Stability of stratified flow and slugging in horizontal gas-liquid flow Stability of stratified flow and slugging in horizontal gas-liquid flow

Stability of stratified flow and slugging in horizontal gas-liquid flow

  • 期刊名字:自然科学进展(英文版)
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  • 论文作者:GU Hanyang,GUO Liejin
  • 作者单位:State Key Laboratory of Multiphase Flow in Power Engineering
  • 更新时间:2020-09-15
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论文简介

PROGRESS IN NATURAL SCIENCEVol. 15, No. 11, November 2005Stability of stratified flow and slugging inhorizontal gas-liquid flowGU Hanyang and GUo LiejinState Key Laboratory of Multiphase Flow in Power Engineering, Xi an Jiaotong University, Xi'an 710049, China)Received February 1, 2005; revised March 28, 2005Abstract A transient one-dimensional two-fluid model is proposed to investigate numerically the interfacial instability and the onsetlugging for liquid-gas flow in a horizontal duct. In the present model, the effects of surface tension and transverse variations in dynamipressure are taken into account. The evolution of interfacial disturbances is displayed and compared with the linear viscous KelyHelmholtz stability analyses. It shows that interfacial wave is more instable due to the non-linear effect. The model predicts well the stability limit of stratified flow in comparison with the experimental data, and also automatically tracks the onset of slugging. The results showthat the initiation of hydrodynamic slugging is related to local interfacial instability. Based on the cycle of slugging, a model for slug fre-quency is presented, which predicts the trends of slug frequencies with gas/liquid flow rate well in comparison with the available data. Thepropertslugging have been examined. It is found that with the increase in the gas viscosity and liquid density theslugging would be inhibited, whereas, with the increase in liquid viscosity and gas density the slugging can be promotedKeywords: two-fluid model, Kelvin-Helmholtz stability, interfacial instability, onset of slugging, gas-liquid stratified flowGas and liquid flowing in a horizontal pipe as- rate results than the previous inviscous theories. Thesumes a number of interfacial configurations. The effects of viscosity in their models were introducedprediction of the type of flow, which will exist, is of through empirical wall and interfacial fraction correcentral importance]lug flow is the predominant tions. But all these authors neglected the normal comflow type for horizontal gas-liquid flow. Slugging in a ponent of viscous stress. They] considered the inhorizontal pipe is, for most applications, an undesir- terfacial instability and the onset of slugging as able phenomenon, so transition from stratified flow to long-wave phenomenon, so surface tension was neslug flow is of particular interest to design and opera- glected in their analysis. Some other investigation of gas and oil pipelines. Various mechanisms for tors[3, 10, however, noticed that slugs were observedthe transition have been proposed 2, however, the to form by a different mechanism from that suggestedproblem remains open. Generally, the instability of waves by VKH theory. Indeed, at a low gas flow rate, theon the gas-liquid interface in the stratified flow is consid- interfacial stability and the initiation of slug wereered as the basic mechanism of the onset of slugging 1Jcaused by a short wave instead of an infinitely longwave. Recently Funada and Joseph l proved thatMany investigators have presented a series of the effect of surface tension was always important andtheoretical studies of the stability of stratified flowdetermined the stability limits for the cases in whichTo our knowledge there is no other theoretical study the volume fraction of gas was not too smallwithout approximations. Viscosity was neglected bKordyban and Rano 3, Wallis and Dobson.43,andBased on the linear analysis, physical interpretaMishima and Ishi 53. Taitel and Duckler6) used a tion for the various unstable regions is suggested. Butcorrection factor in order to take into account the use the linear analysis does not provide information as toof finite waves in their analysis, but still their criteri- the evolution of the interface up to the point of transion was derived by the inviscid fluid theory. Lin and tion中国煤化工HarratBarnea and taiteltionCNMHGS IS Somewhat speculaed viscous K-H analysis using one or other form of tiy et al. llrsuy carried out the non-linone-dimeinclud- ear stability analysis using the method of characteris-ing the effect of shear stress, and showed more accutic. Following, Barnea and Taitel 13], Guo et al. [141四2燃据Natural Science Foon of China( grant No. 50323001)dence should be addressed. E-mail: Ii-guoa mail. xjtu. edu.cnProgressinNaturalScienceVol.15No.112005www.tandf.co.uk/journals1027used a similar technique to examine the system reIn the present work, a full transient one-dimensponse to the finite disturbances of the interface. The sional two-fluid model is used to investigate the internon-linear stability analysis gave an insight into the facial instability and the onset of slugging in horizongrowth and propagation of the interfacial disturbances tal gas-liquid two-phase flow, which takes into acon the interface. The authors employed a simplified count the transverse variations in dynamic pressuretransient form of two-fluid model to make the system surface tension on the interface and phase viscositystrictly hyperbolic as the method of characteristic re- The evolution of finite disturbance on interface is dis-quired. An alternative approach is to numerically played. The result of the non-linear stability analysissolve the complete one-dimensional two-fluid model, is compared with linear theory as well as the experiwhich does not bear any theoretical limitation since it mental data. The onset of slugging is automaticallyis normally based on a direct numerical integration, in tracked by the code and a model of slug frequencyboth space and time, of the full governing equations. presented The effects of physical properties on slug-Ansari 15, 1b. firstly numerically investigated the inter- ging are quantitatively examinedfacial instability and slugging using finite differencemethod. Remarkably in his study, the small random 1 Model descriptionperturbations of short wavelengths arising naturally 1.1 Field equationsmay grow into larger and longer waves on the surfaceof liquid and subsequently, develop into slug. So theConsider a one-dimensionalt stratifiedtransient two-fluid model can automatically track thetwo-phase flow as the one shownFor simof the surface tension and viscosity and a simple hy- plicity, we introduce the followingtionsdrostatic approximation was assumed to the interfacialpressure difference term in his calculation. In order to while the liquid phase is assumed to be impressible 3(i) Gas phase concerned is assumed as ideal gasmatch the experiments growth rate of smallwavemoment and location of the slug initiation etc.(ii) no mass transfer between two phasessome terms, which modify small wave growths, juas Ansari 15)suggested, might have to be added(ii) no heat transfer between two phasesPie (z)士-2g92492Fig. 1. Configuration of gas-liquid two-phase floThe one-dimensional transient two-fluid model isMomentum equationsformulated by considering each phase separately interms of cross section averaged equations governingthe balance of mass and momentum of each phase asPfollows:ax gtA8AContinuity equations中国煤化工a(agog) a(, Ug)THCNMHGa(aro,) a(ap,U)a(, P,)a,+where u ised velocity(m/s)(4)the ph存on,p the deusity(kg/m)1028www.tandf.co.uk/journalsprOgressinNaturalScienceVol.15No.112005a+ag=1.0.(5)o pressure p,()can be expressed byThe subscripts g, l and i refer to the gas, liquidphases, and the interface, respectively. Where S is(y)=pig(ht-)+puy=S(.,v)dywetted perimeter (m), a the cross-sectional area(10)(m2), Pil and pig respectively denote the liquid and withgas interfacial pressure, Pl, Pg are cross-sectional avUt t uvt + v1(tween each phase and the wall, and between thephases themselves (at the interface)Hence the integral of ar-p (y) in pressure term of the1.2 Closure relationliquid phase yieldsliquid-wall, gas-wall and interfacial shear forces in the 0 arp, (y)b(y)dyIt needs closure relations for pressure terms, themodel. Viscous stress of gas over liquid is much lessg ab(y)dimportant than that of liquid, and the adoption of hydrostatic approximation in gas phase could be justifiedin aIo we can express the pressure terms ofthe gas phase by?(z, y)dy b(y)dykg- ag apigV=0.y=y(6) The first term on the right-hand side of(12)correwhere g is gravitational acceleration (m/s2), h the sponds to the hydrostatic term and can be taken asfilm thickness (m)h, ahlb(y)dy= pAl a-g. (13)Most previous investigators employed hydrostatic The other two terms on the right side contain thapproximation to evaluate the pressure terms of the contribution of the transient transverse accelerationliquid phase for the simplicity. Liu[ 17 and Funada terms. Following the approximations presented byand Joseph ll proved that the effect of the transverse the Banerjeel lsI yieldsplayed an important role in the interfacial wave prop(z,h)b(y)dyagation of the two-fluid model. The transverse variation in dyrof the liquid phase is take+U1(x)2(h)(14)into account in the present study. The cross-averagedancpressure is defined aso(z,y)dy o(y)dpi(y)b(y)dy/A(7)Introducing P, (y) as p/(y)=Pil+ p, (y), the presyb(y)dsure term of the liquid phase, using Leibniz rule ofthe derivation, can be taken as+U.-201-23O(15)And the integral term on the right side of (15) is rey=h1 ap, (y)b(y)dy.(8)Using the local momentum balance in the y-directionH中国煤化工C MH Proximation to expressthe difference of liquid and gas interfacial pressurev,+terms and end up with one pressure variable:OPIple '+oO(9)(16)where v数擗y(Ps), t the time(sThe shear stress t for one-dimensional flow is calcuProgressinNaturalScienceVol.15No.112005www.tandf.co.uk/journals1029lated by the following formulawhere D, and D, are hydraulic diameters evaluated infp I Ur I(17)the following manner4A4Awhere the term U stands for the relative velocity be(19)tween the liquid and the wall, the gas and the wall, CI=Cg=Ci=0.46 for turbulent flow and 16 for lamor the liquid and gas.nar one, n=mm=k=0.2 for turbulent flow and 1.0for laminar oneThe liquid and gas friction factors are evaluated2 Numerical solution procedureD,The transport Eq (1)-(5)are solved numerically. The staged grid mesh is chosen to discretize thefgequations where the scalar variables and the pressureare stored at the center of the"continuity control volDn(U。-U1)f(18) umes"and the phase velocities are stored at the facof the scalar control volumes, as illustrated in Fig. 2J-1/2J1/2ig. 2. Typical staggered grids for a pipe sectionThe finite-volume approach is used to integrate 0. 101 MPa at the outlet. The model described is imthe differential transport equations over the length of plemented as a fortran computer codethe control volumes and over time to yield a set of linear algebraic equations, where a full upwind differ- 3 Results and discussionence scheme(UDS) is invoked for the spatial deriva3. 1 Interfacial instabilittives and the Euler implicit scheme is used for thetemporal integration. Although UDs is a first orderThe two- fluid model has been extensively testedscheme in space and may often be less accurate than and validated against data. The results presentohigher order schemes, it eliminates the sources of in- this section include both predictions of dynamic re-stabilities associated with those higher order schemessponses to perturbation on the interface and of the onThe inaccuracy in the solution that results from UDSt-of-instability conditions. In addition, the resultsis removed by successive grid refinement typically of analysis are given concerning comparisons between△x/D≈0.3 is found to be sufficient). The piso althe present numerical results and linear theoriesgorithm is used to solve the system of discretised e-quations at each time step. Once convergence isFigs. 3 and 4 show the propagation of wave onachieved for a given step, a new time increment is gas-liquid two-phase flow interface within a horizontalcalculated based on the dimensionless number 0. 0508 m ID pipe with various liquid flow ratesAt/Ax=c, where the constant c is typically Small perturbations are introduaset at 0. 5. It implies that as the Ug, max increases, thecontinuous sine wave in phase fraction at inlet Aa0.00lsin(t) from initiation. Fig 3 shows that thetime step size is correspondingly reduced to catch the中国煤化工 ance grows as an expowavenentCNMHGbefore 60s at the suconditions are needed. In the present work, the ne y perfacial liquid velocity ji=0.4To complete the numerical model, boundarNeverthelessas the amplitude of the interfacial wave is increasingmass rates for the gas and liquid phases are specified the growth becomes non-linear and the wave front bewhile, at the outlet, zero gradients for the phase ve- comes very sharp. The physical interpretation of thiswww.tandf.co.uk/journalsprOgressinNaturalScienceVol.15No.112005sure generated over the wave due to the bernoulli ef- stable. Actually, some authors previously mademore significantheuristic adjustment for nonlinear effects on linearmately overcomes the stabilizing influence of gravity. analysis by multiplying the critical value of velocity byFig 4 shows that the perturbation decays exponen- a coefficient less than 1.0 to fit experimental datially without evident non-linear phenomenon display- tal6, 11, howbeit it lacks a convincing foundationing at Ji=0.1 m/s1010000.90100750Pressure100500K-H solutionNumerical solution2st=4st=6s‖t=8s06501.53.04.56.0759.024681012Distance along pipe(m)Distance along pipe(m)Fig. 3. Growth of disturbance in space with time (jk=4. 0 m/s,i=0.4m/s)0.395Incompressible gasCompressible gas/=6.7s弓0.380WH0.3750.3700365Distance along pipe(m)6810121416Distance along pipe(m)6. Effect of compressibility on interfacial waveFig. 4. Decay of disturbance in space (jg=4.0m/sTheoretical prediction for the transition fromstratified flow to either slug or annular flow has beenIt is widely acknowledged that nonlinear effects presented by several investigators[6,9,11on the transition from stratified to slug flow are not different assumptions and predicted different stabilitywell understood. Fig. 5 compares the growth rate p limits. In the present study, the numerical calculain space at t=80s predicted by the present numeri- tion yields a transition from a negative to a positivecal calculation with that predicted by linear K-H anal- value of growth rate B, for a constant gas flowrateysis at high superfacial liquid velocity ji=0. 4and at increasing liquid flowrate. We assume that theThe present numerical results vary along the pipe and stratified to non-stratified flow regime transition oc-increase sharply from 7. 5 m downstream to entrance curs when value of growth rate B is zero. Fig. 7comfor the suction effect due to the bernoulli effect, as pares the numerical prediction with the experimentalshown the corresponding interfacial pressure profile, data for air-oil flow in a horizontal pipe with 0. 0508there appears a sharp decrease in interfacial pressureThe identified flow patterns are smoothon wave crest. Moreover, when compressibility of straflow(SS), wavy stratified flow ( SWthe gas is included in the calculation, interfacial wave premature slug flow (PSL, slug flow(SL)and an-grows more readily as shown in Fig. 6. Hence, it isnulimportant to take into account the gas compressibility preseVL中国煤化工, aitel and dublereffect for accurate prediction of interfacial waveCNMHGereafter called bT, TDand FJ respectivelyThe interfacial wave obtained by linear analysis lower when compared with the present numericalig. 7 shows that the TD criteria under-predicth是Rflowrate. So we can conclude that the stability limit when compared with the experits make interfacial wave more in- mental data indicated. Evidently, the F] criterionProgressinNaturalScienceVol.15No.112005www.tandf.co.uk/journals1031fails to predict the instability threshold for the experimental data for j, <4 m/s, which may be due to theshear stress in F] analysis ignored. However, when06FJ critical velocity is multiplied by the TD heuristicPredictionfor-896°correction factor a, the adjusted curve almost over04}∴、-- Predictionfor 8=892laps the bt one for j <4 m/s, and most SL point0.2are above the new curve. But this approach does notaccount for premature slugging due to bifurcationphenomenon, which is intrinsically a non-linear effectj, (m/s)and is not predicted by linear analysis. The stabilitycurve by the present numerical prediction successfullyxperimental vs. calculated transition of stratified to non-stratified flow for downward inclined air/water, D=0.05 mpredicts the instability threshold for j <4 m/s anddrops sharply around jk=5m/s as Fj does. The jk=In the calculations, we take steady air-water5 m/s limit coincides with experimental observastratified-flow in horizontal pipe with 0.0763 m ID astion 19, 20. This reasonable prediction may be due to an initial state. Fig. 9 shows that the wave generatedtaking into account the transverse variations in dy- from interface is captured and the initiation of slugnamic pressure. But it should be noted that the pre- (or slugging) is tracked at different instants undersent model is relative mathematical complexity and /1=0.5m/s, /g=6.5 m/s. It is emphasized that incomputattime-consuming when used to predictthe calculation, interfacial wave and slugging initiatestabilityautomatically and no perturbations need to be introduced artificially. As shown in Fig 9(a) small random perturbations of small amplitudes arise naturallyfrom the interface firstly. Some local waves indicatedBa ANby SI and S2 grow sharply in amplitude by picking upthe liquid flowing ahead of theem, util t=1. 34 s, S10.01 PResent mbridges the pipe cross-section, thereby forms a prelE-ITrDjmature slug and continues to grow due to high liquidlevel downstream. So slugging is thus suggested to bethe result of local interfacial wave instability.Fig. 7. Experimental vs. calculated transition of stratified to non-When SI forms a slug, there is a suddenincreasestratified flow for horizontal air/oil, D=0. 0508 mof the interfacial pressure upstream and a calming ofthe liquid interface behind the slug as illustratedExperiments were carried out in a 0.05 m ID Fig 9( b). The interface behind the slug becomesflow loop facility with 20 m in length in the State Keysmooth for the relative velocity between liquid and gasLaboratory of Multiphase Flow at Xi'an Jiaotong Udecreases due to the slugging. This phenomenon hasniversity. The interfacial profiles along the pipe were been confirmed by an experimental observation[2]The wave indicated by S2 immediately behind themeasured using tow-parallel conductance probes. slug decays soon because it is propagating over a thFig. 8 compares the experimental and calculated transition of stratified to non-stratified flow for downwarder layer and there is no enough liquid to supply itsclinedater two-phase flow. It shows that thestability and growth as shown in Fig 9(cd).Asnodel can predict the transition well when comparedslug propagates down the pipe, the liquid in the stratwith the experimental daified flow is swept up and the liquid level in the pipeug as shown In3.2 SluggingFi中国煤化工CNMHGVarious mechanisms for initiation of slug in the 3. 3 Slug frequencygas-liquid flow have been proposed by woods, butthe problem remains open. In this section, the initiaThe prediction of slug frequency has importanttion of slug (or slusignificance on gas-liquid two-phase flow. Slug frequency is relevant to the onset of slugging Taitel and1032www.tandf.co.uk/journalsprOgressinNaturalScienceVol.15No.11200506162sl0.6l20.6040602Distance along pipe(m)Distance along pipe(m)(a)t=0.74sb)t=1.3481.088760.4Distance along pipe(Distance along pipe(m)(c)t=1.38s(d)t=1.45sFig. 9. Growth of interfacial wave and subsequent slug formation in the air- water pipe flowDukler-21 proposed that the cycle time of slug forma- Fig. 10 with the results calculated according totion at entrance is equal to the inverse frequencEg.(20). The agreement appears satisfactory bothBased on the work of Mishima and Ishi 5 Tron- qualitatively and quantitatively if Cs is set to beconi<]assumed that each interfacial wave generates a 0.47. The mean deviation is less than 10%. Theslug but only half of the slugs survives as single enti- predicted slug frequencies increase with increasing lities while traveling downstream. But the studies car- uid flowrate and exhibit a characteristic minimum andried by Woods and Hanratty] did not support the maximum with increasing gas flowrate for high liquidproposals by Taitel and Dukler and by tronconi. Reflowrate and low liquid flowrate, respectivelycently, on the basis of interfacial wave instability and Fig 11 compares the prediction by Eg.(20)withequilibrium interface theory, Liu-243 formulated slug Cs=0. 47 with the experimental data obtained for arequency as0. 05 m ID horizontal pipe. It displays that the slug=Cs/(t1+t2),(19)frequency model can predict the experimental datawhere ti is time of generation of interfacial wave, t2 well. So we can conclude that Cs=0.47 is appropriis the time that the interfacial wave spent on growing ate for different pipe diametersto bridge the flow conduit. Therefore, ti+ t2 is justthe cycle of slug initiation. Cs is the correlation coef-The dependence of slug frequency on fluid prop-ficient between the frequency of an initial slug and the erties is inspected at fixed flow rates (j=0.5 m/sactual frequency of a fully developed slug. In this jg=6. 5 m/s). Slug frequencies calculated for fourstudy, the period of time for slug formation from different gas density values are shown in Fig. 12.Itsmooth interface can be directly obtained as previoushows that slug frequency increases with increasingsection described. So if we define t3 as the time ofriNerslug initiation from steady state in the inlet region of cord中国煤化工 al calculation, for highthe pipe, following Liu+, we can formmulate slug erCNMH G interface is charaquency asized by waves transporting liquid too efficiently to(20) form high layers, and the formation of shorter(inoods and Hanratty 23] obtained slug frequency data tial) slugs (or larger slug frequency ) The effect offor air and water in a 0. 0763 m ID horizontal pipe us- liquid density on slug initiation and frequency is justIng two-res.These data are comparedopposite as shown in Fig. 13. However, the depenProgressinNaturalScienceVol.15No.112005www.tandf.co.uk/journals1033dency of slug parameter on phase densities is modestL_onsct of slugging(m)compared with that of phase viscosityugH).102Figs 14 and 15, an increase in liquid viscosity, slug0.40initials more readily, while an increase in gas viscosityresults in slugging delayed. Recently rosa et al. [25]0.381935displayed this trend when experimentally inspectingviscosity effect in horizontal slug flows. This trendresults from the higher equilibrium level of the stratified flow near the entry when50300450600750900105032viscosity or decreasing the gas viscosity, according tothe present numerical calculationFig. 13. Dependence of slug frequency and slugging location onliquid derExperiment1.2m!s301--L_onset of slugging(m)8·j,=06m/sFrequency of slug(hz0325‘=0.16m/s官26Prediction1,2m/=0.6m/s2,20.250=0.16m/s200.010.200Ji(m/s)Gas viscosity(X 10 Pa-s)Fig. 10. Experimental vs. calculated values of slug frequency forFig, 14. Dependence of slug frequency and slugging locationExperiment:2. o-Frognset of slugging(m)10.4752.10.6m/Prediction:1.2m!s0.3501.01.52.02.53.03.5404.554681012Liquid viscosity(X10'PasFig. 15. Dependence of slug frequslugging looFig. 11. Experimental vs. calculated values of slug frequency for4 Conclusion2.00r-L_onset of shuggging()10.40a transient one-dimensional two-fluid modelcounting for the transverse variations in dynamicpressure and surface tension is developed and imple0.36pproach. This中国煤化工 h of instabilCN MH Gated interfacial wave0.321.241.61.82.02.22more instable due to non-linear effects in comparisonGas density (kg/m)with analytic solutions from linear stability analysesThe transition from stratified to non-stratified flows isFig. 12. Dependence of slug frequency and slugging location onpredicted quite well in comparison with the availablegas densitdatwww.tandf.co.uk/journalsprOgressinNaturalScienceVol.15No.112005Furthermore, a code is developed in this work II Funada T. and Joseph D D. Viscous potential flow analysis ofthat is able to automatically capture the waves andKelvin- Helmholtz instability in a channel. Int. J. Multiphasetrack their subsequent development into slugs, or onFlow,2001,28(9):263—28312 Crowley C.J., Wallis G. B. and arry JJ. Validation of a one-di-set of slugging. The numerous computations demonmensional wave model for the strartified-to-slug flow regime transi.strate that the onset of slugging may be owing to localtion, with consequences for wave growth and slug frequency. Intinterfacial wave instability. A model is put forwardJ. Multiphase Flow,1992,18(2):249271predict slug frequency on the cycle of slugging. When13 Barnea D. and Yehuda T. Non-linear interfacial instability of separated flow. Chemical Engineering Science, 1994, 49(14)we take the constant Cs as 0. 47, the slug frequenciespredicted by the model accord well with the available 14 Guo L.J., Li G J and Chen X.J. A linear and non-linear analysisinterfacial instability of gas-liquid two-phase flow through a cirular pipe. International Journal of Hear and Mass Transfer, 2002The effects of physical properties of fluids45(7):1525-1534gging are also examined. with an increase in liquid15 Ansari M. R. Dynamical behavior of slug initiation generated byshort waves in two-phase air-water stratified flow. In: Proceedingsviscosity and gas density slug initials more readilof the 1998 ASME International Mechanical Engineering Congresswhile an increase in gas viscosity and liquid densityand Exposition, Anaheim, CA, USA, Nov 15-20, 1998sults in slugging dela28929516 Ansari M. R. Numerical analysis for slugging of steam-water stratiReferencesfied two-phase flow in horizontal duct. Fluid dynamics Research1998,22(6):329344I Hanratty T J, Woods B D, Ilias Iliopoulos et al. The roles of17 Liu w.S. Stability of interfacial waves in two-phase flows. Ininterfacial stability and particle dynamic in multiphase flows: a per-Proceedings of the 1995 16th Annual Conference of the Canadiannal viewpoint. Int. J. Multiphase Flow, 2000, 26(2)muclear Society, Saskatoon, Canada, Jun 4-7, 1995,1-17169-190.18 Banerjee S. Separated flow models Il: Higher order dispersion ef-2 Fan Z, Lusseyran F. and Hanratty. T J. Initiation of slugs infects in the averaged formulation. Int. Journal multiFleorizontal gas-liquid fleAIChE J.,1993,39(11)1741-175319 Mata C., Perayra E, Trallero J. L. et al. Stability of stratified3 Kordyban E. S and Rano T. Mechanism of slug formation in hor-gas-liquid flow. Int. J. Multiphase Flow, 2002, 28(8)izontal two-phase flow. Trans. ASME J. Basic, 1970, 92(41249-1268857-86420 Andritsos N, Williams L. and Hanratty T J. Effect of liquid vis-4 Wallis G. B. and Dobson J E. The onset of slugging in horizontsity on stratified/slug transitions in horizontal pipe flow. Int, Jstratified air-water flow. Int. J. Multiphase Flow, 1973,1(1)Multiphase Flow, 1989, 15(6):877-892173-19321 Taitel Y, and Dukler A. E. A model for slug frequency during gas-5 Mishima K. and Ishii M. Theoretical prediction of onset of hori-iquid flow in horizontal and near horizontal pipes. Int. J. Multizontal slug flow. Trans. ASME J. Fluids Eng, 1980, 102(4)phase Flow,1977,3(6):585-596441-44522 Troniconi E. Predicton of slug frequency in horizontal two-phase6 Taitel Y. and Dukler A. E. A model for predicting flow regimelug flow. AIChe J.,1990,36(5):701-909horizontal and near horizontal gas-liquid flow. AIChE 23 Woods B D. and Hanratty T.J. Influence of Froude number onphysical processes determining frequency of slugging in horizontal7 Lin P.Y. and Hanratty T. J. Prediction of the initiation of slugsgas-liquid flows. IntMultiphase Flow, 2003, 29(3with linear stability theory, Int. J, Multiphase Flow, 19861195-12234 Liu L. A hydrodynamic model for slug frequency in horizontal gas-8 Barnea D. On the effect of viscosity on stability of stratified gas-ligid two-phase flow. Chinese J. Chem. Eng, 2003,11(5)uid flow application to flow pattern transition at various pipe incli508-514ations.Chem.Eng.Sci.,1991,46(8):2123213125 Rosa E.S. and Fagundes J. R. Viscosity effect and flow develop9 Barnea D. and Taitel Y. Kelvin-Helmholtz stability criteria fornent in horizontal slugIn: 5th International Conference onstratified flow: viscous versus non-viscous( inviscid approachesMultiphase Flow, Yokohama, Japan, May 30-Jun 4, 2004Int. J. Multiphase Flow, 1993, 19(4): 639-649203-21410 Woods B D. Slug formation and frequency of slugging in gas-liquidflows. Ph. D. thesis, University of Illinois, Urbana, 1995中国煤化工CNMHG

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