Two-Phase Flow Patterns and Frictional Pressure …/67531/metadc283029/m2/1/high... · An earlier...

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ARGONNE NATIONAL LABORATORY9700 South Cass Avenue, Argonne, Illinois 60439

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Distribution Category:Thermal Sciences

(UC-363)

Two-Phase Flow Patterns and FrictionalPressure Gradients in a Small Rectangular Channel:A Comparison between Two Horizontal Orientations

by

M. W. Wambsganss, J. A. Jendrzejczyk,D. M. France,* and N. T. Obott

Materials and Components Technology Division

November 1990

Work supported by MAS f ERU.S. DEPARTMENT OF ENERGYOffice of Conservation and Renewable Energy

*Department of Mechanicai Engineering, University of llinois at ChicagotDepartment of Chemical Engineering, Clarkson University, Potsdam, NY

'pr

CONTENTS

NOMENCLATURE.............................................................................. vi

ABSTRACT.......................................................................................... 1

1 INTRODUCTION............................................................................... 1

2 PREVIOUS WORK............................................................................. 2

3 EXPERIMENTAL APPARATUS AND PROCEDURES............................ 6

3.1 Flow Apparatus, Test Channel, and Instrumentation.................. 63.2 Procedure: Flow Pattern .......................................................... 63.3 Procedure: Frictional Pressure Gradient.................................. 9

4 R E SU LTS ......................................................................................... 10

4.1 Flow Patterns and Transitions .................................................. 104.2 Frictional Pressure Gradient .................................................... 18

5 ANALYSIS................................................................................... 22

5.1 Flow Patterns and Transitions .................................................. 225.2 Frictional Pressure Gradient ................................................ 28

6 SUMMARY AND CONCLUDING REMARKS.........,......................... 32

ACKNOWLEDGMENTS.........................................................................34

REFERENCES.......................................................................................36

APPENDIX: Measured Values of Pressure Drop andTest-Section Pressure ................................................... 39

FIGURES

1 Schematic diagram of adiabatic two-phase flow apparatus.................. 7

2 Pressure tap locations along flow channel, and camera location for flowpattern photographs......................................................................... 8

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3 Flow patterns, horizontal flow, air/water mixture, channelR-19.05-0.17, G = 50 kg/m2s.............................................................. 11

4 Flow patterns, horizontal flow, air/water mixture, channelR-19.05-0.17, G = 100 kg/m2 s ............................................................ 12

5 Flow patterns, horizontal flow, air/water mixture, channelR-19.05-0.17, G = 200 kg/m2s ............................................................ 13

6 Flow patterns, horizontal flow, air/water mixture, channelR-19.05-0.17, G = 300 kg/m2 s ............................................................ 14



9 Flow patterns, horizontal flow, air/water mixture, channelR-19.05-0..17, G = 700 kg/m2s ............................................................ 17

10 RMS pressure as a function of mass quality and mass flux........... 18

11 RMS pressure as a function of mass quality........................................19

12 Flow pattern map: horizontal air/water flow in channel R-19.05-0.17... 20

13 Two-phase friction multiplier as a function of Martinelli parameter..... 21

14 Two-phase friction multiplier as a function of mass quality............ 23

15 Rectangular cross-section orientations.......................24

16 Flow pattern comparisons .......................................................... . 25

17' Comparison of flow pattern maps ...................................................... 27

18 Comparison between experimental two-phase friction multiplier datafor channels R-19.05-6 and R-19.05-0.17, and with predictions usingthe modified Chisholm correlation................................................ 29

iv

19 Comparison between experimental two-phase friction multiplierdata for channels R-19.05-6 and R-19.05-0.17; low mass qualities ....... 30

20 Comparison between experimental two-phase friction multiplierdata for channels R-19.05-6 and R-19.05-0.17; high mass qualities...... 31

TABLF

1 Error in application of modified Chisholm correlation for 0.05 < x < 1..... 33

V

NOMENCLATURE

A Channel flow area (m2 )

C Flow-regime-dependent factor in Chisholm correlation

Dh Hydraulic diameter (= 4A/P) (m)

Dp Differential pressure transducer; Fig. 2

DPF Measured two-phase frictional pressure gradient (kPa/m)

DPFL Frictional pressure gradient for liquid flowing alone (kPa/m)

DPFLO Frictional pressure gradient for mixture flowing as liquid (kPa/m)

G Total mass flux (kg/m2 s)

L Test channel length (m)

n Exponent in Blasius relationship

P Wetted perimeter (m)

P1, P2 Piezoresistive pressure transducer; Fig. 2

PTS Test section pressure corresponding to midpoint of differentialpressure measurement; Fig. 2

Re Reynolds number

ReLO Reynolds number mixture flowing as liquid

UGS Superficial gas velocity (m/s)

ULS Superficial liquid velocity (m/s)

VG Specific volume gas (m3/kg)

vL Specific volume liquid (m3/kg)

x Mass quality

vi

X Martinelli parameter; Eq. 3

Xtt Martinelli parameter (turbulent-turbulent); Eq. 4

G Viscosity of gas (kg/m-s)

L Viscosity of liquid (kg/m-s)

$FL defined by $FL

FL Two-phase friction multiplier (based on liquid flowing alone)

FLO Two-phase friction multiplier (based on mixture flowing as liquid)

vii

Two-Phase Flow Patterns and FrictionalPressure Gradients in a Small, Rectangular Channel:A Comparison between Two Horizontal Orientations

by

M. W. Wambsganss, J. A. Jendrzejczyk,D. M. France, and N. T. Obot

ABSTRACT

In horizontal flow through a rectangular channel, the channel crosssection can be oriented so that the long side is either vertical or horizontal. Theeffect of cross-section orientation on the fluid dynamic characteristics of two-phase flow is of interest in plate-fin heat exchanger design because a heatexchanger can be similarly oriented to operate in either of the two orientations.An earlier study of two-phase flow patterns and frictional pressure gradients in asmall rectangular channel with the channel cross section oriented with the longside vertical was performed and reported. This report presents the results of acomplementary study of the same channel, but with the channel cross sectionoriented so that the long side was horizontal. Flow patterns were studied and aflow pattern map, using superficial gas and liquid velocities as co-ordinates, wasdeveloped. Measured two-phase frictional pressure drops were analyzed usingthe concept of two-phase flow mrultipliers. Results from the two channelorientations were compared. While there are some notable differences in flowpatterns at low mass qualities and low mass fluxes, in the practical range ofinterest for plate-fin heat exchanger design the effects on frictional pressuregradient are minimal and the modified correlation developed from the earlierstudy is shown to be also applicable for design purposes when the long side ishorizontal.

1 INTRODUCTION

There is an interest in compact plate-fin heat exchangers for applicationsinvolving boiling and condensing in energy conversion and utilization systems.One such application is the use of plate-fin heat exchangers as the evaporatorand condenser in vapor-compression refrigeration cycles that use anonazeotropic refrigerant mixture as the working fluid. To facilitate andoptimize the design of such heat exchangers, information on phase-change heattransfer in flow channels typical of plate-fin heat exchangers is needed.

2

Objectives of the current research program are to investigate and characterize thefluid dynamics and heat transfer in plain-fin corrugations and to develop flow-pattern-dependent prediction methods, thus addressing this need forinformation. To circumvent flow maldistribution problems inherent in allmultichannel flow arrangements, effort is being focused on single channels. Inparticular, studies are being conducted on two-phase flow and frictional pressuregradients in small rectangular channels. The studies are being performed in anadiabatic flow facility using two-component (gas-liquid) mixtures.

The test flow channel is rectangular and 1.14 m in length, with cross-sectional dimensions of 19.05 x 3.18 mm. This report uses the channeldesignation R-x-y, in which R refers to Rectangular, x refers to the longdimension of the rectangle in mm, and y refers to the aspect ratio (in horizontalflow, the vertical dimension is taken as the numerator in calculating an aspectratio).

Previous work in the areas of two-phase flow patterns and pressuregradients was reviewed in some detail in an earlier topical report (Wambsgansset al. 1990). Results were presented in that report from two-phase (air-water)tests of the present test channel in a horizontal orientation with the long sidevertical (channel R-19.05-6). A flow pattern map and a correlation for predictingtwo-phase frictional pressure gradient were given. In this report, results fromtests of the same channel, again, in a horizontal orientation but with the long sidehorizontal (channel R-19.05-0.17), are presented. Information concerningapparatus, test procedure, and background information is summarized from theearlier work of Wambsganss et al. (1990). Results from channel R-19.05-0.17, inthe form of a flow pattern map and frictional pressure gradient data andcorrelation, are compared with those from channel R-19.05-6.

It is of interest to understand and, as necessary, characterize the effects ofchannel orientation on two-phase fluid dynamics because a given plate-fin heatexchanger can be designed to operate in either orientation. Among other things,gravity can be expected to have less effect on two-phase flow in channel R-19.05-0.17, because the height of the flow channel (1/6 that of channel R-19.05-6) is verysmall.

2 PREVIOUS WORK

Two-phase flow in circular tubes has been studied by numerousinvestigators over the last 40 years. Both vertical and horizontal orientations, aswell as inclined orientations, have been studied. Flow patterns have beenidentified and the transitions between flow patterns have been defined, primarily

3

from visual observations. Two-phase pressure drop has been measured andpredictive correlations developed, the majority of which do not distinguish amongflow patterns.

Most of the previous investigations have been performed in circularchannels that are large in cross-sectional area relative to that of the smallrectangular channel of this study. A much more limited number of studiesperformed with rectangular channels also used relatively large cross sections, forthe most part. It was shown by Wambsganss et al. (1990) that the flow pattern andpressure gradient results from the larger-channel data did not agree well withthe results for the small rectangular channel with the orientation of R-19.05-6.

Recent experiments have been performed in small channels, both circularand rectangular, with some cross-sectional areas in the range of the presentchannel. The results of these experiments were also compared to the small-rectangular-channel data of the Wambsganss et al. (1990) study. These recentsmall-channel experiments, as well as the limited number of experiments intwo-phase flow in larger rectangular channels, are discussed briefly since thesegeometries are closest to the present case.

Richardson (1958) investigated the behavior of air/water mixtures inhorizontal rectangular channels. He utilized three different channels, R-50.89-0.125, R-50.8-0.25, and R-50.8-0.50, all with the long side (50.8 mm) forming thebase. Flow pattern maps were presented in terms of liquid and gas flow rates.The channel height of only 6.35 mm minimized the occurrence of stratified andwave flows because of the ease with which liquid reaches the top of the channeland produces slug, plug, or bubbly flows.

Hosler (1968) reported a study to determine the flow patterns in two-phaseflow in a narrow rectangular channel (R-25.4-8) with heat added to boil water athigh pressure (300 to 2,000 psia). The test section was vertically oriented and theflow was upward. Three primary-flow regimes were identified: bubble, slug, andannular. Hosler concluded that the flow patterns observed in boiling flow appearsimilar to flow patterns observed in adiabatic flow. System pressure was shown tohave a significant effect on flow patterns. In particular, as the pressure isincreased the bubble size decreases and the transitions from bubble to slug flowand slug to annular flow occur at higher local qualities. This effect also wasshown by Troniewski and Ulbrich (1984), who replotted Hosler's data as totalmass flux versus quality. While identification of this pressure effect is asignificant contribution of the research, it must be remembered that thepressures and pressure range are very high (reduced pressures to 0.6) comparedto the near-atmospheric pressures of the current study.

4

Jones and Zuber (1975) studied vertical upflow of air/water mixtures in arectangular channel R-63.5-12.7. Their objective was to evaluate theinterrelationship between void-fraction fluctuations (as sensed by a linear X-rayvoid measurement system) and flow patterns. Air(water) was injected into themain stream of water(air) through porous stainless steel plates in the sides of thechannel. The authors presented photographs of the various flow patternsobserved and stressed the "variable nature of some regions of flow" in theirresults. They indicated that the annular flow pattern was not well defined andthat "small ripples and large waves" gave rise to "frothy slugs." While thechannel used by Jones and Zuber was vertically oriented, similar patterns wereseen in the smaller, horizontal, rectangular channel of the study by Wambsgansset al. (1990), with the exception that large waves were never observed in the smallchannel. In this situation, small ripples easily reached the top of the channel,giving rise to slug flow.

Troniewski and Ulbrich (1984) studied 10 different rectangular channelswith aspect ratios ranging from 12 to 0.1 and long-side dimensions of 13.5 to51.1 mm. Investigations were carried out in vertical channels with aspect ratiosin the range 1 to 12 and in horizontal channels with aspect ratios in the range 0.1to 10. The majority of the tests were carried out with air/water; selected testsemployed aqueous solutions of sugar/air mixtures to study the effect of viscosity.

As a result of their research, Troniewski and Ulbrich proposed flow patternmaps for both vertical and horizontal two-phase flows in rectangular channels.For horizontal flow, the channels were divided into rectangular channels andcrevice channels. Crevice channels are distinguished from rectangular channelsby the fact that the vertical dimension of the crevice channel (in the direction ofthe force of gravity) is very small; for this group of channels, stratified and wavyflow regimes were not found. Experiments with aqueous solutions of sugar/airmixtures led to the conclusion that liquid viscosity (up to 0.040 kg/;n-s) has aninsignificant effect on the flow pattern transitions.

Lowry and Kawaji (1988) studied flow patterns associated with verticalupflow of air/water through narrow channels formed by two flat plates. The platespacings were 0.5, 1, and 2 mm and the long channel dimension was 80 mm,yielding channels R-80-160, R-80-80 and R-80-40, respectively. Flow patternmaps were developed showing four main patterns: (1) slug flow, consisting oflarge, irregular shaped, flattened bubbles; (2) churn flow, which wasdistinguished by large gas spaces of irregular shape in the presence of smallerbubbles; (3) bubbly flow with small near-circular bubbles; and (4) annular flow inthe usual sense of liquid film on the channel wall with a continuous gas core.Lowry and Kawaji found that the flow patterns were not well predicted by acorrelation based on larger circular pipe data.

5

As part of an investigation into two-phase flow in compact heatexchangers, Damianides and Westwater (1988) measured two-phase flowpatterns and pressure drop in horizontal capillary tubes of circular cross sectionwith inside diameters of 1, 2, 3, 4, and 5 mm. In general, stratified flow was notobtained in these small-diameter channels, and a wavy flow regime was foundbetween slug and annular flows at lower liquid velocities. Although the capillarytube flow pattern showed only general agreement with the results from the R-19.05-6 rectangular channel of the Wambsganss et al. study (1990), the wavy flowpattern observed in both studies is not characteristic of larger channels.

Fukano et al. (1989) also measured flow patterns and pressure drops inhorizontal capillary tubes with inside diameters ranging from 1 to 4.9 mm.Air/water formed the two-phase mixture and four flow patterns were observed:bubble, plug, slug, and annular. Stratified flow was not observed in these smallchannels, but unlike the experiments of Damianides and Westwater (1988),Fukano did not report a wavy flow pattern. Pressure-drop in the small channelsof Fukano was not well predicted by the larger channel correlation of Chisholmrepresenting the Lockhart and Martinelli (1949) data.

Flow patterns and two-phase pressure drops were measured by Ide andMatsumura (1990) in rectangular channels approaching the dimensions of thepresent channel. Both flow pattern and pressure-drop differences were reportedbetween large and small cross-sectional area channels, with the divisionoccurring at a hydraulic diameter of approximately 10 mm. The importantresults relative to the present study were in the small range of hydraulicdiameter; however, the long sides of the channels were two to eight times largerthan the corresponding 19.05-mm dimension of the channel of the present study.The results of Ide and Matsumura's measurements of small-channel pressuredrop showed a local maximum in the pressure gradient as a function ofMartinelli parameter. The maximum occurred at Xtt in the range of 18-30 forhorizontal flow, which was slightly higher than the range of X = 4-15 found byWambsganss et al. (1990) for the same phenomenon. This local maximumappears to be unique to small channels and has been observed in both circularand rectangular channels. Wambsganss et al. found this result for channelorientation with the short side horizontal, and Ide and Matsumura (1990) found itwith either the long or short side horizontal. In the present experiments, thechannel of Wambsganss et al. (1990) was tested with the long side horizontal, andit will be shown that the local maximum in pressure drop was observed; as foundpreviously, this condition corresponded to a flow pattern transition.

The channel sizes and tests performed by Ide and Matsumura (1990) werethe closest found in the literature to the present study. Still, there were

6

significant differences in cross-sectional dimensions where the channels of Ideand Matsumura approached narrow slits or crevices. Thus, qualitative ratherthan quantitative agreement with the present data would be expected. Therectangular channel pressure-drop data of Ide and Matsumura were not wellpredicted by correlations for relatively large circular tubes. This is in agreementwith the results of Wambsganss et al. (1990) for the R-19.05-6 channel. Also, Ideand Matsumura correlated their pressure-drop data differently for their largeand small channels because of the local maximum in the small channel. Forheat exchanger application of small channels, Wambsganss et al. (1990)correlated the pressure-drop data only at qualities above 0.05, which was abovethe local maximum for the R-19.05-6 channel.

3 EXPERIMENTAL APPARATUS AND PROCEDURES

3.1 Flow Apparatus, Test Channel, and Instrumentation

The flow apparatus is illustrated schematically in Fig. 1. (While the flowchannel is shown in a vertical orientation in Fig. 1, the subject tests wereperformed with the channel horizontally oriented.) Air and water are mixed atthe entrance to the flow channel. Rotameters are used to measure the gas andliquid flow rates. The flow channel is constructed with clear Plexiglass sides toallow for flow visualization and photography of the two-phase flow patterns.

The measured dependent variable is pressure. Both differential pressure,over a specified channel length, and absolute pressures, at two locations, aremeasured. Figure 2 gives the pressure tap locations along the flow channel andthe camera location for flow pattern photographs. The absolute test-sectionpressure, PTS, corresponding to the midpoint of the differential pressure-dropmeasurement location, is calculated from a measured absolute pressure, eitherP1 or P2 , and the calculated pressure gradient obtained from the measuredpressure drop, Dp.

3.2 Procedure: Flow Pattern

The determination of flow pattern by visual observation is a subjectiveprocess. To minimize the subjectivity, it is important to have a clear definition ofthe flow pattern descriptors. The flow descriptors used in this study were definedby Wambsganss et al. (1990) and are reproduced below as an aid to the reader:

7

FlowChanrnl

GasRotametars

Regulator

(Air Supy Air/L< AINL

8 PressureTemperature

Quick-closing 1Valves

Rotameters

Bypass

/TP "\

iquidw a

Sup

Pump

Drain(Water)

Alr/LiquidSeparator

LiquidReservoir

-- Air

- ~ - Two-Phase

Fig. 1. Schematic diagram of adiabatic two-phase flow apparatus

* Stratified: Liquid flows along bottom of channel as gravity forcesdominate; smooth interface exists between liquid and gas (no significantinterfacial waves).

* Wave: Similar to stratified but with waves at the interface traveling indirection of flow; waves do not touch upper surface of channel. Ifdistinct large-amplitude waves occur in the bottom film of an otherwiseannular flow, the flow pattern is defined as wavy.

* Plug: Intermittent plugs of gas (elongated bubbles, generally varied it

size), formed by many bubbles coalescing, flow in a continuous liquidphase; plugs tend to travel in upper half of flow channel.

* Slug: Intermittent slugs of liquid (typically "frothy"), formed, forexample, in "wave" flow by the waves growing to touch upper surface ofchannel, propagate along channel at high velocity; upper surface ofchannel wetted by residual film of liquid that drains back into bulkliquid.

8

CameraLocation

I IDp

Air

I I P1 PTS P2 IWater -+_

14 - 432l

Air 546

718 (UDh - 132)

775

832 (UDh = 153)-----

889

1143

Pressure tap locations referenced to outlet from mixer

Note (1) PTS is calculated from P2 and measured pressure gradientas obtained from Dp

(2) Length dimensions are in mm

Fig. 2. Pressure tap locations along flow channel, and camera location for flowpatter;, photographs

* Bubble: Dispersed vapor distributed as discrete small bubbles (generallyuniform in size) in continuous liquid phase; bubbles tend to travel inupper portion of channel. With increase in vapor velocity, number ofbubbles grows to fill entire channel cross section.

* Annular (Annular Dispersed Liquid): Liquid forms film aroundchannel periphery, with vapor core that may contain entrained droplets;liquid film can be expected to be thicker at channel base. Regular filminterface without surface waves (with large-amplitude waves on bottomfilm, flow pattern is classified as wavy).

An objective of the study is to establish flow pattern maps that characterizethe two-phase fluid dynamics of the flow and ultimately provide a basis for thedevelopment of flow-pattern-dependent methods for predicting pressure dropand heat transfer. In the absence of dimensionless coordinates, which ideallywould include the physical properties of the gas and liquid phases, superficial gas

9

and liquid velocities are used as the map coordinates. Test points are establishedcorresponding to a range of seven different total mass fluxes (50, 100, 200, 300, 400,500, and 700 kg/m2 s) and selected values of mass quality (or superficial gasvelocity). Selection of the test points was based, in part, on experience gained fromexperiments with channel R-19.05-6. Test points were determined with acomputer program developed specifically for experiment design and data analysis(Wambsganss et al. 1990).

In addition to visual observations, supplemented with photographic data,an objective method identified by Wambsganss et al. (1990) is used to establish thetransition-to-slug-flow boundary. The method is based on changes in the root-mean-square (RMS) values of the dynamic pressure-time signals when plottedas a function of quality for a specific total mass flux.

3.3 Procedure: Frictional Pressure Gradient

As noted by Hewitt and Bour6 (1973) and further substantiated byWambsganss et al. (1990), there is much to be gained from systematic testing that,among other things, allows one to study the details associated with the pressuredata. Specifically, testing at selected values of total mass flux allows one toidentify mass velocity effects and facilitates the inclusion of such effects inpressure-drop correlations. Also, obtaining pressure-drop data in the low tovery low quality ranges, where measurements are inherently more difficult,provides the researcher with a data base for studying the effects of flow patterntransitions on pressure, both dynamic and time-averaged mean. These resultsare important because they have the potential to lead to an objective method foridentifying flow pattern transition boundaries.

Pressure data are measured for test runs corresponding to selected valuesof total mass flux, as identified above. At each value of mass flux, data areobtained at preselected values of mass quality ranging from 0 to 1.0 or as high asthe test-section design pressure allows. For mass qualities greater than 0.1, thetest increment is 0.05; for mass qualities less than 0.1, test points are selected toemphasize the range corresponding to the transition to slug flow.

Two-phase pressure data inherently contain a large fluctuatingcomponent that is dependent in part on flow pattern. The reported pressuregradients are calculated from the time-averaged mean pressure drops obtained,in turn, by averaging 10 time signals of 5.12-s duration each; the total samplingtime is 51.2 s and the sampling rate is 200 samples/s. The calculation involvesdividing the time-averaged pressure drop by the spacing between pressure taps.Absolute test-section pressure at the midpoint of the differential pressure

10

measurement is calculated from the point measurement of absolute pressure (P1or P2 in Fig. 2) by interpolating the computed pressure gradient. Absolute test-section pressure is required for determining the specific volume of the gas phaseat the measurement location. The resulting pressure-drop data are analyzedwith the computer program developed specifically for that purpose (Wambsgansset al. 1990).

4 RESULTS

4.1 Flow Patterns and Transitions

Photographs representative of the flow patterns observed, andcorresponding to the selected values of total mass flux tested, are given in Figs. 3-9 for the R-19.05-0.17 channel. These figures also include, for each photograph,the flow pattern descriptor (as determined by applying the definitions given inSection 3.2), mass quality (x), and superficial liquid and gas velocities (ULS andUGS, respectively). It is notable that at the lowest mass fluxes tested (Figs. 3-4),stratified flow was not observed. This result is different from that in the R-19.05-6 channel, where stratified flow was found at low qualities and low mass fluxes.The flow patterns of Figs. 3-8, corresponding to mass fluxes of 50-500 kg/m2 s, allshow a similar progression from plug to slug to annular flow. If a wavy patternexisted, it was not observable because the flow was viewed through the top surfaceof the test section and the condition of the surface of the film on the bottom wall ofthe test section was not discernible. (A wavy pattern was identified in the R-19.05-6 channel; its occurrence between slug and annular flow patterns appearsto be peculiar to small-channel geometry.)

At the highest mass flux of 700 kg/m2 s (Fig. 9), bubble flow is clearly seen atlow quality. This flow pattern was also observed in the R-19.05-6 channel, and itsoccurrence is somewhat surprising considering the small dimension of thechannel, i.e., 3.18 mm. (Preliminary tests using a smaller rectangular channel,R-9.52-6, did not produce a bubble flow pattern.)

Wambsganss et al. (1990) proposed an objective method, based on RMSpressure data, for identifying the transition-to-slug-flow boundary. A compositeplot of RMS pressure, P1 , as a function of mass quality is given in Fig. 10;individual plots corresponding to specific values of total mass flux are given inFig. 11. It has been determined that the transition to slug flow occurs in thequality range corresponding to the well-defined breakpoint in the curve of RMSpressure versus mass quality as mass quality is increased from a low value, e.g.,0.001. For this channel, as with channel R-19.05-6, one can readily observe fromFig. 10 that for the different values of mass flux, the breakpoints occur in the

11

FLOW DIRECTION -Pattern

Annular

Annular

Annular

Slug

Slug

x UIS UGS

0.9 0.005 34.6

0.50 0.03 19.7

0.25 0.04 9.97

0.15 0.04 6.00

0.0256 0.05 1.03

Plug 0.0045 0.05 0.18

Plug 0.0019 0.05 0.08

Fig. 3. Flow patterns, horizontal flow, air/water mixture, channel R-19.05-

0.17, G = 50 kg / m2s

(g)

(f)j

(e)

(d)

(c)

(b)

(a)

0

12


Annular

Annular

Annular

0.15 0.09 12.2

0.09 8.16

-

Slug 0.0512 0.09 4.20

Slug 0.0128 0.10 1.05

Plug 0.0028 0.10 0.23

Plug 0.0008 0.10 0.07


0.17, G = 100 kg / m2s

(g)

x Uis UGS

(f)

0.4 0.06 31.0

(e) 0.1

(d)

(c)

(b)

(a)


Annular

Slug

Slug

x ULs UGS

0.15 0.17 22.3

0.0512 0.19 8.09

0.0256 0.19 4.07

I~q

Slug 0.0045 0.20 0.72

(f)

(e)

(d)

(c)

(b)

(a)

0.0032 0.20 0.51

0.0011 0.20 0.18

0.0004 0.20 0.06

Fig. 5. Flow patterns, horizontal flow, air/water mixture, channel R-19.05-0.17, G = 200 kg / m2s

13

(g)

Plug

Plug

Plug

14

FLOW DIRECTION -+Pattern

Annular

x Uis UGS

0.10 0.27 21.8

Slug 0.0512 0.28 11.9

(

I-

/ N

-~ K~ K) 0

Slug

Slug

0.0064 0.30 1.55

0.0028 0.30 0.67

Plug 0.0023 0.30 0.56

Plug 0.0016 0.30 0.39

Plug 0.0004 0.30 0.10

Fig. 6. Flow patterns, horizontal flow, air/water mixture, channel R-19.05-0.17, G = 300 kg / m2s

(g)

(f)

(e)

(d)

(c)

(b)

(a)

15


Annular

-~ --

Slug

x Uis UGS

0.10 0.36 26.8

(e)

(d)

Slug 0.0045 0.40 1.46

Slug 0.0032 0.40 1.04

r -~~

-~Plug/Slug

Plug

0.0019 0.40 0.63

0.0011 0.30 0.36

Plug 6.0004 0.40 0.13

Fig. 7. Flow patterns, horizontal flow, air/ water mixture, channel R-19.05-

0.17, G = 400 kg / m 2 s

(g)

(f) 0.0256 0.39 7.94

(c)

(b)

(a)

16


Annular(g)

Minwm/

_ yJ.

1 7 T N

Slug/ 0.0256 0.49 9.80

Annular

Slug 0.0128 0.49 5.11

Slug 0.0045 0.50 1.85

Plug/Slug 0.0023 0.50 0.95

(f)

(e)

(d)

(c)

(b)

(a) Plug 0.0008 0.50

0.80

0.34


0.17, G = 500 kg / m2s

X UiS UGS

0.0512 0.47 18.2

Plug 0.0019 0.50

17


Annular(g)

x UiS UGS

0.68 12.4

Slug

V ra .,

- ---U-.

Slug

0.0128 0.69 6.69

0.0045 0.70 2.49

Bubble 0.0032 0.70 1.79

Bubble 0.0023 0.70 1.33(c)A

(b) Bubble 0.0011 0.70 0.62

- -% -. -~ -V.---.-- -'-~-

C ~ -.J~ ~ ~K$)A3dyd ~

Bubble 0.0004 0.70

Fig. 9. Flow patterns, horizontal flow, air/ water mixture, channel R-19.05-0.17, G = 700 kg / m2s

0.0256

(f)

(e)

(d)

(a) 0.23

18

0.001 0.01 0.1

G (kg/m2s)0 50

o 100

o 200

X 300

+ 400

A 500

0 700

1

Mass Quality, x

Fig. 10. RMS pressure P1 as a function of mass quality x and mass flux G

range 0.002 to 0.008, i.e., the RMS pressure begins to rise sharply at qualitiesabove this range. Specific values of the breakpoint for the different mass fluxestested can be determined from the individual plots given in Fig. 11. These valueshave been used in combination with visual observations and photographic data todevelop the flow pattern map for channel R-19.05-0.17 given in Fig. 12. Asdiscussed previously, no stratified or wavy flow patterns are shown in Fig. 12.The stratified flow pattern did not occur as it did in the case of the R-19.05-6channel, and a wavy flow pattern was not observable in this configuration (R-19.05-0.17).

4.2 Frictional Pressure Gradient

The measured test-section pressure drop, DpM, and the correspondingmean test section pressure, pTS, are given in the Appendix. These data wereinput to the computer program for experiment design and data analysis, wherethe frictional contribution to the Tressure gradient was analyzed in terms of thetwo-phase friction multipliers, $FL and 0FLO, and Martinelli parameters, X andXtt, where

4

3.5

3

2.5

2

1.5

1

0.5

CL

al)

C/)

.................................................................................................................................................................

+. .................................................................... ........................ ........... ......... ...................... ................ -

x0 + X +

'X..................................................... o. ............-x -

+ao.00 0 0 00oaf

__ _ _ __ _ _ _

I'

1104

19

0.4

0.35

0.30.

0.25

0.2

0.15

0.1

0.05

0

0.6

0.5

0.4

0.3

0.2

0.1

0

G-50 kg/ms.........- .............. .... 9...... . ......

0

.......... ......... 4a....

-............--.--.

...................i..................... ...................... . .......... ......

00

0 0001 001 01

Mass ual ty x

000-100kg/rn's0000

................... ....... 80..o..0

.. . ......... .......... 4 .........

00

0' 0.001 0.01 0.1

Mass Quality, x

G - 200 kg/m's

0 00

0'' 0.001 0.01 0.1Mass Quality, x

G -2001kg/m0s 0

0

...................... .................. ... ................... ....................

0 .0 0010

.................... ................... .................... .................

0 0

. . .0

0

10

a

0.

3

2.5

2

1.5

0.5

0

14

S3.5

3

2.5

2

1.5

0.5

0

4

3.5

3

2.5

2

1.5

0.5

0

a.j

a.

I

0................... 0...................... ..................... ....................

0

o a 00

0 0.001 0.01 0.1

Mass Quality, x

G-500 kg/mrs..................... {.......................i........ Q............ ....................

.......................................... ........................................-

..................... ..................................................... ......... ......................... .......:.....................

00

00

0 0 00

0- 0.001 0.01 0.1

Mass Quality, x

G - 700 kg/ms

-................................................................ .................... .

8-0

00

A " 00

00 O 0

..010'

0' 0.001 0.01

Mass Quality, x

0.1

0.001 0.01 0.1

Mass Quality, x

Fig. 11. RMS pressure P1 as a function of mass quality x

G - 400 k//ms

1.4

1.2

1

0.8

0.6

0.4

0.2

011

2

1.5

1

I[

3

ac

CL

0.

0.5

0.j"

F

i

ii

i I

1

E

-)-J

0.1

0.01G.( 10 11

G (kg/m2s)

700500400300200

100

50

00

UGS (m/s)

Fig. 12. Flow pattern map: horizontal air/ water flow in channel R-19.05-0.17

L DPF

DPFL

FLO - DPFDPFLO

X= (DPFLDPFG/

and

(1-x VL 2 LJ 2

xtt x G 9G

(1)

(2)

(3)

(4)

In Fig. 13a, following Lockhart and Martinelli (1949), the square root of the

two-phase multiplier, $FL, is plotted as a function of the Martinelli parameter, X.In Fig. 13b, this multiplier is plott:.;d as a function of Xtt, which implies that both

10

1

Bubble

0 +0 00 00 00 0 0 ,0,"-s " " 'C'C'C0 0 0 *d. "" " " " "" 00 0 0 0 0 *S "+ +0++ + 0 0 0 0 "-

+ + +++++++0 o0o 0 0 ,,"-Plug Slug Annular- +* + +".."+ ++ Q Annula

/+E

~~"00

1 I1............I............0.1

'I ' ' ' - - - 1 -- I I I I I I I I I I I I I I u

1 1 l Il l I 1 I l 1 1 1 1 I ll*

I 1 1 1 0 1 9 1

I I

D1l

21

1

Martinelli Parameter, X

(a)

10

2G (kg/m s)

o 50

0 100

o 200

X 300

+ 400

A 500

" 700

100

0.1 1


(b)

Fig. 13. Two-phase friction multiplier AFL as a function of Martinelliparameter X and Xtt

100

LL

1

0

O O0

-

*0

Q Q

00_______I ~ w J p Op

0.10.01

100

I

x

oO 0

o

000000000

OcQO o

o fOu

oo a

0 0 0C,0 O

0 05

______I .... 00 o_ _ _ _ _ _ _ _ _ 0

0.01 10 100

22

the gas and liquid flow are turbulent if each is considered to be flowing alone inthe channel. It is clear that there is a mass flux effect in the data shown inFig. 13, and that there is a local maximum that is more pronounced at highermass fluxes, in the data for Martinelli parameters on the order of 10. The two-phase multiplier, 0FLO' in Fig. 14 exhibits a similar behavior. The two scalesused for mass quality in Figs. 14a and 14b effectively accentuate the low and highquality ranges of the data. In Fig. 14a, a logarithmic scale is used for the massquality and accentuates the results in the low-quality range (0.0001 to 0.1); it isgenerally in this range of mass quality that the various flow pattern transitionsoccur. In Fig. 14b, a linear scale is used, in this case to emphasize the data in thehigh-quality range (0.1 to 1.0), which, for the most part, is the range of practicalinterest for evaporator design.

5 ANALYSIS

In this study, analysis of the results presented in Section 4 were focused oncomparisons between the data obtained from channel R-19.05-0.17 and that fromchannel R-19.05-6. The two channels are physically the same, with the onlydifferences being the orientation of the rectangular cross section, as illustrated inFig. 15, and the associated effect of gravity on a mixture volume of two differentheights.

5.1 Flow Patterns and Transitions

Photographs of flow patterns obtained from this study and the earlier study,representative of the six different flow pattern types (annular, bubble, plug, slug,stratified, and wave) defined in Section 3.2, are given in Fig. 16. As possible, atypical flow pattern from each of the two cross-sectional orientations (aspectratio, or AR, of 6 and 1/6) is shown. As illustrated in Fig. 15, the flow patternswere viewed and photographed from the horizontal (side) position for channel R-19.05-6, and from the vertical (top) position for channel R-19.05-0.17.

Key features of the flow patterns can be observed in Fig. 16 according to thedefinitions given previously. Wave flow was observed only in channel R-19.05-6,where distinct large-amplitude waves occurred in what would otherwise beconsidered annular flow. Wave flow in larger channels occurs as distinct wavesin what would otherwise be considered stratified flow. In both small and largechannels, the wave flow pattern changes to annular flow as quality increases at afixed total mass flux. However, the difference in the wave flow pattern betweenrelatively large and small channels is attributable to the channel dimensionsrather than the geometry, i.e., circular versus rectangular. In the small-

0.01

Mass Quality, x

(a)

0.4 0.6

0.1

0.8

2G (kg/m s)

0 50

0 100

O 200

X 300

+ 400

A 500

0 700

1

1

Mass Quality, x

(b)

Fig. 14. Two-phase friction multiplier (qPFL& 2 as a function of massquality x

1000

100

N

LL

10

I

10-

- x

- O" -p

- . . 4*.

.................... ..................... .. .................. y ......... .....0...

Ex OO

S 0,P 0 0 O ,. o.. 0 .. w.

0.001

0.2

1000

100

N0

-JLL

10

1

x o 000 0 0~0

000'

A0 0O

00

o -

mm .

0I

24

VIEW

I I

Ch. R-19.05-0.17(Aspect ratio = 1/6)

Ch. R-19.05-6(Aspect ratio = 6)

(a) (b)

Fig. 15. Rectangular cross-section orientations: (a) channelR-19.05-6 (aspect ratio = 6), (b) channel R-19.05-0.17(aspect ratio = 1/ 6)

channel R-19.05-6, increasing quality at constant total mass flux in a stratifiedflow produced surface waves that easily reached the top surface of the channeland formed a slug flow pattern. At this stage in the small channel, the slug flowhad little froth and in some cases had long or irregular time periods betweenslugs. In a larger channel, the waves very likely would not be of sufficientamplitude to reach the top wall. The vertical dimension of channel R-19.05-6was of the same order as the wave amplitude, and, instead of a wavy flowprogressing from the stratified flow pattern, a quiescent slug flow patternoccurred as quality increased at constant total mass flux.

If the vertical dimension of channel R-19.05-6 was small enough tosuppress the wavy flow pattern typical of larger channels, then clearly thereshould be no wave pattern of this type for channels of smaller vertical dimensions.In channel R-19.05-0.17, neither wave nor stratified flow patterns were observed.Here, even very small surface waves or random system perturbations causedlow-quality flows to bridge the gap between the top and bottom of the test section.Thus, stratified flow with a smooth or wavy interface did not exist. (A somewhatdifferent wave flow, approaching annular flow, was identified in channel R-19.05-6 but the existence of this pattern could not be determined in channel R-19.05-0.17.) The flow patterns were limited to plug and bubble flows at lowqualities for channel R-19.05-0.17.

25

Ch. R-19.05-6

AR = 6 (side view)

Ch. R-19.05-0.17

AR = 1/6 (top view)

Annular

Af 1 3' t aY

Bubble

Plug

- -i

- --

Slug

Not Observed

Stratified

Not Observed

Wave

FLOW DIRECTION -+

Fig. 16. Flow pattern comparisons: channel R-19.05-6 (aspect ratio = 6) andchannel R-19.05-0.17 (aspect ratio = 1/6)

26

There was some difference between plug flow patterns in channels R-19.05-6 and R.-19.05-0.17; this can be attributed in part to gravitational effects.As shown in Fig. 16, elongated plugs are located near the top of the flow channelfor channel R-19.05-6, while under similar conditions in channel R-19.05-0.17,much more symmetric, more evenly spaced plugs are observed. Considering theabsence of a stratified pattern, observation from the top reveals that, relative toflow patterns, channel R-19.05-0.17 behaves much as one would expect thechannel to behave in vertical flow.

Troniewski and Ulbrich (1984) proposed flow pattern maps for both verticaland horizontal two-phase flows in rectangular channels. The channels forhorizontal flow were divided into "rectangular" and "crevice" channels. Crevicechannels were distinguished from rectangular channels in that the verticaldimension of the crevice channel (in the direction of the force of gravity) was verysmall. In agreement with the findings of this study, for this group of channelsthe stratified and wave flow patterns were not found.

Results from channel R-19.05-6 showed that the initial slug flow pattern,which developed from stratified flow, increased in froth and entrained smallbubbles as quality increased at constant total mass flux. Eventually, a wavy flowwas established before annular flow was achieved. This pattern transition fromwavy to annular flow is similar to that in a large channel. It is the occurrence ofa slug flow regime between stratified and wavy that is peculiar to small channels.

When the flow was in a plug pattern in channel R-19.05-6, it generallyprogressed to typical frothy slug flow and then to annular flow, as happens inlarger channels. This progression was always encountered in channel R-19.05-0.17. Because a stratified flow could not be sustained in this channel, the low-quality flow pattern at low mass flux was always plug flow. Plug flow progressedto slug and then annular flow in the same manner as for channel R-19.05-6 andlarger channels. Thus, the results of the flow patterns, for rectangular channelR-19.05-0.17 with its very small vertical dimension, resemble larger-channelresults in the pattern progression of plug-slug-annular. These results differfrom larger channels in that no stratified flow pattern was obtained in channelR-19.05-0.17. To a large extent, the flow pattern in channel R-19.05-0.17resembled a vertical flow situation as a consequence of the small vertical channeldimension of R-19.05-0.17, which caused channel bridging and suppressed theinfluences of gravity on the patterns.

At higher values of total mass flux, the slug flow pattern is characterized byfroth in the flow; the liquid slugs are not well defined and the pattern therebyclosely resembles the churn flow pattern associated with vertical flow. Plug flow,on the other hand, is considerably more quiescent and the plugs are typically well

27

defined. Bubble flow has numerous clear and relatively uniform bubbles (asopposed to plug flow); small channels can be expected to suppress the bubble flowpattern, and the clear bubble flow found in both channels would not have beenpredicted a priori. (Preliminary tests with a half-scale rectangular cross sectiondid not exhibit a bubble flow pattern.)

The flow pattern map developed for channel R-19.05-0.17 is compared inFig. 17 with that developed for channel R-19.05-6 (Wambsganss et al. 1990).There are some notable differences in addition to the fact that the stratified andwave flow patterns were not observed in channel R-19.05-0.17. While the overalltrends of the transitions are consistent, it is seen that the smaller-aspect-ratiochannel (R-19.05-0.17) produced bubble flow at lower superficial liquid velocities,and the plug-to-slug flow transition occurred at higher superficial gas velocities.It should be noted that the plug-to-slug flow transitions are well defined andsupported by interpretation of the dynamic pressure measurements describedabove. The slug-to-annular flow transitions are more subjective. The

10 -

1

C,)

0.1

0.1 -

0.01 0.1 1 10 100

UGS (m/s)

A - AnnularB - BubbleP - Plug

S - SlugSt - StratifiedW - Wave

Fig. 17. Comparison offlow pattern maps: channel R-19.05-6;--------- channel R-19.05-0.17

I . I I

B

P/ S A

!WSt

I -1 1 1 111 I I 1 1 . .1 1I 1 1 1 1 1 1 1 1 1I

comparison shown in Fig. 17 represents reasonable agreement between the twochannels tested for the transition to annular flow. Researchers who did notdistinguish a wave flow pattern generally interpreted the transition to annularflow according to the trend of the channel R-19.05-0.17 results in which waveflow was not encountered. If wave flow was not recognized in the R-19.05-6results, the transition to annular flow boundary would follow the results ofchannel R-19.05-0.17. (If a wave flow pattern existed between slug and annularflows in channel R-19.05-0.17, it would not have been observed in the presentstudy because of the top viewing.)

Comparisons of the flow pattern map for channel R-19.05-6 with mapsdeveloped for larger rectangular channels and capillary tubes are given byWambsganss et al. (1990). Comparisons with the results for channel R-19.05-0.17 can be inferred from those earlier comparisons with the use of Fig. 17.Wambsganss et al. (1990) showed that good quantitative agreement did not occurbetween the flow patterns of channel R-19.05-6 and the flow patterns of largercircular tubes, larger rectangular channels, and small circular (capillary) tubes.Some qualitative agreement was found and some quantitative agreement wasseen in restricted parameter ranges; the same is true for channel R-19.05-0.17.Agreement between the flow pattern maps of channels R-19.05-6 and R-19.05-0.17 is not good either, considering the absence of stratified flow and thedifferences in the bubble and plug flow transition discussed above.

5.2 Frictional Pressure Gradient

Results of the pressure-drop measurements are presented in Figs. 13 and14 in terms of two-phase frictional multipliers plotted as a function of Martinelliparameter (Fig. 13) and mass quality (Fig. 14). These results are consistent withchannel R-19.05-6 results,.and the data trends are similar between the twochannels, including a mass flux dependence and a well-defined discontinuity inthe curves at a Martinelli parameter of approximately 10, or at a mass quality inthe range 0.002 to 0.007.

Detailed comparisons are made in Figs. 18-20 between the pressure-dropdata of channel R-19.05-6 and channel R-19.05-0.17 for individual values of totalmass flux. Qualitative agreement is excellent over the entire range of massquality (or Martinelli parameter) for all of the mass fluxes. Quantitatively,discrepancies are greatest at the lower values of mass quality and lower values ofmass flux; this is because in this region the flow patterns are often markedlydifferent between channels, e.g., under identical conditions, stratified flow occursin channel R-19.05-6 and plug flow occurs in channel R-19.05-0.17.

100 ~ VYY**- ~ - . .

10

0.1

100

10

0.1

10 1i

100

' 10

0.01

100

L10

10 100

Martinelli Parameter, X0.01

0.1 1Martinelli Parameter, X

0.1 1


10 100

10 100

100 . .

G 200 kg/m a]

10.01 0.1 1

Martinelli Parameter, X10 100

100

*~10

1L

0.01 0.1 1


Fig. 18. Comparison between experimental two-phase friction multiplier ( 5 FJ)

data for channels R-19.05-6 and R-19.05-0.17, and with predictionsusing the modified Chisholm correlation: o channel R-19.05-6; *channel R-19.05-0.17; modified Chisholm correlation

An objective of the overall study is evaluation of state-of-the-artcorrelations relative to their ability to predict two-phase frictional pressure dropin the small rectangular channel of this study and, as necessary, development ofan improved correlation. In the earlier study of channel R-19.05-6, Wambsgansset al. (1990) selected two correlations for evaluation: the Friedel correlation(Friedel 1979) and the Chisholm correlation (Chisholm 1967, 1973); a constant

S G -50 kg/r's

0 "

0.1 1

Martinelli Parameter. X

G "300 kg/rn's

....... .... .. ................. ..........

G - 100 kg/m s.

S

O71

0** :

0.0

G - 400 kg/m's

........... _ _... _....a ............:..........

G -500 kg/m's

.l.l.

10 100

11

h

0i .i .

. .

4

I11

J

0

1

1

1000

100

10

1'

0 0.2 0.4 0.6 0.8Mass Quality, x

G - 300kg/m's

___ ___i I . . _ _ _

------------6 - ---- ------------------------------

0 0.2 0.4 0.6Mass Quality, x

1000

100

10

000

0-560kg/m's

100 .................................................. 0.................. :........

0

P. 0 :

0010 . .. .

1 I I0 0.2 0.4 0.6 0.8

Mass Oualty x

1000 -

G- 100kgm's

0 60204 0

000

1100 ---------------. ---------------. ------. ---. -- --. --. -- ---. ---------------

: . s : :98

1

0 . 04 0. .

Mass Quality, x

1000 -- - - , . . . . . . . . . . . -

G " 200 kg/mra

10 ......... .... S .. . ................... .........

110 --------------- .-------- .--- .---.----------------..----------------t ---------------

10

1000

101

0 0.2 0.4 0.6 0.8Mass Quality, x

G - 500 kg/ms

--. .-. ----....:- ..........-.. -...-.-...-........-.-.-.-- -------- -. --.. ...-

- .L

o

......-.. ..... ......... ........ .........-........ .............. .......-

0 0.2 0.4 0.6 0.8Mass Quality, x

G -700 kg/mse

- - -

4-------+ --------,-------- --------- -------

. L : :

0 0.2 0.4 0.6

Mass Quality, x

0.8 1

0.8 1

Fig. 19. Comparison between experimental two-phase friction multiplier

(OFLO) 2 data for channels R-19.05-6 and R-19.05-0.17; low massqualities: o channel R-19.05-6; e channel R-19.05-0.17

G 400 kg/mas

............. ............... ............... ................. ...............

c

..

Il

1

lb

,uuI

-

I-

1000

1Inn

iI

I

i

1

1

I II

I

31

10'. 0.001 0.01

Mass Quality, x

0.1 1

0. 10' 0.001 0.01 0.1Mass Quality x

G - 200 kg/mrs

0

boo

Pooeg: :-:A

10' 0.001 0.01

Mass Quality, x

oO

104 0.001 0.01

Mass Quality, x

100

21

1L10

1000

100

N

10

1000

10

10

.5

IL0.1 1

.5

G - 400 kg/m's

S~oil

OD .

10. 0.001 0.01

Mass Quality, x

10-4 0.001 0.01

Mass Quality, x

10'

" 0*

".

10"' 0.001 0.01

Mass Quality, x

0.1 1

Fig. 20. Comparison between experimental two-phase friction multiplier

(OFL dataa for channels R-19.05-6 and R-19.05-0.17; high massqualities: o channel R-19.05-6; e channel R-19.05-0.17

1000

100

10

G- 50kg/m's

----.------.. --:------..-...

----.-----.-----.---------1 -.

00 0-

"S1 L10'

1000

100

10

111

G-100kg/m's

*0

o0 0

"i F "

G 500 kg/mrs

cctoo

- . . ..

1000

100

10

0.1 1

0.1 1

0.1 11

G - 700 kg/ms

.e.............. ........ ........... :...........

10.

1000

100

10

IL

G - 300 kg/ms

---------------- + ---------------- +---------------+ ------------ . -----. -------

a

!

10 .*

10m

1 l\ l 11 4 ll"

.J J .J

r " ".- " u- "

L

I

I

6-

value for the C-coefficient was used in the Chisholm correlation. Neithercorrelation satisfactorily predicted the measured pressure-drop results over theentire parameter range for channel R-19.05-6. However, the Chisholmcorrelation has a physical basis and was shown to satisfactorily represent thegeneral trend of the results. The Chisholm correlation was modified byrepresenting the C-coefficient as a function of mass flux and Martinelliparameter. With the channel R-19.05-6 data used as a guide, a modifiedcorrelation was developed over the practical range of interest for plate-fin heatexchangers used as evaporators, i.e., G < 400 kg/m2 s and X < 1 (x > .0.05)(Wambsganss et al. 1990).

The modified Chisholm correlation is given as

FL = 1+C/X+ 1/X2, (5)

where: C = aXb

and a = -2.44 + 0.00939ReLo

b = -0.938 + 0.000432ReLo.

In Eq. 5, ReLo is the Reynolds number corresponding to the mixture flowing as aliquid in the flow channel.

In Fig. 18, the experimentally determined two-phase friction multiplierdata for each of the two channels is compared with predictions using the modifiedcorrelation given by Eq. 5. An assessment of error is given in Table 1, in whichthe error range and average error are given for each of the different mass fluxes.For mass fluxes in the range 100 < G < 500 kg/m2 s, the average error for bothchannels, with one exception, is in the range 20%.

6 SUMMARY AND CONCLUDING REMARKS

In summary, horizontal two-phase flow experiments were performed in asmall rectangular channel with the objective to understand and characterize theeffects of channel orientation on two-phase fluid dynamics. In particular, flowpattern and pressure-drop data were obtained from experiments in which thelong side of the rectangle was horizontal (aspect ratio, or AR, of 1/6). Theseexperiments were designed to provide data to supplement, and allow forcomparisons with, the results of earlier experiments performed with the long sideof the rectangle vertical (AR of 6; Wambsganss et al. (1990). Because the samechannel is used for the two sets of experiments, the only difference is the effect of

Table 1. Error in applicationfor 0.05<x< 1 (%)

of modified Chisholm correlation

MassFlux, G Ch. R-19.05-0.17 Ch. R-19.05-6

(kg/m2 s) Range Average Range Average

50 -36 to -17 -24 -75 to -23 -46

100 -16 to +36 + -49 to +61 +17

200 -8 to +22 +12 -10to +34 +19

300 -11to +1 -5 -10to +17 +3

400 -21to -10 -15 -20 to +2 -7

500 -34 to -3 -27 -26 to -11 -17

gravity acting on3.18 mm).

the same mixture volume but at different heights (19.05 mm vs.

A flow pattern map was developed and compared (in Fig. 17) with the mapdeveloped for the AR-6 channel. Comparison of the two maps revealed that thestratified flow pattern, observed from tests with the AR-6 channel, did not existwith the AR-1/6 channel. However, the overall trends of the remaining flowpattern transitions: although slightly shifted, were consistent. The observeddifferences can be attributed to gravitational effects and the ease with which aperturbation or wave in the liquid tending to flow at the bottom of the channel cancome in contact with the top of the channel R-19.05-0.17 (AR of 1/6), with its verysmall vertical dimension of 3.18 mm.

In agreement with the ARe-6 channel, the pressure gradient data exhibiteda local maximum in the mass quality range 0.001 to 0.008; the critical massquality is a function of mass flux. This phenomenon seems to be unique, or atleast dominant, in channels of small cross-sectional area, because data ofinvestigators of two-phase capillary flows also show a similar behavior (as do thedata of Ide and Matsumura (1990) for small rectangular channels), while datafrom large channels do not show such behavior. As before (Wambsganss et al.1990), it was found in channel R-19.05-0.17 that this local maximum occurred atthe transition from plug, or bubble, to slug flow.

34

As with the AR-6 channel, the transition from plug, or bubble, to slug flowcould also be correlated with a breakpoint in the curve of RMS test sectionpressure when plotted as a function of mass quality. This unique behavior wasused in the development of the flow pattern map as an objective means ofdetermining the transition to slug flow.

The two-phase pressure gradient data from the AR-1/6 channel,expressed in terms of two-phase friction multipliers, were shown generally to bein very good agreement with the AR-6 data taken at corresponding two-phaseflow conditions. The major discrepancies were at low mass fluxes and low massqualities, where the pressure-drop measurements are inherently difficult andthe two-phase flow conditions difficult to establish. The good agreement of thepressure-drop data between the two channels indicated the lack of a gravity orflow transition and pattern effect, at higher qualities. Results from channel R-19.05-6 (AR of 6) also showed that the transition from slug to annular flow did notinfluence the pressure-gradient data trends.

The modified Chisholm correlation was based on the channel R-19.05-6data and was developed by Wambsganss et al. (1990) to include mass velocityeffects; the correlation was developed to predict two-phase pressure drop for massqualities greater than 0.05. Because the pressure gradient data from the twohorizontal orientations of the channel were in very good agreement, thecorrelation also predicted the data of channel R-19.05-0.17 with good accuracy.Further validation is, of course, required before the correlation can be used withconfidence to predict pressure drop in channels of other sizes and aspect ratiosand with different gas/liquid mixtures.

Future plans call for experiments with smaller channels and with differentgas/liquid mixtures. The smaller channels will allow evaluation of size andaspect ratio effects and, as necessary, inclusion of these effects in the correlation.Tests with different gas/liquid mixtures will allow evaluation of fluid propertyeffects and will provide a data base for further modification of the correlation toinclude such effects. In particular, for the very small channels of interest it isexpected that surface tension is a particularly important fluid property.

ACKNOWLEDGMENTS

The authors thank Mr. R. K. Smith for his contributions in fabricating thetest apparatus and flow channel and performing the experiments, and Ms. JoyceStephens for preparing the figures and the overall manuscript for publication.

35

This research is funded by the U.S. Department of Energy, Office ofConservation and Renewable Energy, Advanced Industrial Concepts Division.The continued support and encouragement of Mr. Marvin E. Gunn, Director ofthe Advanced Industrial Concepts Division and Manager of the Thermal SciencesResearch Program, are very much appreciated.

This research represents a U.S. contribution to Annex I of theInternational Energy Agency (IEA) Program on Research and Development inHeat Transfer and Heat Exchangers.

36

REFERENCES

Chisholm, D., (1967), A Theoretical Basis for the Lockhart-Martinelli Correlationfor Two-phase Flow, Int. J. Heat and Mass Transfer 10, 1767-1778.

Chisholm, D., (1973), Pressure Gradients Due to Friction during the Flow ofEvaporating Two-phase Mixtures in Smooth Tubes and Channels, Int. J. HeatMass Transfer 16(2), 347-358.

Damianides, C. A., and Westwater, J. W., (1988), Two-phase Flow Patterns in aCompact Heat Exchanger and in Small Tubes, Proc. 2nd U.K. NationalConference on Heat Transfer, Glasgow, Scotland, Vol. I, 1257-1268.

Friedel, L., (1979), Improved Friction Pressure Drop Correlation for Horizontaland Vertical Two-phase Pipe Flow, Paper 2, European Two-phase Flow GroupMeeting, Ispra, Italy.

Fukano, T., Kariyasaki, A., and Kagawa, M., (1989), Flow Patterns and PressureDrop in Isothermal Gas-liquid Concurrent Flow in a Horizontal Capillary Tube,ANS Proc. 1989 National Heat Transfer Conf., Vol. 4, 153-161.

Hewitt, G. F., and Bour6, J. A., (1973), Some Recent Results and Development inGas-Liquid Flow: A Review, Int. J. Multiphase Flow 1, 139-171.

Hosler, E. R., (1968), Flow Patterns in High Pressure Two-phase (Steam-water)Flow with Heat Addition, AIChE Symposium Series, E. R. Quandt, Jr., ed., 64,54-66.

Ide, H., and Matsumura, H., (1990), Frictional Pressure Drops of Two-phaseGas-liquid Flow in Rectangular Channels, Exp. Therm. Fluid Sci. 3, 362-372.

Jones, 0. C., Jr., and Zuber, N., (1975), The Interrelation between Void FractionFluctuations and Flow Patterns in Two-phase Flow, Int. J. Multiphase Flow 2,273-306.

Lockhart, R. W., and Martinelli, R. C., (1949), Proposed Correlation of Data forIsothermal Two-phase Two-component Flow in Pipes, Chem. Engng. Progress45(1), 39-48.

Lowry, B., and Kawaji, M., (1988), Adiabatic Vertical Two-phase Flow in NarrowFlow Channels, AIChE Symposium Series, 84(263), 133-139.

Richardson, B. L., (1958), Some Problems in Horizontal Two-phase Two-component Flow, Argonne National Laboratory Report ANL-5949.

Troniewski, L., and Ulbrich, R., (1984), Two-phase Gas-liquid Flow inRectangular Channels, Chem. Engng. Sci. 39(4), 751-765.

Wambsganss, M. W., Jendrzejczyk, J. A., France, D. M., and Obot, N. T., (1990),Two-phase Flow Patterns and Frictional Pressure Gradients in a Small,Horizontal, Rectangular Channel, Argonne National Laboratory Report ANL-90/19.

olLIO

APPENDIX

Measured Values of Pressure Drop and Test-Section Pressure

G = 50 kg/m2 s G = 100 kg/m2 s G = 200 kg/m2 s G = 300 kg/m 2 s

x (Mass PTS DPF PTS DPF PTS DPF PTS DPFQuality) (kPa) (kPa/m) (kPa) (kPa/m) (kPa) (kPa/m) (kPa) (kPa/m)

0.00000.00020.00040.00080.00110.00160.00190.00230.00280.00320.00450.00640.01280.02560.05120.10000.15000.20000.25000.30000.35000.40000.45000.50000.55000.60000.65000.70000.75000.80000.85000.90000.9500

0.257

105.3105.3105.3105.3105.3105.3105.3105.3105.4105.4105.6105.7105.9106.0106.2106.4106.6106.9107.2107.5107.8108.2108.5108.8109.2109.6109.9110.3110.8

0.0790.0630.0670.0590.0340.0670.0870.0690.0860.0660.2840.5820.8781.1551.4331.7561.9782.3402.7423.1243.4663.7314.2144.5635.0945.3965.6375.8186.542

105.4105.4105.4105.4105.4105.4105.4105.5105.5105.6105.8106.0106.5107.0107.8108.5109.5110.4111.9113.0114.3115.7116.7117.7118.9120.0121.2122.0122.6123.8

0.2270.2510.2920.3190.2610.2260.2510.2610.2550.2500.5110.9981.6922.4363.4614.3725.5126.2368.0469.13210.76011.84612.26913.15314.29914.92315.60615.88815.80816.391

104.3105.6105.6105.6105.5105.5105.5105.5105.5105.6105.9106.5107.3109.8113.8118.1122.2125.9130.913 C138.5143.0147.2151.4156.4157.8166.2169.1173.3176.1178.8

0.5400.8840.9210.8220.7340.7070.7150.8480.8160.8681.3372.2013.2436.46411.04815.19019.11221.92725.74829.16631.78034.39436.60639.01941.83444.04646.86148.87249.67650.27949.073

102.9103.1103.3103.3103.3103.3103.3103.4103.5103.7103.9104.7106.2109.0116.0125.4134.6143.9152.8161.4167.7176.1185.3194.4204.4213.6220.0229.2238.3248.1255.1

0.4140.6470.9101.2701.3121.2821.2701.4751.5411.7501.6201.9703.0195.0288.346

15.94725.35733.60139.83544.66148.28050.09053.10655.92159.54064.76868.79072.40976.83379.04582.26283.871

MP

G = 400 kg/m2 s G = 500 kg/m2s G = 700 kg/m2s

x (Mass PTS DpF PTS DpF PTS DPFQuality) (kPa) (kPa/m) (kPa) (kPa/m) (kPa) (kPa/m)

0.00000.00020.00040.00080.00110.00160.00190.00230.00280.00320.00450.00640.01280.02560.05120.10000.15000.20000.25000.30000.35000.40000.45000.50000.55000.60000.65000.70000.75000.80000.85000.90000.95001.0000

104.2104.4104.6104.8105.0105.1105.1105.3105.4105.6106.2107.7110.5115.6127.7144.0160.4172.3183.6197.3208.0220.4235.1247.1259.1273.8283.9

0.5341.0281.4261.8022.0242.4462.7072.6872.9893.0612.7783.4595.5229.20214.75226.17340.04851.91158.14560.75964.57966.59070.20975.03579.45985.08988.70995.746

103.8104.1104.5104.9105.4105.6105.6105.6105.6106.2107.0109.5114.1122.9144.8161.5182.5200.2216.2232.8248.8264.9281.7297.2

0.6901.5812.0762.6793.1424.1194.7164.7764.0523.8053.9664.9318.088

13.81923.33042.63353.89466.36174.40478.22479.02981.03984.65989.88794.512

104.1105.5106.9107.9109.3109.0105.3108.0108.3109.5111.2115.9125.0

175.2211.6243.4269.2287.7311.8

1.572.843.645.266.779.069.422.155.786.127.739.62

15.4326.75

63.9584.4698.94104.17101.96100.35

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