Two Phase Flow Splitting in Piping Branches

Two Phase Flow Splitting in Piping Branches

by

Michael Steven Quintana

S.B., Mechanical EngineeringMassachusetts Institute of Technology, 1989

Submitted to the Department of Mechanical Engineering and theDepartment 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 theMASSACHUSETTS INSTITUTE OF TECHNOLOGY

June 1998

© 1998 Massachusetts Institute of TechnologyAll Rights Reserved.

A u th o r ....................................................................................

Certified by..........................................................

Dep

Certified by............................................... ..................

MASSACHUSETTS INSTITUTEOF TECHNOLOGY

JUL 2 0 1999

LIBRARIES

Depart ent of Nuclear ngineering, ~June 1, 1998

Professor Peter O-ith, Emeritusartment of Mechanical Engineering

/) Toes, is Supervisor

Professor Neil Emmanuel TodreasDepartments 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 StudentsDepartment of Nuclear Engineering

Two Phase Flow Splitting in Piping Branches

by

Michael Steven Quintana

Submitted to the Department of Mechanical Engineering and theDepartment of Nuclear Engineering

on June 1, 1998 in Partial Fulfillment of the Requirements for the Degrees ofMaster of Science in Nuclear Engineering

andMaster of Science in Mechanical Engineering

ABSTRACT

The objectives of this research are to evaluate the performance of a flow-splitting tripod, discoverthe factors which most affect the flow distribution; and quantify the effects of geometry, qualityand flow rate on the distribution. Knowing all this allows one to predict the distribution forgiven conditions. An R-22 test apparatus was constructed for carrying out the experiments. Thefactors examined were tripod orientation, Froude number, void fraction, and swirl induced byhelical grooves in the tube supplying the two-phase flow to the tripod. The flow regime ofconcern 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 theirperformance 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 eliminatethis variable a number of tripods were tested, using an air-water rig, to find a tripod that was notdefective. Tests using R-22 were then run on this tripod and it was found that inlet swirl hadlittle or no affect on the flow distribution. The factors that had the greatest effect on the flowdistribution 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 GriffithTitle: 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 Intro du ctio n ....................................................................................................................... 9

1.1 Problem Statement ......................... .......... ............................... 9

1.2 Geom etric and Property V ariables ...................................................... ......... 101.2.1 Swirl .................................................... ................ 10

1.2.2 O rientation .................. ....................................................................... 10

1.2.3 Geometry of Tripod ............................... . ................. 111.2.4 Refrigerant ............................................................... 11

1.2.5 Property V ariables ........................................ 11

1.3 Current Work ........................ ................ ................. 12

1.3.1 Flow Regimes of Interest ........................................ 12

1.3.2 Refrigerant 23 Tests ..................................................... 13

1.3.3 D efective Tripods ........................................ .................. 13

1.3.4 Comparison to Air-W ater Tests ...................................... ........ .. 13

2 Flow Regimes and Conditions of Interest ........................................ ... 15

2.1 Range of Pressures, Qualities and Flow Rates of Interest ................................ 15

2.2 Taitel-Dukler Flow Regime M ap ........................................ .... ............ 15

2.3 Conditions for the Range of Param eters ............................................................. 16

2.4 Range of Void Fractions and Froude Numbers ..................................... 17

2.5 The Selection of the Correlation Factors .................................. 17

3 Refrigerant 22 Experiments ...................................... ........... 19

3 .1 A pparatu s ....................................................................... 19

3.1.1 Flow Loop ...................................................................... 19

3.1.2 Test Section ................................................................. ............... 24

3.1.3 Cooling System ........................................................... 24

3.1.4 Instrum entation ..................................................... 24

3.2 Parameters Varied ................................................................... 27

3 .3 R esu lts .......................................................................................................... 2 7

4 Comparison of Refrigerant 23 to Air-Water Experiments .......................................... 31

4.1 Air-Water Experiment Results ......................... .. ............... 31

4.2 Direct Comparison of Refrigerant 23 and Air-Water Experiments ................. 31

4.3 Air-Water System's Limitations ........................................ 32

5 C o nclu sio n s ....................................................................................................................... 3 45.1 Geometric Variations ....................................... .................. 34

5.2 Unnecessary R-23 Tests ........................................ 35

5.3 Stratified Flow R egim e ................................................................ ................. 35

5.4 Optimum Conditions .......................... ............................................ 35

Table of Contents (cont.)

R eferences ........................ .......... . ..................................................................................... 36Appendix A Nomenclature and Subscripts ........................................ 37Appendix B Raw Data .............................................................................. 38Appendix C Calculations ...................................... ........................... 46Appendix D Empirical Correlation Derivation ................................ 57

List of Figures

Figure 1.1: Typical Tripod ......................................... ....... ........... 10Figure 1.2: Tripod Orientation and Swirl Rotational Direction ......................................... 12Figure 1.3: Defective Tripod ........................................ .......................... 14Figure 1.4: Comparison of Distribution Between Defective and Non-defective Tripods ....... 14Figure 2.1: Flow Regim e M ap .................................................................. ......................... 16Figure 2.2: Flow Regime Schematics ......................................... 17Figure 2.3: Slip Ratio versus Specific Volume ....................................... ............ 18Figure 3.1: Test Apparatus Schematic .............................................. 20Figure 3.2: Test A pparatus ....................................................... 21Figure 3.3: Inside the Pressure Vessel......................................................................... 22Figure 3.4: Test Section ................................................................ 23Figure 3.5: Rotating Brass Guide .......................................................................... ................ 25Figure 3.6: Cooling System Schem atic .................................. ............................ ... 26Figure 3.7: Comparison of Measured and Calculated Liquid Flow Split Using Equation 3.1 . 29Figure 3.8: Comparison of Measured and Calculated Liquid Flow Split Using Equation 3.2. 30Figure 4.1: Comparison at Low Froude Number ..................................... .......... 32Figure 4.2: Comparison at Intermediate Froude Number .................. ......................... 33Figure 4.3: Comparison at High Froude Number ........................................ 33

List of Tables

Table 2.1: Conditions of Interest ........................... ................................... 15Table 2.2: Approach Tube Parameters ........................................ .................... 15Table 5.1: Defective Tripod Distribution .......................................................................... 34Table 5.2: Stratified Flow Distribution ........................................ .................... 35

8

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 u-

tube. 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

Right 0 00 0 Left

2700 900

Left 1800 * Right

Left Right g

c' Swirl Rotational Direction

Figure 1.2: Tripod Orientation and Swirl Rotational Direction

1.3 Current Work

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 non-

defective 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.

0 ]drilled hole 0.275" 1

Ifeed tube ID 0.281" I.edtb I .8

- brazed flarejoint

Figure 1.3: Defective Tripod

100

90 -

80 -

70

60

50o

40 -

30 -

20 -

10 -

- -- - Defective Tripod(avg)

-- - - - Non-defective

Tripod (avg)

0 90 180 270 360

rotation angle (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 Range Nominal Value

Temperature, 'F 40 to 55 45

Pressure, psia 83.2 to 107.3 90.7

103 -lbMass Flux, 20 to 100 80

S hr ft 2

Superficial Velocity ft/sec 1.05 to 5.2 4.22

Quality, % 18 to 60 30

Back Pressure Imbalance, psi 0 to 3 0

Table 2.1: Conditions of Interest

Variable Range Nominal Value

Diameter, inches 0.3 to 0.7 0.375

Inside Surface smooth to enhanced enhanced

Tube Orientation horizontal 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).

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.

1 10 100Gas Velocity (ft/sec)

OOOOO OOO OOO OOAAAoOOOOOOOO OOOO O o00

OO OOOOO OOOO OAO OOOOOOOOOOOOOOOA AAO OOAAAAAAAAAAAAA Ao [ 00 0AAAAAAAAAAAAAOOOO0oo

AAAAAAAAAAAOOOOOOOOOOAAAAAAAAAAOoo ooooooo

AAAAAAAAAOOOOoooooooAAAAAAAAO EMOooooooo

000000000 on0 000000000000000000E n 0000000000000000OOOO000000000000 0000000000 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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.

100

10

1

0.1

0.01

0001 I

0.01

0 ANNULAR

OBUBBLE

AINTERMITTENTOSTRATIFIED

)000.1Superficial

The four regimes that are identified are

1

O 0 0** z*0 o a o C:0 4

Bubbly Flow Stratified Flow

.D 0 0

Intermittent Flow Annular 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.

1 Pg SX P

where (2.2)

(2.3)V

S VI9V,'

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

64

S

1 2 4 6 10 20 40 60 100 200 4006001,000 2,000

VSpecific volume ratio 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 ApparatusA 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. The

hoses in the pressure vessel are high quality neoprene.

TEST SECTION

TRIPOD RETURN TUBES BRASS GUIDE

METERINGVALVES

(NEEDLE VALVES)

HEATER

PRESSURE VESSEL

GLASSESI

DRAINAGEA I SYSTEM

ISOLATIONVALVE

FILTER/DRYER

ISOLATIONVALVE

TO AND FROMCOOLING

SURGESUPPRESSER

Figure 3.1: Test Apparatus Schematic

II ENHANCED TUBE

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 INCHESSCALE 1:1O-RING GROOVE SCALE: 4:1

00 TO 50 0.280 BREAK CORNERAPPROX. 0.280 R

4.875

Figure 3.5: Rotating Brass Guide

E

Pressure Vessel

Drain Valve

Pump Discharge

CoolingPump

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 ResultsThe 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= 0.5 - 0.145 sin 0(1 - a) °0

2 Fr-024, (3.1)w

- 0.5- 0.155 sin 0, (3.2)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%

-6%70% +

60% -

I-

I. 50%

La 40%

30%E

8%

20% +

0% I I I I I I I I

0.00% 10.00% 20.00% 30.00% 40.00% 50.00% 60.00%

Calculated

70.00% 80.00%

Flow 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 0 2 Fr- 24.

o% +

10% -

0%

-6%

0.00% 10.00% 20.00% 30.00% 40.00% 50.00% 60.00%

70% -

60%

Calculated Flow Split

Figure 3.8: Comparison of Measured and Calculated Liquid Flow Split

Using Equation 3.2 = 0.5 - 0.155 sin 0.W

8 AO

70.00 9%

70.00% 80.00%

Ia 50% -

0

La 40% -

" 30% -Et

20% +

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 air-

water 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 air-

water 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

50

40

30

20

10

00 90 180

rotation angle

270

(deg)

360

Figure 4.1: Comparison at a Low Froude Number

X11

- -

I I

-- X- -Air/Water-Fr0.4, voidfraction 88%

--- 0-- R 22-Fr 0.4,void fraction84%

100

80t70

60

50 4

40 -

30

20

10

0 90 180 270 360


Figure 4.2: Comparison at an Intermediate Froude Number

100

90 -

80

70

60

50 I

40

30

20 +

0 90 180 270 360


Figure 4.3: Comparison at a High Froude Number

- -

a

-- K- -Air/Water-Fr0.7, voidfraction 93%

-- 4- - R 22-Fr 0.7,void fraction93%

- -X- -Air/Water-Fr1.0, voidfraction 96%

----- R 22-Fr 1.0,void fraction95%

I I

t

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 0O just as one

would expect. The effect of the swirl on the flow split in all tripods is overwhelmed by the

manufacturing defects.

Angle Mass Velocity Velocity Quality Split (%

(deg) (104 lb/hr ft2) (ft/sec) (%) Left Right

90 10.22 4.18 22.72 52.47 47.5390 9.30 5.87 33.18 58.72 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 R-

22, and does not correlate well.

Angle Flow Fr Left Right x Slip a

(deg) (1041b/hr-ft) (%) (%) (%) ratio (%)

0 4.58 0.62 52.33 47.67 52.70 2.13 96.50

90 4.14 0.62 16.84 83.16 57.90 2.13 97.15

180 4.08 0.62 46.67 53.33 58.88 2.13 97.25

270 5.07 0.61 71.15 28.85 47.51 2.11 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 Horizontal Pipes. MS Thesis, Massachusetts Instituteof 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-water Modeling ofRefrigerant Distribution Tripods. BS Thesis,Massachusetts Institute of Technology, Cambridge, MA.

Taitel, Yehuda, 1990, "Flow Pattern Transition in Two-Phase Flow", Proceedings of the 9th

International Heat Transfer Conference, The Assembly for International Heat TransferConferences, Hemisphere Publishing Corporation, Washington.

Whalley, P.B., 1997, Boiling, Condensation, and Gas-Liquid Flow, 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 T 1 T2 T3 T4 P2 P 3 P4 Left th, Right rz,

(deg) (volts) (OF) (OF) (OF) (OF) (psi) (psi) (psi) (lb/hr) (lb/hr)

1 0 50.1 47.93 49.82 38.43 38.77 95.70 82.20 81.97 8.67 7.58

2 0 50.0 48.56 49.08 38.38 39.00 95.70 80.70 82.20 9.18 8.03

3 0 50.0 48.38 50.22 38.68 39.91 96.70 80.70 83.12 10.55 8.57

4 0 49.8 48.16 49.15 38.34 38.77 95.70 80.70 81.97 10.52 8.55

5 0 50.0 47.56 52.86 39.17 41.81 101.70 83.70 85.87 15.27 12.41

6 0 49.9 47.74 52.90 39.07 39.93 101.70 82.70 83.14 15.14 12.30

7 0 49.9 47.76 53.11 39.11 39.67 102.20 83.70 82.87 14.91 13.05

8 0 49.8 47.85 52.97 39.01 41.20 102.20 83.70 84.97 15.89 12.91

9 0 65.1 47.99 61.48 39.58 40.80 117.70 84.70 84.38 9.49 8.31

10 0 65.0 47.96 61.08 39.55 40.72 117.70 84.70 84.26 10.26 8.98

11 0 65.0 47.92 61.14 39.56 39.67 117.70 84.70 82.87 9.57 8.50

12 0 64.9 48.03 61.09 39.40 39.40 117.70 84.70 82.60 9.25 8.10

13 0 49.9 43.73 53.13 40.67 39.84 102.20 84.70 83.05 28.27 26.51

14 0 50.4 43.87 53.48 40.80 39.92 103.70 85.70 83.13 29.75 27.89

15 0 50.3 43.97 53.68 40.89 40.03 103.70 85.70 83.25 30.60 28.69

16 0 50.3 44.06 53.85 41.01 40.08 103.70 85.70 83.32 30.63 28.71

17 0 65.4 43.40 58.03 40.00 38.56 112.20 85.70 81.76 22.42 18.21

18 0 65.5 43.45 58.29 40.07 38.81 112.20 85.70 82.01 21.96 19.22

19 0 65.5 43.43 57.96 40.01 38.87 112.20 85.70 82.07 23.18 21.73

20 0 65.5 43.44 58.38 39.95 38.76 112.20 85.70 81.96 21.25 19.92

Table B.I: R-22 Experiment Raw Data

Run Angle Heater Voltage TI T2 T3 T4 P2 P 3 P 4 Left rm, Right ri,

(deg) (volts) (oF) (oF) (OF) (OF) (psi) (psi) (psi) (lb/hr) (lb/hr)

21 0 77.5 43.89 64.08 40.84 39.39 124.70 88.70 82.59 16.44 15.41

22 0 77.6 43.98 65.40 40.82 39.34 124.70 88.70 82.54 19.20 16.80

23 0 77.6 43.98 64.05 40.87 39.39 124.70 88.70 82.59 18.35 17.21

24 0 77.6 44.06 63.49 40.90 39.32 123.70 88.70 82.52 15.56 14.59

25 90 78.0 44.11 65.88 40.88 39.31 127.20 89.70 82.51 10.23 23.39

26 90 78.0 44.03 65.99 40.81 39.51 127.20 89.70 82.71 12.92 22.96

27 90 78.0 43.95 65.90 40.91 39.59 127.20 89.70 82.79 14.38 23.02

28 90 77.9 43.98 65.74 40.87 39.57 127.20 89.70 82.77 12.26 21.80

29 90 65.6 43.64 57.54 39.98 39.51 112.20 87.20 82.71 11.65 23.30

30 90 65.8 43.65 57.42 39.95 38.73 112.20 87.20 81.93 11.17 22.34

31 90 65.9 43.67 57.25 40.00 38.78 112.20 86.70 81.98 10.37 23.70

32 90 65.8 43.70 57.39 40.01 38.62 112.20 86.70 81.82 10.21 23.34

33 90 50.2 43.62 51.40 39.94 38.74 102.20 85.70 81.94 15.28 30.56

34 90 50.3 43.62 52.05 39.46 38.27 102.20 85.70 81.47 17.88 35.77

35 90 50.4 43.50 52.04 39.24 38.28 102.20 84.70 81.48 19.50 34.67

36 90 50.4 43.26 52.08 39.23 38.11 101.70 84.70 81.30 16.63 33.26

37 0 49.9 42.04 51.40 37.91 39.45 98.70 82.70 82.65 29.18 27.46

38 0 49.9 42.10 51.38 37.92 39.10 98.70 82.20 82.30 29.48 29.48

39 0 49.9 42.07 51.50 37.90 38.61 98.70 80.70 81.81 27.85 27.85

40 0 49.9 42.01 51.65 37.94 38.86 98.70 80.70 82.06 27.50 27.50

Table B.1: R-22 Experiment Raw Data (continued)

Run Angle Heater Voltage T 1 T2 T3 T 4 P 2 P3 P 4 Left Mh, Right m,

(deg) (volts) (OF) (oF) (OF) (oF) (psi) (psi) (psi) (lb/hr) (lb/hr)

41 0 65.3 42.04 60.48 38.60 39.93 116.70 83.70 83.14 26.57 26.57

42 0 65.2 42.15 60.46 38.58 39.19 116.70 83.70 82.39 26.90 26.90

43 0 65.2 42.20 60.50 38.61 40.74 116.70 82.70 84.29 28.23 28.23

44 0 65.2 42.20 60.48 38.59 39.92 116.70 82.70 83.13 27.42 27.42

45 0 74.7 42.19 66.68 39.18 39.69 127.20 84.70 82.89 25.91 25.91

46 0 74.7 42.48 66.44 39.18 39.50 127.20 84.70 82.70 25.84 25.84

47 0 74.8 42.58 66.32 39.19 39.61 127.20 84.70 82.81 25.78 25.78

48 0 74.7 42.61 66.25 39.20 39.86 127.70 84.70 83.07 25.23 25.23

49 0 65.0 43.61 55.16 38.96 42.04 106.70 82.70 86.21 16.56 15.52

50 0 65.0 43.61 55.00 39.00 40.14 106.70 82.70 83.41 17.00 15.94

51 0 65.0 43.75 55.27 38.99 41.37 106.70 82.70 85.22 16.65 15.61

52 0 65.0 43.71 55.58 39.00 42.11 106.70 82.70 86.32 17.50 16.41

53 0 80.0 43.94 63.01 39.81 39.32 120.70 85.70 82.52 12.85 12.05

54 0 80.0 44.07 63.27 39.89 42.19 120.70 85.70 86.44 12.77 11.97

55 0 80.0 44.09 63.32 39.88 39.65 120.70 85.70 82.85 13.60 11.90

56 0 80.0 44.05 63.30 39.86 39.01 120.70 85.70 82.21 13.36 11.69

57 0 60.4 44.76 48.49 38.44 39.06 94.70 81.70 82.26 8.35 7.83

58 0 60.4 44.71 48.45 38.43 40.61 94.70 84.70 84.10 8.91 7.97

59 0 60.4 44.58 48.66 38.39 39.20 94.70 82.70 82.40 8.53 7.99

60 0 60.4 44.63 48.42 38.43 37.90 94.70 82.70 81.09 8.49 7.42


Run Angle Heater Voltage T 1 T 2 T3 T4 P2 P 3 P4 Left mi Right iz,

(deg) (volts) (OF) (OF) (OF) (OF) (psi) (psi) (psi) (lb/hr) (lb/hr)

61 0 75.1 44.91 53.80 39.45 41.63 103.70 83.70 85.60 3.08 3.85

62 0 75.0 45.09 53.50 39.33 40.71 103.70 83.70 84.25 3.53 4.12

63 0 75.0 45.00 53.99 39.36 41.39 103.70 83.70 85.25 3.62 4.22

64 0 74.9 45.14 53.40 39.42 41.45 103.70 83.70 85.34 3.50 4.08

65 90 75.4 45.95 52.72 39.82 39.21 102.70 82.70 82.41 1.46 2.93

66 90 74.8 45.95 52.28 39.74 39.38 102.70 83.70 82.58 1.47 2.45

67 90 74.8 45.90 52.75 39.44 39.01 102.70 83.70 82.21 1.45 2.41

68 90 75.0 45.97 52.90 39.28 38.77 102.70 83.70 81.97 1.42 2.36

69 90 60.4 45.37 48.29 38.61 39.31 95.70 82.70 82.51 2.66 10.63

70 90 60.3 45.28 48.37 38.80 40.12 96.70 82.70 83.38 2.18 11.63

71 90 60.3 45.48 47.90 38.56 39.08 95.70 82.70 82.28 1.94 10.34

72 90 60.2 45.18 48.31 38.48 37.71 95.70 81.70 80.90 2.12 11.28

73 90 49.9 41.70 51.27 37.91 40.46 100.70 81.70 83.88 18.20 36.40

74 90 49.9 41.99 51.34 37.93 40.16 98.70 81.70 83.44 19.61 39.23

75 90 50.4 42.01 51.74 37.96 39.17 100.70 81.70 82.37 19.94 39.89

76 90 50.7 42.10 51.71 38.03 38.86 100.70 82.20 82.06 19.36 38.72

77 90 65.3 42.48 59.95 38.74 39.52 114.70 83.70 82.72 16.98 33.96

78 90 65.4 42.50 59.76 38.78 39.68 114.70 83.70 82.88 16.87 33.74

79 90 65.4 42.51 60.26 38.71 39.99 114.70 83.70 83.20 17.62 35.25

80 90 65.4 42.52 59.97 38.73 40.17 114.70 83.70 83.45 17.29 34.59


Run Angle Heater Voltage T 1 T2 T3 T4 P 2 P3 P 4 Left mth Right ri,(deg) (volts) (oF) (oF) (oF) (OF) (psi) (psi) (psi) (lb/hr) (lb/hr)

81 90 75.1 42.46 65.56 39.22 40.80 125.70 85.70 84.38 15.54 31.07

82 90 75.0 42.60 65.27 39.34 39.71 125.70 85.70 82.91 15.39 30.77

83 90 75.1 42.75 65.71 39.31 40.16 125.70 85.70 83.44 16.63 29.56

84 90 75.1 42.81 65.64 39.32 40.74 125.70 85.70 84.29 13.07 29.86

85 90 65.3 43.92 53.92 38.72 41.35 104.70 83.70 85.19 7.61 20.30

86 90 65.4 43.74 54.35 38.71 38.38 105.70 83.70 81.58 9.23 21.11

87 90 66.3 43.65 55.05 38.74 39.51 106.70 83.70 82.71 7.67 20.46

88 90 66.3 43.49 55.19 38.80 39.35 106.70 83.70 82.55 7.74 20.65

89 90 80.0 43.97 62.32 39.74 39.62 118.70 84.70 82.82 8.08 12.94

90 90 80.0 44.06 61.32 39.76 39.91 118.70 84.70 83.12 6.13 12.26

91 90 80.0 44.20 61.32 39.65 39.82 119.70 85.70 83.02 7.95 14.14

92 90 80.0 44.14 62.01 39.73 39.83 119.70 85.70 83.03 7.85 13.96

93 180 50.0 42.15 51.99 37.91 38.57 101.70 82.70 81.77 28.90 28.90

94 180 50.6 42.21 51.84 37.90 38.35 101.70 82.70 81.55 30.19 28.41

95 180 49.9 42.04 51.85 37.85 38.47 101.70 82.70 81.67 26.92 30.77

96 180 50.5 42.01 51.97 37.83 37.19 101.70 82.70 80.38 30.87 30.87

97 180 65.2 42.04 59.75 38.56 39.53 114.70 83.70 82.73 25.97 27.70

98 180 65.2 42.24 59.47 38.53 38.91 114.70 84.70 82.11 24.33 27.80

99 180 65.5 42.30 59.86 38.55 39.03 114.70 84.70 82.23 22.97 26.25

100 180 67.0 42.35 60.90 38.68 39.18 116.70 84.70 82.38 26.87 26.87


Run Angle Heater Voltage T 1 T2 T3 T4 P2 P3 P4 Left t , Right ith

(deg) (volts) (OF) (OF) (oF) (OF) (psi) (psi) (psi) (lb/hr) (lb/hr)

101 180 75.1 42.46 66.02 39.21 39.71 126.70 86.70 82.91 22.90 26.17

102 180 75.0 42.71 65.53 39.26 39.54 125.70 86.70 82.74 21.09 24.10

103 180 74.9 42.88 65.30 39.29 39.38 125.70 85.70 82.58 22.54 24.04

104 180 74.8 42.80 65.80 39.24 39.48 125.70 86.70 82.68 25.59 25.59

105 180 65.1 43.71 54.26 38.74 40.51 104.70 83.70 83.95 12.93 14.77

106 180 65.0 43.69 54.10 38.60 40.00 104.70 83.70 83.21 13.12 16.15

107 180 64.9 43.62 54.73 38.61 39.29 105.70 83.70 82.49 14.47 16.54

108 180 64.9 43.46 54.64 38.61 39.71 105.70 83.70 82.91 15.22 17.40

109 180 79.9 43.35 61.60 39.50 40.19 118.70 85.70 83.48 9.69 11.63

110 180 79.9 43.56 61.74 39.55 40.05 118.70 85.70 83.28 10.18 11.10

111 180 80.1 43.83 62.28 39.62 39.55 118.70 85.70 82.75 11.43 11.43

112 180 80.0 44.00 61.15 39.79 40.30 118.70 85.70 83.65 11.04 11.04

113 180 60.2 44.92 47.53 38.45 39.01 93.70 80.70 82.21 5.86 6.70

114 180 60.3 45.11 47.40 38.50 39.54 94.70 80.70 82.74 6.31 7.21

115 180 60.3 45.21 47.70 38.47 38.68 94.70 80.70 81.88 5.73 6.55

116 180 60.3 45.28 47.49 38.41 40.08 94.70 80.70 83.32 5.79 6.61

117 180 75.0 45.24 52.38 39.48 40.26 102.70 82.70 83.59 2.67 2.13

118 180 74.9 45.27 52.90 39.52 39.49 102.70 82.70 82.69 2.88 1.44

119 180 75.2 45.27 52.80 39.48 40.46 102.70 82.70 83.88 2.77 1.38

120 180 75.3 45.27 53.02 39.53 41.45 102.70 82.70 85.34 2.63 1.31


Run Angle Heater Voltage T 1 T2 T3 T4 P2 P3 P 4 Left m, Right ih,

(deg) (volts) (oF) (OF) (OF) (OF) (psi) (psi) (psi) (lb/hr) (lb/hr)

121 270 49.8 41.74 52.71 37.95 40.01 101.70 81.70 83.22 40.26 22.65

122 270 49.7 41.78 52.55 37.92 40.90 100.70 81.70 84.52 37.12 18.56

123 270 49.7 41.90 52.39 37.97 40.09 100.70 81.70 83.34 37.98 18.99

124 270 49.7 41.94 52.50 37.96 39.12 101.70 81.70 82.32 39.05 19.52

125 270 65.1 42.04 60.61 38.68 39.30 115.70 84.70 82.50 35.58 17.79

126 270 65.4 42.24 60.81 38.78 39.50 116.70 84.70 82.70 33.85 19.04

127 270 64.7 42.35 60.55 38.75 39.86 115.70 84.70 83.07 34.69 17.35

128 270 65.1 42.41 60.59 38.81 39.61 115.70 84.70 82.81 33.84 19.03

129 270 75.2 42.60 66.55 39.34 39.80 127.70 86.70 83.00 28.89 18.06

130 270 74.8 42.78 66.24 39.40 39.13 126.70 85.70 82.33 30.13 18.83

131 270 75.0 42.85 66.36 39.48 39.59 126.70 86.70 82.79 30.84 15.42

132 270 75.8 42.89 66.51 39.44 39.52 127.70 86.70 82.72 30.22 17.00

133 270 65.2 43.49 55.88 39.04 40.88 107.70 84.70 84.49 19.76 9.88

134 270 65.0 43.52 55.65 39.05 38.42 106.70 84.70 81.62 20.93 10.46

135 270 65.1 43.64 55.62 38.91 39.24 106.70 84.70 82.44 21.61 12.15

136 270 65.2 43.50 55.77 38.85 40.20 106.70 84.70 83.50 20.37 8.91

137 270 79.8 43.51 62.67 39.66 39.83 119.70 85.70 83.03 13.28 8.30

138 270 79.8 43.80 62.20 39.72 39.84 119.70 86.70 83.05 12.62 9.46

139 270 79.8 43.89 61.90 39.57 40.32 119.70 86.70 83.67 13.86 8.66

140 270 79.9 43.84 62.60 39.61 38.85 119.70 86.70 82.05 12.33 8.48


Run Angle Heater Voltage T 1 T2 T3 T4 P2 P3 P4 Left ri, Right rill

(deg) (volts) (oF) (oF) (OF) (OF) (psi) (psi) (psi) (lb/hr) (lb/hr)

141 270 60.0 44.89 48.96 38.50 39.87 95.70 80.70 83.08 13.92 5.22

142 270 59.9 44.82 48.93 38.54 41.47 95.70 80.70 85.37 14.25 6.24

143 270 60.1 44.74 49.14 38.44 40.38 95.70 80.70 83.76 14.28 5.36

144 270 60.0 44.69 49.34 38.43 40.18 95.70 80.70 83.47 14.78 6.46

145 270 75.4 45.56 53.69 39.59 40.31 102.70 82.70 83.66 3.51 1.75

146 270 74.9 45.71 52.22 39.67 39.95 101.70 82.70 83.16 3.76 1.88

147 270 75.2 45.70 52.77 39.37 40.56 102.70 82.70 84.03 3.49 1.75

148 270 74.8 45.74 52.67 39.40 39.96 102.70 80.70 83.17 3.52 1.76

149 270 74.9 45.67 52.75 39.34 40.62 102.70 82.70 84.11 3.66 2.74

150 270 74.8 45.55 52.96 39.30 41.20 102.70 82.70 84.97 3.59 2.69

151 270 74.8 45.62 52.85 39.41 41.27 102.70 82.70 85.07 3.63 2.72

152 270 74.8 45.58 53.30 39.34 40.05 102.70 82.70 83.28 3.88 2.91


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-------------------- iL ---------

TestThrottle Section

Valve

I 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

(C.1)A= h4 (p -p4).

Using assumption 1 and substituting it into equation C.1 we get

A = h4 + v(2 - ).

Now looking at the energy balance between points 1 to 2 we have

+m

(C.2)

(C.3)

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

(C.5)S=h 4 V 4(p 2 4 )+ .m

The R-22 is at saturated conditions at point 3 and we have

(C.6)h = I +Xhg.

Assumption 3, h3 = , allows us to equate equations C.5 and C.6 to get

h4 + v4(p2 -4 p,)+ - = i + Xgm

Since the mass flow rate of the liquid, mi, is measured substitute

I-x

into equation C.7

h4 + v4(p2 -4) X+ 1m,, -+ ,

and solve for X

Calculated data is given in Table C.1 below.

(C.7)

(C.8)

(C.9)

[(h4 - ,) + v4(), - P,)z + QmA,, +Q

(C.10)

Run Angle Mass Flux Fr Left Right x Slip at jl jg Flow

(deg) (1041b/hr-ft2) (%) (%) (%) Ratio (%) (ft/sec) (ft/sec) Regime

1 0 3.80 0.43 53.33 46.67 43.48 2.14 95.04 0.08 3.08 stratified

2 0 3.93 0.43 53.33 46.67 42.02 2.14 94.75 0.08 3.07 stratified

3 0 4.19 0.43 55.17 44.83 39.64 2.13 94.23 0.09 3.08 stratified

4 0 4.16 0.42 55.17 44.83 39.33 2.14 94.17 0.09 3.05 stratified

5 0 5.35 0.43 55.17 44.83 31.61 2.13 91.96 0.13 3.12 stratified

6 0 5.28 0.42 55.17 44.83 31.31 2.13 91.87 0.13 3.05 stratified

7 0 5.35 0.42 53.33 46.67 30.84 2.13 91.70 0.13 3.04 stratified

8 0 5.48 0.43 55.17 44.83 30.49 2.13 91.58 0.13 3.09 stratified

9 0 5.17 0.72 53.33 46.67 54.45 2.12 96.72 0.08 5.16 stratified

10 0 5.35 0.72 53.33 46.67 52.44 2.12 96.46 0.09 5.15 stratified

11 0 5.18 0.71 52.94 47.06 53.84 2.12 96.64 0.08 5.12 stratified

12 0 5.07 0.71 53.33 46.67 54.75 2.13 96.76 0.08 5.10 stratified

13 0 8.87 0.41 51.61 48.39 18.31 2.11 84.55 0.25 2.93 annular

14 0 9.28 0.42 51.61 48.39 17.84 2.11 84.11 0.27 2.98 annular

15 0 9.49 0.42 51.61 48.39 17.37 2.10 83.66 0.28 2.96 annular

16 0 9.49 0.42 51.61 48.39 17.34 2.10 83.62 0.28 2.96 annular

17 0 8.16 0.71 55.17 44.83 34.15 2.12 92.73 0.19 5.09 annular

18 0 8.24 0.72 53.33 46.67 33.96 2.12 92.67 0.19 5.11 annular

19 0 8.74 0.72 51.61 48.39 32.05 2.12 92.07 0.21 5.11 annular

20 0 8.24 0.72 51.61 48.39 33.97 2.12 92.68 0.19 5.12 annular-0 - -.2 -.7 -16 8.9 3

Table C.1: R-22 Calculated Data

Run Angle Mass Flux Fr Left Right x Slip tg j jg Flow


21 0 8.14 1.00 51.61 48.39 48.30 2.11 95.79 0.15 7.08 annular

22 0 8.70 1.00 53.33 46.67 45.30 2.11 95.28 0.17 7.10 annular

23 0 8.64 1.00 51.61 48.39 45.61 2.10 95.33 0.16 7.09 annular

24 0 7.93 1.00 51.61 48.39 49.72 2.10 96.01 0.14 7.09 annular

25 90 8.43 1.01 30.43 69.57 47.25 2.10 95.62 0.16 7.16 annular

26 90 8.73 1.01 36.00 64.00 45.67 2.11 95.35 0.17 7.18 annular

27 90 8.93 1.01 38.46 61.54 44.64 2.10 95.15 0.17 7.17 annular

28 90 8.48 1.01 36.00 64.00 46.91 2.10 95.56 0.16 7.16 annular

29 90 7.45 0.72 33.33 66.67 37.97 2.12 93.77 0.16 5.17 annular

30 90 7.26 0.72 33.33 66.67 38.97 2.12 94.02 0.16 5.17 annular

31 90 7.34 0.73 30.43 69.57 38.65 2.12 93.94 0.16 5.18 annular

32 90 7.26 0.72 30.43 69.57 38.91 2.12 94.00 0.16 5.16 annular

33 90 7.69 0.42 33.33 66.67 21.24 2.12 86.90 0.21 2.99 annular

34 90 8.73 0.42 33.33 66.67 18.75 2.12 85.07 0.25 3.01 annular

35 90 8.81 0.42 36.00 64.00 18.71 2.13 85.06 0.25 3.04 annular

36 90 8.24 0.42 33.33 66.67 19.96 2.13 86.06 0.23 3.03 annular

37 0 9.17 0.43 51.52 48.48 18.33 2.14 84.88 0.26 3.15 annular

38 0 9.47 0.43 50.00 50.00 17.66 2.14 84.28 0.27 3.13 annular

39 0 9.02 0.43 50.00 50.00 18.37 2.14 84.91 0.26 3.10 annular

40 0 8.93 0.43 50.00 50.00 18.61 2.14 85.11 0.25 3.11 annular

Table C.1: R-22 Calculated Data (continued)

Run Angle Mass Flux Fr Left Right x Slip a jl jg Flow


41 0 9.88 0.73 50.00 50.00 28.86 2.13 90.98 0.25 5.29 annular

42 0 9.93 0.73 50.00 50.00 28.39 2.14 90.79 0.25 5.24 annular

43 0 10.33 0.74 50.00 50.00 27.77 2.13 90.53 0.26 5.33 annular

44 0 10.09 0.73 50.00 50.00 28.16 2.13 90.70 0.25 5.28 annular

45 0 10.55 0.95 50.00 50.00 35.05 2.13 93.04 0.24 6.82 annular

46 0 10.52 0.95 50.00 50.00 35.07 2.13 93.04 0.24 6.81 annular

47 0 10.52 0.95 50.00 50.00 35.21 2.13 93.08 0.24 6.83 annular

48 0 10.37 0.95 50.00 50.00 35.69 2.13 93.22 0.23 6.83 annular

49 0 7.09 0.73 51.61 48.39 40.19 2.13 94.34 0.15 5.27 annular

50 0 7.16 0.72 51.61 48.39 39.19 2.13 94.11 0.15 5.19 annular

51 0 7.10 0.73 51.61 48.39 39.93 2.13 94.28 0.15 5.24 annular

52 0 7.34 0.73 51.61 48.39 38.90 2.13 94.04 0.16 5.27 annular

53 0 7.50 1.08 51.61 48.39 56.11 2.12 96.92 0.12 7.70 annular

54 0 7.55 1.09 51.61 48.39. 56.67 2.12 96.99 0.11 7.82 annular

55 0 7.59 1.08 53.33 46.67 55.57 2.12 96.85 0.12 7.71 annular

56 0 7.51 1.07 53.33 46.67 55.93 2.12 96.90 0.12 7.69 annular

57 0 4.54 0.62 51.61 48.39 52.92 2.14 96.55 0.07 4.47 stratified

58 0 4.66 0.63 52.78 47.22 52.11 2.14 96.44 0.08 4.52 stratified

59 0 4.59 0.62 51.61 48.39 52.43 2.14 96.49 0.08 4.48 stratified

60 0 4.49 0.62 53.33 46.67 53.18 2.14 96.58 0.07 4.45 stratified


Run Angle Mass Flux Fr Left Right x Slip ca j jg Flow


61 0 4.66 0.96 44.44 55.56 80.36 2.12 99.02 0.03 6.88 stratified

62 0 4.73 0.95 46.15 53.85 78.65 2.13 98.91 0.04 6.85 stratified

63 0 4.77 0.96 46.15 53.85 78.26 2.13 98.89 0.04 6.87 stratified

64 0 4.73 0.95 46.15 53.85 78.78 2.13 98.92 0.04 6.85 stratified

65 90 4.32 0.96 33.33 66.67 86.56 2.12 99.37 0.02 6.84 stratified

66 90 4.20 0.94 37.50 62.50 87.64 2.12 99.43 0.02 6.74 stratified

67 90 4.19 0.94 37.50 62.50 87.81 2.12 99.44 0.02 6.76 stratified

68 90 4.19 0.95 37.50 62.50 88.10 2.13 99.46 0.02 6.80 stratified

69 90 4.16 0.62 20.00 80.00 57.81 2.13 97.15 0.06 4.47 stratified

70 90 4.23 0.62 15.79 84.21 56.88 2.13 97.04 0.06 4.46 stratified

71 90 4.02 0.62 15.79 84.21 59.60 2.14 97.35 0.06 4.45 stratified

72 90 4.14 0.61 15.79 84.21 57.24 2.14 97.09 0.06 4.41 stratified

73 90 8.93 0.44 33.33 66.67 19.14 2.14 85.54 0.25 3.20 annular

74 90 9.48 0.44 33.33 66.67 17.96 2.14 84.55 0.27 3.19 annular

75 90 9.62 0.44 33.33 66.67 17.75 2.14 84.36 0.28 3.19 annular

76 90 9.39 0.44 33.33 66.67 18.26 2.14 84.80 0.27 3.21 annular

77 90 9.57 0.73 33.33 66.67 29.60 2.13 91.26 0.24 5.25 annular

78 90 9.53 0.73 33.33 66.67 29.83 2.13 91.35 0.23 5.27 annular

79 90 9.85 0.74 33.33 66.67 29.01 2.13 91.04 0.24 5.30 annular

80 90 9.72 0.74 33.33 66.67 29.44 2.13 91.20 0.24 5.31 annular


Run Angle Mass Flux Fr Left Right x Slip at j jg Flow(deg) (1041b/hr-ft2) (%) (%) (%) Ratio (%) (ft/sec) (ft/sec) Regime

81 90 9.93 0.97 33.33 66.67 37.95 2.13 93.80 0.22 6.95 annular

82 90 9.82 0.95 33.33 66.67 37.88 2.13 93.78 0.21 6.85 annular

83 90 9.85 0.96 36.00 64.00 38.02 2.13 93.82 0.21 6.90 annular

84 90 9.44 0.97 30.43 69.57 39.86 2.13 94.25 0.20 6.93 annular

85 90 6.55 0.74 27.27 72.73 43.65 2.13 95.06 0.13 5.30 annular

86 90 6.82 0.72 30.43 69.57 41.16 2.13 94.56 0.14 5.20 annular

87 90 6.63 0.75 27.27 72.73 43.88 2.13 95.10 0.13 5.39 annular

88 90 6.66 0.75 27.27 72.73 43.61 2.13 95.05 0.13 5.38 annular

89 90 6.99 1.08 38.46 61.54 60.27 2.12 97.40 0.10 7.72 annular

90 90 6.65 1.08 33.33 66.67 63.45 2.12 97.72 0.09 7.73 annular

91 90 7.14 1.08 36.00 64.00 59.12 2.12 97.27 0.10 7.74 annular

92 90 7.10 1.08 36.00 64.00 59.41 2.12 97.30 0.10 7.73 annular

93 180 9.30 0.43 50.00 50.00 17.88 2.14 84.48 0.27 3.11 annular

94 180 9.44 0.44 51.52 48.48 17.97 2.14 84.56 0.27 3.18 annular

95 180 9.28 0.43 46.67 53.33 17.83 2.14 84.45 0.27 3.10 annular

96 180 9.82 0.43 50.00 50.00 16.88 2.14 83.55 0.29 3.11 annular

97 180 9.92 0.73 48.39 51.61 28.51 2.14 90.84 0.25 5.26 annular

98 180 9.70 0.72 46.67 53.33 28.97 2.14 91.03 0.24 5.22 annular

99 180 9.35 0.73 46.67 53.33 30.38 2.14 91.56 0.23 5.28 annular

100 180 10.08 0.77 50.00 50.00 29.50 2.13 91.23 0.25 5.52 annular- - mmm


Run Angle Mass Flux Fr Left Right X Slip a j jg Flow


101 180 10.22 0.96 46.67 53.33 36.54 2.13 93.44 0.23 6.89 annular

102 180 9.69 0.95 46.67 53.33 38.36 2.13 93.90 0.21 6.85 annular

103 180 9.86 0.95 48.39 51.61 37.55 2.13 93.70 0.22 6.82 annular

104 180 10.46 0.95 50.00 50.00 35.34 2.13 93.12 0.24 6.82 annular

105 180 6.49 0.73 46.67 53.33 43.53 2.13 95.04 0.13 5.23 annular

106 180 6.68 0.72 44.83 55.17 42.04 2.13 94.75 0.14 5.21 annular

107 180 6.88 0.72 46.67 53.33 40.45 2.13 94.41 0.14 5.17 annular

108 180 7.11 0.72 46.67 53.33 39.32 2.13 94.16 0.15 5.19 annular

109 180 7.04 1.08 45.45 54.55 59.96 2.12 97.37 0.10 7.76 annular

110 180 7.03 1.08 47.83 52.17 59.99 2.12 97.37 0.10 7.74 annular

111 180 7.25 1.08 50.00 50.00 58.32 2.12 97.18 0.11 7.75 annular

112 180 7.15 1.08 50.00 50.00 59.18 2.12 97.28 0.10 7.75 annular

113 180 4.05 0.62 46.67 53.33 58.97 2.14 97.28 0.06 4.44 stratified

114 180 4.19 0.62 46.67 53.33 57.33 2.14 97.10 0.06 4.47 stratified115 180 4.01 0.62 46.67 53.33 59.56 2.14 97.34 0.06 4.45 stratified116 180 4.05 0.62 46.67 53.33 59.50 2.14 97.34 0.06 4.48 stratified

117 180 4.35 0.95 55.56 44.44 85.41 2.12 99.31 0.02 6.82 stratified

118 180 4.26 0.95 66.67 33.33 86.62 2.12 99.38 0.02 6.78 stratified

119 180 4.28 0.96 66.67 33.33 87.19 2.12 99.41 0.02 6.86 stratified

120 180 4.28 0.96 66.67 33.33 87.83 2.12 99.44 0.02 6.90 stratified


Run Angle Mass Flux Fr Left Right x Slip cc jl jg Flow


121 270 10.01 0.44 64.00 36.00 16.94 2.14 83.60 0.29 3.17 annular

122 270 9.07 0.44 66.67 33.33 18.84 2.14 85.30 0.26 3.20 annular

123 270 9.22 0.44 66.67 33.33 18.29 2.14 84.83 0.26 3.15 annular

124 270 9.40 0.43 66.67 33.33 17.64 2.14 84.26 0.27 3.10 annular

125 270 9.87 0.72 66.67 33.33 28.49 2.13 90.83 0.25 5.22 annular

126 270 9.83 0.73 64.00 36.00 28.89 2.13 90.98 0.24 5.26 annular

127 270 9.67 0.72 66.67 33.33 28.86 2.13 90.97 0.24 5.17 annular

128 270 9.81 0.72 64.00 36.00 28.73 2.13 90.91 0.24 5.22 annular

129 270 9.95 0.96 61.54 38.46 37.63 2.13 93.72 0.22 6.89 annular

130 270 10.16 0.94 61.54 38.46 36.26 2.13 93.36 0.23 6.78 annular

131 270 9.83 0.95 66.67 33.33 37.79 2.12 93.75 0.21 6.83 annular

132 270 10.04 0.97 64.00 36.00 37.80 2.12 93.76 0.22 6.97 annular

133 270 6.76 0.73 66.67 33.33 42.00 2.13 94.72 0.14 5.24 annular

134 270 6.92 0.71 66.67 33.33 40.01 2.13 94.29 0.15 5.11 annular

135 270 7.26 0.72 64.00 36.00 38.52 2.13 93.96 0.16 5.17 annular

136 270 6.70 0.73 69.57 30.43 42.19 2.13 94.77 0.14 5.23 annular

137 270 7.05 1.08 61.54 38.46 59.56 2.12 97.32 0.10 7.70 annular

138 270 7.12 1.08 57.14 42.86 59.00 2.12 97.26 0.10 7.70 annular

139 270 7.19 1.08 61.54 38.46 58.59 2.12 97.22 0.10 7.74 annular

140 270 6.94 1.07 59.26 40.74 60.37 2.12 97.41 0.10 7.69 annular


Run Angle Mass Flux Fr Left Right x Slip a jl jg Flow


141 270 4.92 0.61 72.73 27.27 48.53 2.14 95.91 0.09 4.44 stratified

142 270 5.11 0.62 69.57 30.43 47.03 2.14 95.67 0.09 4.47 stratified

143 270 5.00 0.62 72.73 27.27 48.07 2.14 95.84 0.09 4.47 stratified

144 270 5.20 0.62 69.57 30.43 46.01 2.14 95.50 0.10 4.45 stratified

145 270 4.45 0.96 66.67 33.33 84.36 2.12 99.25 0.02 6.89 stratified

146 270 4.44 0.95 66.67 33.33 83.24 2.12 99.19 0.03 6.78 stratified

147 270 4.43 0.96 66.67 33.33 84.37 2.13 99.26 0.02 6.88 stratified

148 270 4.39 0.95 66.67 33.33 84.09 2.13 99.24 0.02 6.79 stratified

149 270 4.56 0.95 57.14 42.86 81.44 2.13 99.09 0.03 6.83 stratified

150 270 4.54 0.95 57.14 42.86 81.70 2.13 99.10 0.03 6.83 stratified

151 270 4.55 0.95 57.14 42.86 81.53 2.13 99.09 0.03 6.82 stratified

152 270 4.59 0.95 57.14 42.86 80.45 2.13 99.03 0.03 6.80 stratified


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

( wl\0.5 - -

nI WIIn sinO| m=Incq + c2 In(1- a) + c3 In(Fr)

This was put into a matrix for using the data for annular flow conditions.

0.5 -

b, = In .sinO

a,1 =1

a, = In(Fr)

(D.2)

(D.3)

rln c,

X= C2

C3(D.4)

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,

(ATA)I ATAx =(ATA)-I ATb,

x= (ATA)IA b,

(D.6)

(D.6)

(D.8)

giving

[ -1.93 1x= 12.2710 - 3 i,

[ -0.24 ]

c = e

x'

C2 = X 2

C 3 = 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.

Two Phase Flow Splitting in Piping Branches

Documents

Transcript of Two Phase Flow Splitting in Piping Branches