Modeling Two-Phase Flow in Pipe

8/13/2019 Modeling Two-Phase Flow in Pipe

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Savalaxs Supa-AmornkulDepartment of Chemical Engineering, University

of New Brunswick Fredericton, N.B. E3B5A3,

Canada

e-mail: [email protected]

Frank R. StewardCentre for Nuclear Energy Research, Enterprise

UNB Building, University of New Brunswick,

Fredericton, N.B. E3B6C2, Canada


Derek H. ListerDepartment of Chemical Engineering, University

of New Brunswick Fredericton, N.B. E3B5A3,

Canada


Modeling Two-Phase Flow in PipeBends

In order to have a better understanding of the interaction between the two-phase steam-water coolant in the outlet feeder pipes of the primary heat transport system of someCANDU reactors and the piping material, themalhydraulic modelling is being performedwith a commercial computational fluid dynamics (CFD) codeFLUENT6.1. The modeling

has attempted to describe the results of flow visualization experiments performed in atransparent feeder pipe with air-water mixtures at temperatures below 55C. The CFDcode solves two sets of transport equationsone for each phase. Both phases are firsttreated separately as homogeneous. Coupling is achieved through pressure and inter-

phase exchange coefficients. A symmetric drag model is employed to describe the inter-action between the phases. The geometry and flow regime of interest are a 73 deg bend

in a 5.9 cm diameter pipe containing water with a Reynolds number of1E5-1E6. Themodeling predicted single-phase pressure drop and flow accurately. For two-phase flowwith an air voidage of 550%, the pressure drop measurements were less well predicted.Furthermore, the observation that an air-water mixture tended to flow toward the outsideof the bend while a single-phase liquid layer developed at the inside of the bend was not

predicted. The CFD modeling requires further development for this type of geometry withtwo-phase flow of high voidage. DOI: 10.1115/1.1904063

Keywords: Two-Phase Flow Experiment, CFD Modeling, Film Inversion

Introduction

There have been a number of studies of vertical and horizontal

two-phase flow in straight pipes as well as single-phase flow in

curved pipes. In two-phase flow, the curved pipe geometry tendsto give rise to inhomogeneous phase distribution, flow reversal,flooding, secondary flow, and film inversion. These phenomena

can cause problem such as burn-out, corrosion, and tube failure inindustrial components, resulting in costly outages, repairs, andearly replacement affecting plant reliability and safety.

This project began with the discovery of unexpectedly high

corrosion rates of several carbon steel feeder pipes at the reactor

outlet in the primary coolant system of a CANDU reactor in1996as high as 120 m/year. It should be noted that the antici-pated corrosion rate of carbon steel obtained from laboratory stud-

ies 1was 10 m/year. A program of in situ monitoring of feed-ers has since been carried out. Results of a program of laboratoryexperiments and modeling have indicated that the phenomenon is

flow-accelerated corrosionFAC. In general, FAC of carbon steelcan be described by processes in series, magnetite film dissolutionand erosion, and mass transport of dissolved iron into the bulkcoolant. The last two processes are enhanced by the relative

movement between the liquid and the surface. High turbulenceareas such as sharp bends, elbows and entrances are susceptible tohigh FAC rates 24. It is therefore desirable to understand thehydrodynamics of the coolant in the complex geometry and ag-

gressive conditions at the reactor outlets. The feeders are prima-

rily 2.5

nominal size 2.3

inner diameter 5.9 cm connected to ahorizontal reactor fuel channel with a Grayloc fitting. The fuelchannel has an annular geometry at that point and the feeders havesingle or double bends just after the Grayloc connector see Fig.1. The coolant is heavy water at 310 C with Re of 1E5-1E6 andsteam quality up to 4%.

In this paper, the results of modeling the hydrodynamics of an

experimental mock-up of an outlet feeder operating with air-watermixtures at room temperature are described. The modeling wascarried out with the FLUENT 6.1 computational fluid dynamicscode. The model describes three-dimensional turbulent flow in theend fitting and feeder pipe. The results are compared with mea-sured pressure distributions. Phase distributions predicted fromthe modelling were compared with observations from flow visu-alization. Particular attention was paid to the two-phase flow char-acteristics in the bend since there have been few studies 5in thisarea. Discrepancies between the predictions and observations oc-curred for two-phase flow.

Modeling the Experiments

The mock-up was a full-scale fuel-channel end fitting con-nected to an acrylic feeder pipe that had a single bend. The end-fitting geometry was an annulus that was supplied with air-water

mixtures at temperatures up to 55C, flow rates up to 0.047 m 3/ sliquid and void fractions up to 0.6. Pressure taps were fixed ateight positions along the bend extrados and eight positions alongthe intrados. Two additional taps were positioned at the connectorto the end fitting. Flow patterns were visualized during severalruns with a video camera and a high-speed movie camera andduring other runs with the observation of the pattern in a previ-ously applied viscous oil film.

The modeling used FLUENT

version 6.1, which incorporates anEulerian treatment of three-dimensional, two-phase flowssingle-phase flows are treated similarly but with a simplified approach.The following concepts and assumptions were made: 1 a singlepressure is shared by both phases; 2 momentum and continuityequations are solved for each phase; 3 the secondary phase con-sists of uniform and unchanging bubbles dispersed in a continuous

phase; 4 the bubble size is assumed to be 0.1 mm; 5 the tur-bulent flow is everywhere isotropic; 6 a two-equation turbulentmodel is solved for the mixture; and 7 physical properties areuniform throughout.

The following conservation equations are the basis for the mod-eling:

Contributed by the Pressure Vessels and Piping Division for publication in the

JOURNAL OFPRESSUREVESSEL TECHNOLOGY. Paper presented at the 2004 ASME Pres-

sure Vessels and Piping Division Conference PVP2004, July 25, 2004-July 29,2004, San Diego, California, USA. Manuscript received November 4, 2004; Final

manuscript received December 8, 2004. Review conducted by: Sam Zamrik.

204 / Vol. 127, MAY 2005 Copyright 2005 by ASME Transactions of the ASME

wnloaded From: http://pressurevesseltech.asmedigitalcollection.asme.org/ on 04/08/2013 Terms of Use: http://asme.org/terms


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Mass:

k

t+ kuk= 0 1

Momentum:

ku

k

t+ kuk

uk

= T

+ kg 2

where, T= pkI+k

Equations of jump conditions to ensure that mass and momen-tum are conserved at the phase interface are included. The inter-face force which is caused by the relative motion between phasesis represented by the symmetric drag model 6.

The Reynolds stress terms are averaged using Boussinesqs as-

sumption. The standard k model was used to solve for the

turbulent viscosity,t, using the properties of the mixture. TheReynolds stress model RSM 6 was also used for single-phaseflow modeling.

A three-dimensional domain of the end fitting and the feederpipe was constructed for the modeling. The mesh was made todescribe a large aspect ratio. The domain consisted of 360,714elements. Several cells were placed close to the wall within the

region y + 30 to account for wall functions. The hydraulic diam-eter DH of the annulus was 2.8 cm and its length from the inlet

to the centerline of the feeder pipe was approximately 50 times

DH. The feeder pipe diameter was 5.9 cm. The ratio of the bend

radius of curvature R to the pipe cross section diameter D,

R/D, was 1.61. The straight section after the bend was 30 cm.Independence of the modeling results from the chosen mesh could

not be proven because of computing limitations. Instead, the re-sults of single-phase flow modeling with the chosen mesh werevalidated by experiment.

Results and Discussions

Single-Phase.Figure 2 presents the pressure measurements andmodeling predictions for a single-phase flow experiment. Thepressure distribution is presented in terms of the pressure coeffi-

cient, Cp, which is defined as p pref/1

2ave

2 . The local staticpressure is p and p refis an upstream reference pressure located at

56 cm from the centerline of the feeder pipe in this experiment.The average Reynolds number for the pipe bend in this experi-ment was 370,000. The circumferential position at 0 deg repre-sents the data along the intrados of the bend whereas 180 degrepresents the data along the extrados of the bend. At the connec-tor zero on the abscissa the additional two measurements weremade. The 1 position supplies the reference pressure. The overallpressure drop across the bend shows good agreement between theexperiment and the predictions except at the location ahead of thebend. The RSM did not make a significant difference on the pres-sure distribution prediction. The RSM was able to predict circularmotions after the pipe bend; however, such a result can not bemeasured from the experiment at this time.

When the flow follows a bend the static pressure and velocitydistributions change; thus secondary flows are generated and tur-bulence structure is affected by the curvature. The static pressureincreases with the radius of curvature to balance the centrifugalforce. Centrifugal and pressure forces acting on the faster fluid inthe core cause the core to shift towards the extrados of the bend.Low energy fluid near the wall tends to move around the wall

towards the low static pressure region at the intrados of the bend.This tends to separate the low energy fluid from the core flow andcause it to accumulate at the intrados. Figure 3 presents the Fluentrepresentation of this phenomenon.

Two counter-rotating recirculation flows of the fluid at the en-trance to the feeder pipe were predicted by the modeling Fig. 3;they are due to the adverse pressure gradient and the abruptchange in area ratio. The entrainment of recirculating fluid in-duces a flow reattachment downstream7. This recirculating fluidwas observed in the flow visualization experiments. Thus, twocounter-rotating vortices over the intrados portion of the feederinlet downstream from the recirculation region were generated.The line where these two flow systems meet can be seen in the oilflow visualization patterns Fig. 4.

Two-Phase Flow Pressure Distribution. The average Rey-nolds number in the feeder pipe for these two-phase experiments

varies from 7E5 to 1E6using a volume-weighted average toestimate physical properties and a homogeneous model to esti-mate the average velocity of the mixture. Since there is no uni-versal model8,9 that can represent properties of two-phase flowat the bend, the pressure measurements are presented as absolutepressure values.

Pressure data at 16 points along the feeder pipe are shown inFigs. 5 and 6 for both the experiment and the predictions. Figure5 shows the pressure data for 14% volume fraction air at averageReynolds number across the pipe bend of 780,000. The agreementis good for the extrados portion of the pipe except for a single

Fig. 1 aEnd fitting and feeder pipe geometry,bend view ofend fitting and feeder pipe, showing actual orientation, and cgrid system

Journal of Pressure Vessel Technology MAY 2005, Vol. 127 / 205



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Fig. 2 Pressure distribution along tube bend, experiment, and prediction single-phase, flow rate=0.019 m3 / s, temperature=25C

Fig. 3 Predicted velocity distribution along the pipe bendFig. 4 Oil pattern from flow visualization experiment

Fig. 5 Pressure distribution along tube bend, experiment, and prediction volume fraction of air=14%, liquid flow rate=0.0312 m3 /s, temperature=25C

206 / Vol. 127, MAY 2005 Transactions of the ASME



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point at 6 cm from the connection. However, numerical modelingtends to overpredict the pressure values at the intrados portion ofthe feeder pipe.

Experimental conditions in Fig. 6 are 49% volume fraction ofair with a Reynolds number of 930,000 in the feeder pipe. Theagreement for the extrados again is good except for a single point

at 6 cm from the connector, where the experimental value is sub-stantially lower, and downstream of the bend midpoint. The val-ues for the intrados of the feeder pipe are consistently higher forthe simulation than for the experiment. The difference is less thanthat for the lower void fraction Fig. 5.

Phase Distribution. The flow pattern is considered to dependon the flow rate of each phase, the interaction of the phases, thetransport properties and the geometry of the bend.

Figure 7 presents photographs of the phase distribution for a

void fraction of 15%. The bubbles are smaller than the recordingresolution of the high-speed movie camera of about 0.1 mm. Theflow regime was difficult to determine in the two-phase regionnear the intrados. While there is generally an accumulation of airtowards the intrados, there also appears to be an accumulation ofa slower liquid film underneath the faster core. This originatesfrom the start of the bend and extends to 0.5 diameters down-stream from the bend before the core flow reattaches. This couldbe caused by a radial pressure gradient generated by the fastercore of the lower density mixture causing the slow-moving liquidphase near the wall to move toward the intrados. Other workers1016 observed a similar phenomenon at high gas flow rates;most of them offer the same explanation and invoke the ratio ofcentrifugal force to gravity force.

The criterion which is used to predict the accumulation of

liquidthe Froude number

16failed to predict these experi-mental conditions. A similar concept using slip velocity ratio10,

which was based purely on centrifugal force and gravity force,does not apply here because the slip velocity was observed to betoo low. From the flow visualization, it was deduced that the sec-ondary flowvortices that originated from the inlet portion of thefeeder pipe could be an important factor in this type of flow 15.As found in the single phase experiment, the secondary flow nor-mally originated in a pair of counter-rotating vortices at the intra-dos portion of the feeder inlet. These vortices leave the intradosand contact the extrados immediately downstream of the bend.The vortices then merge downstream of the bend intrados seeFig. 8a.

Fig. 6 Pressure distribution along tube bend, experiment and prediction volume fraction of air=49%, liquid flow rate=0.0224 m3 /s, temperature=25C

Fig. 7 a,bPhase distribution at the bend volume fraction ofair=15%, Re=7.0E5, temperature=25C




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The apparent layer of slow moving liquid at the intrados of thebend is larger at higher void fractions compare Figs. 7a and8b and becomes less stable as the void fraction increases. Sub-sequent measurements have shown that these liquid films are thin-ner than they appear. Quantitative measurements are needed toconfirm the layer thickness.

The phase distribution predicted by FLUENT for similar condi-tions fails to represent this development of a liquid film at theintrados of the bend. Figure 9a shows the prediction of an accu-mulation of air at the intrados of the bend. FLUENT predicts themovement of the high density fluid to the extrados of the bend dueto the centrifugal force. The inability of FLUENT to predict the

pressure distribution measured for two-phase flow may then berelated to these discrepancies in predicting film development atthe bend. The inconsistency implies that the current two-fluidmodel and/or above assumptions need to be improved, in particu-lar, surface tension effects on the nature of two-phase flow shouldbe considered. Bubble size and velocity and spatial variations involume fraction would influence the drag coefficient term in themodel, which may account for the discrepancy.

On the other hand, the predominantly liquid layer predicted byFLUENTto develop at the bend extrados and to extend downstreamand around the wallsee Figs. 9a and 9b was observed in theflow tests. Figure 9a shows a liquid film at one diameter down-stream from the intrados of the bend which extends further down-

stream. In the experiment this liquid film was found earlier at theintrados of the bend.

Conclusions

1. The simulation with the CFD code, FLUENT, for single phaseflow gives a representation of the pressure distribution along afeeder pipe test section that is in reasonable agreement with theexperimental data.

2. The simulation by FLUENT for two-phase flow was signifi-cantly different from the experimental data. The predicted pres-sures along the intrados of the bend were higher than the experi-mental values. The overall pressure drop across the test sectionwas significantly less for the simulation than for the experimentaldata.

3. The chosen models withinFLUENTpredicted an accumulation

of air at the intrados of the bend in general agreement with flowobservations but did not predict the development of the liquid filmnear the intrados that was observed. This may be related to theinability of FLUENT to predict pressure drop in two-phase flowaccurately, possibly because it does not consider bubble evolutionin any detail.

Acknowledgments

The authors would like to acknowledge the CANDU OwnersGroup and thank Atomic Energy of Canada Limited for conduct-ing the experiments and providing the experimental data and pho-tographs. In particular, Bruce Smith and John Pietralik are

Fig. 8 a,bPhase distribution at the bend volume fraction ofair=52%, Re=12.0E5, temperature=40C

Fig. 9 a Air distribution at the middle plane of the feeder pipevolume fraction of air=49%, Re=9.3E5, temperature=25C,and b water distribution around the wall volume fraction ofair=49%, Re=9.3E5, temperature=25C

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thanked for their assistance and valuable discussions. The NaturalSciences and Engineering Research Council of Canada is thankedfor providing financial support.

Nomenclaturey+ dimensionless distance from the wall

g gravitational acceleration, m/s2

ui interface velocity, m/sRe Reynolds number

pk thermodynamic pressure, Pa

I unit tensor

uk

velocity of phase k, m/s

Greek Symbols

density, kg/m3

k stress tensor of phase k, kg/s2

Subscript

k liquid or gas phase in governing equations

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