西南石油大学英语翻译作业.doc

Paper NoS5_Tue_D_296th International Conference on Multiphase FlICMF 2007, Leipzig, Germany, July 9 13,S5_Tue_D_29Simulation of multiphase flows composed of large scale interfaces and dispersed fields1)Harald Laux, Ernst A. Meese and Stein Tore Johansen, Yves Ladam,1)1)1)2)Kris M. Bansal and Thomas J. Danielson, Alexandre Goldszal and Jon Ingar Monsen2)3)3)1)SINTEF, Trondheim, Norway , ConocoPhillips, Houston,USA, 3)TOTAL, Stavanger,Norway2)Corresponding author: Stein.T.Johansensintef.noKeywords: Turbulence, large scale interface, slug flow, droplets, bubbles, pipelinesAbstractIn the present paper we present a 3D multiphase flow model that is capable of predicting flow with coexisting continuous anddispersed phases. A quasi-3D (Q3D) pipe flow version of the 3D model has been developed by averaging the flow overhorizontal slices, reducing the computational time dramatically without losing the pipe geometry and too much of the criticalflow physics. By this basically two-dimensional approach it is possible to simulate sufficiently long sections of a pipe toanalyze flow development and flow regime transitions. It is shown that this type of model can predict, both qualitatively andquantitatively, different types of two-phase pipe flows without a priori flow regime information.Introductionmain features of the 3D model and a particularimplementation of this model.Multiphase flows in pipelines are important for a variety ofindustries, ranging from nuclear power plants, plants forfood processing, to oil and gas pipelines. These flows canTheorycontain(different physical realizations of a phase). Typically, in oilnumerousphasesandcorrespondingfieldsIn our model approach we derive Eulerian volume- andensemble-averaged turbulent transport equations for allpresent fields. The starting point for the model are thesingle-phase volume-averaged Navier-Stokes equations(Whitaker, 1969, Prosperetti & Jones, 1984, Slattery, 1999).In addition we split the multiphase flow into differentfields. Our field concept assumes that the flow consists ofdifferent regions in which particles, droplets and bubblesare suspended by only one fluid. Each fluid-continuousregion and all possible types of dispersed particulatescomprise the total number of fields. Hence, we normallyhave four fields in a two-phase flow without solid particles(Figure 1) and nine fields in a corresponding three-phaseflow. However, by introducing a thin wall film of liquid weadd one more field to our description.andgas pipelines the flow could contain water,hydrocarbon liquid (oil or condensate) and gas. In additionnumerous solids phases may be present. The flow patternsmay take any of a number of different regimes, such asslug flow, flows with large waves, bubbly flow, stratifiedflow, annular flow and churn flow.To predict these flows one-dimensional models have beendeveloped over the last 50 years. These models have beensuccessful in assisting the industrial development but stillhave significant shortcomings due to crude simplificationsand the use of empirical correlations. At the same time,new 3D modeling techniques are developing fast, madepossiblebythecontinuousgrowthinavailablecomputational power. Already now we see that 3DComputational Fluid Dynamics (CFD) models can giveinformation that both qualitatively and even quantitativelysurpass information obtained from 1D models.A major problem with most current 3D approaches is thatthey are based on direct simulation of interface evolution.Due to the span in length scales in industrial problems amulti-scale approach has to be devised. Such an approachneeds to handle large-scale interfaces representing waves,coexistingwith transport of bubbles and droplets,including deposition and entrainment. In addition themodels should be able to represent large-scale spatial andtemporal features of the real flows without using anyassumptions about flow organization (flow regime).To meet these challenges we started the development ofLedaFlow (Danielson et al, 2005), a next generationtransient multiphase flow simulator that has 1D capability(Goldszal et al., 2007) in addition to the herein presented3D modeling approach. In the present paper we present theFigure 1. Typical topology of a gas-liquid flow. The threeinterface types between the four fields (bubbles, droplets,gas-continuous region and liquid continuous region) areshown.1 Paper NoS5_Tue_D_296th International Conference on Multiphase FlICMF 2007, Leipzig, Germany, July 9 13,S5_Tue_D_29Turbulence is modeled by a filter-based (Johansen, Wu &Shyy) multiphase model, where turbulent dissipation isrepresented by an algebraic closure (Schumann, 1975).The conservation equations for turbulent flows areobtained after conditional ensemble averaging of theprevious transport equations. Now we average over thepossible turbulent realizations of the flow. Flow featuressmaller than the applied filter size are now modeled whilethe large-scale features are resolved. This approach isimplemented for all of the four-field transport equations.By adding together the field transport equations, we obtainphase transport equations for phase-specific quantities. Wenote that mass transfer terms due to transfer betweenbubble and continuous liquid fields disappear formally. Onthe other hand we introduce an inaccuracy as in interfacialTo derive our model we apply volume-averaging to eachcontinuous region to obtain generic transport equations forthe continuous and the dispersed fields. The mass equationreads: ktKk kF,(1)k+ u =kjkj=1jkwhere the inter-field mass transfer term is given by:K K ( uk w n dsk kjK)k1V S.(2) kjkjEThe integral (2) in the mass transfer term represents bothcellswe cannot discriminate between bubble andmolecularmasstransfer(diffusion,evaporation,continuous gas velocity. The resulting momentum equationfor the gas phase is:condensation) and mechanical mass transfer (depositionand entrainment of droplets and bubbles at interfacesbetween continuous regions (Figure 1).t( u ) + ( ug, jug,i) = g P + giThe resulting momentum equation is:,(4)ggg,ix jggxiggKll + fl t g ltp,droplet g,i fl t g utK K (- ul,i) fggufuul,i+ ( u u).kkk(3)kkkktp,dropletg,igp,bubblep,bubble= p + gK + 16eff ,gG l, jix jnAg,CV + flgkkkkV CVCVfaces1FKKK w )kjK (uunkdsfgwhere and fl denote the local volume fraction ofVkkkj=1 Sjkkjspace that is gas- and liquid-continuous, respectively.The turbulent dispersion fluxes (only bubble flux is shown)are modeled by:EFK1 (pkI + )knkdsVj=1 S t,gScd gjkkjE,(5)u= gK Ku1Vg,i+ (u*k)drkkVand for the turbulent dispersion Schmidt number we followthe proposal of Gouesbet et al. (1984).EWe note that the third line in Equation (3) is due tointer-field mass transfer, the term on the fourth line is thephase interaction term, containing drag, lift, virtual mass,large-scale pressure and large-scale viscous stresses. Thefifth line contains the mixing stresses, a result of thevolume- and ensemble-averaging of the convective terms.This term is usually neglected in models, even if it may beof crucial importance in some flow situations. We furthernote that the phase pressure pk does not exist fordispersed phases as long as inter-particle collisional effectscan be neglected. By applying appropriate closure modelsfor the integral terms in Equation (3) we may obtain amodel for the transient 3D flow inside the differentcontinuous regions of the flow.The turbulent flux, including internal stresses at the LSI, isrepresented by:1V6GnCV Ag,CV,(6)eff ,gCV faceswhereis the effective laminar and turbulent stresseff ,gGdue to continuous gas and LSI, and where n is theCVnormal vector pointing out of the liquid-continuous regionin the computational cell with volume V , where Ag,CVis the face area.The corresponding momentum equation for the liquidphase contains the same and symmetric terms with the gasphase momentum equation.We now focus on the two-phase flows with only fourfields: continuous liquid, continuous gas, droplets andbubbles. In addition we introduce the concept of thelarge-scale interface that may have unresolved structures.The role of the large-scale interface (LSI) is to separategas- and liquid-continuous regions. Furthermore, the LSI isresponsible for transfer of shear stresses between differentfluid-continuous regions, delivering droplets and bubblesto the respective continuous regions and at the same timereceiving depositing bubbles and droplets. The LSI isidentified as the physical interface where local volumefractions pass the phase inversion boundary. The LSI isillustrated by the second box from the top in Figure 1.The joining of fields into phase transport equations is alsoperformed for the turbulent energy fields. Turbulentsub-filter energy is then represented by (here only liquidphase is shown):t2.(7)Kl+xk lul,kKl x = ( + l,t)x j 3 KKlfllu + flll,tSl2llllj3 gltp,bubbleg gk K 1 u u2l l,i g ,iKl2+ CBP fl fl0.845(u - u ) f l2ltp,bubble llglgk pltpltp,droplet 1+ f gKgul,i g,iu flul,i(ul,i u )+ PLSIg,i2In Equation (7) we see two production terms, after the2 Paper NoS5_Tue_D_296th International Conference on Multiphase FlICMF 2007, Leipzig, Germany, July 9 13,S5_Tue_D_29equality sign, the dissipation term, the bubble-inducedenergy production term, two interphase energy exchangeterms, a drag-like term that represents gravitationalproduction and finally the added production caused bylarge-scale interfaces (LSI). The two-phase correlationappropriate for a pipe flow. The slice average is describedby:z1/ 2 ( y) dz .(8)z1/ 2 ( y)kuuis modeled according to Zhou et al. (2002).l,i g ,iwhere z(y) is the slice width. By a formal averaging of thetransport equations we obtain new Q3D-averaged fields. InAt the large-scale interfaces (LSI) we use the concept ofwall functions, where the shear stresses from both sides ofthe interface are approximated by the rough-wall wallfunctions described by Asrafian & Johansen (2007). Thesame wall functions are used to calculate the addedparticularweobtainQ3Dmass-averagedvelocitycomponents:ugQ,3i D ug,i / g.g(9)turbulenceproduction in LSI cells. The effect ofnon-resolved waves is modeled by a density correctedCharnok (1955) model.The revised gas momentum equation now reads:The dispersed droplet and bubble sizes are treated by theirlocal Sauter mean diameters. The spatial development ofbubble and droplet sizes is described with convectiveevolution equations (Laux & Johansen 1999, Laux, 2003),where the droplet size entrained from the LSI needs aspecific model.tx j P.(10)( ) +( gug, jug,i) = g x+ ggug,iggggiil glg fl+ fg(u u ) f-ug,i fltul,igtltg,il,igtp,dropletp,bubble p,dropletp,bubbleG) nCV Ag,CV6 l, jix j1V CV (+ gug,l g,iu+ fleff ,gggfacesThe flow interaction with solid walls is treated by thewell-established concept of wall functions used in CFD(Computational Fluid Dynamics). The actual model used isdescribed in Asrafian & Johansen (2007).In this Q3D-averaged equation all fields are slice-averaged(over pipe width). The only retained, but most important ofthe new terms that has arrived is u u, whereggg ,l g ,iug,iis the deviation between the local 3D velocityThe quasi-3D approximationcomponent and the Q3D-averaged value. This new term isa mixing stress that is a result of the flow geometry.Similar terms appear in scalar transport equations and mayhave a significant impact on axial dispersion. At presentwe cannot offer a specific closure model for this term, andwe use an effective stress model for the total stress term:A quasi-3D (Q3D) version of the 3D model has beendeveloped by averaging the flow over horizontal slices.The motivation was to reduce the computational timedramatically without losing relevant pipe geometry and toomuch of the critical flow physics. By this basicallytwo-dimensional approach, it is possible to simulatesufficiently long sections of a pipe to analyze flowdevelopment and flow regime transitions. The slicing ofthe pipe cross section is illustrated in Figure 2 below, andthe flow transport equations are spatially averaged overeach slice. The result of this averaging is that we obtainprimarily 2-dimensional (Q3D) transport equations wherethe fluxes at the walls are treated as boundary conditions. ggug,l g,iu=eff ,g,(11) ug, j+ ug,ix j2 g K ijg g3() + g.l g,tgxiwhere the turbulent viscosity is here given by: = 0.103 f ()Kg1/ 2(12)g,tgHere, the function f depends on , the ratio betweenKolmogorov wave number and filter cut-off wave number.Numerical solution methodThe transport equations are solved using a coupledpressure based technique that is similar to the Vasquez &Ivanov (2000) method. This is an extension of the SIMPLEclass of algorithms (Patankar, 1980). The implicit solveruses first order-time discretization and up to third-order inspace (convective terms). The linear equations are solvedby either a Gaussian elimination or a selection fromKrylov subspace methods.Figure 2. Outline of the Q3D geometry. The walls coloredred are the external boundary to the grey colored slice.The slice averaging is however not unproblematic as wehave to reduce the model dimension from 3 to 2, still being3 Paper NoS5_Tue_D_296th International Conference on Multiphase FlICMF 2007, Leipzig, Germany, July 9 13,S5_Tue_D_29Experimental dataA large number of experimental data have been availableto the model development through the TILDA database atthe Tiller Large-Scale Multiphase Flow Facility at SINTEFPetroleum Research. In particular we have acquired owndata for 8“ and 12“ two-phase pipe flows. An optical testsection was developed that made it possible to performLDV (Laser Doppler Velocimetry) measurements andintrusive probe measurements. In several campaigns in the8” SINTEF Tiller flow loop we obtained detailedinformation about velocity profiles and droplet informationthat has been of great importance in the validation work ofthe present model.Figure3.Predictedliquidvolumefraction,flowconfiguration (LSI, shaded surface), and liquid phasevelocity vectors in a 12 inch diameter pipeline having aGas-Oil-Ratio of 100. The pipe inclination is 10 upward.ResultsThe model has initially been run on a number of cases tovalidate the performance when it comes to turbulent energy,and pressure drop in single-phase flows. We then havevalidated the performance for two-phase flows includingstratified and slug flows and low liquid loading flows witha droplet flux distribution. Results from the two-phasecases are presented and discussed below.For the Q3D model we typically apply 10 40 grid-pointsin the cross-sectional direction of a pipe. Axially wetypically use 50 to 1000 grid points, depending on the flowsituation. Much finer grids can be used, but are usuallyavoided as we wish to compute flow development overrelative long times (several minutes of real time).Figure 4. Time averaged liquid volume fraction versus pipelength. The flow is the same