Valvula tipo S

Chemical Engineering and Processing 52 (2012) 74 84

Contents lists available at SciVerse ScienceDirect

Chemical Engineering and Processing:Process Intensication

j ourna l h o me pa ge: www.elsev ier .co

Modeli s udynam

Shuo Jian g ZSchool of Chem

a r t i c l

Article history:Received 13 MReceived in reAccepted 20 NAvailable onlin

Keywords:Triangular xeCFD simulatioClear liquid heAverage gas ho

D) may. ThBasedptedried ar liqliquida.

1. Introdu

Trayed column is an important type of gasliquid contact equip-ments in chemical industry. Fixed valve tray, one of the majorresearch and industrial interest recently, draws more and moreattention as a hybrid of oating valve tray and sieved tray. How-ever, the industrial application of the xed valve tray has beenalso limitedor insufcieknown, theis of great imnamics, thepredicted fosystem prop

Nowadatool in chemmodel trayLiu et al. [8two-dimenhydrodynamdirection ofQuarini [9] hydrodynamwhich was acient was

CorresponE-mail add

s opeVan Baten [10] described the hydrodynamics of sieve trays by esti-mating a new drag coefcient correlation for the liquid hold-upon the basis of the correlation of Bennett et al. [11], which wasappropriate for a swarm of large bubbles. Because the correlationof Bennett et al. over-predicted the liquid hold-up fraction in thefroth regime, Gesit et al. [12] chose the correlation of Colwell [13]

0255-2701/$ doi:10.1016/j. to some degree due to its imperfect mechanical designnt empirical structural optimization [1,2]. As is well

description of the hydrodynamics of xed valve trayportance in industrial practice. Based on its hydrody-

separation efciency and overall performance can ber a given set of operating conditions, tray geometry anderties.ys CFD is becoming a powerful research and designical engineering. There have been many attempts to

hydrodynamics by use of CFD [36]. Yu et al. [7] and] tried to simulate the two-phase ow behavior with asional model, which focused on the description of theics of liquid phase but ignored the variations in the

gas ow along the height of the dispersion. Fischer andsimulated the three-dimensional transient gasliquidics; they assumed a constant drag coefcient of 0.44,ppropriate for uniform bubbly ow. Yet, this drag coef-not appropriate for description of the hydrodynamics

ding author. Tel.: +86 022 27891755; fax: +86 022 27891755.ress: [email protected] (J. Sun).

to predict the ow patterns and hydraulics of a commercial-scalesieve tray, which worked well in the froth regime. As a result ofthe previous researches focusing on the sieve tray with a sim-plest quasi two-dimensional structure, Li et al. [14] attempted toinvestigate the hydrodynamics of a full-open valve tray which hadmore complicated three-dimensional cubic structure for the rsttime. Their work extended the scope of application of the CFDmodel.

In this work, a three-dimensional transient CFD model wasdeveloped for hydrodynamics of a new xed valve tray withinthe two-phase Euler framework, whose three-dimensional struc-ture was shown as Fig. 1. The xed valve opening area is1.746 103 m2, and the height of valve cap was 8 mm, and prop-legs inclined to the surface of valve tray at an angle of 30 degrees.Some other dimensions of the xed valves are shown as Fig. 2,as well as the conguration of different valves. Several simula-tions were carried out with varying supercial gas velocity, weirheight and liquid strength. Finally, a simulative comparison ofcorrespondent liquid velocity components between two differentarrangements of trays, with arrays of xed valves in respectivelypositive and reverse directions, was done to study their inuenceon liquid ow near the arcuate region.

see front matter 2011 Elsevier B.V. All rights reserved.cep.2011.11.009ng xed triangular valve tray hydraulicics

g, Hong Gao, Jinsheng Sun , Yanhong Wang, Lininical Engineering and Technology, Tianjin University, Tianjin 300072, PR China

e i n f o

ay 2010vised form 3 September 2011ovember 2011e 28 November 2011

d valve traynightld-up

a b s t r a c t

A computational uid dynamics (CFhydraulics of triangular xed valve trmodeled in the Eulerian framework. correlation for liquid hold-up was adoculated. Several simulations were carconditions. Velocity distributions, clefor various combinations of gas and agreement with the experimental dat

ction of traym/locate /cep

sing computational uid

hang

odel was developed for describing the ow patterns ande gas and liquid phase, as two interpenetrating phases, were

on the clear liquid height obtained by experiments, a new, and the interphase momentum transfer source was also cal-out for a triangular xed valve tray with varying operationaluid height, froth height, and phase hold-up were predicted

ow rates, and the results were found to be in reasonable

2011 Elsevier B.V. All rights reserved.

rating in either the froth or spray regimes. Krishna and

S. Jiang et al. / Chemical Engineering and Processing 52 (2012) 74 84 75

ed val

2. Experim

The mactray, such aheight and a plexiglassimental facheight weretube (commtappings weof the tray outlet zonewell as to e

A pitot the superfrom 0.42 mby a rotam3.97 m3/(m30, 40, 50, 6

mo

odel

modorkFig. 1. Structure diagram of the x

3. CFD

3.1. M

TheframewFig. 2. The dimensions of the xed valve.

ent

roscopic hydrodynamic performances of this xed valves pressure drop, entrainment, weeping and clear liquidso on, were investigated by use of air-water system in

column with an inner diameter of 600 mm. The exper-ilities were shown in Fig. 3, and the data of clear liquid

obtained by the method of installing a static pressureunicating pipe with scale). What is more, ve pressurere mounted at different positions, including the centeroor, both sides of the column, and the liquid inlet ands, in order to obtain the average clear liquid height, asliminate the effects of liquid distribution on the tray.tube was used to measure the gas ow rate, andcial gas velocity, US, used in the experiments ranged/s to 1.04 m/s. The liquid ow rate was controlledeter, and the liquid strength, QL/W, ranged from

h) to 39.70 m3/(m h). Various heights of weir, hw, of0 mm, were, respectively, chosen in the experiments.

continuumfocusing onhas been trecontinuousomitted to port equatiare shown

t(GG) +

t(LL) +

G + L = 1

t(LLuL)

t(GGuG

Simultanphases. MGterm, and e

3.2. Closure

In orderume fractiointerphase cosities to tthe tray, thforce, virtutwo other fignored [5,MGL is

MGL = 34

C

dve tray.

del development

equations

el includes the ow of gas and liquid in the Eulerian- in which each phase is treated as interpenetrating

with separate transport equations. With the model the froth region of the xed valve tray, the gas phaseated as the disperse phase, while the liquid phase as the

one. Like other authors, energy and mass transfer arefacilitate hydrodynamic behavior research. The trans-ons of gas (subscript G) and liquid (subscript L) phaseas follows:

(GGuG) = SGL (1)

(LLuL) = SGL (2)

(3)

+ (L(LuLuL)) = (Leff,L(uL + (uL)T )) LpL + MGL + LLg (4)

) + (G(GuGuG)) = (Geff,G(uG + (uG)T )) GpG MGL + GGg (5)

eously, the same pressure eld was assumed for bothL in above equations is interphase momentum transferqual to the sum of force between two phases.

relationships to solve Eqs. (1)(5) for velocities, pressure, and vol-ns, additional equations are indispensable to relate themomentum transfer term MGL and the turbulent vis-he mean ow variables. For gasliquid bubbly ows one interphase momentum transfer term includes dragal mass force and lift force. Compared to drag force, theorces which do not affect the hydraulics greatly can be15]. To the gas as the disperse phase, the equation for

D

GGL|uG uL|(uG uL) (6)

76 S. Jiang et al. / Chemical Engineering and Processing 52 (2012) 74 84

Fig. 3. Schem e-me6experiment 9en13communi outle

where CD isFor the specbulent regias

CD =43

L

where Vslipthe liquid, a

Vslip =Us

averG

Substituting

MGL = G(

For sieve trathe gas hold

averageL

= exp[

For full operelation wa

averageL

= exp[

For this novage gas hoConsequentexperimenttray, the cleby the supenew correla

obtalable

averagL

matatic diagram of experimental apparatus: 1water pump; 2rotameter; 3wiral tray; 7gas distributor and weeping-gathered tray; 8water storage tank; cating pipe with scale; 14U-tube manometer; 15U-tube manometer; 16water

the interphase momentum transfer (drag) coefcient.ial case of rising large bubble swarms in the churn tur-me, Krishna et al. [15] estimated the drag coefcient

GL

gdG1

V2slip

(7)

tray is is avai

hcl =

The foris the slip velocity of the bubble swarm with respect tond is shown as

age (8)

Eqs. (8) and (7) into Eq. (6)

L G)g(averageG )

2

U2s|uG uL|(uG uL) (9)

y, Bennett et al. [11] proposed a correlation to estimate-up:

12.55Us(

GL G

)0.91], average

G= 1 average

L(10)

n V1 Glitsch valve tray, an appropriate gas hold-up cor-s developed by Li et al. [14]:

1.44Us(

GL G

)0.74], average

G= 1 average

L(11)

el xed valve tray, however, no correlations of the aver-ld-up fraction were proposed in previous researches.ly, a new correlation would be introduced based onal data of clear liquid height.Like sieve tray and valvear liquid height of xed valve tray is mainly inuencedrcial gas velocity, liquid weir load and weir height. If ation of clear liquid height on the triangular xed valve

lations are:

C = a1 + a2

averageL = e

Accordincorrelationfor every oues of the oSubsequentted vs. thethe 10% dried out a lovalues whi10% deviaclear liquidmined paraa3 = 120.8, result, the cas follows:

averageG = 1

Turbulenuation on thphase and dsh demister; 4entrainment-gathered tray; 5experimental tray;trainment exit; 10weeping exit; 11pitot tube; 12air blower;t; 17ow control valve.

ined, the liquid hold-up, the averageL in Eq. (14) [11,14],. The general formula is shown as follows:

e

[hw + C

(QL

averageL

)2/3](12)

s assumed for the C, weir coefcient, and averageL corre-exp [a3hw] (13)

xp

[a4Us

(G

L G

)a5](14)

g to the values of the ve parameters in Bennett et al. [11] and Li et al. correlation [14], we rst set a rangene. And then, one coefcient was tted while the val-ther four were xed on the basis of experimental data.ly, the experimental clear liquid height data was plot-

calculated values using the tted correlation withineviation chart, as shown in Fig. 4. Similarly, we car-t of attempts, and sought the most suitable parameterch enable more experimental data located within thetion lines. Taking advantage of such approach, the new

height correlation was established, and the undeter-meters (a1,. . .,a5) were conrmed, a1 = 1.18, a2 = 0.536,a4 = 10.2, a5 = 0.74. The average error was 4.7%. As aorrelation of average gas hold-up fraction was obtained

exp[

10.2Us(

GL G

)0.74](15)

ce is taken into account for the mixture phase. The sit-e tray becomes quite complicated between continuousispersed phase, since the presence of dispersed phase


Fig. 4. Calculated values of clear liquid height using new correlation comparedagainst experiment.

can affect the turbulence in the continuous phase. For k model,robustness, economy, and reasonable accuracy for a wide rangeof turbulent ows explains its popularity in industrial ow. Bir-cgers et al. for gasliqusimulation characteriststandard kin this workin the publi

3.3. Mesh g

The numaccuracy ofunstructuremany CFD been chosenvalve tray ging to Tu etexibility aregions. Theand prisms mesh intervfor those aw

Fig. 6. Figure of geometric model and boundary of simulation.

doptput

g froas baliquray [

of t in Fi

unda

modtheir

comtructientolveary cnd a,17].[16] have assessed the applicability of the k modelid ows in the bubble columns. Considering of the labconditions, the level of ow accuracy required, and theics of fully turbulent ows on the xed valve tray, the model with default model coefcients was adopted. This kind of standard k model has been well treatedshed literature [3,4,5,10,12,14,17].

eneration

ber of meshes signicantly impacts convergence and the results. Tu et al. [18] reported that the use of and mesh was more prevalent and widespreadly used inapplications. For our case, unstructured meshes have

in simulations due to the complexity of this novel xedeometry by use of pre-processor GAMBIT 2.4.6. Accord-

al. [18], the use of hybrid grids can provide maximumnd permit to allocate various cell types in complex owrefore in this work, unstructured tetrahedral volumesmeshes were applied adjacent to the vapor inlet, and theal size of 5 mm is used to obtain the detail of ow eld;ay from the tray deck, hexahedron and wedge elements

were athe comranginsize wof gasvalve tulationshown

3.4. Bo

Theuse of to savesolid sconven

To sboundaries a[10,15Fig. 5. The grid map of CFD simulatioed with mesh size 8 mm. The total number of grids inational domain was 516,983 with the element volumesm 1.61 109 m3 to 1.25 107 m3. Such choice of gridsed on the experience gained in the Eulerian modelingid bubble column [2,3], MVG tray [17] and V1 Glitsch14], where grid convergence was satised for the sim-wo-phase ow on the trays. The meshing of the tray isg. 5 as well as the whole computational domain.

ry conditions and initialization

el geometry and boundaries are shown in Fig. 6. Making observations, only half of the tray was modeled so asputational time and physical memory. In addition, theure of xed valve was simplied to face structure for

meshing. the continuity and momentum equations, appropriateonditions should be specied at all external bound-ny specic internal boundaries of the ow geometryn.


0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18h c

l /m

0 9F

Fig. 7. Transieloading factorheight hw = 0.0where u0 is ga

3.4.1. LiquiA unifor

UL,in =QL

hapL

where hap iThe liquid vassuming thance. This isentrainmen

3.4.2. Gas inThe gas i

a uniform g

UG,in =Q

NhA

The gas volu

3.4.3. LiquiThe liqui

boundariesthat only liq

Liquid o

uix

= 0k

x= 0

x= 0

L = 1; GGas outl

uiz

= 0k

z= 0

z= 0

L = 0; G0 2 4 6 8 10 12

Tray parameters averagedover this time interval

Time /s0.5 33.71 ; 19.85 ; 0.05wWLm s kg m Q L m m h h m

nt clear liquid height monitored as a function of time. Gas phase F0 = 9.71 (m/s) (kg/m3)0.5; liquid weir load QL/Lw = 19.85 m/m h; weir5 m. (It is noted that F0 is calculated by use of the formula, F0 = u0 ,s velocity through valve holes, and is gas density.)

d inletm liquid inlet velocity prole was recommended [19]:

W(16)

s the downcomer clearance and Lw is the weir length.olume fraction at the liquid inlet was taken to be unity,at only liquid entered through the downcomer clear-

a reasonable approximation, since the amount of vaport is small.

letnlet holes of the model were captured by cell faces, andas velocity was supposed:

G

hole(17)

me fraction at the inlet holes was specied to be unity.

d and gas outletd and gas outlets boundaries were specied as pressure

with volume fraction specications, and it was assumed

uid or gas could leave the ow geometry, respectively.utlet:

= 0

(18)

et:

= 1

(19)

Fig. 8. Comparison of experimental clear liquid height with results of CFD simula-tions.


Fig. 9. Snapshots of the front view y = 0 m of the simulations.

3.4.4. Wall and symmetry boundary conditionsAll walls in the ow eld were specied as no-slip wall bound-

ary, and the stand wall functions were used near wall regions. At theplane of symmetry, the normal velocity is zero and the gradients ofthe other variables in the transverse coordinate direction are takento be zero. Since the tray is symmetric in structure, only half of thetray was simfor the studet al. [12], Z

Wall:

uqi = 0kq = 0q = 0

Plane of symmetry:

uqiy

= 0

kqy

= 0

0

0

(21)

q is g

ow-

d inid a sulated. Such approach applied on the distillation traysy of gasliquid ow has been already reported by Gesitarei et al. [17] and Liu et al. [20].

(20)

qy

=

qy

=

where

3.5. Fl

Gooto avoiFig. 10. Snapshots of the top view of different heights includias phase or liquid phase.

eld initialization

tial guesses of the ow variables are important not onlyignicantly longer computational time but also in someng gas hold-up scale prole.


Fig. 11. Average gas hold-up at different elevations.

cases to avoid divergence. Air (at ambient pressure conditions) andwater were used as the gas and liquid phases respectively. At thestart of a slled with a

4. Results

A commtions of conpackage is athe cell centhe Phase CdifferencingConsideringtime incremto simulatethe simulatsteady stateheight remthe time-avwas achieveas shown in

To validaclear liquid

data. Clear liquid height is dened as the height of liquid that wouldexist on the tray in the absence of vapor ow. Using this denition,it can be calculated as the tray spacing multiplied by the volume-averaged of the liquid-volume fraction. Besides, it should be notedthat the calculation of this parameter is independent of the volumefraction constraints at the outlet conditions.

Fig. 8 compares the experimental data, the calculations of clearliquid height from CFD simulations with the correlation in thiswork.

hcl = averageL

[hw + C

(QL

averageL

)2/3]C = 1.18 + 0.536 exp[120.8hw]

averageL = exp[

10.2Us(

GL G

)0.74] (22)

It is remarkable that the clear liquid height determined fromCFD simulations does not only match the correlation quite closelybut also have the same changing trends as experimental data.The predicted clear liquid height decreases with F0 factor at givenliquid ow rate and weir height in Fig. 8A, increases with liq-uid ow at a given F0 factor and weir height in Fig. 8B and

ses with weir height at a given F0 factor and liquid ow Figmulaiquiduse in ttionelowtionight hich

. 9 tatio, thes.

10 p at d

divi. Neas phases atinuimulation, the tray conguration shown in Fig. 2 was uniform gasliquid dispersion, with 60% gas hold-up.

and discussion

ercial CFD package FLUENT was used to solve the equa-tinuity and momentum for the two-uid mixture. This

nite volume solver, and all variables are evaluated atter. The pressure-velocity coupling was obtained usingoupled SIMPLE algorithm. A fully implicit backward

scheme was used with the time step size of 0.005 s. of the accuracy required and the simulation time, suchent adopted in the simulation is appropriate enough

the gasliquid ow on the xed valve tray [12]. Duringion, the clear liquid height was monitored, and quasi-

was assumed to prevail if the value of the clear liquidained constant for a long enough period to determineeraged values of the various parameters. Steady stated approximately in 4 s after the start of the simulations,

Fig. 7.te the simulation results against the experimental data,height was computed and compared with experimental

decrearate inCFD siclear lis becalished interaceld binteracuid helines, wdegree

Fig.compushownpicture

Fig.resultscan beregiontinuoudecreaing conFig. 12. Enlarge view of liquid velocity prole. 8C. It is also important to point out that both thetions and the correlation tend to underpredict the

height, compared with the experimental data. Thisthe interphase momentum transfer term, MGL, estab-his work cannot fully reect the realistic gasliquid

on the xed valve tray. The reason lies in that the ow the valve caps is lled with gas phase without the

resulting from liquid phase. Besides, our new clear liq-correlation was established within the 10% deviation

may result in a less perfect tting accuracy to some

presents the snapshots of the front view of then results at different times. With chaotic behavior

process of quasi-steady state is described in the

resents the snapshots of the top view of the simulationifferent heights. The two-phase regime above the trayded into liquid continuous region and gas continuousr the tray deck, the gas is dispersed by the liquid, con-se, after thrusting out the xed valve. Liquid hold-ups vertical height increases while gas is gradually becom-ous phase. At the transition of the two regions, there is

at z = 2 mm.


no clear intzone of gas as well.

Fig. 11 pthe gas holhold-up couFig. 13. Snapshots of the top view of gas and liquid ow e

erface between gas and liquid phase. In addition, a deadappearing above the valve cap is revealed in the pictures

resents typical simulation results for the variation ofd-up along the height of the dispersion. The values ofld be obtained after averaging in the cross section over

a sufcientwere establat which ththis denitilayer augma given liquld at different elevations.

ly long time interval once quasi-steady state conditionsished. The height of foam layer is dened by the heighte average liquid hold-up will be below 10%. Based onon, the simulation results show that the height of foaments along with the increasing supercial gas velocity atid ow rate and weir height, and the values of 120 mm


and 160 mmlines. Besidvalve cap (8gas.

Liquid hin Figs. 12 a

Below thliquid is dravalve holes,to valve hol

In the sptop view at shown in FiAs a result,inlet to outof rising gaeasily foundin Fig. 13A.Fig. 14. Snapshots of front view of liquid phase ow eld

can easily be read by use of the additional referencees, a descent point of hold-up appears at the height of

mm) which implies the existence of dead zone of the

as diverse ow regimes at different heights, as shownnd 13.e valve caps, as presented in Fig. 12, a great amount ofgged up vertically by the upward vapor injected from

which results in the liquid nearby ows from all aroundes.ace between valve cap and top of the weir (50 mm), thea height of 20 mm above the tray deck was selected andg. 13A, where the rise and fall of liquid reach a balance.

when the liquid, with initial momentum, ows fromlet, it would bypass the valve zones due to the effects injected from valve orices. This phenomenon is also

in the simplied picture of liquid velocity component

Above thselected anthe valve horest of liquwhy the velgally from picture in F

Fig. 14 sliquid circu

The owof researchregion is bthe xed vitive layouow patteinvestigatevelocity onthat with at different elevations.

e weir height, the top view at a height of 60 mm wasd shown in Fig. 13B. It is found that only the liquid aboveles keeps the uptrend with a weakened degree, and theid ows downwards to the tray deck. This can explainocity components in the cross section all point centrifu-the tray center, which was described in the simpliedig. 13B.hows the snapshots of the front view of ow eld. Thelation cells are clearly visible in the vertical direction.

eld in arcuate region of tray is always the focuses [6,10]. A most common phenomenon during thisackow. In this work, two kinds of arrangements ofalve trays with different directions, namely the pos-t and the reverse layout, were devised. Then, therns in arcuate region of both the two trays wered. Fig. 15 shows that the x-component of liquid

the tray with reverse xed valve is greater thannormal xed valve. In addition, the values on the


e in ar

tray with backow.

5. Conclus

In this pinvestigatedtwo-phase based on thwas obtaine

The simutal counterow eld o

In the pterns in thvalves can abackow. Band weepin40% and 38under the narrangemenmore attent

Moreoveall of the sima half-tray a simpliedputational which is moeld on thetation cost computatioon the adop

s undin theFig. 15. Liquid x-direction-component velocity prol

reverse xed valve are positive, which indicate no modelfor us ions

aper, the ow hydraulics of novel xed valve tray was experimentally by means of CFD; a three-dimensionalCFD model was developed in the Eulerian frameworke experimental data. A new correlation of gas hold-upd.lation results, in good agreement with the experimen-

parts, exhibit some known features of the two-phasen trays.resent work, the simulative investigation on ow pat-e arcuate regions reveals that reverse arranged xedccelerate the liquid ow in arcuate region and restrainesides, on basis of experimental data, the entrainmentg of the reverse arranged xed valve tray decrease by% respectively, yet the pressure drop increases by 8.2%ormal operating conditions compared to the positivet [21]. In general, this reverse one is deserved to attractions for eld application.r, there is one signicant point needed to mention thatulations involved in this work were completed under

situation with an ifthen symmetric condition. This is approach to save simulative time under limited com-ability by virtue of the previous published researches,re or less inappropriate for such actual turbulent ow

full xed valve tray. It is well known that the compu-will be reduced dramatically along with the increasednal power. In the light of these considerations, the studytion and comparison of different kinds of turbulence

Appendix A

NotationsAhole ara1,. . .a5 paCD drC wdG diF0 gag achap dohcl clhw wk tuLW wM inNh nup prQG gaQL liqt timu veUS suVslip slx coy coz cocuate region, y = 0.25 m.

er a full-tray condition will be greatly concentrated on following research.. Nomenclature

ea of hole (m2)rameters used in Eqs. (13) and (14)ag coefcient, dimensionlesseir coefcientameter of gas bubble (m)s phase loading factor ((m/s) (kg/m3)0.5)celeration due to gravity (9.81 m/s2)wncomer clearance (m)ear liquid height (m)eir height (m)rbulent kinetic energy (m2/s2)eir length (m)terphase momentum exchange term (N/m3)mber of holesessure (N/m2)s ow rare across tray (m3/s)uid ow rare across tray (m3/s)e (s)

locity vector (m/s)percial gas velocity (m/s2)ip velocity between gas and liquid (m/s)ordinate (m)ordinate (m)ordinate (m)


Greek letters volume fraction of phase, dimensionless turbulent dissipation rate (m2/s3) viscosity of phase (Pa s) density of phases (kg/m3)

Subscriptscl clear liquideff effectiveG referring to gas phaseG,in gas inletL referring to liquid phaseL,in liquid inletq gas/liquid phaseslip slip

Superscriptaverage average

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Modeling fixed triangular valve tray hydraulics using computational fluid dynamics1 Introduction2 Experiment3 CFD model development3.1 Model equations3.2 Closure relationships3.3 Mesh generation3.4 Boundary conditions and initialization3.4.1 Liquid inlet3.4.2 Gas inlet3.4.3 Liquid and gas outlet3.4.4 Wall and symmetry boundary conditions

3.5 Flow-field initialization

4 Results and discussion5 ConclusionsAppendix A NomenclatureReferences

Valvula tipo S

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