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Some of the most importantand challenging problems in two-phase flow today have to do with the understandingand prediction of multidimensional phenomena, in particular,lateral phase distribution in both simple and complex geometry conduits. A prior review paper [I] summarized the state-of-the-art in the understanding of phase distribution phenomena, and the ability to perform mechanistic multidimensional predictions. The purpose of this paperis to updatethatreview, with particularemphasis on complex geometry conduitpredictivecapabilities. Previous experimental studies have shown that pronounced lateral phase distribution may occur. Serizawa et al [2] and Michiyoshi et al [3] havemeasured pronouncedwall peakingof the local void fractionfor turbulentbubbly air/watertwo-phase upflow in a pipe. Similar results were foundby Valukina et al [4] for laminarbubblyair/watertwo-phase upflow in a pipe. These results were laterconfirmedin a studyby Wang et al [5], and were extended to show that, in contrast to the bubbly upflow results; void coring (ie, void concenwafionnearthepipe'scenteriine) occurredforturbulentbubblytwo-phaseair/waterdownflow in a pipe. Recently, the developmentof these lateralphasedistributionprofiles hasbeen studiedby Class et al [6] and Liu [7], where it was found thatbubble size effects are importmi_.This may explain why wall peaking in verticalc_x:ur_ntupflow is not always observed. The importance of bubble size on lateral void phase distributionhas also been recognized by other investigawrs, including Sekoguchi et al [8] andZun [9]. Moreover, Monji et al [10] have foundthatfor bubbly air/waterupflows thatsmall bubbles (Db < 0.5 nun) tend to be uniformly distributedacross the conduits, while large bubbles (Db • 6 ram)tend to core, and it is only the intermediate size bubbles that concentrate near the wallofthe conduit. Interestingly, similar lateral phasedistribution phenomenahavealsobeenobserved incomplex geometry conduits. Sadatomi etal[II]havefound pronounced wall peaking for turbulent bubbly air/water twophaseupflow invertical triangular andrectangular conduits. Moreover, theyfoundthat forslugflow, void coting occurred. Similar voidcoring "has beenobserved bySire etal[12] for bubbly/slug air/water upflows ina verticaltriangularduct. Okhawa et al [13] made measurementsof bubbly air/water two-phase upflow in an eccentric annular test section. Theyobserved significant lawxal phase distribution, withthevoid fraction being larger inthemore openregion oftheflowarea. Similar results werefound by Shiralkar etal[14] using boiling Freon-114. Itisclear that there arestrong lateral forces on thedispersed (ie, vapor) phasewhichleadto the observed phasedistributions. Thuslet usnext consider whatisknownabout the physics ofthese lateral forces. Drew & Laheyhavedemonstrated theunique relationship between theturbulence field oftheliquid phase andthe voiddistribution for pipes [15] andfor complex geometry conduits [16]. Similar result3 havealso beenfound byKataoka etal[17]. Wang etal[5] haveextended these analyses ...

An extension of the k-ε model for bubbly two-phase flow is proposed and tested against experimental data. The basic assumption made is that the shear-induced turbulence and bubble-induced turbulence may be linearly superposed. This assumption results in a model with two time constants that matches both homogeneous two-phase turbulence data (Lance and Bataille, 1991) and pipe data (Serizawa, 1986). The coefficients of the single-phase k-ε model have not been modified and only one additional coefficient is required: the virtual volume coefficient of the bubbles, which may be determined from first principles. This model not only agrees with the data trends, but it also predicts the turbulence suppression which has been measured for high Reynolds number bubbly air/water flows in pipes.

The void fraction distribution for turbulent bubbly air/water upflows and downflows in a pipe was analyzed using a three-dimensional two-fluid model. A τ − ε (i.e., Reynolds stress) turbulence model was used for the continuous (liquid) phase. The τ − ε transport equations yield all components of the Reynolds stress tensor for the liquid phase momentum equations. The effect of these stresses is to create a lateral pressure gradient that acts on the bubbles and effects their distribution. The lateral lift force on the bubbles has also been modelled. This lift force arises due to the relative motion of the bubble with respect to a nonuniform liquid velocity field. It has been observed experimentally that for upflows the bubbles concentrate near the wall while for downflows they move toward the center of the conduit. The model presented herein predicts these trends.