Two Phase Flow Splitting in Piping Branches
by
Michael Steven Quintana
S.B., Mechanical Engineering
Massachusetts Institute of Technology, 1989
Submitted to the Department of Mechanical Engineering and the
Department of Nuclear Engineering
in Partial Fulfillment of the Requirements for the Degrees of
Master of Science in Nuclear Engineering
and
Master of Science in Mechanical Engineering
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
June 1998
© 1998 Massachusetts Institute of Technology
All Rights Reserved.
MASSACHUSETTS INSTITUTE
OF TECHNOLOGY
JUL 2 0 1999
LIBRARIES
Auth o r....................................................................................
Depart ent of Nuclear ngineering
~June 1, 1998
,
Certified by..........................................................
Professor Peter O-ith, Emeritus
Dep artment of Mechanical Engineering
/) Toes, is Supervisor
Certified by............................................... ..................
Professor Neil Emmanuel Todreas
Departments of Nuclear and Mechanical Engineering
Thesis Reader
A ccepted by ........................................ .....................................................................................
Professor Anthony Tyr Patera
Acting Chairman, Departmental Committee on Graduate Students
epartment of Mechanical Engineering
/
Accepted by........................
Professor Lawrence Lidsky
Chairman, Departmental Committee on Graduate Students
Department of Nuclear Engineering
Two Phase Flow Splitting in Piping Branches
by
Michael Steven Quintana
Submitted to the Department of Mechanical Engineering and the
Department of Nuclear Engineering
on June 1, 1998 in Partial Fulfillment of the Requirements for the Degrees of
Master of Science in Nuclear Engineering
and
Master of Science in Mechanical Engineering
ABSTRACT
The objectives of this research are to evaluate the performance of a flow-splitting tripod, discover
the factors which most affect the flow distribution; and quantify the effects of geometry, quality
and flow rate on the distribution. Knowing all this allows one to predict the distribution for
given conditions. An R-22 test apparatus was constructed for carrying out the experiments. The
factors examined were tripod orientation, Froude number, void fraction, and swirl induced by
helical grooves in the tube supplying the two-phase flow to the tripod. The flow regime of
concern is primarily annular. Experiments were run and data was collected and analyzed.
The two piece tripods were generally found to have manufacturing defects which made their
performance unpredictable. The hole through which the flow was provided was often off center.
This defect greatly affected the distribution and masked other geometric factors. To eliminate
this variable a number of tripods were tested, using an air-water rig, to find a tripod that was not
defective. Tests using R-22 were then run on this tripod and it was found that inlet swirl had
little or no affect on the flow distribution. The factors that had the greatest effect on the flow
distribution were the tripod's orientation, the Froude number of the flow, and the void fraction.
An empirical correlation for flow splitting was derived including these factors.
Thesis Supervisor: Professor Peter Griffith
Title: Professor of Mechanical Engineering, Emeritus
Acknowledgments
I would like to thank my advisor, Professor Peter Griffith, without his patience, kindness,
and guidance this thesis would not have been completed. I learned a lot from him during the
course of my research from him.
His tremendous knowledge and engineering intuition are
remarkable. His ability to see a problem in its simplest form came as a great help to me. I am
indebted to him.
I would also like to thank the Carrier Corporation for funding my research. As well I
would like to thank the very knowledgeable and skillful technicians at the Pappalardo
Laboratory: Mr. Norman Berube, Mr. Norman MacAskill, and Mr. Robert Nuttall, I am grateful
for all the time, skill, and effort that they have given me.
Their help with the design and
construction of the experimental apparatus was invaluable. I am also indebted to Dr. Wayne
Bidstrup and Mr. Richard Fenner, for their time and council.
A special thanks goes to Mike
Demaree for his advice and help dealing with the refrigerant.
A special thanks goes to Professor Ronald M. Latanision for his support. I would not
have finished this thesis without him. I would also like to thank Constance Beal, Clare Egan, and
Leslie Regan. They truly make the Institute run smoothly.
Many thanks go to my friends in the Heat and Mass Transfer Lab: Richard Nelson, Marc
Hodes, and Andres Pfahnl and those in the Corrosion Lab: Jason Cline, Dr. Gary Leisk, and Dr
Bryce Mitton for their support, encouragement and friendship.
Finally, I want to thank my wife Tiffany for all the support that she has given me. This
thesis is dedicated to her.
To my wife.
Table of Contents
...............................
..........
1.1 Problem Statement .........................
.........
1.2 Geom etric and Property V ariables ......................................................
1.2.1 Swirl .................................................... ................
1.2.2 Orientation .................. .......................................................................
.................
.
1.2.3 Geometry of Tripod ...............................
1.2.4 Refrigerant ...............................................................
1.2.5 Property V ariables ........................................
.................
................
1.3 Current Work ........................
1.3.1 Flow Regimes of Interest ........................................
1.3.2 Refrigerant 23 Tests .....................................................
..................
1.3.3 Defective Tripods ........................................
..
1.3.4 Comparison to Air-W ater Tests ...................................... ........
...
2 Flow Regimes and Conditions of Interest ........................................
2.1 Range of Pressures, Qualities and Flow Rates of Interest ................................
............
....
2.2 Taitel-Dukler Flow Regime M ap ........................................
2.3 Conditions for the Range of Param eters .............................................................
2.4 Range of Void Fractions and Froude Numbers .....................................
2.5 The Selection of the Correlation Factors ..................................
...........
3 Refrigerant 22 Experiments ......................................
3 .1 A pparatu s .......................................................................
3.1.1 Flow Loop ......................................................................
...............
3.1.2 Test Section .................................................................
3.1.3 Cooling System ...........................................................
3.1.4 Instrum entation .....................................................
3.2 Parameters Varied ...................................................................
3 .3 Resu lts ..........................................................................................................
9
9
10
10
10
11
11
11
12
12
13
13
13
15
15
15
16
17
17
19
19
19
24
24
24
27
27
4 Comparison of Refrigerant 23 to Air-Water Experiments ..........................................
31
...............
4.1 Air-Water Experiment Results ......................... ..
4.2 Direct Comparison of Refrigerant 23 and Air-Water Experiments .................
4.3 Air-Water System's Limitations ........................................
5 C o nclu sio n s .......................................................................................................................
..................
5.1 Geometric Variations .......................................
5.2 Unnecessary R-23 Tests ........................................
5.3 Stratified Flow Regime ................................................................ .................
5.4 Optimum Conditions .......................... ............................................
31
31
32
34
34
35
35
35
1 Intro du ctio n .......................................................................................................................
Table of Contents (cont.)
References ........................
..........
. .....................................................................................
Appendix A Nomenclature and Subscripts ........................................
Appendix B Raw Data
..............................................................................
Appendix C Calculations ......................................
...........................
Appendix D Empirical Correlation Derivation ................................
36
37
38
46
57
List of Figures
...........
Figure 1.1: Typical Tripod ......................................... .......
Figure 1.2: Tripod Orientation and Swirl Rotational Direction .........................................
..........................
Figure 1.3: Defective Tripod ........................................
Figure 1.4: Comparison of Distribution Between Defective and Non-defective Tripods .......
.........................
Figure 2.1: Flow Regim e Map ..................................................................
Figure 2.2: Flow Regime Schematics .........................................
............
Figure 2.3: Slip Ratio versus Specific Volume .......................................
Figure 3.1: Test Apparatus Schematic ..............................................
Figure 3.2: Test Apparatus .......................................................
Figure 3.3: Inside the Pressure Vessel.........................................................................
Figure 3.4: Test Section ................................................................
................
Figure 3.5: Rotating Brass Guide ..........................................................................
...
Figure 3.6: Cooling System Schem atic .................................. ............................
3.1
.
Using
Equation
Flow
Split
Calculated
Liquid
and
of
Measured
3.7:
Comparison
Figure
Figure 3.8: Comparison of Measured and Calculated Liquid Flow Split Using Equation 3.2.
..........
Figure 4.1: Comparison at Low Froude Number .....................................
.........................
Figure 4.2: Comparison at Intermediate Froude Number ..................
Figure 4.3: Comparison at High Froude Number ........................................
10
12
14
14
16
17
18
20
21
22
23
25
26
29
30
32
33
33
List of Tables
...................................
Table 2.1: Conditions of Interest ...........................
....................
........................................
Table 2.2: Approach Tube Parameters
Table 5.1: Defective Tripod Distribution ..........................................................................
....................
Table 5.2: Stratified Flow Distribution ........................................
8
15
15
34
35
Chapter 1
Introduction
1.1 Problem Statement
Flow splitting tripods are needed to complete the U-turn end connections found in the
finned tube heat exchangers used in the evaporator of an air conditioning unit. The refrigerant
enters the evaporator from the throttle valve. At this point there is a flowing two phase mixture
which is below ambient temperature and at various pressures, mass velocities, and qualities. The
tripods, which can vary in rotational orientation, are usually connected to horizontal tubes. The
Carrier Corporation uses tripods to split the refrigerant flow in the evaporator between two or
more parallel tubes to reduce the overall pressure drop across the evaporator. By using a tripod,
the velocity in each parallel tube is halved compared to a single pass tube of the same total length.
Therefore, in the ideal case of uniform distribution the overall pressure drop is reduced and the
thermal efficiency of the system is increased.
In general, the flowing refrigerant does not split evenly. Since the liquid refrigerant has a
much greater potential for absorbing heat than does the vapor, the tube receiving less liquid often
does not absorb as much heat as it was designed to. The tube that receives additional liquid often
does not make efficient use of it and can send some liquid refrigerant back to the compressor.
A typical tripod, such as is illustrated in Figure 1.1 and is used in this experiment, is
made of two pieces which are brazed together. One piece consists of a u-tube with a hole on one
side that is slightly smaller than the inner diameter of the supply tube. The supply tube of the
tripod is a half of a u-tube that is brazed to the side of the full u-tube as depicted in the Figure
1.1. The flow through the tripod enters the half u-tube and is split as it enters the full u-tube.
1.2 Geometric and Property Variables
1.2.1 Swirl
The tube supplying the tripod has helical grooves within it. These are fine grooves which
are used to improve heat transfer. This improvement is accomplished by using swirl the grooves
induce to throw liquid to the walls and keep them wet. The helically grooved tube has a slightly
larger inside diameter than the tripod outer diameter; and is flared for receiving the tripod and
providing clearance for the braze. Figure 1.1 shows the dimensions while Figure 1.2 shows the
swirl rotational direction for the tripods tested in these experiments.
0.5"
0. 5" R
.0.3125"
Figure 1.1: Typical Tripod
1.2.2 Orientation
The experiments were carried out using four tripod rotational orientations with all supply
and discharge tubes always being in the horizontal orientation. The tripod orientations were at
00, 900, 1800, and 2700 and are as illustrated in Figure 1.2. The left and right labels indicate
which collection glass in the pressure vessel will receive the tube's discharge. The collection
glasses were viewed through a window at the end of the pressure vessel. (See Chapter 3.) The
gravity vector is down in this figure and flow is into the paper with an X and out with a e.
1.2.3 Geometry of Tripod
The tripod's tubing is a nominal 3/8 inch outside diameter (OD), 0.364 inches actual OD,
with a 0.0394 inches wall thickness. The distance between the centers of the full u-tube is 1 inch.
The vertical distance from the full u-tube centers to the half (supply) u-tube center is 0.75 inches
and the horizontal distance is 0.5 inches. The tips of the tripod tubing are straight for 0.3125
inches then curve forming a semi circle for the full u-tube and a quarter of a circle for the half utube. The centerline radius of the bends is 0.5 inches.
1.2.4 Refrigerant
Refrigerant 22 was used in all experiments conducted.
R-22 is a very aggressive
refrigerant, in that it greatly effects the elasticity of many elastomer materials and is very
permeable in many elastomers. These properties greatly affected the design of the test system.
They also lead us to look for other simpler and less difficult-to-handle fluids to test the tripods.
Air and water were found to be suitable when the experiments were properly scaled.
The
counterpart air-water experiments were conducted by Richard Perkins (1997) and are used as a
comparison to the R-22 experiments.
1.2.5 Property Variables
The property variables that were recorded for each experiment were pressure,
temperature, and mass flow rate. Velocity, quality, phase densities and viscosities, and, surface
tension were then determined from these values. See Table 2.1 for ranges tested.
Left
Right
0
Right
00
2700
Left
c'
Left
*
Right
900
1800
Left
0
Right
g
Swirl Rotational Direction
Figure 1.2: Tripod Orientation and Swirl Rotational Direction
1.3 CurrentWork
1.3.1 Flow Regimes of Interest
The main flow regime of interest for these flow splitting experiments was annular flow.
The range of flow variables was set by the conditions in use at the Carrier Corporation in their air
conditioning units. For some of the low velocity runs there was stratified flow present. The
flow regimes were determined using 'unified.f, a computer code written by Marc Hodes (1994)
based on the Taitel-Dukler (1990) unified model for two-phase flow regimes. The model uses
vapor and liquid densities, viscosities, surface tension, tube diameter, and angle of inclination to
predict what the flow regime is.
1.3.2 Refrigerant 22 Tests
Tests were run at the various orientations described earlier and shown in Figure 1.2. The
range of states experienced under normal operating conditions were encompassed in this test
matrix. A set of data was taken at each condition. The experimental variables tested were the
mass flow rate and the quality of the R-22.
1.3.3 Defective Tripods
The first set of results did not match our expectation that gravity was the major factor
determining the uniformity of the flow split. At the 00 orientation the left tube (see Figure 1.2)
was receiving over 70% of the liquid. The tripod was dismantled and it was found that the hole
in the full u-tube was off center, as shown in Figure 1.3. Since the flow regime was annular the
liquid was deflected to the left tube from the right tube (of Figure 1.3) by the ridge created by
the offset. Figure 1.4 shows the disparity in flow distribution between a defective and a nondefective tripod.
The average difference between the flow splits from the two tripods was
20.8%, which is unacceptable.
Air-water tests were run on all the tripods. The split at an orientation of 00 varied by as
much as 50%±10% for either side (Perkins, 1997). There were however two out of the twelve
tripods that gave flow splits that were 50%+1%. One of these tripods was used for the rest of
the experiments. The same tripod was used for both the air-water and R-22 experiments.
1.3.4 Comparison to Air-Water Tests
The results of the air-water experiments matched the R-22 experiments in shape when the
Froude number and void fraction were the same. The magnitude of the amplitude was not quite
the same, however. The correlation between the air-water and R-22 tests was only found to be
valid in the annular flow regime. With this limitation, the simpler air-water tests could be used to
give information about the flow distribution on untested tripods which would be useful for
screening the quality of the tripods from various suppliers and selecting the good ones from a
batch.
]drilled hole 0.275" 1
0
Ifeed tube ID 0.281"
'
I
.edtb
-
I
.8
brazed flarejoint
Figure 1.3: Defective Tripod
100
90 80 70
60
50o
40
-
30
-
- --
-
%%
- Defective Tripod
(avg)
-- -
- - Non-defective
Tripod (avg)
20 10 0
90
180
rotation angle
270
360
(deg)
Figure 1.4: Comparison of Distribution Between Defective
and Non-defective Tripods
Chapter 2
Flow Regimes and Conditions of Interest
2.1 Range of Pressures, Qualities and Flow Rates of Interest
The Carrier Corporation chose the range of R-22 conditions which was tested. This range
encompassed the range that is found in their products. This range is given in Table 2.1. The
range of geometric parameters tested for the smooth and the swirl enhanced supply tube are given
Table 2.2.
Variable
Temperature, 'F
Pressure, psia
103 -lb
Mass Flux,
Shr ft 2
Range
40 to 55
83.2 to 107.3
Nominal Value
45
90.7
20 to 100
80
1.05 to 5.2
18 to 60
0 to 3
4.22
30
0
Superficial Velocity ft/sec
Quality, %
Back Pressure Imbalance, psi
Table 2.1: Conditions of Interest
Variable
Diameter, inches
Inside Surface
Tube Orientation
Range
0.3 to 0.7
smooth to enhanced
horizontal
Nominal Value
0.375
enhanced
horizontal
Table 2.2: Approach Tube Parameters
2.2 Taitel-Dukler Flow Regime Map
A flow regime map using a nominal pressure and a horizontal tube with a diameter of
0.375 inches is shown in Figure 2.1. Marc Hodes' 'unified.f program was used to generate the
map (Hodes, 1994). It is based on the Taitel-Dukler unified model presented at The Ninth
International Heat Transfer Conference (Taitel, 1990). The four regimes that are identified are
annular, bubble, intermittent, and stratified as depicted in Figure 2.2. The primary regime of
interest is the annular regime. Using the ranges for R-22 given in Table 2.1, the experimental data
mostly falls within the annular regime and just borders the stratified regime.
100
OOAAAo
OOOOO OOO OOO
o00
OOOOOOOO OOOO O
OOO
OO OOOOO OOOOOAO
OO
OOOOOOOOOOOOA AAO
[ 0
AAAAAAAAAAAAA Ao00
AAAAAAAAAAAAAOOOO0oo
10
AAAAAAAAAAAOOOOOOOOOO
AAAAAAAAAAOoo ooooooo
1
0 ANNULAR
AAAAAAAAAOOOOooooooo
AAAAAAAAO EMOooooooo
on0
000000000
00000000000E
000000000OOOO0000000
0000000000
00000
00000000000000000000
00000000000000000000
00000000000000000000
00000000000000000000
00000000000000000000
0.1
0.01
0001
n
OBUBBLE
AINTERMITTENT
OSTRATIFIED
0000000
0000000
000
I
0.01
0.1
Superficial
1
Gas
10
Velocity
100
(ft/sec)
1 )00
Figure 2.1: Flow Regime Map. A Single Shape Identifies Each Flow Regime.
Filled Shapes Indicate Experimental Operating Conditions
2.3 Conditions for the Range of Parameters
The range of parameters given in Table 2.1. set the conditions of a saturated system
where annular flow dominates the flow regime.
O
0
0** z*0
o
a
o C:0
4
Stratified Flow
Bubbly Flow
0
.D
0
Annular Flow
Intermittent Flow
Figure 2.2: Flow Regime Schematics
2.4 Range of Void Fractions and Froude Numbers
Once the conditions were set to meet the range of the parameters given in Table 2.1, the
void fractions and Froude numbers could be calculated. Void fractions ranged between about
83% to 99% and were calculated using the methods described in the next section. The Froude
number in these experiments ranged from about 0.4 to 1.
2.5 The Selection of the Correlation Factors
The Froude number and void fraction were selected as the correlation factors needed to
scale the air-water experiments to the R-22 experiments. These are the dimensionless variables
that are dominate in annular flow. The Froude number was calculated using the equation below:
Fr= jg
- p )gd
(2.1)
wherejg is the superficial velocity of the gas, pg and pl are the densities of the gas and liquid R-22
respectively, g is the gravitational constant, and d is the inside diameter of the tube. The gas
phase superficial velocity is almost the mixture velocity. It isn't clear which is appropriate.
The void fraction is the volume fraction of the gas phase in a two-phase system.
The
void fraction, a, was calculated using the Thornm correlation.
where
(2.2)
Pg S
X P
1
V
S
(2.3)
VI9
V,'
S, which is plotted as phase velocity ratio on Figure 2.3, is called the slip ratio, Vg and V are the
phase velocities, pg and Pt are the densities of the gas and liquid respectively, and X is the quality.
The slip ratio was obtained using Figure 2.3.
10
6
4
S
1
2
4 6
10
20
40 60 100 200 4006001,000 2,000
Specific volume ratio
V
i
O Conditions of Interest for R-22 Experiment
Figure 2.3: Slip Ratio versus Specific Volume
These are the dimensionless groups found by Flores (1992) and Taitel (1990) among
others to be the best descriptors of annular flow. The details of how the flow variables were
calculated are given in Appendix C. These variables are given in Table C.1 of Appendix C.
Chapter 3
Refrigerant 22 Experiments
3.1 Apparatus
A schematic drawing of the apparatus is shown in Figure 3.1 and a photo in Figure 3.2.
The apparatus is broken down into four sections; 1) flow loop, 2) test section, 3) cooling system,
and 4) instrumentation as described below.
3.1.1 Flow Loop
The metering pump draws R-22 from an internally located sump/reservoir and passes the
R-22 through the filter/dryer, the surge suppresser, the heater, metering valves, test section and
finally into the measurement glasses. The metering pump is a Barnant PTFE diaphragm pump.
The pump can be controlled to meter accurately ( 2% volume variation) from 30 to 300 gallons
per day (0.02 to 0.2 gpm). This range covers the desired mass fluxes for this project. There is
also very little pressure level effect on pump performance. The heater is a 2000 watt screw plug
immersion heater (Omega TMW-1200).
It has a 7.9 Ohm resistance. A variac was used to
control the heater input by varying the voltage across the heater. Two separate metering valves
are used to cover the range of mass fluxes. The high flow-rate metering valve (Whitey 31 Series)
covers the range of 0.1 to 0.28 gpm and the low flow-rate valve (Nupro M Series) covers the
range of 0.02 to 0.15 gpm. The combination of the heater and metering valves gives the necessary
energy increase and
pressure drop, respectively, to achieve the desired qualities.
The
measurement glasses are 5 inches tall and nominal 3 inches in diameter glass cylinders. These
cylinders are fastened to an aluminum plate containing drainage ports. Both ports are connected
to a single three-way valve that allows for simultaneous isolation and draining of both glasses, see
Figure 3.3. The glasses have a level indicator that is read through the viewing window.
hoses in the pressure vessel are high quality neoprene.
The
TEST SECTION
PRESSURE VESSEL
TRIPOD
RETURN TUBES
BRASS GUIDE
GLASSES
II
I
ENHANCED TUBE
A I
DRAINAGE
SYSTEM
ISOLATION
VALVE
METERING
VALVES
(NEEDLE VALVES)
FILTER/DRYER
ISOLATION
VALVE
TO AND FROM
COOLING
HEATER
SURGE
SUPPRESSER
Figure 3.1: Test Apparatus Schematic
Figure 3.2: Test Apparatus
Figure 3.3: Inside the Pressure Vessel
Figure 3.4: Test Section
3.1.2 Test Section
The test section, (enhanced approach tube, tripod (Figure 1.1), return tubes, and brass
guide) can be rotated to adjust the orientation of the tripod, see Figure 1.2. In the drawing,
hoses (high pressure refrigerant for external hoses) are depicted by thick black lines. The hoses
give the flexibility necessary for rotation. The whole test section is supported by a single PVC
pipe with oak supports to eliminate any twisting of the copper tubing. There is a brass guide for
the return tubes penetration of the pressure vessel. This guide has an o-ring seal and a Teflon
bearing. The Teflon has a very low coefficient of friction which is necessary for rotating the
brass guide while the vessel is under pressure. See Figure 3.4 for a photo of the installed test
section. A detailed drawing of the brass guide is shown in Figure 3.5.
3.1.3 Cooling System
The cooling system is comprised of a pump, coils, and a reservoir as shown in Figure
3.6. The coils are internal to the pressure vessel and made from a single piece of copper tubing as
shown in Figure 3.3. The inlet to and outlet from the coils is via penetrations in the bottom of
the vessel sump/reservoir. The pump takes the suction off the bottom of the cooling reservoir
(ice bath), pumps water through the coils, then back to the reservoir. There is a bypass valve on
the discharge of the pump to control the flow through the coils.
3.1.4 Instrumentation
There were four thermocouple locations: pump discharge, heater outlet, the enhanced tube
inlet, and the pressure vessel. There were four pressure gauge locations: the pressure vessel
sump, the pressure vessel, the metering valves inlet, and the metering valves outlet. A volt meter
was attached to the heater leads to read the heater's electrical resistance and voltage.
NOTE: ALL DIMENSIONS IN INCHES
SCALE 1:1
O-RING GROOVE SCALE: 4:1
00 TO 50
0.280
BREAK CORNER
APPROX. 0.280 R
4.875
Figure 3.5: Rotating Brass Guide
E
Pressure Vessel
Pump Discharge
Cooling
Pump
Drain Valve
Isolation Valve
Figure 3.6: Cooling System Schematic
3.2 Parameters Varied
Mass flow rate and quality were varied. The mass flow rate was varied by adjusting the
metering pump. The quality was varied by varying the voltage applied to the heater and the
pressure drop across the metering (needle) valves. After the system reached a steady state, the
mass flow rate and quality were calculated. When in the proper range, several data runs were
taken. The test section was then rotated and another set of data was collected. The angles used
were 00, 900, 1800, and 2700 as depicted in Figure 1.2.
3.3 Results
The distribution of the liquid R-22 as a function of the tripod orientation had a roughly
sinusoidal shape about the 50% distribution line. The amplitude of the imbalance was affected
by both the Froude number and the void fraction. It increased with a decreasing Froude number
and/or void fraction. The raw data are given in Table B.1 of Appendix B.
An empirical
correlation, given in equation 3.1, was developed using the dimensionless parameters of void
fraction and Froude number given in Table C.1 of Appendix C, and the angle of orientation. The
calculated flow splits using this correlation are within +8% and -6% of the measured data, shown
in Figure 3.7. Equation 3.2, developed using the same method as used for equation 3.1 but
only using angle of orientation as a factor, gives a correlation of within +9% and -6% of the
measured data, shown in Figure 3.8. Both correlations used only the data where the flow was
annular.
As stated earlier, stratified flow gives very poor distribution.
The derivation of
equation 3.1 is given in Appendix D.
w=
w
° 0 2Fr-024,
(3.1)
0.5- 0.155 sin 0,
(3.2)
0.5 - 0.145 sin 0(1 - a)
-
W
where wl is the mass of liquid distributed to the left tube of the tripod, w is the total mass of
liquid distributed, 0 is the tripod's angle of orientation, a is the void faction, and Fr is the Froude
number.
The main results of these experiments are; 1) manufacturing tolerances are very
important. This is the dominate factor in the maldistribution in the annular flow regime. 2) The
swirl induced by the helical ribbing in the approach tube has little or no effect of the flow
distribution. 3) Tripod orientation is very important, due to gravitational forces. It affects both
direction and magnitude of the imbalance.
4) The Froude number and void fraction are also
important and affect the magnitude of the maldistribution. 5) Stratified flow regime gives very
poor distribution particularly in the air-water experiments because of the effects of non-wetting
on the tube.
80%
70%
-6%
+
60% -
8%
II.
50%
La 40%
E
30%
20% +
o% +
I
I
I
I
I
I
I
I
0.00%
10.00%
20.00%
30.00%
40.00%
50.00%
60.00%
70.00%
0%
Calculated Flow
80.00%
Split
Figure 3.7: Comparison of Measured and Calculated Liquid Flow Split
Using Equation 3.1 1= 0.5 - 0.145 sin (1- a)0
02
Fr- 24.
8AO
-6%
70% -
60%
Ia
70.00
9%
50% -
0
t
La 40% -
" 30% E
20% +
10% -
0%
0.00%
10.00%
20.00%
30.00%
40.00%
Flow
Calculated
50.00%
60.00%
70.00%
80.00%
Split
Figure 3.8: Comparison of Measured and Calculated Liquid Flow Split
Using Equation 3.2
W
= 0.5 - 0.155 sin 0.
Chapter 4
Comparison of Refrigerant 22 and Air-Water Experiments
4.1 Air-Water Experiment
The air-water experiments were conducted by Perkins (1997).
It was found that there
was too much variation in the brazed tripods due to manufacturing defects for us to use as
received. A random variation in the flow split up to ±10% existed from tripod to tripod with the
tripods tested. An acceptable tripod was selected. The flow distribution for an acceptable
tripod was found to be symmetric with respect to the tripod's orientation. This symmetry
showed that swirl had little effect on the flow distribution. A unibody tripod was also tested. It
did not show the manufacturing deviations observed in the brazed two piece tripods.
The
unibody tripod's distribution mirrored the distribution of a brazed two piece tripod. The airwater system flow split results for all tripods were found to be erratic at low Froude numbers.
The high Froude number air-water tests were useful, however.
4.2 Direct Comparison of Refrigerant 22 andAir-Water Experiments
The air-water system using the suggested scaling methodology was found to be a good
predictor at high Froude numbers of the flow distribution for R-22. The Froude numbers and
void fractions were controlled in order to compare the experiments performed on the two
systems. Figures 4.1 through 4.3 give a graphical comparison of the two systems' distribution.
The shapes of the distribution curves are the same but the magnitudes, to some extent, differ.
The air-water system is far easier to build and manipulate than the R-22 system and as it gives
relevant data it therefore serves as an attractive screening tool when looking at geometric variables
in the flow splitting system.
4.3 Air-Water System's Limitations
The air-water system is limited to annular flow which means Froude numbers as defined
in this work must be equal to or above 0.4. The air-water flow distribution in the stratified
regime does not correlate at all well with the R-22 data. Wetting effects also come into play in
the air-water experiments at low Froude numbers. (This would be a contact angle and Webber
number effect). R-22 has a low surface tension and more easily wets the tube walls. The airwater system experienced incomplete wetting of the tube walls. These differences were obvious
when looking at the experiments. As the velocity (and Froude number) were increased, the R-22
and air-water experiments came into line.
100
90
80
70
60
X- -Air/Water-Fr
0.4, void
fraction 88%
--- 0-- R 22-Fr 0.4,
void fraction
84%
--
50
X11
40
-
-
30
20
10
0
0
I
I
90
180
rotation angle
270
360
(deg)
Figure 4.1: Comparison at a Low Froude Number
100
80t
70
60
-
K- -Air/Water-Fr
0.7, void
fraction 93%
-- 4- - R 22-Fr 0.7,
void fraction
93%
--
-
50 4
40 30
20
10
a
0
90
180
270
360
rotation angle (deg)
Figure 4.2: Comparison at an Intermediate Froude Number
100
90 80
70
60
-
-X-
50 I
40
-----
t
30
20
-Air/Water-Fr
1.0, void
fraction 96%
R 22-Fr 1.0,
void fraction
95%
+
0
I
I
90
180
270
360
rotation angle (deg)
Figure 4.3: Comparison at a High Froude Number
Chapter 5
Conclusions
5.1 Geometric Variations
Geometric variations due to manufacturing defects dominate the flow maldistribution.
Table 5.1 shows just how much this affects the distribution. The left side should have less when
the tripod is in the 900 orientation, but with the defective tripods it sometimes had more. The
offset hole in an asymmetrical tripod, Figure 1.3, creates a barrier that deflects the liquid film
flow to one side. As the quality and void fraction are increased, giving a smaller film thickness,
the distribution becomes even worse. Figure 1.4 gives a comparison of the liquid flow
distribution between a defective tripod and an acceptable tripod.
Annular flow in a defective
tripod clearly makes the distribution worse rather than better. A symmetrical tripod has the right
side flow rate at its maximum at 900 with a 50%-50% split at an orientation of 0Ojust as one
would expect. The effect of the swirl on the flow split in all tripods is overwhelmed by the
manufacturing defects.
Angle
(deg)
Mass Velocity
(104 lb/hr ft 2)
Velocity Quality
(%)
(ft/sec)
Split (%
Right
Left
90
90
10.22
9.30
4.18
5.87
22.72
33.18
52.47
58.72
47.53
41.28
0
7.31
6.76
49.40
68.09
31.91
0
6.82
7.60
59.92
73.59
26.41
Table 5.1: Defective Tripod Distribution
5.2 Unnecessary R-22 Tests
The R-22 experiments are not essential for identifying defective tripods. It has been
shown that properly scaled air-water tests suffice.
An air-water test would save time and
money, yet provide a quick and easy way to screen different tripod designs or monitor a
supplier's quality control.
5.3 Stratified Regime
The R-22 flow distribution in the stratified regime is often very poor. Even at a high
quality, if the mass flow rate is low, the distribution is poor. An example of this is given in
Table 5.2. Even with the high quality the low flow rate dominated the distribution because the
flow was stratified. The air-water flow distribution in the stratified regime is worse than the R22, and does not correlate well.
Angle
(deg)
0
90
180
270
Flow
Fr
4
(10 1b/hr-ft)
4.58
4.14
4.08
5.07
0.62
0.62
0.62
0.61
Left
(%)
52.33
16.84
46.67
71.15
Right
(%)
47.67
83.16
53.33
28.85
x
(%)
52.70
57.90
58.88
47.51
Slip
ratio
2.13
2.13
2.13
2.11
a
(%)
96.50
97.15
97.25
95.68
Table 5.2: Stratified Flow Distribution
5.4 Optimum Conditions
The empirical equation, equation 3.1, developed from the raw data for a symmetrical
tripod shows that a tripod orientation of either 00 or 1800 is optimal. If this is not possible,
operating at a higher Froude number and void fraction will decrease the magnitude of the
imbalance. Flow splitting at very high quality outside the range of desired operation and the
correlating equations 3.1 and 3.2, where the films are quite thin, is likely to be poor.
References
Flores, Aaron, 1992, Dry Out Limits in HorizontalPipes. MS Thesis, Massachusetts Institute
of Technology, Cambridge, MA.
Hodes, Marc Scott, 1994, Gas Assisted Evaporative Cooling in Downflow Through Vertical
Channels. MS Thesis, University of Minnesota.
Perkins, Richard, 1997, Air-waterModeling ofRefrigerantDistributionTripods. BS Thesis,
Massachusetts Institute of Technology, Cambridge, MA.
Taitel, Yehuda, 1990, "Flow Pattern Transition in Two-Phase Flow", Proceedingsof the 9th
InternationalHeat Transfer Conference, The Assembly for International Heat Transfer
Conferences, Hemisphere Publishing Corporation, Washington.
Whalley, P.B., 1997, Boiling, Condensation,and Gas-LiquidFlow, Claredon Press, Oxford.
Appendix A
Nomenclature and Subscripts
Nomenclature:
h: enthalpy (BTU/lb)
j : superficial velocity (ft/sec)
r : mass flow rate (lb/hr)
p : pressure (psia)
Q
: heat input (BTU/hr)
R: electrical resistance (ohm)
T : temperature (F)
V: phase veolicty
v : specific volume
VD
: voltage applied to the heater (volts DC)
x : quality
subscripts:
1 : denotes outlet of pump and inlet to heater
2 : denotes outlet of heater and inlet to throttle valve
3 : denotes outlet of throttle valve and inlet to test section
4 : denotes pressure vessel (outlet of test section and inlet of pump)
g: gas
1: liquid
Ig : difference between liquid and gas
Appendix B Raw Data
Run
Angle
Heater Voltage
T1
T2
T3
T4
P2
P3
P4
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
(deg)
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
(volts)
50.1
50.0
50.0
49.8
50.0
49.9
49.9
49.8
65.1
65.0
65.0
64.9
49.9
50.4
50.3
50.3
65.4
65.5
65.5
65.5
(OF)
47.93
48.56
48.38
48.16
47.56
47.74
47.76
47.85
47.99
47.96
47.92
48.03
43.73
43.87
43.97
44.06
43.40
43.45
43.43
43.44
(OF)
49.82
49.08
50.22
49.15
52.86
52.90
53.11
52.97
61.48
61.08
61.14
61.09
53.13
53.48
53.68
53.85
58.03
58.29
57.96
58.38
(OF)
38.43
38.38
38.68
38.34
39.17
39.07
39.11
39.01
39.58
39.55
39.56
39.40
40.67
40.80
40.89
41.01
40.00
40.07
40.01
39.95
(OF)
38.77
39.00
39.91
38.77
41.81
39.93
39.67
41.20
40.80
40.72
39.67
39.40
39.84
39.92
40.03
40.08
38.56
38.81
38.87
38.76
(psi)
95.70
95.70
96.70
95.70
101.70
101.70
102.20
102.20
117.70
117.70
117.70
117.70
102.20
103.70
103.70
103.70
112.20
112.20
112.20
112.20
(psi)
82.20
80.70
80.70
80.70
83.70
82.70
83.70
83.70
84.70
84.70
84.70
84.70
84.70
85.70
85.70
85.70
85.70
85.70
85.70
85.70
(psi)
81.97
82.20
83.12
81.97
85.87
83.14
82.87
84.97
84.38
84.26
82.87
82.60
83.05
83.13
83.25
83.32
81.76
82.01
82.07
81.96
Table B.I: R-22 Experiment Raw Data
Left th, Right rz,
(lb/hr)
8.67
9.18
10.55
10.52
15.27
15.14
14.91
15.89
9.49
10.26
9.57
9.25
28.27
29.75
30.60
30.63
22.42
21.96
23.18
21.25
(lb/hr)
7.58
8.03
8.57
8.55
12.41
12.30
13.05
12.91
8.31
8.98
8.50
8.10
26.51
27.89
28.69
28.71
18.21
19.22
21.73
19.92
Run
Angle
Heater Voltage
TI
T2
T3
T4
P2
P3
P4
Left rm,
Right ri,
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
(deg)
0
0
0
0
90
90
90
90
90
90
90
90
90
90
90
90
0
0
0
0
(volts)
77.5
77.6
77.6
77.6
78.0
78.0
78.0
77.9
65.6
65.8
65.9
65.8
50.2
50.3
50.4
50.4
49.9
49.9
49.9
49.9
(oF)
43.89
43.98
43.98
44.06
44.11
44.03
43.95
43.98
43.64
43.65
43.67
43.70
43.62
43.62
43.50
43.26
42.04
42.10
42.07
42.01
(oF)
64.08
65.40
64.05
63.49
65.88
65.99
65.90
65.74
57.54
57.42
57.25
57.39
51.40
52.05
52.04
52.08
51.40
51.38
51.50
51.65
(OF)
40.84
40.82
40.87
40.90
40.88
40.81
40.91
40.87
39.98
39.95
40.00
40.01
39.94
39.46
39.24
39.23
37.91
37.92
37.90
37.94
(OF)
39.39
39.34
39.39
39.32
39.31
39.51
39.59
39.57
39.51
38.73
38.78
38.62
38.74
38.27
38.28
38.11
39.45
39.10
38.61
38.86
(psi)
124.70
124.70
124.70
123.70
127.20
127.20
127.20
127.20
112.20
112.20
112.20
112.20
102.20
102.20
102.20
101.70
98.70
98.70
98.70
98.70
(psi)
88.70
88.70
88.70
88.70
89.70
89.70
89.70
89.70
87.20
87.20
86.70
86.70
85.70
85.70
84.70
84.70
82.70
82.20
80.70
80.70
(psi)
82.59
82.54
82.59
82.52
82.51
82.71
82.79
82.77
82.71
81.93
81.98
81.82
81.94
81.47
81.48
81.30
82.65
82.30
81.81
82.06
(lb/hr)
16.44
19.20
18.35
15.56
10.23
12.92
14.38
12.26
11.65
11.17
10.37
10.21
15.28
17.88
19.50
16.63
29.18
29.48
27.85
27.50
(lb/hr)
15.41
16.80
17.21
14.59
23.39
22.96
23.02
21.80
23.30
22.34
23.70
23.34
30.56
35.77
34.67
33.26
27.46
29.48
27.85
27.50
Table B.1: R-22 Experiment Raw Data (continued)
Run
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
Angle
(deg)
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Heater Voltage
(volts)
65.3
65.2
65.2
65.2
74.7
74.7
74.8
74.7
65.0
65.0
65.0
65.0
80.0
80.0
80.0
80.0
60.4
60.4
60.4
60.4
T1
(OF)
42.04
42.15
42.20
42.20
42.19
42.48
42.58
42.61
43.61
43.61
43.75
43.71
43.94
44.07
44.09
44.05
44.76
44.71
44.58
44.63
T2
(oF)
60.48
60.46
60.50
60.48
66.68
66.44
66.32
66.25
55.16
55.00
55.27
55.58
63.01
63.27
63.32
63.30
48.49
48.45
48.66
48.42
T3
(OF)
38.60
38.58
38.61
38.59
39.18
39.18
39.19
39.20
38.96
39.00
38.99
39.00
39.81
39.89
39.88
39.86
38.44
38.43
38.39
38.43
T4
(oF)
39.93
39.19
40.74
39.92
39.69
39.50
39.61
39.86
42.04
40.14
41.37
42.11
39.32
42.19
39.65
39.01
39.06
40.61
39.20
37.90
P2
(psi)
116.70
116.70
116.70
116.70
127.20
127.20
127.20
127.70
106.70
106.70
106.70
106.70
120.70
120.70
120.70
120.70
94.70
94.70
94.70
94.70
P3
P4
Left Mh,
Right m,
(psi)
83.70
83.70
82.70
82.70
84.70
84.70
84.70
84.70
82.70
82.70
82.70
82.70
85.70
85.70
85.70
85.70
81.70
84.70
82.70
82.70
(psi)
83.14
82.39
84.29
83.13
82.89
82.70
82.81
83.07
86.21
83.41
85.22
86.32
82.52
86.44
82.85
82.21
82.26
84.10
82.40
81.09
(lb/hr)
26.57
26.90
28.23
27.42
25.91
25.84
25.78
25.23
16.56
17.00
16.65
17.50
12.85
12.77
13.60
13.36
8.35
8.91
8.53
8.49
(lb/hr)
26.57
26.90
28.23
27.42
25.91
25.84
25.78
25.23
15.52
15.94
15.61
16.41
12.05
11.97
11.90
11.69
7.83
7.97
7.99
7.42
Table B.1: R-22 Experiment Raw Data (continued)
Run
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
Angle
(deg)
0
0
0
0
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
Heater Voltage
(volts)
75.1
75.0
75.0
74.9
75.4
74.8
74.8
75.0
60.4
60.3
60.3
60.2
49.9
49.9
50.4
50.7
65.3
65.4
65.4
65.4
T1
(OF)
44.91
45.09
45.00
45.14
45.95
45.95
45.90
45.97
45.37
45.28
45.48
45.18
41.70
41.99
42.01
42.10
42.48
42.50
42.51
42.52
T2
T3
T4
P2
P3
P4
(OF)
53.80
53.50
53.99
53.40
52.72
52.28
52.75
52.90
48.29
48.37
47.90
48.31
51.27
51.34
51.74
51.71
59.95
59.76
60.26
59.97
(OF)
39.45
39.33
39.36
39.42
39.82
39.74
39.44
39.28
38.61
38.80
38.56
38.48
37.91
37.93
37.96
38.03
38.74
38.78
38.71
38.73
(OF)
41.63
40.71
41.39
41.45
39.21
39.38
39.01
38.77
39.31
40.12
39.08
37.71
40.46
40.16
39.17
38.86
39.52
39.68
39.99
40.17
(psi)
103.70
103.70
103.70
103.70
102.70
102.70
102.70
102.70
95.70
96.70
95.70
95.70
100.70
98.70
100.70
100.70
114.70
114.70
114.70
114.70
(psi)
83.70
83.70
83.70
83.70
82.70
83.70
83.70
83.70
82.70
82.70
82.70
81.70
81.70
81.70
81.70
82.20
83.70
83.70
83.70
83.70
(psi)
85.60
84.25
85.25
85.34
82.41
82.58
82.21
81.97
82.51
83.38
82.28
80.90
83.88
83.44
82.37
82.06
82.72
82.88
83.20
83.45
Table B.1: R-22 Experiment Raw Data (continued)
Left mi
(lb/hr)
3.08
3.53
3.62
3.50
1.46
1.47
1.45
1.42
2.66
2.18
1.94
2.12
18.20
19.61
19.94
19.36
16.98
16.87
17.62
17.29
Right iz,
(lb/hr)
3.85
4.12
4.22
4.08
2.93
2.45
2.41
2.36
10.63
11.63
10.34
11.28
36.40
39.23
39.89
38.72
33.96
33.74
35.25
34.59
Run
Angle
Heater Voltage
T1
T2
T3
T4
P2
P3
P4
Left mth
Right ri,
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
(deg)
90
90
90
90
90
90
90
90
90
90
90
90
180
180
180
180
180
180
180
180
(volts)
75.1
75.0
75.1
75.1
65.3
65.4
66.3
66.3
80.0
80.0
80.0
80.0
50.0
50.6
49.9
50.5
65.2
65.2
65.5
67.0
(oF)
42.46
42.60
42.75
42.81
43.92
43.74
43.65
43.49
43.97
44.06
44.20
44.14
42.15
42.21
42.04
42.01
42.04
42.24
42.30
42.35
(oF)
65.56
65.27
65.71
65.64
53.92
54.35
55.05
55.19
62.32
61.32
61.32
62.01
51.99
51.84
51.85
51.97
59.75
59.47
59.86
60.90
(oF)
39.22
39.34
39.31
39.32
38.72
38.71
38.74
38.80
39.74
39.76
39.65
39.73
37.91
37.90
37.85
37.83
38.56
38.53
38.55
38.68
(OF)
40.80
39.71
40.16
40.74
41.35
38.38
39.51
39.35
39.62
39.91
39.82
39.83
38.57
38.35
38.47
37.19
39.53
38.91
39.03
39.18
(psi)
125.70
125.70
125.70
125.70
104.70
105.70
106.70
106.70
118.70
118.70
119.70
119.70
101.70
101.70
101.70
101.70
114.70
114.70
114.70
116.70
(psi)
85.70
85.70
85.70
85.70
83.70
83.70
83.70
83.70
84.70
84.70
85.70
85.70
82.70
82.70
82.70
82.70
83.70
84.70
84.70
84.70
(psi)
84.38
82.91
83.44
84.29
85.19
81.58
82.71
82.55
82.82
83.12
83.02
83.03
81.77
81.55
81.67
80.38
82.73
82.11
82.23
82.38
(lb/hr)
15.54
15.39
16.63
13.07
7.61
9.23
7.67
7.74
8.08
6.13
7.95
7.85
28.90
30.19
26.92
30.87
25.97
24.33
22.97
26.87
(lb/hr)
31.07
30.77
29.56
29.86
20.30
21.11
20.46
20.65
12.94
12.26
14.14
13.96
28.90
28.41
30.77
30.87
27.70
27.80
26.25
26.87
Table B.1: R-22 Experiment Raw Data (continued)
Run
Angle
Heater Voltage
T1
T2
T3
T4
Left
t,
Right ith
P2
P3
P4
(psi)
82.91
82.74
(lb/hr)
22.90
21.09
(lb/hr)
26.17
24.10
101
102
(deg)
180
180
(volts)
75.1
75.0
(OF)
42.46
42.71
(OF)
66.02
65.53
(oF)
39.21
39.26
(OF)
39.71
39.54
(psi)
126.70
125.70
(psi)
86.70
86.70
103
180
74.9
42.88
65.30
39.29
39.38
125.70
85.70
82.58
22.54
24.04
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
180
180
180
180
180
180
180
180
180
180
180
180
180
180
180
180
180
74.8
65.1
65.0
64.9
64.9
79.9
79.9
80.1
80.0
60.2
60.3
60.3
60.3
75.0
74.9
75.2
75.3
42.80
43.71
43.69
43.62
43.46
43.35
43.56
43.83
44.00
44.92
45.11
45.21
45.28
45.24
45.27
45.27
45.27
65.80
54.26
54.10
54.73
54.64
61.60
61.74
62.28
61.15
47.53
47.40
47.70
47.49
52.38
52.90
52.80
53.02
39.24
38.74
38.60
38.61
38.61
39.50
39.55
39.62
39.79
38.45
38.50
38.47
38.41
39.48
39.52
39.48
39.53
39.48
40.51
40.00
39.29
39.71
40.19
40.05
39.55
40.30
39.01
39.54
38.68
40.08
40.26
39.49
40.46
41.45
125.70
104.70
104.70
105.70
105.70
118.70
118.70
118.70
118.70
93.70
94.70
94.70
94.70
102.70
102.70
102.70
102.70
86.70
83.70
83.70
83.70
83.70
85.70
85.70
85.70
85.70
80.70
80.70
80.70
80.70
82.70
82.70
82.70
82.70
82.68
83.95
83.21
82.49
82.91
83.48
83.28
82.75
83.65
82.21
82.74
81.88
83.32
83.59
82.69
83.88
85.34
25.59
12.93
13.12
14.47
15.22
9.69
10.18
11.43
11.04
5.86
6.31
5.73
5.79
2.67
2.88
2.77
2.63
25.59
14.77
16.15
16.54
17.40
11.63
11.10
11.43
11.04
6.70
7.21
6.55
6.61
2.13
1.44
1.38
1.31
Table B.1: R-22 Experiment Raw Data (continued)
Run
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
Angle
(deg)
270
270
270
270
270
270
270
270
270
270
270
270
270
270
270
270
270
270
270
270
Heater Voltage
(volts)
49.8
49.7
49.7
49.7
65.1
65.4
64.7
65.1
75.2
74.8
75.0
75.8
65.2
65.0
65.1
65.2
79.8
79.8
79.8
79.9
T1
(oF)
41.74
41.78
41.90
41.94
42.04
42.24
42.35
42.41
42.60
42.78
42.85
42.89
43.49
43.52
43.64
43.50
43.51
43.80
43.89
43.84
T2
(OF)
52.71
52.55
52.39
52.50
60.61
60.81
60.55
60.59
66.55
66.24
66.36
66.51
55.88
55.65
55.62
55.77
62.67
62.20
61.90
62.60
T3
(OF)
37.95
37.92
37.97
37.96
38.68
38.78
38.75
38.81
39.34
39.40
39.48
39.44
39.04
39.05
38.91
38.85
39.66
39.72
39.57
39.61
T4
P2
P3
P4
Left m,
Right ih,
(OF)
40.01
40.90
40.09
39.12
39.30
39.50
39.86
39.61
39.80
39.13
39.59
39.52
40.88
38.42
39.24
40.20
39.83
39.84
40.32
38.85
(psi)
101.70
100.70
100.70
101.70
115.70
116.70
115.70
115.70
127.70
126.70
126.70
127.70
107.70
106.70
106.70
106.70
119.70
119.70
119.70
119.70
(psi)
81.70
81.70
81.70
81.70
84.70
84.70
84.70
84.70
86.70
85.70
86.70
86.70
84.70
84.70
84.70
84.70
85.70
86.70
86.70
86.70
(psi)
83.22
84.52
83.34
82.32
82.50
82.70
83.07
82.81
83.00
82.33
82.79
82.72
84.49
81.62
82.44
83.50
83.03
83.05
83.67
82.05
(lb/hr)
40.26
37.12
37.98
39.05
35.58
33.85
34.69
33.84
28.89
30.13
30.84
30.22
19.76
20.93
21.61
20.37
13.28
12.62
13.86
12.33
(lb/hr)
22.65
18.56
18.99
19.52
17.79
19.04
17.35
19.03
18.06
18.83
15.42
17.00
9.88
10.46
12.15
8.91
8.30
9.46
8.66
8.48
Table B.1: R-22 Experiment Raw Data (continued)
Run
Angle
Heater Voltage
T1
T2
T3
T4
P2
P3
P4
Left ri,
Right rill
141
142
(deg)
270
270
(volts)
60.0
59.9
(oF)
44.89
44.82
(oF)
48.96
48.93
(OF)
38.50
38.54
(OF)
39.87
41.47
(psi)
95.70
95.70
(psi)
80.70
80.70
(psi)
83.08
85.37
(lb/hr)
13.92
14.25
(lb/hr)
5.22
6.24
143
270
60.1
44.74
49.14
38.44
40.38
95.70
80.70
83.76
14.28
5.36
144
145
146
147
148
149
150
151
152
270
270
270
270
270
270
270
270
270
60.0
75.4
74.9
75.2
74.8
74.9
74.8
74.8
74.8
44.69
45.56
45.71
45.70
45.74
45.67
45.55
45.62
45.58
49.34
53.69
52.22
52.77
52.67
52.75
52.96
52.85
53.30
38.43
39.59
39.67
39.37
39.40
39.34
39.30
39.41
39.34
40.18
40.31
39.95
40.56
39.96
40.62
41.20
41.27
40.05
95.70
102.70
101.70
102.70
102.70
102.70
102.70
102.70
102.70
80.70
82.70
82.70
82.70
80.70
82.70
82.70
82.70
82.70
83.47
83.66
83.16
84.03
83.17
84.11
84.97
85.07
83.28
14.78
3.51
3.76
3.49
3.52
3.66
3.59
3.63
3.88
6.46
1.75
1.88
1.75
1.76
2.74
2.69
2.72
2.91
Table B.1: R-22 Experiment Raw Data (continued)
Appendix C
Calculations
The schematic in Figure C.1 was used to calculate the quality, X, of the flow in the
approach tube, point 3. Nomenclature and subscript definitions are given in Appendix A.
3r--------------------
i
L ---------
Throttle
Valve
I
Test
Section
Sectio
Pump
Figure C.I: Schematic of Refrigerant Cycle
Assumptions
1. A
P2, negligible pressure drop across the heater because of the low velocity.
2. v,
v4 , specific volume change across the pump is minimal
3. h3
1, constant enthalpy across the throttle valve.
Calculations
An energy balance across the pump between points 4 and 1 and assumption 2 gives
A= h4
(C.1)
(p -p4).
Using assumption 1 and substituting it into equation C.1 we get
A = h4 + v(2 -
).
(C.2)
Now looking at the energy balance between points 1 to 2 we have
+
(C.3)
m
where
V2
R
(C.4)
Q is the heat input from the heater, V is the voltage applied to the heater, and R is the electrical
resistance of the heater, 7.9 ohms, and th is the total mass flow rate. Substituting equations C.2
into equation C.3 the result is
S=h
4
V 4(p
2
4)+ m .
(C.5)
The R-22 is at saturated conditions at point 3 and we have
h = I +Xhg.
(C.6)
Assumption 3, h3 = , allows us to equate equations C.5 and C.6 to get
h4 + v4(p2 p,)+
-4
- =
m
(C.7)
+ Xg
i
Since the mass flow rate of the liquid, mi, is measured substitute
(C.8)
I-x
into equation C.7
h4
+ v4(p2 -4)
1 -+
m,,
X+ ,
(C.9)
and solve for X
[(h4 - ,) + v4(), - P,)z + Q
mA,, +Q
Calculated data is given in Table C.1 below.
(C.10)
Run
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
-0
Angle
(deg)
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0-
Mass Flux
(1041b/hr-ft2 )
3.80
3.93
4.19
4.16
5.35
5.28
5.35
5.48
5.17
5.35
5.18
5.07
8.87
9.28
9.49
9.49
8.16
8.24
8.74
8.24
2
Fr
0.43
0.43
0.43
0.42
0.43
0.42
0.42
0.43
0.72
0.72
0.71
0.71
0.41
0.42
0.42
0.42
0.71
0.72
0.72
0.72
-.7
Left
(%)
53.33
53.33
55.17
55.17
55.17
55.17
53.33
55.17
53.33
53.33
52.94
53.33
51.61
51.61
51.61
51.61
55.17
53.33
51.61
51.61
Right
(%)
46.67
46.67
44.83
44.83
44.83
44.83
46.67
44.83
46.67
46.67
47.06
46.67
48.39
48.39
48.39
48.39
44.83
46.67
48.39
48.39
8.9
x
(%)
43.48
42.02
39.64
39.33
31.61
31.31
30.84
30.49
54.45
52.44
53.84
54.75
18.31
17.84
17.37
17.34
34.15
33.96
32.05
33.97
3 -.
Slip
Ratio
2.14
2.14
2.13
2.14
2.13
2.13
2.13
2.13
2.12
2.12
2.12
2.13
2.11
2.11
2.10
2.10
2.12
2.12
2.12
2.12
-16
Table C.1: R-22 Calculated Data
at
(%)
95.04
94.75
94.23
94.17
91.96
91.87
91.70
91.58
96.72
96.46
96.64
96.76
84.55
84.11
83.66
83.62
92.73
92.67
92.07
92.68
jl
(ft/sec)
0.08
0.08
0.09
0.09
0.13
0.13
0.13
0.13
0.08
0.09
0.08
0.08
0.25
0.27
0.28
0.28
0.19
0.19
0.21
0.19
jg
(ft/sec)
Flow
Regime
3.08
3.07
3.08
3.05
3.12
3.05
3.04
3.09
5.16
5.15
5.12
5.10
2.93
2.98
2.96
2.96
5.09
5.11
5.11
5.12
stratified
stratified
stratified
stratified
stratified
stratified
stratified
stratified
stratified
stratified
stratified
stratified
annular
annular
annular
annular
annular
annular
annular
annular
Angle
Mass Flux
(deg)
(1041b/hr-ft 2)
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
0
0
0
0
90
90
90
90
90
90
90
90
90
90
90
90
0
0
0
8.14
8.70
8.64
7.93
8.43
8.73
8.93
8.48
7.45
7.26
7.34
7.26
7.69
8.73
8.81
8.24
9.17
9.47
9.02
40
0
8.93
Run
Fr
1.00
1.00
1.00
1.00
1.01
1.01
1.01
1.01
0.72
0.72
0.73
0.72
0.42
0.42
0.42
0.42
0.43
0.43
0.43
0.43
j
jg
Flow
(%)
(ft/sec)
(ft/sec)
Regime
95.79
95.28
95.33
96.01
95.62
95.35
95.15
95.56
93.77
94.02
93.94
94.00
86.90
85.07
85.06
86.06
84.88
84.28
84.91
85.11
0.15
0.17
0.16
0.14
0.16
0.17
0.17
0.16
0.16
0.16
0.16
0.16
0.21
0.25
0.25
0.23
0.26
0.27
0.26
0.25
7.08
7.10
7.09
7.09
7.16
7.18
7.17
7.16
5.17
5.17
5.18
5.16
2.99
3.01
3.04
3.03
3.15
3.13
3.10
3.11
annular
annular
annular
annular
annular
annular
annular
annular
annular
annular
annular
annular
annular
annular
annular
annular
annular
annular
annular
annular
Left
Right
x
Slip
tg
(%)
(%)
(%)
Ratio
51.61
53.33
51.61
51.61
30.43
36.00
38.46
36.00
33.33
33.33
30.43
30.43
33.33
33.33
36.00
33.33
51.52
50.00
50.00
50.00
48.39
46.67
48.39
48.39
69.57
64.00
61.54
64.00
66.67
66.67
69.57
69.57
66.67
66.67
64.00
66.67
48.48
50.00
50.00
50.00
48.30
45.30
45.61
49.72
47.25
45.67
44.64
46.91
37.97
38.97
38.65
38.91
21.24
18.75
18.71
19.96
18.33
17.66
18.37
18.61
2.11
2.11
2.10
2.10
2.10
2.11
2.10
2.10
2.12
2.12
2.12
2.12
2.12
2.12
2.13
2.13
2.14
2.14
2.14
2.14
Table C.1: R-22 Calculated Data (continued)
Left
Right
x
Slip
a
jl
jg
Flow
(%)
(%)
(%)
Ratio
(%)
(ft/sec)
(ft/sec)
Regime
0.73
0.73
0.74
0.73
0.95
0.95
0.95
0.95
50.00
50.00
50.00
50.00
50.00
50.00
50.00
50.00
50.00
50.00
50.00
50.00
50.00
50.00
50.00
50.00
28.86
28.39
27.77
28.16
35.05
35.07
35.21
35.69
2.13
2.14
2.13
2.13
2.13
2.13
2.13
2.13
90.98
90.79
90.53
90.70
93.04
93.04
93.08
93.22
0.25
0.25
0.26
0.25
0.24
0.24
0.24
0.23
5.29
5.24
5.33
annular
annular
annular
5.28
6.82
6.81
6.83
6.83
annular
annular
annular
annular
annular
7.09
0.73
51.61
48.39
40.19
2.13
94.34
0.15
5.27
annular
0
0
0
0
0
7.16
7.10
7.34
7.50
7.55
0.72
0.73
0.73
1.08
1.09
51.61
51.61
51.61
51.61
51.61
48.39
48.39
48.39
48.39
48.39.
39.19
39.93
38.90
56.11
56.67
2.13
2.13
2.13
2.12
2.12
94.11
94.28
94.04
96.92
96.99
0.15
0.15
0.16
0.12
0.11
5.19
5.24
5.27
7.70
7.82
annular
annular
annular
annular
annular
55
0
7.59
1.08
53.33
46.67
55.57
2.12
96.85
0.12
7.71
annular
56
57
58
59
60
0
0
0
0
0
7.51
4.54
4.66
4.59
4.49
1.07
0.62
0.63
0.62
0.62
53.33
51.61
52.78
51.61
53.33
46.67
48.39
47.22
48.39
46.67
55.93
52.92
52.11
52.43
53.18
2.12
2.14
2.14
2.14
2.14
96.90
96.55
96.44
96.49
96.58
0.12
0.07
0.08
0.08
0.07
7.69
4.47
4.52
4.48
4.45
annular
stratified
stratified
stratified
stratified
Angle
Mass Flux
(deg)
(1041b/hr-ft2)
41
42
43
44
45
46
47
48
0
0
0
0
0
0
0
0
9.88
9.93
10.33
10.09
10.55
10.52
10.52
10.37
49
0
50
51
52
53
54
Run
Fr
Table C.1: R-22 Calculated Data (continued)
Slip
Ratio
2.12
2.13
ca
(%)
99.02
98.91
j
(ft/sec)
jg
(ft/sec)
Flow
Regime
55.56
53.85
x
(%)
80.36
78.65
0.03
0.04
6.88
6.85
stratified
stratified
Right
4.66
4.73
0.96
0.95
Left
(%)
44.44
46.15
0
4.77
0.96
46.15
53.85
78.26
2.13
98.89
0.04
6.87
stratified
0
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
90
4.73
4.32
4.20
4.19
4.19
4.16
4.23
4.02
4.14
8.93
9.48
9.62
9.39
9.57
9.53
9.85
9.72
0.95
0.96
0.94
0.94
0.95
0.62
0.62
0.62
0.61
0.44
0.44
0.44
0.44
0.73
0.73
0.74
0.74
46.15
33.33
37.50
37.50
37.50
20.00
15.79
15.79
15.79
33.33
33.33
33.33
33.33
33.33
33.33
33.33
33.33
53.85
66.67
62.50
62.50
62.50
80.00
84.21
84.21
84.21
66.67
66.67
66.67
66.67
66.67
66.67
66.67
66.67
78.78
86.56
87.64
87.81
88.10
57.81
56.88
59.60
57.24
19.14
17.96
17.75
18.26
29.60
29.83
29.01
29.44
2.13
2.12
2.12
2.12
2.13
2.13
2.13
2.14
2.14
2.14
2.14
2.14
2.14
2.13
2.13
2.13
2.13
98.92
99.37
99.43
99.44
99.46
97.15
97.04
97.35
97.09
85.54
84.55
84.36
84.80
91.26
91.35
91.04
91.20
0.04
0.02
0.02
0.02
0.02
0.06
0.06
0.06
0.06
0.25
0.27
0.28
0.27
0.24
0.23
0.24
0.24
6.85
6.84
6.74
6.76
6.80
4.47
4.46
4.45
4.41
3.20
3.19
3.19
3.21
5.25
5.27
5.30
5.31
stratified
stratified
stratified
stratified
stratified
stratified
stratified
stratified
stratified
annular
annular
annular
annular
annular
annular
annular
annular
61
62
Angle
(deg)
0
0
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
Run
Mass Flux
Fr
(1041b/hr-ft2)
(%)
Table C.1: R-22 Calculated Data (continued)
Run
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
Angle
Mass Flux
(deg)
(1041b/hr-ft2 )
90
90
90
90
90
90
90
90
90
90
90
90
180
180
180
180
180
180
180
180
-
9.93
9.82
9.85
9.44
6.55
6.82
6.63
6.66
6.99
6.65
7.14
7.10
9.30
9.44
9.28
9.82
9.92
9.70
9.35
10.08
Fr
0.97
0.95
0.96
0.97
0.74
0.72
0.75
0.75
1.08
1.08
1.08
1.08
0.43
0.44
0.43
0.43
0.73
0.72
0.73
0.77
j
jg
Flow
Ratio
at
(%)
(ft/sec)
(ft/sec)
Regime
2.13
2.13
2.13
2.13
2.13
2.13
2.13
2.13
2.12
2.12
2.12
2.12
2.14
2.14
2.14
2.14
2.14
2.14
2.14
2.13
93.80
93.78
93.82
94.25
95.06
94.56
95.10
95.05
97.40
97.72
97.27
97.30
84.48
84.56
84.45
83.55
90.84
91.03
91.56
91.23
0.22
0.21
0.21
0.20
0.13
0.14
0.13
0.13
0.10
0.09
0.10
0.10
0.27
0.27
0.27
0.29
0.25
0.24
0.23
0.25
6.95
6.85
6.90
6.93
5.30
5.20
5.39
5.38
7.72
7.73
7.74
7.73
3.11
3.18
3.10
3.11
5.26
5.22
5.28
5.52
-
Left
Right
x
Slip
(%)
(%)
(%)
33.33
33.33
36.00
30.43
27.27
30.43
27.27
27.27
38.46
33.33
36.00
36.00
50.00
51.52
46.67
50.00
48.39
46.67
46.67
50.00
66.67
66.67
64.00
69.57
72.73
69.57
72.73
72.73
61.54
66.67
64.00
64.00
50.00
48.48
53.33
50.00
51.61
53.33
53.33
50.00
37.95
37.88
38.02
39.86
43.65
41.16
43.88
43.61
60.27
63.45
59.12
59.41
17.88
17.97
17.83
16.88
28.51
28.97
30.38
29.50
Table C.1: R-22 Calculated Data (continued)
annular
annular
annular
annular
annular
annular
annular
annular
annular
annular
annular
annular
annular
annular
annular
annular
annular
annular
annular
annularmmm
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
Angle
(deg)
180
180
180
180
180
180
180
180
180
180
180
180
180
180
180
117
118
119
120
180
180
180
180
Run
116
180
Mass Flux
(1041b/hr-ft2 )
10.22
9.69
9.86
10.46
6.49
6.68
6.88
7.11
7.04
7.03
7.25
7.15
4.05
4.19
4.01
4.35
4.26
4.28
4.28
4.05
Right
(%)
53.33
53.33
51.61
50.00
53.33
55.17
53.33
53.33
54.55
52.17
50.00
50.00
53.33
53.33
53.33
X
(%)
36.54
38.36
37.55
35.34
43.53
42.04
40.45
39.32
59.96
59.99
58.32
59.18
58.97
57.33
59.56
Slip
Ratio
2.13
2.13
2.13
2.13
2.13
2.13
2.13
2.13
2.12
2.12
2.12
2.12
2.14
2.14
2.14
a
(%)
j
(ft/sec)
jg
(ft/sec)
Flow
Regime
0.96
0.95
0.95
0.95
0.73
0.72
0.72
0.72
1.08
1.08
1.08
1.08
0.62
0.62
0.62
Left
(%)
46.67
46.67
48.39
50.00
46.67
44.83
46.67
46.67
45.45
47.83
50.00
50.00
46.67
46.67
46.67
93.44
93.90
93.70
93.12
95.04
94.75
94.41
94.16
97.37
97.37
97.18
97.28
97.28
97.10
97.34
0.23
0.21
0.22
0.24
0.13
0.14
0.14
0.15
0.10
0.10
0.11
0.10
0.06
0.06
0.06
6.89
6.85
6.82
6.82
5.23
5.21
5.17
5.19
7.76
7.74
7.75
7.75
4.44
4.47
4.45
annular
annular
annular
annular
annular
annular
annular
annular
annular
annular
annular
annular
stratified
stratified
stratified
0.95
0.95
0.96
0.96
55.56
66.67
66.67
66.67
44.44
33.33
33.33
33.33
85.41
86.62
87.19
87.83
2.12
2.12
2.12
2.12
99.31
99.38
99.41
99.44
0.02
0.02
0.02
0.02
6.82
6.78
6.86
6.90
stratified
stratified
stratified
stratified
Fr
0.62
46.67
53.33
59.50
2.14
97.34
Table C.1: R-22 Calculated Data (continued)
0.06
4.48
stratified
Left
Right
x
Slip
cc
jl
jg
Flow
(%)
(%)
(%)
Ratio
(%)
(ft/sec)
(ft/sec)
Regime
0.44
0.44
64.00
66.67
36.00
33.33
16.94
18.84
2.14
2.14
83.60
85.30
0.29
0.26
3.17
3.20
annular
annular
9.22
0.44
66.67
33.33
18.29
2.14
84.83
0.26
3.15
annular
9.40
9.87
9.83
9.67
9.81
9.95
10.16
9.83
10.04
6.76
6.92
7.26
6.70
7.05
7.12
7.19
6.94
0.43
0.72
0.73
0.72
0.72
0.96
0.94
0.95
0.97
0.73
0.71
0.72
0.73
1.08
1.08
1.08
1.07
66.67
66.67
64.00
66.67
64.00
61.54
61.54
66.67
64.00
66.67
66.67
64.00
69.57
61.54
57.14
61.54
59.26
33.33
33.33
36.00
33.33
36.00
38.46
38.46
33.33
36.00
33.33
33.33
36.00
30.43
38.46
42.86
38.46
40.74
17.64
28.49
28.89
28.86
28.73
37.63
36.26
37.79
37.80
42.00
40.01
38.52
42.19
59.56
59.00
58.59
60.37
2.14
2.13
2.13
2.13
2.13
2.13
2.13
2.12
2.12
2.13
2.13
2.13
2.13
2.12
2.12
2.12
2.12
84.26
90.83
90.98
90.97
90.91
93.72
93.36
93.75
93.76
94.72
94.29
93.96
94.77
97.32
97.26
97.22
97.41
0.27
0.25
0.24
0.24
0.24
0.22
0.23
0.21
0.22
0.14
0.15
0.16
0.14
0.10
0.10
0.10
0.10
3.10
5.22
5.26
5.17
5.22
6.89
6.78
6.83
6.97
5.24
5.11
5.17
5.23
7.70
7.70
7.74
7.69
annular
annular
annular
annular
annular
annular
annular
annular
annular
annular
annular
annular
annular
annular
annular
annular
annular
Angle
Mass Flux
(deg)
(1041b/hr-ft2)
121
122
270
270
10.01
9.07
123
270
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
270
270
270
270
270
270
270
270
270
270
270
270
270
270
270
270
270
Run
Fr
Table C.1: R-22 Calculated Data (continued)
Angle
Mass Flux
(deg)
(1041b/hr-ft 2)
141
142
143
144
145
146
147
148
270
270
270
270
270
270
270
270
4.92
5.11
5.00
5.20
4.45
4.44
4.43
4.39
149
270
150
151
152
270
270
270
Run
Fr
Left
Right
x
Slip
a
jl
jg
Flow
Regime
(%)
(%)
(%)
Ratio
(%)
(ft/sec)
(ft/sec)
0.61
0.62
0.62
0.62
0.96
0.95
0.96
0.95
72.73
69.57
72.73
69.57
66.67
66.67
66.67
66.67
27.27
30.43
27.27
30.43
33.33
33.33
33.33
33.33
48.53
47.03
48.07
46.01
84.36
83.24
84.37
84.09
2.14
2.14
2.14
2.14
2.12
2.12
2.13
2.13
95.91
95.67
95.84
95.50
99.25
99.19
99.26
99.24
0.09
0.09
0.09
0.10
0.02
0.03
0.02
0.02
4.44
4.47
4.47
4.45
6.89
6.78
6.88
6.79
stratified
stratified
stratified
stratified
stratified
stratified
stratified
stratified
4.56
0.95
57.14
42.86
81.44
2.13
99.09
0.03
6.83
stratified
4.54
4.55
4.59
0.95
0.95
0.95
57.14
57.14
57.14
42.86
42.86
42.86
81.70
81.53
80.45
2.13
2.13
2.13
99.10
99.09
99.03
0.03
0.03
0.03
6.83
6.82
6.80
stratified
stratified
stratified
Table C.1: R-22 Calculated Data (continued)
Appendix D
Empirical Correlation Derivation
First an equation, equation D.1, was assumed. The Froude number, void fraction, and the
angle of orientation were used as correlating factors because, from the data, it could be seen that
they had the largest effects on the flow distribution. A least squares solution to was used to
derive the empirical correlation.
-= 0.5- c sinO (1- a)2 Frc
(D.1)
The natural log of equation D.1 was taken
( 0.5 -
wl\
-
InnIsinOWI=Incq + c2 In(1- a) + c3 In(Fr)
| m
This was put into a matrix for using the data for annular flow conditions.
0.5 b, = In
sinO
.
(D.2)
a, 1 =1
(D.3)
a, = In(Fr)
rln c,
X= C2
(D.4)
C3
where i = 1... n, n being the number of data points, b, is the ith term in the vector b, ai, is the
component of the matrix A in the ith row andjth column. We now have the matrix equation
(D.5)
Ax = b.
We can now use the least squares method as follows
A TAx =A Tb,
(D.6)
(ATA)I ATAx =(ATA)-I ATb,
(D.6)
x= (ATA)IA b,
(D.8)
giving
1
[ -1.93
x= 12.2710
[
-0.24
-3
i,
]
c
=
e
x'
C2 = X 2
C3 = X
3
Finally we have c = 0.145, c2 = 2.27- 10- 3 , and c3 = -0.24 and Equation 3.1.
= 0.5 - 0.145 sin 01 - a) 002Fr-04
(3.1)
w
A comparison between the measured and correlated data is illustrated in Figure 3.7. The
calculated data is within +8% and -6% of the experimental data. An equation, equation 3.2, was
derived using the method as above with the exceptions of using the void fraction and Froude
number as factors.
-= 0.5 - 0.155 sin 80,
(3.2)
This equation gives calculated data within +9% and -6% of the experimental data as illustrated in
Figure 3.8.