7.1 Flow distribution
Algorithms based on the flow distribution model were written (see Appendix J). Computer simulation was run to compare the model and the experimental results. The mass
flow rate input for the flow distribution model was based on the Henry-Fauske's model.
The useful values generated by the simulation and experiments were tabulated in Appendix K.
7.1.1 Measured results vs. model
Figure 7.1 through 7.12 show the comparison between the model and experimental
results on the flow distribution for each of the flow distribution tests. In this section, the
limitation of the model and the effects of friction pressure drop in feeder tube inlet plenum
are also discussed.
E4-1
1.q-
1.2-
t
-
1.0-
~'8ei08
-- experiment
-
- - model
'i
-o- tubelength(m)
l0.4-
I
0
a
b
l
11
_.
I
0.2
0.0
c
feedertube
d
e
Figure 7.1: Experimental and model flow distribution results for E4-1.
50
E4-2
14
-
1.2-
-
1.0
>
._
0R
E
-0- experiment
cr ~.0.8
c
~7'
to
e
- model
=
D 0.6
-O- tubelength(m)
-
E O 0.4 0
0-
C
0.2 0.0 w
a
a
I
b
c
I
d
e
e
feedertube
Figure 7.2: Experimental and model flow distribution results for E4-2.
E4-3
1.4
1.2>
1.0-
Z e0.8 -
--o- experiment
o-
-0- model
-- tubelength(m)
0-
E 0=.
N '
E
0.4-
I
c
0.2 - I
0.0
a
a
I
b
C
feeder
tube
d
e
e
feedertube
Figure 7.3: Experimental and model flow distribution results for E4-3.
51
E4-4
IA
1.2 -
1.21.0
0
.-c ,0.g
0.8 -
-
-~~~~~-a--~~~~~~~--
i I
-0- experiment
- 0- model
--O-tube length(m)
0-
,W W
13----
,- .0.6a
N 'I
c= U
R
0.4-
0.2
0.2 I- {I
a
a
I
I
b
C
d
e
e
feedertube
Figure 7.4: Experimental and model flow distribution results for E4-4.
E4-5
1.4
i _
1.2 -
1.0-
- s0.8
o
'
-0- experiment
O.._
…~
-
model
-- tube length(m)
0.4-
z0 0
0.2 0.0
)
a
a
b
b
d
C
d
e
e
feedertube
Figure 7.5: Experimental and model flow distribution results for E4-5.
52
E4-6
IA
1.2-
~2 1.0>
0.8-
-- experiment
-0- model
--- tubelength(m)
0
00~~X
0.6-
s2 z
E 0.4 0I
0.2 0.0
b
a
b
d
d
c
e
feedertube
Figure 7.6: Experimental and model flow distribution results for E4-6.
E5-2
1
1.2 1.2-
D,----->
1.0
0
'-0.8=
z
--------
"
"
-0- experiment
-0- model
0\w
oG
cO
)=
o .o0.6
E
N
-- tubelength(m)
-80.46
0
0.2 u.u
a
a
I
b
b
C
feeder
tube
d
d
e
e
feedertube
Figure 7.7: Experimental and model flow distribution results for E5-2.
53
E5-4
1.4 1.2-
0
1.0-
,
0/
*0.4-
a---------
------------
-
--0- experiment
model
0.2I 0. '=
0
.
r
-- tubelength(m)
E 0.40
0.2 -
n
a
i
b
b
a
d
C
e
e
feedertube
Figure 7.8: Experimental and model flow distribution results for E5-4.
E6-1
I
1.2>
1.0-
-
13
/'
-
-0- experiment
2 -0O.8-
-- model
o
-0- tubelength(m)
0.-
•20
50 t 0.6 aO D .4-
0.2 0.0
I
a
b
c
Ceeder
tube
d
d
e
e
feeder tube
Figure 7.9: Experimental and model flow distribution results for E6-1.
54
E6-5
1.4-
1.2!
1
1.0-0- experiment
i ~o1s0.8
-
-- model
-0- tube length(m)
0 .
S0.4
0
0.2 noili
a
a
b
b
I
d
e
d
C
e
feeder tube
Figure 7.10: Experimental and model flow distribution results for E6-5.
E7-1
1.4
rl
1.2·
..-.
1.0
0
--
ad -n
experiment
- - model
0.6
-0- tubelength(m)
- 0.4-
0.2
U.U
a
b
b
feedertube
d
e
feeder tube
Figure 7.11: Experimental and model flow distribution results for E7-1.
55
E7-4
I A
1.42-
I
1.21.0-
2 ,0.8 Ct
-0- experiment
b
-0- model
h5n
Z.2
. P, (_6
i:;,
.
__
-O- tube length (m)
-
N E
a
0.4
0.2 0.0 -
I
I
I
I
I
a
b
c
d
e
feedertube
Figure 7.12: Experimental and model flow distribution results for E7-4.
It can be seen that the model and measured results agree within certain accuracy in
predicting the flow distribution. Generally, a shorter feeder tube gets more liquid refrigerant due to lower back pressure at the feeder tube inlet plenum.
In experiments E7-1 and E7-4 (Figure 7.11 and 7.12), the shortest tube (tube "e") did
not get as much refrigerant flow as predicted by the model. It is suspected that the flow in
the short tube might have choked at the exit as the sharp pressure drop in the feeder tube
could cause a second choked plane to form in the flow. Although there is no existing critical flow model that predicts the choked flow in long tubes (the L/D ratio of the feeder tube
is too large to be considered to be the short tube in Henry-Fauske model), I used the
Henry-Fauske model anyway as a reference to predict the likelihood of the occurrence of
the second choked plane. With the temperature, pressure, and quality at the throttle discharge used as the stagnation conditions to Henry-Fauske's model, the critical pressure
56
ratio is about 0.7. The implication is that the freedom to control the flow distribution by
adjusting the tube length is limited by the onset of choking in the shortest tube. If we allow
a lower pressure drop across the throttle, the large pressure drop across the feeder tubes
can create a choked plane which will nullify the prediction of the proposed flow distribution model.
If 0.8 is used as the high value for the critical pressure ratio in the feeder tubes, a pressure of more than 1/0.8=1.25 times the absolute evaporator pressure in the feeder tubes
will subject the flow to a second choked plane in the feeder tubes. In other words, to safely
use the model to predict the flow distribution, the pressure in the feeder tubes should not
be more than 25% higher than that of evaporator.
From Figures 7.7 through 7.10, in which the feeder tubes are in configuration (ii) or
(iii), the friction pressure drop in the feeder tube inlet plenum has a negligible impact on
flow distribution.
7.1.2 Subcooling effect on flow distribution
Figure 7.13 and 7.14 show that the flow distributions are almost the same for different
E4-1 (Po=184.9psia.To=94.0F. subcooled=-3.4F)
E4-2 (Po=227.0psia,To=94.8F, subcooled=10.6F)
E4-3 (Po=240.5psla,To=80.2F, subcooled=29.5F)
1.4
1.2-
_X
X
1.0-
So.8
.25 =
-0- experimentE4-1
--- experimentE4-2
._
-- experimentE4-3
-.- tubelength(m)
0.4 -
00
I
0.2 0.0 -
0.0
I
I
I
I
I
a
b
c
d
e
feedertube
Figure 7.13: Experimental flow distribution results with the same throttle size (Dt = 0.080
in) but different stagnation conditions.
57
E4-4 (Po=201.4psia,To=97.6F, subcooled=-1.0F)
E4-5(Po=254.3psla,To=84.1F. subcooled=29.8F)
E4-6(Po=207.7psia,To=98.3F, subcooled=0.6 F)
1.4
1.2
4
1.0
0.4.60.8 s .s
a.
-0- experimentE4-4
-0- experimentE4-5
V
-- experimentE4-6
-- tube length(m)
0.4
C)-
0
0.2 0.0 -
A
I
a
a
I
b
c
d
I
e
feedertube
Figure 7.14: Experimental flow distribution results with the same throttle size (Dt = 0.052
in) but different stagnation conditions.
degree of refrigerant subcooling. The flow distribution model also predicts the same result
as shown in Figure 7.15 and 7.16. For the range of stagnation conditions run in the experiments, the degree subcooling did not have observable effects on the flow distribution.
E4-1(Po=184.9psia,To=94.0F, subcooled=-3.4F)
E4-2(Po=227.0psia,To=94.8F. subcooled=10.6F)
E4-3(Po=240.5psia,To=80.2F. subcooled=29.5F)
1.41.2-
2
-
1.0-
0.-
-0- modelE4-1
--- modelE4-2
c :90.8 -
(a as
V
-o- modelE4-3
, -0 0.6 s
Z
-7- tube length(
0.4
0
0.2 0.0
a
I
b
b
feeder
tube
d
d
e
e
feedertube
Figure 7.15: Model flow distribution results with the same throttle size (Dt = 0.080 in) but
different stagnation conditions.
58
E4-4 (Po=201.4psla, To=97.6F, subcooled=-l.0F)
E4-5 (Po=254.3psla,To=84.I F, subcooled=29.8F)
E4-6 (Po=207.7psia,To=98.3F, subcooled=0.6 F)
1.4
1.2 -
*0
.
o.8
E0
0
;0.4 -
,, 0
-0- modelE4-4
--o- modelE4-5
--- modelE4-6
-v tube length(m)
i
I
a
b
I
0.2
0.0
c
d
e
feedertube
Figure 7.16: Model flow distribution results with the same throttle size (Dt = 0.052 in) but
different stagnation conditions.
7.1.3 Mass flow rate on flow distribution
In Figure 7.17, the flow distribution does not vary much for the two runs which have
almost the same stagnation conditions but different flow rates (using different throttle
sizes). The flow distribution model also predict the same trend as shown in Figure 7.18.
In Figure 7.19 through 7.21, although the flow distribution vary between runs with different stagnation conditions and flow rates, it can be seen that the flow distribution is
essentially dictated by the feeder tube lengths. The corresponding flow distribution model
results are shown in Figure 7.22 through 7.24.
59
E4-3(Po=240.5psia,To=80.2F, subcooled=29.5F massflowrate=0.1971Ibmls)
E4-5 (Po=254.3psia,To=84.1F, subcooled=30.0F. massflow rate=0.0914Ibm/s)
1 . AI
1.2 5,
.
.- g
1.0--
'0.8
=
8; to.
' °
30.
=
VI
experimentE4-3
-0- experimentE4-5
-v- tube length(m)
NU
U04
0
::~
0.2 0.0
a
a
b
b
!
c
feedertube
feeder
tube
d
e
d
e
Figure 7.17: The experimental flow distribution results for two runs with similar stagnation conditions but different mass flow rates.
E4-3 (Po=240.5psia,To=80.2F, subcooled=29.5F. massflowrate=0.1971lbm/s)
E4-5 (Po=254.3psia,To=84.1F, subcooled=30.0F, massflowrate=0.0914lbm/s)
1.4 1.25.r
.
1.0-
,G _
ct0.8Iez
_
-- modelE4-3
-0- modelE4-5
VI
-m- tube length (nm)
0.
0.20.0 -
I
a
b
b
I
feeder
tube
feeder
tube
d
d
e
e
Figure 7.18: The model flow distribution results for two runs with similar stagnation conditions but different mass flow rates.
60
E5-2 (Po=241.5psla,To=97.2F. subcooled=12.8F, massflow rate=0.0821Ibms)
Ibms)
E5-4 (Po=215.9psia,To=98.8F, subcooled=2.9F, massflow rate=--0.1409
1.4 -
1.2
1.0
-
0.8
-- experimentE5-2
-0-experimentE5-4
-v-- tubelength(m)
b to4
=0.6
0lu "Z
4
0.2 0.0
a
a
b
b
C
feeder
tube
d
e
e
feedertube
Figure 7.19: The experimental flow distribution results for E5-2 and E5-4.
E6-1 (Po=215.5psia,To=95.8F, subcooled=5.9F, massflowrate=0.1879Ibm/s)
E6-5 (Po=250.2psia,To=97.2F. subcooled=15.5F. massflow rate=0.0963bm/s)
1.4 1.21.0
.
~ ~0
-0- experiment
E6-1
-0- experimentE6-5
-- tubelength(m)
,rs
'Ili 55
5-z
5~
o0.8
'2 B0.4
0
0.2 U.0
a
a
b
I
I
c
d
Ceeder
tube
e
e
feedertube
Figure 7.20: The experimental flow distribution results for E6-1 and E6-5.
61
E7-1 (Po=216.0psia,To=93.5F, subcooled=8.3F, massflow rate=0.26Ibm/s)
Ibm/s)
E7-4 (Po=245.3psia,To=96.9F. subcooled=14.3F. massflow rate--=0.0911
14
1.24
1.0-
vff
b
.b
-0-experiment E7-4
.- tube length(m)
0
oZ
E. Z
:50.
N
.14
-o- experimentE7-1
!aO.8 -
-
06
a0.40
.2
VI
0.2 0.0
a
a
b
b
I
d
d
c
e
e
feedertube
Figure 7.21: The experimental flow distribution results for E7-1 and E7-4.
E5-2(Po=241.5psia,To=97.2F. subcooled=12.8F, massflow rate=0.0821lbm/s)
E5-4 (Po=215.9psia,To=98.8F. subcooled=2.9F. massflow rate=0.1409bm/s)
a
I
/I
I
1.2 -
2
1.0n
n
--- modelE5-2
--- modelE5-4
--v- tubelength(m)
,= 0.8 -
t'~ :s00.4. 0.2 au)
u.u
a
a
I
b
C
feeder
tube
d
e
feedertube
Figure 7.22: The model flow distribution results for E5-2 and E5-4.
62
E6-1 (Po=215.5psla,To=95.8F, subcooled=5.9F, massflow rate=0.1879Ibm/s)
E6-5 (Po=250.2psia,To=97.2F, subcooled=15.5F, massflow rate=0.0963lbm/s)
1.4 1.2 -,
.O
1.0-
ca
--
modelE6-1
-- modelE6-5
-v- tubelength(m)
0.2
Of.8-
cO -04
::0.
k
-
E
0.2
0.0
a
a
I
d
d
b
e
e
feedertube
Figure 7.23: The model flow distribution results for E6-1 and E6-5.
E7-1 (Po=216.0psia,To=93.5F, subcooled=8.3F, massflow rate=--0.26
Ibm/s)
E7-4 (Po=245.3psia.To=96.9F, subcooled=14.3F. massflow rate=0.0911Ibm/s)
1.4
1.2
1.0
'2
0
C1
0. 8
t00.8
-0- modelE7-1
' 0.6
-O- modelE7-4
-.- tubelength(m)
. 0.4
0.2
0.0
a
b
c
d
e
feedertube
Figure 7.24: The model flow distribution results for E7-1 and E7-4.
63
7.2 Mass flow rate
The mass flow rates in the experiments were determined by two methods: stop watch
measurement and reservoir hydrostatic pressure change measurement. Figure 7.25 shows
the measurement results from both methods.
0.3
E
o
"
.S = 0.2
ct
3."
E:
q)
tct 2 0.
;: .s
0.
0.0
0.1
0.2
Stop watch measured mass flow rate (Ibm/s)
0.3
Figure 7.25: Mass flow rates determined by stop watch measurement vs. mass flow rates
from reservoir hydrostatic pressure change measurement.
There are small discrepancies between these two measurements. I believe the stop
watch measurement is more reliable because the reading at the pressure differential transducer can be affected easily by the formation of condensate at one end of the transducer,
especially for the small range of pressure differential it measured.
Therefore, the stop
watch measured mass flow rate is used to compare to that predicted by Henry-Fauske's
model, as shown in Figure 7.26.
64
0.3
=I's 0.2
E
.:o
0
-o
a
-.
0
0.1
E
0
0
=0.0
0.0
0.1
0.2
Stop watch measured mass flow rate (Ibm/s)
0.3
Figure 7.26: Mass flow rates predicted by Henry-Fauske's model vs. mass flow rate determined by stop watch measurement.
It can be noted that Henry-Fauske's model predicts the mass flow rate quite well for
small flow rates. However, it tends to overestimate the flow rate for higher mass flow
rates.
7.3 Pressure drops across the throttle and feeder tubes
The flow distribution model predicted the pressure drops across the throttle within certain accuracy as shown in Figure 7.27.
Figure 7.28 shows the pressure drops across the feeder tubes. The discrepancies are
likely due to the poor measurement taken by one of the pressure transducers used. As it
can be seen from the pressure drop across feeder tubes vs. time plots in Appendix F, or
65
160
150
140
130
*Z'120
! 110
S100
v1
e 90
; 80
0~
2 70
60
E
, 50
0- 40
30
0
0
20
10
0
0 0 0C-.4 0Ad 0or 0A \S0 0 000 0\0 oo 0-_ 0 0et 01 0_ 0_
Measured pressure drop across throttle (psi)
Figure 7.27: Model predicted and measured pressure drop across the throttle.
50
,-,40
U:
.0
_R
a)1020
130
Ct0
22
0
0)
0
10
20
30
40
Measured pressure drop across feeder tubes (psi)
50
Figure 7.28: Model predicted and measured pressure drop across the feeder tubes.
66
table K.7 in Appendix K, the zero offsets of the transducer varied between -7.7 psi and 0.2 psi. The diaphragm in the differential pressure transducer could have been sticky,
causing the zero offset fluctuation.
67
Chapter 8
Conclusions
The major findings of this research are as follows:
(1) The flow regime, in both the distributor throttle discharge and feeder tubes for all conditions tested, was in the high velocity, intermittent flow regime, as shown in Figures 4.1
through 4.5. The maps also show the velocity level where stratification becomes important.
(2) The approach pipe orientation upstream to the distributor made virtually no difference
in the flow distribution for the type II distributor (see Figure 3.5).
(3) Individual distributor tube differences, probably burrs on the inlet, gave rise to variations (as high as 10% from the mean) in the mass flow rates into the feeder tubes (see Fig-
ures 3.5 and 3.7 for type II distributor, and Figures B.2, B.4, B.5, B.6, and B.7 for type I
distributor).
(4) When the feeder tube pressure drop is greater than 25% of the evaporator inlet pressure, a feeder tube may choke and the use of feeder tube length to control distribution
becomes impossible (see Figures 7.11 and 7.12). Note how, as tube "e", the short tube,
gets shorter in proceeding from Figure 7.10 to 7.11 and 7.12, the deviation from the
Baroczy theory becomes more severe.
(5) The flow distribution model (based on the Baroczy pressure drop model), used as indicated, does a fine job of predicting the distribution (see Figures 7.1 through 7.10). However, the model has not been proven to give good absolute pressure drop predictions due to
68
poor pressure drop measurements from one of the differential pressure transducers used
(see Figures 7.27 and 7.28).
(6) The Henry-Fauske critical flow model gave good predictions for low flows but poor
ones for large flows (see Figure 7.26). This appears to be due to flashing upstream of the
distributor which greatly reduces the choked flow values.
69
References
Chapra, Steven C., Canale, Raymond P., Numerical Methods for Engineers, 2nd edition,
McGraw-Hill, Inc., New York, 1988.
Ely, J., Gallagher, J., Huber, M., McLinden, M.,Morrison, G., NIST Thermodynamic Prop-
erties of Refrigerantsand RefrigerantMixtures,Version3.04a,computerprogram,
National Institute of Standards and Technology, Gaithersburg, 1989.
Henry, Robert E., Fauske, Hans K., "The Two-Phase Critical Flow of One-Component
Mixtures in Nozzles, Orifices, and Short Tubes", Journal of Heat Transfer, vol 93,
series C, The American Society of Mechanical Engineers, May 1971.
Hodes, Marc S., Gas Assisted Evaporative Cooling in Down Flow through Vertical Channels, M.S. thesis in the Department of Mechanical Engineering, University of Minnesota, 1994.
Howell, John R., Buckius, Richard O., Fundamentals of Engineering Thermodynamics,
McGraw-Hill, Inc., New York, 1987.
Munson, Bruce R., Okiishi, Theodore H., Young, Donald F., Fundamentals of Fluid
Mechanics, John Wiley & Sons, New York, 1990.
Smith, Heather G., Design of Test Apparatus to Analyze Two-Phase Refrigerant Flow Distribution for Furnace Coil Applications, M.S. thesis in the Department of Mechanical Engineering, Massachusetts Institute of Technology, 1994.
Taitel, Yehuda, "Flow Pattern Transition in Two-Phase Flow", Proceedings of the 9th
International Heat Transfer Conference, The Assembly for International Heat Transfer Conferences, Hemisphere Publishing Corporation, Washington, 1990.
Wallis, Graham B. One-dimensional Two-phase Flow, McGraw-Hill, Inc., New York,
1969.
Whalley, P. B., Boiling. Condensation, and Gas-Liquid Flow, Clarendon Press, Oxford,
1987.
70
Appendix A
Nomenclature
A: area; cross-sectional area
a : y-axis intercept
slope
a:
D: diameter
e: error
f: friction factor
G: mass flux
height; feeder tube inlet plenum height; enthalpy
j: superficial velocity
h:
entrance loss coefficient
L: length
KL:
m:
mass flow rate
N:
experimental parameter
P: pressure
R:
radius
Reynolds number
s: entropy
T: temperature
Re:
V: velocity
v: specific volume
x: quality
a: critical pressure ratio
0: sector angle
g: viscosity
p: density
2: Baroczy correction factor
02
fo
: Baroczy multiplier
71
subscripts:
1: denotes section 1; area of section 1 = 27RAh
2: denotes section 2; area of section 2 = 2R/zjh
3: denotes section 3; area of section 3 = tRf2
4: denotes section 4; area of section 4 =1Rf
a: denotes feeder tube "a"
B:
Baroczy model
b: denotes feeder tube "b"
c: denotes feeder tube "c"; critical flow
d: denotes feeder tube "d"
equilibrium (corresponding to local static pressure)
e: denotes feeder tube "e"
E:
f: feeder tube
g: gas; vapor
(guess)
a guessed value
1: liquid
m: model
o: stagnation conditions
T: throttle discharge
t: throat
v: main vessel
72
Appendix B
ApparatusEvaluation
Apparatus Consistency Test
To ascertain the experimental apparatus can effectively measure the performance of
the distributors, I first ran a set of redundancy experiments to evaluate the apparatus and to
gain a preliminary insight of the flow distribution in the distributor assembly. I used a
Type I distributor to do the test and it was mounted in the main vessel in an orientation as
that shown in Figure 2.4 in Chapter 2. Each feeder tube was labeled and their arrangement
with respect to the approach pipe is shown in Figure B. 1. The feeder tubes were all 26.5
inches (0.6731 m) long and 0.0975 inches (2.4765e-3 m) in inner diameter (ID).
tor
approachpi
Pe
"e"1
feeder
tube "a"
refrigerant
n1
Figure BAI:Top view of the distributor assembly
To begin with the experiments, R-22 was conditioned to 95°F and 240 psia in the reservoir while the main vessel was filled with R-22 vapor at 90 psia. Once the valve was
opened, the subcooled R-22 entered the approach pipe and then flowed horizontally before
73
making a 90° turn and entered vertically into the distributor. The refrigerant then flowed
spirally and smoothly into the glass containers. No splash, nor leakage of the liquid from
the containers were observed. Once the refrigerant liquid entered the glass containers,
evaporation occurred immediately. However, the evaporation rate was not fast enough to
affect the liquid level readings (the liquid level dropped about an negligible amount of 1/
32 inch after all the measurements were made). Therefore, the order of recording the liquid level was not critical.
Three identical runs were done. As shown in Figure B.2, glass "d" consistently had the
lowest liquid level, and either glass "a" or "e" received the most liquid. The plot for each
run shows a consistent trend in the distribution of the liquid. It is noted that the feeder
tubes at the far side of the approach pipe tend to get higher liquid level. The variation of
liquid level in each individual glass for different runs was within about 6%.
(feeder tube "a" points straight away from approach pipe)
1.2
>01.0
f0.8
--
i 0.7
&0.6
2 0.5
S0.4
1st run
0- 2nd run
-- 3rd run
-
0.3
0.2
Z0.1
0.0
I
I
I
I
a
b
c
d
'
e
feeder tube
Figure B.2: Normalized refrigerant liquid level in each glass container with feeder tube
"a" pointing straight away from the approach pipe.
74
Bias test
I turned the distributor 180° horizontally and had feeder tubes "a", "b", and "e" on the
near side of the approach pipe (see Figure B.3). The results show that feeder tube "a" and
"e" did not receive the most liquid with this orientation and feeder tube "c", which was on
the far side, had the highest liquid level (see Figure B.4). I repeated the experiments with
different arrangements by having different feeder tube pointing straight away from the
approach pipe. Figure B.5, B.6, and B.7 show the results respectively. I observed that all
the glass containers on the far side (with the exception of "d") consistently received more
liquid than those on near side. Glass "d" received less liquid no matter how the distributor
was positioned with respect to the approach pipe.
feeder
approachpi
tube "c"
refrigerant
Figure
view
B.3:
ofTop
distributor assembly after 180 degree turn.
Figure B.3: Top view of distributor assembly after 180 degree turn.
75
(feeder tube "a" points towards approach pipe)
1.2
_ 1.1
1.0
.r0.9
V0.8
00.7
00.6
20.5
-0--1strun
- 0- 2nd run
O0.4
i0.3
- 0.2
Z0.1
0.0
.~~
_
I
a
I
b
I
c
~
~I _
I
d
~
~~
I
e
feeder tube
Figure B.4: Normalized refrigerant liquid level in each glass container with feeder tube
"a" pointing towards the approach pipe.
(feeder tube "b" points straight away from approach pipe)
1.2
- 1.1
'1.0
.0.9
0.8
0.7
.o0.6
~0.5
20.4
N
0.3
$ 0.2
E
0.1
0.0
I
a
-
I--
I
b
c
II
I
II
d
d
e
e
feeder tube
Figure B.5: Normalized refrigerant liquid level in each glass container with feeder tube
"b" pointing straight away from the approach pipe.
76
(feeder tube "d" points straight away from approach pipe)
1.2
1.1
' 1.0
~.
.
0.9
"O.8
o 0.7
I-.
~0.6
20.5
A 0.4
N
10.3
80.2
0.1
0.0
I-V
a
-
I
d
Ii
b
c
I
e
feeder tube
Figure B.6: Normalized refrigerant liquid level in each glass container with feeder tube
"d" pointing straight away from the approach pipe.
(feeder tube "e" pointing straight away from approach pipe)
1.2
_1.1
_ 1.0
0.9
.
;0.8
0.7
e0.6
~0.5
`0.4
'0.3
0.2
Z0.1
0.0
a
a
I
b
I
c
-
I-d eI
d
e
feeder tube
Figure B.7: Normalized refrigerant liquid level in each glass container with feeder tube
"e" pointing straight away from the approach pipe.
77
Apparatus Evaluation Conclusion
The redundancy experiments verified that the test apparatus used is reliable and is
capable of indicating the flow distribution of a distributor assembly. Care has to be taken
when evaluating the data because the apparatus introduces bias in the measurement with
the far-side glasses generally receiving more liquid. The bias is likely due to the non-fullydeveloped flow as a result of the 90° bend of the pipe right before entering the distributor.
However, the bias was only found in type I distributor and the later experiments on type II
distributor mounted in the same orientation did not show such bias.
The redundancy experiments also showed that one of the holes in the distributor tested
allowed less liquid flow. The disparity might be caused by the distributor fabrication process or defects that were associated with this particular distributor used. However, by
looking at all the plots, it can be noted that none of the liquid level variations was larger
than 10% from the mean. This small degree of variation indicates that the distributor used
in fact did distribute the flow quite uniformly.
78
Appendix C
Henry and Fauske's Two-Phase Critical Flow Model
(Henry, 1971)
The Henry-Fauske model is developed for the two-phase critical flow of one-component mixtures through convergent nozzles. The model is extended to the orifices and short
tubes. It accounts for the nonequalibrium nature of the two-phase critical flow.
The model can predict the critical mass flux based on the stagnation conditions. For
subcooled stagnation conditions where quality, x o, is zero, the square of the critical mass
flux is
~G2
Cv
Evo
.
(VgE-Vl
N
)T_
(C.1)
dslE
Ni dszE
SgE -SIE
where
.XEt
N =
4
'(C.2)
0.14'
and
x
(C.3)
oSgE - SIE
The predicted critical pressure ratio, ilm,,is
V
Vlo
= 1- 2
79
G2
'CG
.,
P(C.4)
The knowns are the stagnation conditions: vo, s, and Po. Since equation (C.1) is
evaluated at the throat conditions, first the pressure at the throat, Pt(guess) has to be
guessed. Based on this value, the remaining terms can be evaluated and d-sE can be
dP
obtained by interpolation.
Next, equation (C.4) can be evaluated. By comparing 11rm
to l (guess) where
Pt(guess)
Po
(guess}
(C.)
(C.5)
if the two values are equal, then G is the critical mass flux. Otherwise, keep guessing
Pt(guess)
and iterate until
tm
and T1(guess) are equal.
80
Appendix D
Throttle Discharge Quality Iteration
Similar to the iteration in the Henry-Fauske model, an initial guess for the pressure at
the throttle discharge, PT(gues.s)is required. Since the enthalpy at the discharge remains
constant as long as the exit kinetic energy can be neglected (as it can here), we get
xT
h - hi]
(D.1)
h-
hig
P (gue.s)
Next, I use Baroczy correlation (see Appendix E) to formulate the pressure drop across the
feeder tubes, A Pf .
APf
(2f)
f
lpV
=
f
o
g
Q
R)f
GL
(D.2)
Note that I only use one equation to account for the pressure drop across the feeder tubes
even though the feeder tubes can be of different lengths and each can have different mass
flux. In order to simplify this preliminary calculation, I believe taking the average value
for the feeder tube lengths and mass flux is sufficient. The final model developed in this
thesis takes into account the variation in the feeder tube lengths and mass flux. In addition,
the model considers the Bernoulli pressure drop in the feeder tube inlet plenum and
entrance loss.
In equation (D.2), the feeder tube length is determined by
Lf =
La +Lb +L c + Ld +Le
5(D.3)
81
(D.3)
The feeder tube mass flux is obtained by
Gf = Aff
Gf = A
,DA
'
(D.4)
where
m
r
rh5T
.(D.5)
To determine f, I need to calculate the Reynolds number, Re, in the feeder tubes.
Ref
=
Gf. ( 2 Rf)
(D.6)
where g is the viscosity of the refrigerant evaluated at PT(guess) . With Reynolds number,
we can look up Moody Chart to get the friction factor. The two-phase multiplier, 0 2 , and
correction factor, Q, can be obtained from Baroczy correlation charts.
Another assumption is made in equation (D.2). I assume the thermal property changes
are small from throttle discharge to the end of feeder tube. That is the reason the viscosity
in equation (D.6) is evaluated at throttle discharge conditions. For the same reason, the
specific volume of the refrigerant in the feeder tube is obtained by
Vf
VI) I
(D.7)
PT(guess)-Pv
(D.8)
VT = V+ X (Vg -
The iteration continues until
P
=
where Pv is the pressure in the main vessel (which simulates the conditions of the evaporator inlet).
82
Appendix E
Baroczy Correlation Model (Wallis, 1969)
As shown in equation (E. 1), the Baroczy model uses a correlation factor -- the Baroczy
correlation factor, fB, to replace the friction factor in a single-phase pressure drop equation.
AP =fB( L)IpV2
(E.1)
p is the density of the two-phase mixture and is obtained by taking the inverse of the mixture's specific volume. The specific volume is expressed as,
v = v+x
(g-
v)
(E.2)
V is the velocity of the two-phase mixture. It can be determined by
V -
(E.3)
p.A
The Baroczy correlation factor,fB, is a product of single-phase Moody chart friction factor, f, two-phase multiplier, Of, and correction factor, a, i.e.
f8fB == f f-0j2
0o2f*Q
(E.4)
Figure E. 1 shows the chart for getting the two-phase multiplier values for G = 10E6lb/
(hr)/(ft2 ). The two-phase multiplier is expressed as a function of property index
(I/Ag)
0.2/ (pl/Pg)
(which is denoted as
(gg)
83
0 2 / (p/pg)
in Wallis). When G =
O10E6
lb/(hr)/(ft2 ), the correction factor is not necessary and thus is equal to 1. Figure E.2
shows the chart for correction factor values for other mass flux values.
14
'S,
-.9
0
E
0
u~
I
Propertyindex, /f/
Sodium,°F
1200
Potossium,"F
I
1400
1600
I
1800 2000
S)2/{p//p
g)
Freon-22,°F
40
I
80 00
_I
! I
1000
1200
1400 1600 18002000
L
iL
L
Rubidium F '
1000
1200
1400 1600 1800
I
I
Mercury, F
600
800
1000 1200 400
I
.
Woter,F
212
328
467 545
140
180
205
I
636
705
Figure E.1: Baroczy's correlation of two-phase multiplier for G = 10E6 lb/(hr)(ft2 ) (Wallis, 1969).
84
1.
I
0
'
1
:. c
-.
A
'1.8
0
1.6
1.4
1.2
1.0
0.8
0.6
0.0001
0.01
0.001
Property index,(/F/)
0
O.
1
2/ (pf/Pg)
Figure E.2: Correction factor versus property index for Baroczy correlation (Wallis,
1969).
85
Appendix F
Experimental Result Plots
Experiment E2-20
E2-20
0O
time second]
Figure F.1: Reservoir hydrostatic pressure vs. time for E2-20.
E2-20
R.
111!
.
.
.
.
.-
.
.
.-
.
.
.
.
.
105
100
111L I.,
7111IFTIVIIII
1,111,11id
I 11 11.1. 11
1 95
V 90
E
85
80
75
ill
I
0
5 10 15 20 25
30 35 40
4550
55 60 65
time second]
Figure F.2: Reservoir temperature vs. time for E2-20.
86
70
E2-20
time[second]
Figure F.3: Pressure drops across the throttle and feeder tubes vs. time for E2-20.
E2-20
.
.
.
.
.
.
.
.
.
.
.
..
300
280
260
240
220
200
A 180
0
solidline: reservoir
dottedline: mainvessel
160
0 140
-120
;
100
80
.....
.......
60
40
20
.,
0
5
~ ~~ ~ ~~~~~~~~~~
I'
,.
10
i
'
,
15
20
i
25
,
i'
*
I&
,
,
30 35 40
time [second]
45
50
55
*
·
60
65
70
Figure F.4: Reservoir and main vessel pressure vs. time for E2-20.
87
Experiment E3-1
E3-1
time [second]
Figure F.5: Reservoir hydrostatic pressure vs. time for E3-1.
E3-1
llU
I
I
I
I
I
I
I
I
I
105
-all
100
E
&"il -
llimilmirli
95
.
0
i5 90
E
,.,
00
80
75
/fl
7 ~A
0
!
5
,
I l ,
10
[
,
15
,
I.
20
25
30 35 40
time [second]
45
50
55
60
Figure F.6: Reservoir temperature vs. time for E3- 1.
88
65
70
E3-1
40n
EOV
11
solid line: acrossthrottle
dottedline: acrossfeeder tube
160
140
120
A.100
ou
-o 80
(I
·
60
...-
<~~~~~~...~~~~I
¢.
...
40
20
0
0
5
10
15
20
25
30 35 40
time [second]
45
50
55
60
65
70
Figure F.7: Pressure drops across the throttle and feeder tubes vs. time for E3-1.
E3-1
Juu
---
,
i
.
.
.
.
.
.
280
260
240
220
200
. 180
solid line: reservoir
dottedline: mainvessel
2160
c
140
0-120
100
80
60
40
20
t3
v00
I
5
I
10
I
15
I
20
I
25
I
30 35 40
time [second]
I
I
I
I
I
45
50
55
60
65
70
Figure F.8: Reservoir and main vessel pressure vs. time for E3-1.
89
Experiment E3-2
E3-2
0
'n
atL
5
0
10
15
20
25
30 35 40
time [second]
45
50
55
b5
60
Figure F.9: Reservoir hydrostatic pressure vs. time for E3-2.
E3-2
I
, lu
I
I
!
I
I,
I
I
I
I
I
105 F
100
f
I
I
I II
9
95
Al
I IIIIIII161
1111
1.1IIIIIIIIIIIII
I I.IIIIII III
WISMAINM
111
I -111111-11
11
1111111
-I 11I 111
1 IFITT7
qI I 101
P -IIFIIIIIli
11I
1I I
I
E)
aE
C.
E
C)
90
f-1
00
_
so80
75
/(!
0
I.
5
I
10
.
.
.
15
20
25
.
.
.
30 35 40
time [second]
.
.
.
.
I
45
50
55
60
65
Figure F.10: Reservoir temperature vs. time for E3-2.
90
70
70
E3-2
Q.
.o
'0
-0
'a2
0
2.
(/
0
time [second]
Figure F.11: Pressure drops across the throttle and feeder tubes vs. time for E3-2.
E3-2
.,
300
280
260
240
220
200
· 180
solid line: reservoir
dottedline: mainvessel
O.
0 160
0 140
I
.19l
100
.....
~..,......
......
80
60
40
20
I!,
0
I
I
I
I
5
10
15
20
i
25
i
i
I
30 35 40
time [second]
I
45
i
50
i
55
Ii
60
65
70
Figure F.12: Reservoir and main vessel pressure vs. time for E3-2.
91
Experiment E3-5
E3-5
0
time [second]
Figure F.13: Reservoir hydrostatic pressure vs. time for E3-5.
E3-5
.4d
1 l
105
100
E
I ,1
I
I
I
IIII, III Ad
11
J
-i..
L111111.,1114
95 5 qlqq
llil'
ll
,.,n'r''r''
" II l
.
I
I I IIII
90
213.
a
E
85
80
75
/fn
7 ~A
0S0
,,
l
5
l
i
i
10
15
i
20
l
25
30 35 40
time [second]
45
50
55
60
65
Figure F.14: Reservoir temperature vs. time for E3-5.
92
70
E3-5
180
II
I
~I
i
!
I
160
140
I
IT
I
I
solid line: acrossthrottle
dottedline acrossfeedertube
i
120
. 100
0L
02
-o 80I
0
e 60I
0.
40
20
4-" ..-.
0
-
worl
0
I.
.
.
5
10
15
.
20
I
I
30 35 40
time [second]
.
.
25
.
.
.
.
45
.
50
55
I
60
.
65
70
Figure F.15: Pressure drops across the throttle and feeder tubes vs. time for E3-5.
E3-5
300
.
.
I
.
.
.
.
.
280
260
240
220
200
Y180
solid line: reservoir
dotted line: mainvessel
0
a160
e
' 140
0
e 120
,
100
..........
80
.
.....
.....-
I
.,
I
15
20
25
'....'
60
40
20
A
I13
,
5
,
10
,
,
I
30 35 40
time [second]
,
*
45
50
I
55
*
60
I
65
70
Figure F.16: Reservoir and main vessel pressure vs. time for E3-5.
93
Experiment E3-6
E3-6
0.45
0.4
0.35
0.3
0
Q
w0.25
2
0.2
a-)
a-O.
0.15
0.1
0.05
0
5
10
15
20
25
30 35 40
time [second]
45
50
55
60
65
70
Figure F.17: Reservoir hydrostatic pressure vs. time for E3-6.
E3-6
110
105i1 00
M4%
L'L".
I
T MMIMNIIIIII F
I
_ U-
V 90
a)
E
85
80
75
70
0
I
l
.......
---
I
5
....
--
I
10
I
--
15
m
20
--
I
25
I
I
f
30 35 40
time [second]
I
45
I
50
I
~
f
55
60
65
Figure F.18: Reservoir temperature vs. time for E3-6.
94
70
E3-6
w
0)
.
0.,0
U)
0.
time[second]
Figure F.19: Pressure drops across the throttle and feeder tubes vs. time for E3-6.
E3-6
rrll I! I
,
*
.
,
.
.
.
I
I
,
,
*
,
l
10
solid line: reservoir
i0
dotted line: mainvessel
28
10
26
24
2210
Io
10
'1E
a.1E
a-)
14
0 2
ic10
. ....
....
...........
;~ .....
830
t0
40
6
. .
..
.........
..
............-
..
..........
.........
.
-..........
... ..
.
4
2
0
I
I
5
10
.
.
15
1I1
20
I
I
25
I
I
30 35 40
time [second]
I
I
I
I
I
45
50
55
60
65
70
Figure F.20: Reservoir and main vessel pressure vs. time for E3-6.
95
Experiment E3-7
E3-7
.Le
0
o.
0
0
aVD
0
time [second]
Figure F.21: Reservoir hydrostatic pressure vs. time for E3-7.
E3-7
110
I
[I
I
I
I
105
100
E
95
0
0
90
III
I
E
No
111U11111,11
Mrip11111?
11q1
fill"
111111 i
II
II I I
sINO'"11'"''1 luimhqi11
85
80
75
"'Jn'
IEI
0
I
I
I
I
I
5
10
15
20
25
30 35 40
time [second]
45
50
55
60
Figure F.22: Reservoir temperature vs. time for E3-7.
96
65
70
E3-7
- I -
.
I
I
I
I
I
I
I
I
-
I
I
200
~
[\~~~~~~~~
150
solid line: acrossthrottle
dottedline: acrossfeedertube
,
0
0.
I
CL.
2 100I
a
I
0
0
I.
0.
50I
0I
I
I
0
5
10
15
20
I
I
25
30 35 40
time [second]
I
I
45
50
55
60
65
70
Figure F.23: Pressure drops across the throttle and feeder tubes vs. time for E3-7.
E3-7
.
,
....
.
.
.
.
.
..
3C
3O
10
28
10
26
24
2260
0
2C40
2
·.r 18-0
solid line: reservoir
dottedline: mainvessel
16
10
aX21210
n
1 80
40
.........
860
.
.
...
.
640
...
420
io
.
2-0
0
5
10
15
20
25
30 35 40 45
time second]
50
55
60
65
70
Figure F.24: Reservoir and main vessel pressure vs. time for E3-7.
97
Experiment E4-1
E4-1
0
5
10
15
20
25
30 35 40
time [second]
45
50
55
60
65
70
Figure F.25: Reservoir hydrostatic pressure vs. time for E4-1.
110
.
.
.
.
10
15
20
25
..
E4-1
.
.
.
50
55
60
105
100
1-:
90
E
CD
85
80
75
70
0
5
30 35
40
time [second]
45
Figure F.26: Reservoir temperature vs. time for E4-1.
98
65
70
E4-1
iduu
solid line: reservoir
dottedline: mainvessel
260
240
220
200
180
*' 160
E 140
07
E 120
0.
100
80
60
40
20
II
I
0
5
10
15
20
25
30 35 40
time [second]
45
50
55
60
65
70
Figure F.27: Reservoir and main vessel pressure vs. time for E4-1.
E4-1
1.4
-
. 1.2=
'El1.0
-Z
0.8 10
0.6 -
b0
.N 0.4E0.2-
0.0
0.0
-
a
a
i
c
feedertube
b
b
d
d
feeder tube
Figure F.28: Flow distribution for E4-1.
99
e
e
Experiment E4-2
E4-2
c
to
a
2
a.
0
5
10
15
20
25
30 35 40
time [second]
45
50
55
60
65
70
Figure F.29: Reservoir hydrostatic pressure vs. time for E4-2.
E4-2
]
,I
105 IAll
n
l%
L
95
II
El
)
95
IL LIIILIjw
1.1.11I 11,1111h
1.111
111101111"I"
ai
i
- I - -,
MIM"I
90
E
a)
85
80
75
f(I
#TJ.......
0
I
5
I
10
I
15
I
20
&
25
f
r
I
30 35 40
time [second]
I
I
45
50
W
I
55
60
Figure F.30: Reservoir temperature vs. time for E4-2.
100
I
65
70
E4-2
3001
,
solid lne reser
,
280
260
240
220
200
._
solid line: reservoir
180
160
dotted line ·main vessel
2160F
140
120
100
80-
60
40
20
il
I
0
5
,
,
10
15
.
,
20
Io
25
F
Is
30 35 40
time [second]
I,
45
50
I
I,
55
60
65
Figure F.31: Reservoir and main vessel pressure vs. time for E4-2.
E4-2
1.4 > 1.2%2
'0)
-
. I9 0.8
0,6
5 0.2 -
z
0.0 a
I
c
feedertube
b
b
d
d
feeder tube
Figure F.32: Flow distribution for E4-2.
101
e
e
70
Experiment E4-3
E4-3
0
5
10
15
20
25
30 35 40
time [second]
45
50
55
60
65
70
Figure F.33: Reservoir hydrostatic pressure vs. time for E4-3.
E4-3
441'
[IV
l l1
105
100
95
.u.
.
E
0
90
_
85
80 11
iII
grflir'Ial-l
I
ill
r1l1
I I I l 1ni'i
-PI
I q - il- I Il
75
·,7f~.
,..I
v
_
5
10
15
20
25
30 35 40
time [second]
45
50
55
60
Figure F.34: Reservoir temperature vs. time for E4-3.
102
65
70
E4-3
300
280
260
240
220
200
solid line: reservoir
dottedline: mainvessel
'18 0
16 0
140
co)
02
120
100
8;0
60
40
2_0
0
I
I
I
I
I
5
10
15
20
25
I
I
I
30 35 40
time [second]
I
I
I
45
50
55
I
60
65
70
Figure F.35: Reservoir and main vessel pressure vs. time for E4-3.
E4-3
1.4 > 1.2-
d
0.8 -
0.6
· 0.4 c 0.4 -~
CO
° 0.20.0 a
b
d
feeder tube
Figure F.36: Flow distribution for E4-3.
103
e
e
Experiment E4-4
E4-4
0.45
0.4
0.35
0.3
'a
CL)
._
_ 0.25
.5
0)
2
0.2
.
a0.15
0.1
0.05
tn
I1 __
0
5
10
15
20
25
30 35 40
time [second]
45
50
55
60
65
70
Figure F.37: Reservoir hydrostatic pressure vs. time for E4-4.
E4-4
U
11en
I
I
I
I
I
I
I
I
1065
10)0
E
9}5
.Q
90
.11J. U
L wI&
.
'ITIllp
.
60
70
ITI111111111101171
I 1111
E
a)
85
80
75
7n
v
_I
5
I
10
15
I
I
20
25
I
I
____________
30 35 40
time [second]
I
45
50
55
Figure F.38: Reservoir temperature vs. time for E4-4.
104
65
E4-4
280
solid line: reservoir
dottedline: mainvessel
260
240
220
200
. 180
a160
=. 1 40
u)
0.120
100
80
60
40 :
20
0
0
5
10
15
20
25
30 35 40
time lseco
45
50
55
60
65
70
Figure F.39: Reservoir and main vessel pressure vs. time for E4-4.
E4-4
1.4
_.
>
1.2 -
"31.0-
p
3
.=~
'~0.6 .~ 0.4-
z 0.0 00
a
a
I
b
b
c
feeder tube
d
d
Figure F.40: Flow distribution for E4-4.
105
e
e
Experiment E4-5
E4-5
co
n
a
0
5
10
15
20
25
30 35 40
time [second]
45
50
55
60
5b
70
Figure F.41: Reservoir hydrostatic pressure vs. time for E4-5.
E4-5
al ale~,
Il
105
100
95
E! 90
a>
E
85
Ilkiak
I'lliI.Addil
85
80
75
I
II
7
0
5
10
15
I
I
II
20
25
30 35 40
time[second]
I
45
I
I
50
55
-
I
60
Figure F.42: Reservoir temperature vs. time for E4-5.
106
65
70
E4-5
300
_s
~ll,,
iI
I
I
Ii!
i
280
260
240
220
200
solid line: reservoir
dottedline: mainvessel
W180
-160
a)
co 140
C.120
100
80
60
40
20
0
5
10
15
20
25
30 35 40
time [second]
45
50
55
60
65
70
Figure F.43: Reservoir and main vessel pressure vs. time for E4-5.
E4-5
1.4 > 1.2 -
' o.1.0 ;=
C
0----
0.8 -
-0 0.6
I-
IQ0.4 cd
;0.2 0.0
a
a
b
b
I
c
feedertube
feeder
tube
d
d
Figure F.44: Flow distribution for E4-5.
107
e
e
Experiment E4-6
E4-6
0
5
10
15
20
25
30 35 40
time [second]
45
50
55
60
65
70
Figure F.45: Reservoir hydrostatic pressure vs. time for E4-6.
E4-6
110
105
100
1,111,1,14iia
117
E
14,IT 111,1117
,11110
95
I
'10
e 90
C
E
e 85
80
75
7n
0t
.
.
10
15
I
20
25
.
. 35 40
30
time [second]
.
45
I
50
.
55
.
60
Figure F.46: Reservoir temperature vs. time for E4-6.
108
.
65
70
E4-6
-uv
280
260
240
220
200
solid line: reservoir
dottedline: mainvessel
.180
160
3 140
C
..... I
.-.......
......
........
120
120
100
O/*
Ou
A.... ... "..
60
40
20
0
5
10
15
20
25
30 35 40
time[second]
45
50
55
60
65
70
Figure F.47: Reservoir and main vessel pressure vs. time for E4-6.
E4-6
1.4 -
>.20.
'S 1.0 -
z
§0.8
;-
-
.m
40.6 .N 0.4 -
;< 0.2 0.0 a
a
b
b
d
feeder tube
Figure F.48: Flow distribution for E4-6.
109
e
e
Experiment E5-1
E5-1
C?
I~,
In
8 |
.h
11
v
-
t
i
l
l
0.45
MIAA.L.,Illj
0.4 ."I"
F
I
Wk. - L ..
I .
. . 1,
A
thujh
0.35
'n 0.3
a
._.
20.25
a0)
a- 0.2
0.15
0.1
0.05
t
I
0I
5
I
10
15
20
I
25
30 35 40
time [second]
I
I
45
50
55
60
70
65
Figure F.49: Reservoir hydrostatic pressure vs. time for E5-1.
E5-1
_
l
Ill it}wv
1 .,
{
4
l
|
.
ffi
ffi
z
X
i
i
l
l
-
l
-
l
l
-
-
105
100
ili
W, II
I
U' 95
.)
,ia)
C 90I
0
E
- 85
80
75
,.".
I
Co
I I
5
10
15
20
I
25
I
30 35 40
time [second]
45
I
50
55
I
60
65
Figure F.50: Reservoir temperature vs. time for E5-1.
110
70
E5-1
I
I
I
I
I
I
200
solid line across throttle
dotted line across feeder tube
150
a,
.
- 100
I_
0
i
0
Q
03.
50
0
0
5
10
15
20
25
30 35 40
time [second]
45
50
55
60
65
70
Figure F.51: Pressure drops across the throttle and feeder tubes vs. time for E5-1.
E5-1
30)0
2880
2660
2440
2220
20
0(
2000
*1
0.
1880
solid line: reservoir
dottedline : mainvessel
1660
ap
1 40
D14
30
0.1220
tO
1000
..
880
.0
60
6)0
430
40
2
0
.
,..-
~~~~~~~~~~~~~.,
I
,
I
I
5
10
I
I
I
15
20
25
I
I
I
30 35 40
time [second]
I
45
I
50
I
55
I I
60
65
70
Figure F.52: Reservoir and main vessel pressure vs. time for E5-1.
111
Experiment E5-2
E5-2
0)
a
0
a.-
0
time[second]
Figure F.53: Reservoir hydrostatic pressure vs. time for E5-2.
E5-2
110
I
I
I
I
I
I
I
105
100
[III
IM
95
1ARIIIA
l
111,Iq
IllrMlIMM7171111111
i
'Irl"
J-111-fil
.
I I- .1 r IT
-
0)
0
0..
:3
90
E
02
85
80
75
0
5
10
15
I
20
25
I
30 35 40
time [second]
45
I
50
55
I
60
Figure F.54: Reservoir temperature vs. time for E5-2.
112
I
65
70
E5-2
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
300
............
28 0
260
240
220
200
solid line: reservoir
dottedline: mainvessel
30
._18
0.
-16
E
c14
So 60
s.1
8 0
......
.0
00
E20
80
6
60
4
4-0
2
0
5
10
..
15
20
25
30 35 40
time [second]
45
....
50
55
65
60
70
Figure F.55: Reservoir and main vessel pressure vs. time for E5-2.
E5-2
1.4 > 1.2 -
' .) 1.0 -r
0.8 a.
0.6 . 0.4 -
z0 0.20.0
-
a
a
I
C
b
b
d
d
feeder tube
Figure F.56: Flow distribution for E5-2.
113
e
e
Experiment E5-3
E5-3
C,
.5
5)
2
CL
0)
0
5
10
15
20
25
30 35 40
time [second]
45
50
55
60
65
70
Figure F.57: Reservoir hydrostatic pressure vs. time for E5-3.
E5-3
110
105 t100 F
_
il
1I IIn 1 111
II1 1
III"
I 111
'a 90
E
c)
A,
I"111
ItI
11ill III IIIAll ill1011
9r
vvm
a_
fire"IRMI"TIUR"Iff,
.. l '
'"I.'.
M-T--
'.' '
85
80
7J::
fi^
Jn
0
10
15
20
25
30 35 40
time [second]
45
50
55
60
Figure F.58: Reservoir temperature vs. time for E5-3.
114
65
70
E5-3
............
I
200
180
solid line: across throttle
dottedline: acrossfeedertube
160
140
120
-C
.100
~, 8o
ED 40
60
2 80
0D
CD
a2-60
40
20
..........
'''.oo......
0
-20
.
0
5
10
~~~~~ ~ ~ ~ ~ ~ ~. ~ . ~..~. ~ .
15
20
25
30 35 40
time [second]
45
.
.. ...
50
.
55
.
60
.
65
70
Figure F.59: Pressure drops across the throttle and feeder tubes vs. time for E5-3.
E5-3
300
..
,
.
.
l
l
....
l
l
280
260
240
220
200
I
· 180
solid line: reservoir
dottedline: mainvessel
2 160
' 140
0-120
;
100
80
60
40
,,"''"'.-'""''
I
0
5
10
I
15
20
I
25
I
I
30 35 40
time [second]
I
45
50
55
60
65
I
70
Figure F.60: Reservoir and main vessel pressure vs. time for E5-3.
115
..-
Experiment E5-4
E5-4
U,
.5
a
I=
0
a-
a.
0
5
10
15
25
20
30 35 40
time[second]
45
50
55
60
65
70
Figure F.61: Reservoir hydrostatic pressure vs. time for E5-4.
11..I
E5-4
,
A.
,
,
,
,
,
,
,
.
.
.
.
.
1A.Ub
100
E
a)
a)
.
E
_D
,
i
lia 11.;,a,11IJ.1
1ll
95
90
85 ,
l,
I...'LuiIIIl
l
...
,l ,l ,
l
lla
la
l,
,l,
l
l
80
75
7t3
0
I
I
I
I
5
10
15
20
I
25
I
I
30 35 40
time [second]
I
I
I
I
I
45
50
55
60
65
Figure F.62: Reservoir temperature vs. time for E5-4.
116
70
E5-4
to,%
if l
I
I
I
- I
I
I
I
I
28ouu
280
260
240
220
200
solid line: reservoir
dottedline : mainvessel
180
' 160
'a) 140
2 120
100
80
60
40
20
0
5
10
15
20
25
30 35 40
time [second]
45
50
55
60
65
70
Figure F.63: Reservoir and main vessel pressure vs. time for E5-4.
E5-4
1.4 > 1.2 ©
ra
. 1.0 cr
.O
."U 0.6 te
z 0.
0.0
-
a
a
I
c
feedertube
b
b
d
d
feeder tube
Figure F.64: Flow distribution for E5-4.
117
e
e
Experiment E6-1
E6-1
0.5
0.45
0.4
0.35
'a 0.3
.
e0
I0.2
llkMAd'A.IU.Wl
a)
77`17
0.15
0.1
0.05
0
.
.
I
.
I
5
10
15
20
25
.
I
I
30 35 40
time [second]
I
I
.
.
.
45
50
55
60
65
70
Figure F.65: Reservoir hydrostatic pressure vs. time for E6-1.
E6-1
110
105
100
cS95
Ia) 90
I
I
ii ,
I
i
I
i
I
i
I
i
[
,
I
,
I
,~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
0.
E
G)
85
80
75
'I
-
7f
I
0
5
I
10
15
l
20
25
30 35 40
time [second]
45
l
l
l
l
50
55
60
65
Figure F.66: Reservoir temperature vs. time for E6- 1.
118
70
E6-1
300
280
260
240
220
200
solid line: reservoir
dotted line: main vessel
X 180
160
' 140
a 120
100
80
60
40
20
n
v0
I
5
10
.
I
15
20
25
.
30 35 40
time [second]
,
I
45
50
55
60
65
70
Figure F.67: Reservoir and main vessel pressure vs. time for E6- 1.
E6-1
1.4,-.
> 1.27:)
-
1.0-
To
.00 0.8 -oP
0.2 0.0 a
b
C
d
feeder tube
Figure F.68: Flow distribution for E6-1.
119
e
e
Experiment E6-3
E6-3
0
5
10
15
20
25
30 35 40
time [second]
45
50
55
60
65
70
Figure F.69: Reservoir hydrostatic pressure vs. time for E6-3.
E6-3
441~x
ILU
105
100
lljwj,Jjj
ilwab
E 95
166,1"
VTP-111-1
11
i
II PT"
-
0
E 90
E
0
85
80
75
7n
'0
I
I
I
5
10
15
I
20
25
30 35 40
time [second]
I
I
45
50
55
60
Figure F.70: Reservoir temperature vs. time for E6-3.
120
65
70
E6-3
On~t'
iH(l
solid line: acrossthrottle
dottedline: acrossfeedertube
160
140
120
!
._
oA100
'g 1O0
a
80
) 60
40
40
..............................
20
. .. ... .... ......
0
-1
I
.o
0
5
I
10
I
15
t
I
20
25
l
I
l
I
30 35 40
time [second]
i
45
50
l
55
l
60
65
70
Figure F.71: Pressure drops across the throttle and feeder tubes vs. time for E6-3.
E6-3
300
280
260
240
......
220
-
200
solidline: reservoir
dottedline: mainvessel
a,180
.
. 160
' 140
.120
100
80
60
40
20
I
0
5
.
10
.
15
.
.
20
25
.
.
I.
30 35 40
time [second]
I.
45
i
.I
50
55
60
65
70
Figure F.72: Reservoir and main vessel pressure vs. time for E6-3.
121
Experiment E6-4
E6-4
a
.0
a
In
II
CL
time [second]
Figure F.73: Reservoir hydrostatic pressure vs. time for E6-4.
E6-4
,An
lit
TV
11
'
'
'
s
l
-
.
'
'
'
105I
100t
I
I
95 I
NIAI1illt
La ,1l ,11FTlII90
l 11
11
I
lI
I
,
I II'l
.
,
,I
I11
,
I
ITIT"FrTI11,11'1i1II
Wrwl"
,.
lrI..qIIIIlllII Ill
I
0)
0,)
0-
E
w
85H80
I
75
/t
I_
0
5
10
15
20
25
30 35 40
time [second]
45
50
55
60
Figure F.74: Reservoir temperature vs. time for E6-4.
122
65
70
E6-4
200
180
solid line across throttle
dotted line across feeder tube
160
140
c 120
2 100
80
en 80
w
60
40
"
20
- , , , -.- .....
- .........- .-.- .... I -- .-,
- . - 1. ..
-
0
nor
mf~m
.
0
5
10
15
20
25
.
.
.
30 35 40
time [second]
.
45
.
50
.
55
.
60
65
70
Figure F.75: Pressure drops across the throttle and feeder tubes vs. time for E6-4.
E6-4
300
i
,I
iI
,I
,
,
,
,I
i
,
,
,
i
280
260
240
220
200
· 180
solid line: reservoir
dottedline: main vessel
.
E 160
° 140
120
100
80
60
40
20
0
5
10
15
20
25
30 35 40
time [second]
45
50
55
60
65
70
Figure F.76: Reservoir and main vessel pressure vs. time for E6-4.
123
Experiment E6-5
E6-5
CD
a
0
2CD
._
%
0
time[second]
Figure F.77: Reservoir hydrostatic pressure vs. time for E6-5.
E6-5
.
.
I.110
.
.
.
.
15
20
25
.
.
.
.
.
.
.
I
I
I
I
30 35 40
time [second]
45
50
55
60
65
1105
I100
95
E
0
0.
90
E
a)
85
80
75
I7
I
0'
5
10
I
I
Figure F.78: Reservoir temperature vs. time for E6-5.
124
70
E6-5
300
I
I
I
I
I
I
I
I
I
I,
280
260
240
220
200
solidline: reservoir
dottedline: mainvessel
5.180
160
2
' 140
(o
120
100
80
60
40
20
n
0
I
I
I
I
I
5
10
15
20
25
I
I
t
30 35 40
time [second]
I
I
I
I
I
45
50
55
60
65
70
Figure F.79: Reservoir and main vessel pressure vs. time for E6-5.
E6-5
1.4
-
1.2aI)
,1.0
-
0.8 I'l
._..
U0.6 .i
- 0.4 -
zo O.20.0-
I
I
a
b
I
I
I
c
d
e
feeder tube
Figure F.80: Flow distribution for E6-5.
125
-
Experiment E7-1
E7-1
0
5
10
15
20
25
30 35 40
time[second]
45
50
55
60
65
70
Figure F.81: Reservoir hydrostatic pressure vs. time for E7-1.
E7-1
1v110
l
l
l
l
105F
100h
-
95
I
!L
'
I III
1
11611110
TN
90
Ec)
85
80
75
71
O
I
I
I
5
10
15
I
20
Ir
25
I
I
30 35 40
time [second]
I
I
45
50
I
55
I
60
Figure F.82: Reservoir temperature vs. time for E7- 1.
126
65
70
--- I
:4. I
-1
~~~~~~~~~~I
T
T
r
I
E7-1
r
I
I
rI
I
I
280
260
240
220
200
.'180
solid line: reservoir
dottedline: mainvessel
0.
-160
.e
3 140
ID
c120
,.................
., ................................
80
.....................
A
....
100
...
,.
". ..
60
40
20
0
i
i
5
10
i
15
i
I
20
25
i
i
i
30 35 40
time [second]
i
i
i
i
!
45
50
55
60
65
70
Figure F.83: Reservoir and main vessel pressure vs. time for E7-1.
E7-1
1.4 -
z.
g 1.2-
,
' 1.0 -
=0.8 -!0.6
. 0.4 -
o0.2
0
0.0
a
a
i
b
b
d
d
feeder tube
Figure F.84: Flow distribution for E7-1.
127
e
e
Experiment E7-2
E7-2
0
5
10
15
20
25
30 35 40
time [second]
45
50
55
60
65
70
Figure F.85: Reservoir hydrostatic pressure vs. time for E7-2.
E7-2
1 110
l
l
105
100
L1,1,LJ1JJJikL
,A,=
A_
E
a)
iL
E
U)
(1
I LI8IIII'llllIi'I
1101
wmwi
M
IM111,111,11
"I" I I I 'r 1,RI ""I I 11 II 11I I
25
30 35 40
time [second]
90
85
80
75
7(.
5
0
5
10
15
20
45
50
55
60
Figure F.86: Reservoir temperature vs. time for E7-2.
128
I
65
70
E7-2
a.
0
0
a.
0-3
0
5
10
15
20
25
30 35 40
time [second]
45
50
55
60
65
A
70
Figure F.87: Pressure drops across the throttle and feeder tubes vs. time for E7-2.
E7-2
iI
,
-
l
I
300
280
260
240
220
200
· 180
solid line: reservoir
dottedline: mainvessel
a.
. 160
C
140
Q14
,e
o-120
100
,....................................
....-
, ,~~~~~~~~~~.
8
...
.....
.~~.
--
6tO
4.0
.
.
.
.
.
10
15
20
25
.
.
.
.
.
.
45
50
55
60
2 0l
0
5
30 35 40
time [second]
65
70
Figure F.88: Reservoir and main vessel pressure vs. time for E7-2.
129
Experiment E7-3
E7-3
0.45
0
time[second]
Figure F.89: Reservoir hydrostatic pressure vs. time for E7-3.
E7-3
44^
11U
105 k
100 I-
Irl
E 95
G)
1111
1 i III
I I
UU
I
li
I,
I 11
111
1 I11iiII
III M
1111.11
II
H
, 171"R4,941TIM11
111111will
o
E
)
85
80
75
t0
On
_
I
I
5
10
15
I
I
I
I
I
20
25
30 35 40
time [second]
45
50
55
60
Figure F.90: Reservoir temperature vs. time for E7-3.
130
65
70
E7-3
time [second]
Figure F.91: Pressure drops across the throttle and feeder tubes vs. time for E7-3.
E7-3
|
g
l
8
300
280
260
240
220
200
solid line: reservoir
dottedline: mainvessel
· 5 180
.
2 160
= 140
0120
100
80
60
40
20
n1
0
il
5
10
il
15
l
20
l
25
i
!
l
30 35 40
time [second]
a
l
E
l
i
45
50
55
60
65
70
Figure F.92: Reservoir and main vessel pressure vs. time for E7-3.
131
Experiment E7-4
E7-4
f, r-
U.
0.4
0.
0.3
to o.
2 0.2
a)
coi
%
0.1
0.
0.0
To
time[second]
Figure F.93: Reservoir hydrostatic pressure vs. time for E7-4.
E7-4
11
E,
a)
C.E
U)
time[second]
Figure F.94: Reservoir temperature vs. time for E7-4.
132
D
E7-4
JU
280
260
240
220
200
W180
solidline: reservoir
dottedline: mainvessel
0.A
160
140
C0
0.
120
100
80
l
~~~~~..........
....
... ,......
.................
--..............
-'
60
40
20
II
0
I
5
I
10
I
15
I
I
20
25
I
I
I
30 35 40
time [second]
I
I
A
I
I
45
50
55
60
65
70
Figure F.95: Reservoir and main vessel pressure vs. time for E7-4.
E7-4
I.41 A
-
> 12 n.:
' 1.0 -I 0.8 0.
0.6 0)
. 0.4 E
z0.2
0.0 -
-
I
I
a
b
I
I
c
d
feeder tube
Figure F.96: Flow distribution for E7-4.
133
e
Appendix G
Calculations of Mass Flow Rate
The mass flow rate, m, of a liquid flowing out of a container can be described as
= pA .ddh
dt
(G.1)
where p is the liquid density, A is the cross-sectional area, and
dh
-
is the rate of change of
container.
liquid level in the
liquid level in the container.
dh
We can use the liquid hydrostatic pressure measurement to determine dt
Since
P = p -g -h
,
(G.2)
by differentiating it with respect of time, we get
dP
dt
dh
(G.3)
Pgdt
Thus, once we know the rate of hydrostatic pressure change, we can determine the mass
dP
flow rate. Appendix H shows the calculation to get dP from the experimental data. The
calculation for the reservoir's cross-sectional area is discussed in Appendix I.
Another method of getting dh is by using a stop watch or any time-measuring device
to record the liquid level change rate.
134
Appendix H
Slope Determination through Least-Squares Regression
(Chapra, 1988)
As discussed in Appendix G, we are interested in determining the slope, dPinesr
P in reservoir hydrostatic pressure vs. time plots. To fit a line to the plots, I use Least-Squares
Regression. Since I expect the line to be a straight line, linear regression, which fits a
straight line to a set of paired data:
(x, ly),
(x 2, 2)
... ,
(x, yn)
,
is used. The mathe-
matical expression for the straight line is
y = a + alx + e
(H.1)
where a is the intercept at the y-axis, a is the slope of the straight line, and e is the error.
By linear regression approximation, the slope, a, is
nExiyi al = nEx2 _
i
(xiHY
(H.2)
and the summations are from i = 1 to n.
The y-axis intercept, a, is given by
ao =
where
-ax
(H.3)
and x are the means of y and x, respectively.
The error, e, which is the discrepancy between the true value of y and the approximate
value, is expressed as
135
e = y-a,-a!X
136
(H.4)
Appendix I
Reservoir Cross-Sectional Area Calculation
The coils in the reservoir complicate mass flow rate calculation in equation (G-1) since
the cross-sectional area is not uniform throughout the height. In order to simplify the calculation, I approximate the reservoir with another constant cross-sectional area cylinder.
The coils occupy the space in the reservoir up to a height of 7.25 inches. The outer
diameter of the coils is 0.375 inches. Therefore, if all the coils are packed adjacently without space in between, there will be approximately
7.25
725= 19 coils
0.375
in the reservoir. Assume the spacing between the coils is about the size of the coil diameter, then there are approximately 10 coils.
The volume occupied by a single coil is approximated by
(coil cross-sectional area)
2. X.
(coil radius)
0.375 2 .2.'.i- 5.25
T= . (-T-Z)
-
1.8216 in3 .
Therefore the total volume taken by the 10 coils is 18.216 in3 .
The total volume of liquid the reservoir can take up to a height of 7.25 inch is therefore
(n. (4)2. 7.25) - 18.216 = 346.21
in3
and thus the constant area cylinder which approximates the reservoir has a cross-sectional
area of
346.21
7.25
47.75
5i
137
in 2.
Appendix J
Computer Simulation and Codes
All computer programs in this thesis were written and run in MATLAB. The R-22
property table used was generated by NIST's database program (Ely 1989). In order to
read the values from the Baroczy correlation multiplier and correction factor figures, I
took data points on the figures and put them in matrix form. Two-dimensional interpolation was used to get the values from the matrices. The friction factor in a pipe was evaluated by using Colebrook formula (Munson, 1990).
%**
* ***
**
****
***
***
***
* ******
**
* **
**
**
***
**
* ***
**
**
**
* ****
**
****
% Program: Integrated Henry-Fauske and Flow Distribution Model
%
written by,
%
Sheit Sheng Chen
%
Massachusetts Institute of Technology
%
1995
%
This program calculates the mass flow rate based on
%
Henry-Fauske model.The flow rate is then used as an input
%
to the flow distribution model to predict the mass flow
%
rate in each feeder tube and pressure drop across
%
the feeder tubes.
% ---- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - % external files used:
% R22 : R22 property table
: Baroczy correlation multiplier table
% M
: Baroczy correlation correction factor table for mass
% C2
%
flux = 2e6 lbm/(hr*ft^2)
: Baroczy correlation correction factor table for mass
% C3
flux = 3e6 lbm/(hr*ft^2)
%
% external functions used:
: evaluates the friction factor
% evalffactor()
: evaluates the correction factor in Baroczy
% eval_Omega()
%
correlation
: evaluates the multiplier in Baroczy correlation
% eval_Phi()
% solve-model() : solves the 6-equation, 6-unknowns refrigerant flow
distribution model
%
% variables:
%
Dt : diameter of throttle (inch)
%
138
%
%
f : friction factor in feeder tube
FBa
Baroczy friction factor for feeder tube "a";
%
FBb
Baroczy friction factor for feeder tube "b";
%
FBa = f*Phi*Omega at b
FBc : Baroczy friction factor for feeder tube c";
%
%
FBa = f*Phi*Omega
%
%
%
FBa = f*Phi*Omega
at c
FBd : Baroczy friction factor for feeder tube "d";
%
FBa = f*Phi*Omega at d
FBe : Baroczy friction factor for feeder tube "e";
%
%
%
at a
FBa = f*Phi*Omega
G_SI
Geg
~~% ~
at e
average mass flux in feeder tube in SI unit (kg/m^2/s)
average mass flux in feeder tube in British
unit (lbm/hr/ft^2)
%
%
%
%
%
%
hh
height of the distributor feeder tube inlet plenum (meter)
hg
enthalpy of vapor R-22 (Btu/lbm)
hl : enthalpy of liquid R-22 (Btu/lbm)
hlgs
guessed liquid enthalpy (Btu/lbm)
hlggs
guessed (hg - hl) (Btu/lbm)
hlo : stagnation liquid enthalpy (Btu/lbm)
%
K
%
La
%
La
%
%
%
%
Lb : feeder tube length
Lc : feeder tube length
Ld : feeder tube length
Le
feeder tube length
%
%
%
%
%
%
%
%
%
mdot :total mass flow rate (lbm/s)
mdot_a : mass flow rate in feeder tube "a" (kg/s)
mdot_b
mass flow rate in feeder tube "b" (kg/s)
mdot_c
mass flow rate in feeder tube "c" (kg/s)
mdot_d
mass flow rate in feeder tube "d" (kg/s)
mdote
: mass flow rate in feeder tube "e" (kg/s)
mdot_SI : total mass flow rate in SI unit (kg/s)
mdotf : average mass flow rate in a feeder tube (kg/s)
Mu : viscosity of liquid R-22 (N*s/m^2)
%
Omega : Barozcy correction factor
entrance loss factor
feeder tube length for tube "a
: feeder
tube
length
"a"
(meter)
for
for
for
for
"b"
"c"
"d"
"e"
(meter)
(meter)
(meter)
(meter)
tube
tube
tube
tube
%
P : pressure
%
%
%
%
P12_a
pressure drop from section 1 to 2 in feeder tube "a"
P23_a
pressure drop from section 2 to 3 in feeder tube "a"
P34_a
pressure drop from section 3 to 4 in feeder tube "a"
PdropSI
: model predicted pressure drop across the feeder
~% ~tubes
in SI unit (Pa)
Pdropeg
model predicted pressure drop across the feeder
~% ~tubes
in British unit (psi)
Phi
Baroczy multiplier
Po : stagnation pressure (psia)
Po_index : row number of Po in R-22 property table file
%
%
%
%
of R-22
(meter)
for tube
(psia)
139
%
%
%
%
%
%
Pratioguess : guessed critical pressure ratio
PT : throttle discharge pressure (psia)
PT_m : model predicted pressure at throttle discharge (psia)
throat pressure (psia)
Pt
main vessel pressure (psia)
Pv
Pv_index : row number of Pv in R-22 property table file
%
%
%
%
%
%
Regs : guessed Reynolds number
Re_T : Reynolds number at throttle discharge
rho_l : density of liquid R-22 (lbm/ft^3)
rho : density of R-22 mixture (kg/m^3)
Rf
feeder tube radius (meter)
RT : radius of the throttle discharge (meter)
%
%
%
Sg : entropy of vapor R-22 (Btu/lbm/R)
S1 : entropy of liquid R-22 (Btu/lbm/R)
Slo : stagnation liquid entropy (Btu/lbm/R)
(degree
T : temperature
%
%
%
%
%
Ta
Tb
Tc
Td
Te
: angle subtended at the distributor hole by feeder tube "a"
%
To
: stagnation
%
%
%
%
%
%
%
%
V1 : R-22 velocity at section 1 (m/s)
vgs
: guessed specific volume of R-22 mixture (m^3/kg)
v_T : specific volume at throttle discharge (ft^3/lbm)
vl : specific volume of liquid R-22 (ft^3/lbm)
vl_gs :guessed liquid specific volume (ft^3/lbm)
vlo : stagnation liquid specific volume (ft^3/lbm)
vg : specific volume of vapor R-22 (ft^3/lbm)
vggs
: guessed vapor specific volume (ft^3/lbm)
%
%
x : quality
xgs : guessed quality
:
:
:
:
angle
angle
angle
angle
of R-22
F)
%
subtended
subtended
subtended
subtended
at
at
at
at
the
the
the
the
distributor
distributor
distributor
distributor
**
by
by
by
by
feeder
feeder
feeder
feeder
tube
tube
tube
tube
(degree F)
temperature
%*********************
hole
hole
hole
hole
*********
****
***********************
clear;
% input variables
Dt
Po
To
Pv
=
=
=
=
0.080;
226.2;
103.9;
97.38;
%
%
%
%
throat diameter
stagnation pressure
stagnation temperature
main vessel pressure
La
Lb
Lc
Ld
=
=
=
=
0.65786;
0.65786;
0.5715;
0.50292;
%
%
%
%
feeder
feeder
feeder
feeder
tube a" length
tube "b" length
tube "c" length
tube d" length
140
"b"
"c"
"d"
"e"
Le = 0.50292;
% feeder tube "e".length
RT = 0.0027432;
Rf = 0.00124;
% t hrottle discharge radius
% feeder tube radius
% feeder tube inlet plenum height
% e ntrance loss factor
hh = 0.001;
K = 0.8;
Lavg
% average feeder tube length
= (La+Lb+Lc+Ld+Le)/5;
if Po <= Pv
error('stagnation pressure is lower or equal to vessel pressure')
end
% initialization
global
C2 C3 M;
load R22;
load M;
load C2;
load C3;
% Initialize variables
%
- - - - - - -
-
T = R22(:,2);
% temperature
rho_l = R22(:,6);
% density (liquid)
-
-
-
P = R22(:,3);
% pressure
hl = R22(:,8);
%
%
%
%
%
%
hg = R22(:,9);
Sl = R22(:,10);
Sg = R22(:,11);
vl = R22(:,4);
vg = R22(:,5);
Mu = R22(:,12)*le-7;
vlo = interpl(T,vl,To);
Slo = interpl(T,Sl,To);
hlo = interpl(T,hl,To);
-
-
-
-
-
-
-
-
-
enthalpy (liquid)
enthalpy (vapor)
entropy (liquid)
entropy (vapor)
specific volume (liquid)
specific volume (vapor)
% viscosity
% interpolate to get stagnation
%
specific volume
% interpolate to get stagnation entropy
% interpolate to get stagnation enthalpy
%**********************************
*************
*********
% PART 1: Henry-Fauske's model:
%
predict the mass flow rate
%***************************************************************
% 1.1 locate the row numbers of stagnation pressure value and
%
main vessel pressure value on R22 property table.
if Po > 274.70
141
error('stagnation pressure is out of range on the R22\
property table file')
elseif
Po > 250
= 726;
Po_start_search_index
= 800;
Po_stopsearch_index
elseif Po > 230
= 663;
Po_start_search_index
= 727;
Postopsearch_index
elseif Po > 200
= 561;
Po_start_search_index
= 664;
Postop_search_index
elseif Po > 180
= 487;
Po_start_search_index
= 562;
Po_stopsearch_index
else
Po_start_search_index
= 1;
Postop_search_index
= 487;
end
if Pv < 83.61
error('main vessel pressure is out of range on the R22\
property table file')
elseif
Pv < 90
Pv_start_search_index
Pv_stop_search_index
elseif
= 2;
= 45;
Pv < 100
= 44;
Pv_start_search_index
= 107;
Pv_stop_search_index
elseif Pv < 110
= 107;
Pv_start_search_index
= 165;
Pvstop_search_index
elseif Pv < 120
= 165;
Pv_start_search_index
= 219;
Pvstop_search_index
else
Pv_start_search_index
Pvstopsearch_index
=
= 218;
Po_start_search_index;
end
for i = Po_start_search_index:Postopsearch_index
P_Po_difference(i) = abs(P(i)-Po);
end
[num, Po_relatv_index]
= min(PPo_difference(Po_start_search_\
index:Po_stopsearchindex));
Po_index =
Po_relatv_index + Po_start_search_index - 1;
if Po_index > 599
Po_index = 599
% to avoid Tgs > lOOF since the range of Phi
% is from 40 to lOOF in M file
end
for i = Pv_start_search_index:Pvstopsearch_index
P_Pv_difference(i) = abs(P(i)-Pv);
end
142
= min(P_Pv_difference(Pv_start_search_\
[num, Pv_relatv_index]
Pv_index =
index:Pv_stop_search_index));
Pv_relatv_index + Pv_start_search_index -1 ;
% 1.2 Henry-Fauske model iteration: select the critical mass
flux where the difference between the guessed and model
%
%
predicted critical pressure ratio is the smallest.
for i= Pv_index:Po_index
derivative(i) = (Sl(i+l)-Sl(i-l))/(P(i+l)-P(i-1));
x(i) = (Slo-Sl(i))/(Sg(i)-Sl(i));
N(i) = x(i)/0.14;
Gsquare(i) = 1/((vg(i)-vlo)*N(i)*derivative(i)/(Sg(i)-Sl(i)));
Pratioguess(i) = P(i)/Po;
Pratio(i) = 1 - vlo*Gsquare(i)/(2*Po);
Pdifference(i) = abs(Pratioguess(i)- Pratio(i));
end
[minvalue, Ptrelatv_index] = min(Pdifference(Pv_index:Po_index));
Pt_index = Pt_relatv_index + Pv_index - 1;
% 1.3
Output the mass flow rate and related variables to a file
diary OUTPUT.txt
fprintf('Henry-Fauske Model result\n')
fprintf('Po
fprintf('To
fprintf('Pv
= %g.\n',
= %g.\n',
= %g.\n',
Po)
To)
Pv)
fprintf('throat pressure is %g.\n', P(Pt_index))
mdot = (sqrt(Gsquare(Pt_index)*0.2234))*pi*(Dt/2)^2
fprintf('derivative is %g.\n',derivative(Ptindex))
fprintf('x is %g.\n', x(Pt_index))
fprintf('N is %g.\n', N(Pt_index))
fprintf('Gsquare is %g.\n',Gsquare(Ptindex))
fprintf('Pratioguess is %g.\n',Pratioguess(Ptindex))
fprintf('Pratio is %g.\n',Pratio(Pt_index))
% mass flow rate in SI unit, i.e. kg/s
mdot_SI = mdot*0.4526
diary off
% PART 2: Quality Iteration at Throttle Discharge
%*******************
******
******
% 2.1 Initialize the relevant variables
i= Pv_index:Po_index;
143
*******
******************
hlgs = hl(i);
hlggs = hg(i) - hl(i);
vlgs = vl(i);
vggs = vg(i);
Mugs = Mu(i);
T_gs = interpl(P,T,P(i));
dPgs = P(i)-Pv;
x_gs = (hlo-hl_gs)./(hlggs);
mdotf = (mdot/5)*0.4536;
% 1 lbm/s = 0.4536 kg/s
G_SI = mdotf/(pi*(Rf)^2);
Geg = G_SI*737.5;
% 1 kg/s*m^2 = 737.5 lbm/hr*ft^2
if Geg
> 3.5e6
fprintf('Warning:
Geg
is too big')
end
vgs = (vlgs + x_gs.*(vggs-vl_gs)).*1/16.0185;
%
1 lbm/ft^3 = 16.0185 kg/m^3
Regs = G_SI*2*Rf./Mugs;
% 2.2 Evaluate the friction factor, multiplier, and correction factor
j = zeros(l,Poindex-Pv_index+l); % preallocate the vectors to make
f = zeros((Poindex-Pv_index+l),l); % the for loop go faster
f((Poindex-Pv_index+l),l)=1000;
Phi((Po_index-Pv_index+l),1)=1000;
Omega((Po_index-Pv_index+1),l)=1000;
for j= l:(Poindex-Pv_index+1)
if xgs(j)
< 0.001
break;
else
f(j,1) = evalfjfactor(Regs(j));
Phi(j,1) = evalPhi(Tgs(j),xgs(j));
Omega(j,1) = evalOmega(Tgs(j),x_gs(j),G_eg);
end
end
% 2.3 select the quality that gives the smallest difference
%
between the guessed and Baroczy model predicted pressure
%
drop across the feeder tubes
dP_Baroczy = f.*Phi.*Omega.*L_avg.*(G_SI^2).*v_gs.*((0.145/1000)\
/(2*2*Rf)); % 1 kPa = 0.145 psi
dPdifference= abs(dP_gs - dP_Baroczy);
[min_value, PTrelatv_index] = min(dPdifference);
PT_index = PT_relatv_index + Pv_index - 1;
144
PT = P(PT_index);
x_T = xgs(PT_relatv_index);
%***********************
**
*******************
****************
% PART 3: Flow Distribution Model
------
%------
------
------
-----
**************-*****-*********
---
% 3.1 Initialize with the values calculated in the quality iteration
v_T = v_gs(PT_relatv_index);
Re_T = Regs(PT_relatv_index);
dP_T = dP_Baroczy(PT_relatv_index);
dPdifference_T = dPdifference(PT_relatvindex);
Vl= (mdot*0.4536/(2*pi*RT*hh))*v_T;
rho = l/vT;
FBa = f(PTrelatv_index)*Phi(PT_relatv_index)*Omega(PTrelatv_index);
FBb
FBc
FBd
FBe
=
=
=
=
FBa;
FBa;
FBa;
FBa;
dumvarl = (Vl*RT/(2*pi*Rf))^2;
dumvar2 = (Vl*RT*hh/(pi*Rf^2))^2;
termla =
termlb =
termlc =
termld =
termle =
term2 =
0.5*rho*(dumvarl
0.5*rho*(dumvarl
0.5*rho*(dumvarl
0.5*rho*(dumvarl
0.5*rho*(dumvarl
0.5*rho*Vl^2;
+
+
+
+
+
K*dumvar2
K*dumvar2
K*dumvar2
K*dumvar2
K*dumvar2
% define dummy variable 1
% define dummy variable 2
+FBa*(La/(2*Rf))*dumvar2);
+FBb*(Lb/(2*Rf))*dumvar2);
+FBc*(Lc/(2*Rf))*dumvar2);
+FBd*(Ld/(2*Rf))*dumvar2);
+FBe*(Le/(2*Rf))*dumvar2);
% 3.2 Call the function that solves the flow distribution model
equations
%
[dP,Ta,Tb,Tc,Td,Te]=solve_model(termla,termlb,termlc,termld,termle,\
term2);
% 3.3 send the results to the output file
diary OUTPUT.txt
mdot_a
mdot_b
mdot_c
mdot_d
mdot_e
=
=
=
=
=
rho*Vl*RT*hh*Ta
rho*Vl*RT*hh*Tb
rho*Vl*RT*hh*Tc
rho*Vl*RT*hh*Td
rho*Vl*RT*hh*Te
145
P12_a = 0.5*rho*(dumvarl.*Ta.^2-(Vl).^2)
P23_a = 0.5*K*rho*dumvar2*Ta^2
P34_a = FBa*(La/(2*Rf))*rho*dumvar2*0.5*Ta^2
= P12_a + P23_a + P34_a
= (PdropSI/1000)*.145
PdropSI
Pdropeg
% pressure drop across feeder\
tube in psi.
% pressure at throttle discharge\
predicted by flow distribution model.
PT_m = Pdrop_eg + Pv
diary off
External functions called from the main program:
function y = eval_ffactor(x)
% This function returns the friction factor for a given Reynolds
%
number in a smooth pipe (roughness = 0) based on Colebrook
%
Formula which is valid for the entire nonlaminar range
%
of the Moody
chart.
% written by Sheit Sheng Chen, MIT, 1995.
% input: Reynolds number
% output: friction factor
f_lower_bound = 0.014;
f_upper_bound
Re_lower_bound
Re_upper_bound
Re
% this is the range of interest
= 0.030;
= e4;
= 3e5;
= x;
if Re <
e4
I Re > 3e5
error('Reynolds number is out of range')
end
f=f_lower_bound:0.0002:f_upperbound;
difference = abs((l./sqrt(f)) +2.*loglO((2.51)./(Re.*sqrt(f))));
[num, f_relatv_index]
= min(difference);
- 1)*0.0002;
f_factor = 0.014+(frelatv_index
y = f_factor;
function y = eval Omega(xl,x2,x3)
% This function evaluates the correction factor in the Baroczy's
%
correlation.
% written by Sheit Sheng Chen, MIT, 1995.
146
% inputs:
xl: temperature (degree F)
%
x2: quality
%
x3: mass flux (lbm/(hr*ft^2)
% output:
y: correction factor
% The correction factor tables C2 (For mass flux = 2e6 lbm/(hr*ft^2))
%, and C3 (For mass flux = 3e6 lbm/(hr*ft^2) ) have to be placed
% in the same directory as eval_Omega.m
T = xl;
x = x2;
Geg
= x3;
G_eg_lower_bound
= 0.75e6;
Gegupperbound
= 4.00e6;
if Geg
< Geglower_bound
I Geg > Gegupperbound
error('Geg is out of bound')
end
if 0.75e6 < G_eg & G_eg <= 1.5e6
Omega
elseif
=
1;
y = Omega;
return;
1.5e6 < G_eg & Geg
<= 2.5e6
tab = C2;
else
tab = C3;
end
Tarray = tab(:,1);
[rownum,columenum]
= size(tab);
x_lower_bound = tab(1,2);
xupper_bound = tab(1,colume_num);
T_lower_bound = tab(2,1);
Tupper_bound
= tab(rownum,
if T < T_lower_bound
1);
I T > Tupperbound
error('correction factor chart temperature out of range')
elseif x < x_lower_bound I x > xupperbound
error('correction factor chart quality out of range')
end
i = zeros(1,rownum);
% preallocate the vectors to make the
T_array_diff = zeros(1,rownum);
% for loop go faster
% perform 2-D interpolation
for i = 2:row_num
Tarraydiff(i)
if
= T - Tarray(i);
T_arraydiff(i)
Tmarkl
Tmark2
== 0
= i;
= i + 1;
break;
147
elseif
< 0
T_array_diff(i)
= i - 1;
= i;
Tmarkl
Tmark2
break;
end
end
Omegal = interpl(tab(l,:),tab(Tmarkl,:),x);
Omega_2 = interpl(tab(1,:),tab(Tmark2,:),x);
Omega_interpr = [Omega_l, Omega_2];
T_interpr = [tab(Tmarkl,l), tab(Tmark2,1)];
Omega = interpl(Tinterpr,Omega_interpr,T);
y = Omega;
function y = eval_Phi(xl,x2)
% This function evaluates the multiplier in the Baroczy's
correlation.
%
% written by Sheit Sheng Chen, MIT, 1995.
% inputs:
xl:
temperature
(degree F)
x2: quality
%
% output:
y: multiplier
% The Multiplier table M (For mass flux = e6 lbm/(hr*ft^2)) has
% to be placed in the same directory as eval_Phi.m
T = xl;
x = x2;
Tarray = M(:,);
[rownum,columenum]
= size(M);
x_lower_bound = M(1,2);
x_upper_bound = M (l,columenum);
T_lower_bound = M(2,1);
= M(rownum, 1l);
Tupper_bound
if T < T_lower_bound
I T > Tupperbound
error('multiplier table temperature out of range')
elseif
x < x_lower_bound
I x > x_upper_bound
error('multiplier table quality out of range')
end
% preallocate the vectors to make the
i = zeros(1,rownum);
% for loop go faster
T_array_diff = zeros(l,rownum);
% perform 2-D interpolation
148
for
i = 2:row_num
Tarraydiff(i)
if
= T - Tarray(i);
T_arraydiff(i)
Tmarkl
Tmark2
=
=
== 0
i;
i + 1;
break;
elseif
Tarray_diff(i)
Tmarkl
Tmark2
< 0
= i - 1;
= i;
break;
end
end
Phil = interpl(M(l,:),M(Tmarkl,:),x);
Phi_2 = interpl(M(l,:),M(Tmark2,:),x);
Phi_interpr
= [Phi_l,
Phi_2];
T_interpr = [M(Tmarkl,l), M(Tmark2,1)];
Phi = interpl(Tinterpr,Phi_interpr,T);
y = Phi;
function [u,v,w,x,y,z] = solvemodel(xl,x2,x3,x4,x5,x6)
%-_
__
_
_
_
_
_
_
% This function solves the 6-equation, 6-unknowns refrigerant flow
%
distribution model
% written by Sheit Sheng Chen, MIT, 1995.
_
%-_
_
_
_
_
_
_
_
mpa('termla',int2str(xl));
mpa('termlb',int2str(x2));
mpa('termlc',int2str(x3));
mpa('termld' int2str(x4));
mpa('termle',int2str(x5));
mpa('term2',int2str(x6));
eqnl
eqn2
eqn3
eqn4
eqn5
eqn6
=
=
=
=
=
=
'Ta
'dP
'dP
'dP
'dP
'dP
+ Tb + Tc + Td + Te - 2*pi ';
- termla*(abs(Ta)*Ta) + term2
termlb*(abs(Tb)*Tb) + term2
termlc*(abs(Tc)*Tc) + term2
termld*(abs(Td)*Td) + term2
- termle*(abs(Te)*Te) + term2
';
'
';
';
';
[u,v,w,x,y,z]=solve(eqnl,eqn2,eqn3,eqn4,eqn5,eqn6,'dP,Ta,Tb,Tc,\
Td,Te');
u = str2num(u);
v
w
x
y
=
=
=
=
str2num(v);
str2num(w);
str2num(x);
str2num(y);
z = str2num(z);
149
R22 file:
R22 file is the R-22 property table. The temperature ranges from 40.1 °F to 120.0 °F in an
increment of 0.1 °F.
M file:
0.
0.001
0.005
0.01
0.02
0.035
0.05
0.075
0.10
0.15
40
1.1220
1.349
1.6218
2.1878
3.000
3.7154
5.000
6.6069
9.3325
60
80
100
1.2882
1.3490
1.8197
2.3714
3.000
3.8019
4.6774
6.4565
7.9433
1.0715
1.047
1.2023
1.1092
1.3183
1.2162
1.6596
1.3804
2.000
1.737
2.3988
2.000
3.000
2.3174
3.5481
2.6915
4.7863
3.4674
6.000
4.2658
C2 file:
0.
40
60
0.001
0.90
0.91
0.01
0.83
0.86
0.05
0.775
0.78
0.10
0.80
0.815
0.20
0.76
0.76
80
100
0.92
0.94
0.88
0.895
0.79
0.78
0.80
0.77
0.74
0.70
70
0.915
0.87
0.80
0.815
0.755
C3 file:
0.
0.001
0.01
0.05
0.10
0.20
40
0.87
0.77
0.67
0.68
0.645
70
0.885
0.8125
0.70
0.70
0.635
100
0.90
OR0.85
0.8,n
a.... _
0. . _
V
nV . An
VV
60
80
0.20
11.12
1.0965
0.88
0.89
0.80
0.825
0.69
0.69
150
0.69
0.69
0.64
0.63
Appendix K
Experimental Data and Model Predicted Results
experiment
name
stagnation stagnation
temperature pressure
(degree F)
_
_
_ _
_
_
_
~~
_
_
Idegree
subcooled
(psia)
_
_
I
I
_
(degree F)
1
__
__
_
vessel
pressure
_
_
98.11
208.62
13-1
96.6j
3-2
__
_
(psia)
_.__
_
I
I
_
1.1000
99.79
243.031
13.9000
103.831
96.55
235.64
11.6500
105.2
97.89
244.87
13.110
95.791
194.79
-. 1900
96.87
3-7
85.57
251.9
27.4300
97.95
4-1
93.97
184.94
-3.3700
102.82
4-2
94.81
227.03
10.5900
99.1
4-3
80.21
240.54
29.4900
101.44
4-4
97.62
201.36j
-1 .0200
89.23
4-5
84.06
254.31
29.8400
91.18
f2-20
3-5
3-6
4-6
1
1
103.14
98.31
207.721
0.60001
5-1
98.171
237.791
10.73001
88.591
5-2
97.24
241.47
12.7600
93.89
5-3
94.17
217:14]
~-
05-4
~ 8
98.831
6-1
95.75
6-3
~
5
~
215.871
90.43
7.9300
~
8
2.87001
94.85]
o
s
~
95.51l
215.51
5.8500
95.19
95.491
222.541
8.4100
93.18
6-4
94.5
251.8
18.7000
79.62
6-5
97.22
250.171
15.4800
94.77
7- 1
93.451
215.98
8.2500
7-2
96.181
245.83
15.2200
7-3
74
495.71
96.911
101.5J
96.891
225.5
9.2000
93.98
245.32
14.2900
91.69
Table K.1: Experiment stagnation conditions
151
experiment
stop watch
reservoir fHenry-FauskeHenry-Fauske
name
measurement
mass flow
rate
(lbm/s)
hydrostatic
pressure
measurement
mass flow
rate
model
predicted
mass flow
rate
(lbm/s)
model
predicted
mass
flux
lbm/hr/ft^2
..........
__ _ _(lbm/s)
~
i~
2-20
0.0863
0 0
2-2
.6
0.0806
!
-
0.1782
_ ,..
2.4747e+06
..
3-1
0.1576
0.1304
0.2285
3.1736e+06
3-2
0.1113
0.1006
0.21861
3.0363e+06
3-5
0.0767
0.0675
0.0958
1.3306e+06
3-6
0.0603
0.0639
0.0726
1o0077e+06
3-7
0.0898
0.0882
0.1174
1.6302e+06
4-1
0.1135
0.0916
0.1606
2.2310e+06
4-2
0.1721
0.1128
0.2130
2.9583e+06
0.1971
0.1497
0.28271
3.9260e+06
4-4
0.0591
0.0633
0.0683
9.4837e+05
4-5
0.09141
0.0854
0.1205
1.6735e+06
4-6
0.0646
0.0643
0.0761
1.0564e+06
5-1
0.0677
0.0662
0.0926
1.2864e+06
5-2
0.08211
0.07881
0.0948
1.3163e+06
0.1817
0.1409
0.17321
0.11061
0.2013
0.1850
2.7967e+06
2.5692e+06
6-1
0.1879
0.1213
0.19791
2.7487e+06
6-3
0.1814
0.1586
0.2051
2.8485e+06
6-4
0.0982
0.0891
0.1054
1.4635e+06
6-5
0.0963
0.0925
0.0997
1.3854e+06
7-1
0.26
0.228
0.2057
2.8572e+06
7-2
0.0957
0.089
0.0990
1.3746e+06
7-3
0.1987
0.1874
0.2083
2.8926e+06
0.0911
0.0846|
0.0973
1.3517e+06
.4-3
5-3
5-4
|
7-4
|
Table K.2: Measured and model predicted mass flow rates.
152
experiment
name
Henry-Fauske Henry-Fauske Henry-Fauske
model
model
model
predicted
predicted
predicted
critical
throat
quality
pressure
pressure
at throat
ratio
2-20
13-1
3-2
3-5
_______
(psia)
0.81
169.1
0.0517338
0.73
178.4
0.0326966
0.74
174.9 _______
0.0376115
_________________
0.74
181.3j
0.0335994
I~~~~~~~~~~~~
.
l
|~~~~~~~~~~
3-6
0.81
158.5
0.0583728
3-7
0.63
158.8
0.0202502
4-1
4-2
4-3
0.831
0.75
0.61
153.4
171.1
147.3
0.0592321
0.036493
0.0185531
4-4
0.84
168.9
0.0502421
4-5
0.61
4-6
0.8
167.21
5-1
0.75
178.2
0.039058
5-2
0.741
179.21
0.034052
5-3
5-4
6-1
6-3
6-4
6-5
0.77
0.8
0.78
0.77
0.7
0.72
166.9
173.1
167.2
170.9
174.9j
181.3
1
7-1
0.76
7-2
7-3
0.72
0.76
0.73
~7-4
156
164
178.4
172.1
179.5
0.0189995
0.0552486
0.0400937
0.0488181
0.0457025
0.0393365
0.0297543
0.0310037
0.0416985
0.0311082
0.0383447
0.0323182
Table K.3: Henry-Fauske's model predicted conditions at throat.
153
experiment
name
flow
flow
flow
low
distribution distribution distribution distribution
model
model
model
predicted
predicted
predicted
predicted
throttle
quality
Reynolds
velocity
discharge
at throttle number
at section
pressure
discharge
in feeder
1
!model
(psia)
2-20
._
___
_,_
tube
139.3339
_1
3-1
144
_
_
(m/s)
0.0993
_
4.7190e+04
0.0861
6.1316e+041
15.04491
15. 449
16.9788
3-2
143.2987
0.0873
5.8529e+04
16.4746
3-5
3-6
3-7
4-1
4-2
4-3
4-4
127.7614
117
118.3074
136.1734
140.6438
133.1608
114.2281
0.1169|
0.1267
0.0871
0.0888
0.0847
0.0424
0.1381
2.4563e+04
1.8028e+04
2.9273e+04
4.2158e+04
5.6604e+04
7.3609e+04
1.6823e+04
9.8036
8.4946
10.1518
12.7066
15.9237
14.0610
8.7560
4-5
115.9298
0.0860
2.9827e+04
10.4766
4-6
117.7094
0.1347
1.8939e+04
5-1
115.2475
0.1385
2.2879e+04
11.8291
5-2
117.81191
0.13081
2.3599e+04
11.3336
5-3
129.4717
0.1001
5.1884e+04
18.0730
5-4
130.8932
0.1154
4.7850e+04
18.3601
127.9294
127.8317
110
117.6384
125.5518
0.1086
0.1077
0.1337
0.1311
0.1040
5.0771e+04
5.2613e+04
2.5622e+04
2.4825e+04
5.2399e+04
19.0931
19.6513
13.5719
11.9629
19.4704
7-2
114.3836
0.1325
2.4397e+04
12.2507
7-3
123.6312
0.1152
5.2790e+04
21.6000
111.4692
0.1401
2.3777e+04
12.8921
6-1
6-3
6-4
6-5
7-1
7-4
|
1
9.3144
Table K.4: Flow distribution model predicted values at throttle discharge and feeder
tubes.
154
experiment
name
flow
flow
flow
flow
distribution distribution distribution distribution
model
model
model
model
predicted predicted
predicted
predicted
density of
friction
multiplier
correction
R-22
factor
in feeder
factor
mixture
in
in feeder
tubes
in feeder
feeder tubes tubes
tubes
(kg/m3)
2-20
311.6584
0.0212
4.0142
0.8127
3-1
354.14381
0.0200
3.5454
0.6964
3-2
349.1953
0.0202
3.5964
0.6968
3-5
257.15241
0.0246
4.8991
1
1
3-6
224.7708
0.0266
5.6055
3-7
304.2450
0.0236
4.1789
0.8065
4-1
332.6614
0.0218
3.7974
0.8116
352.0005
0.0204
3.5844
0.6980
529.02131
0.0192
2.47521
0.7198
205.2134
0.0270
6.1907
1
4-5
302.6460
0.0236
4.2083
0.8050
4-6
214.8841
0.0262
5.8586
1
5-1
206.0370
0.0250
6.1413
1
220.0512
0.02481
5.72361
11
5-3
293.18771
0.0208
4.3026
0.6966
5-4
265.1311
0.0210
4.7449
0.6880
6-1
272.76701
0.0208
4.6234
0.6908
6-3
274.6369
0.0206
4.5925
0.6914
6-4
204.3054
0.0244
6.3267
11
6-5
219.4199
0.0246
5.7400
11
7-1
278.0326
0.0206
4.5441
0.69241
7-2
212.5942
0.0246
5.9750
1
7-3
253.7340
0.0206
4.9739
0.6853
198.65891
0.0248
6.4662
4-2
1
4-3
4-4
15-2
7-4
1
1
1
Table K.5: Flow distribution model predicted values at feeder tubes.
155
1
experiment
name
flow
measured
pressure
distribution
drop across model
throttle
jpredicted
( after
pressure
drop across
offset
adjustment ) throttle
pressure
transducer
( which
measured
pressure
drop across
throttle )
zero offset
(psi)
(psi)
(psi)
2-20
-4
95.35
69.2861
3-1
3-2
-3.71[l
-3.424
11l.99
109.67
99.0811
92.3413
3-5
3-6
3-7
5-1
5-3
-4.3
-4.39
-4.69
.
-4.98
-4.39
133.68
88.36
146.96
135.48
77.94
117.1086
77.7805
133.5926
122.5425
87.6683
85.49
94.7083
-4.10
-4.20
149.28
142.12
-. 91
86.21
141.8527
131.4464
101.8688
6-3
6-4
7-2
7-3
~~~
.......
5.71
~
-4.10
Table K.6: Measured and model predicted pressure drop across throttle.
156
experiment
name
=____
_
pressure
measured
flow
transducer pressure
distribution
( which
drop across model
measured
feeder tube predicted
pressure
( after
pressure
drop across offset
drop across
feeder tube) adjustment ) feeder tubes
(psi)
(psi)
zero offset
(psi)
2-20
-0.19
12.03
39.5439
3-1
-7.64
29.87
40.1189
3-2
-4.95
15.24
38.0987
3-5
-0.34
9.64
24.6214
13-6
-0.33
5.74
20.1395
3-7
-0.36
7.761
20.3574
5-1
-7.13
6.95
26.6575
5-3
-7.64
24.61
34.6217
6-3
-0.31 out of range
34.6517
6-4
-0.27
30.3273
7-2
1
7-3
1
-7.58
7.631
16.78
7.811
17.4936
26.68(
29.6512
Table K.7: Measured and model predicted pressure drop across the feeder tubes.
157
experiment
name
flow
distribution
model
predicted
flow
distribution
model
predicted
flow
distribution
model
predicted
flow
distribution
model
predicted
model
predicted
sector
angle "a"
(radian)
sector
angle "b"
sector
angle "c"
sector
angle "d"
sector
angle "e"
(radian)
(radian)
(radian)
(radian)
flow
distribution
.,~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
4-1
4-2
4-3
4-4
4-5
4-6
5-2
5-4
6-1
6-5
7-1
7-4
_1.2206
1.1857
1.1870
1.1896
1.1830
1.1850
1.1831
1.0858
1.0946
1.1857
1.1870
1.1896
1.1830
1.1850
1.1831
1.0858
1.0946
1.2684
1.2682
1.2679
1.2686
1.2684
1.2686
1.0858
1.0946
1.3217
1.3205
1.3180
1.3243
1.3224
1.3241
1.5129
1.4996
1.3217
1.3205
1.3180
1.3243
1.3224
1.3241
1.5129
1.4996
1.0290
1.0167
1.2310
1.4084
1.4166
1.2310
1.2206
1.0290
1.0167
0.9002
0.8743
1.4084
1.4166
1.2310
1.2206
1.4084
1.4166
1.6899
1.7471
Table K.8: Model predicted feeder tube inlet plenum sector angles.
158
experiment
name
flow
distribution
model
predicted
flow
distribution
model
predicted
flow
distribution
model
predicted
flow
distribution
model
predicted
flow
distribution
model
predicted
mass flow
mass flow
mass flow
mass flow
mass flow
rate in
rate in
rate in
rate in
rate in
feeder tube feeder tube feeder tube feeder tube feeder tube
"a"
"b"
(lbm/s)
(lbm/s)
"c"
"d"
(lbm/s)
(lbm/s)
"e
(lbm/s)
I
4-1
4-2
4-3
4-4
4-5
4-6
5-2
0.030269554
0.040433053
0.053689792
0.012814848
0.022757402
0.014361467
0.016349978
0.030269554
0.040433053
0.053689792
0.012814848
0.022757402
0.014361467
0.016349978
0.03247901
0.043084401
0.057224923
0.013919576
0.024304021
0.015466195
0.016349978
0.033804684
0.044851966
0.059434379
0.014361467
0.025408749
0.016129032
0.022978347
0.033804684
0.044851966
0.059434379
0.014361467
0.025408749
0.016129032
0.022978347
5-4
6-1
6-5
7-1
7-4
0.032258065
0.03247901
0.016129032
0.040433053
0.019001326
0.032258065
0.044410075
0.022536456
0.040433053
0.019001326
0.032258065
0.03247901
0.016129032
0.029606717
0.013477684
0.044189129
0.044410075
0.022536456
0.040433053
0.019001326
0.044189129
0.044410075
0.022536456
0.055457357
0.027176315
Table K.9: Model predicted feeder tube mass flow rate.
159