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Chemical Engineering and Processing 48 (2009) 145–151

Contents lists available at ScienceDirect

Chemical Engineering and Processing:Process Intensification

journa l homepage: www.e lsev ier .com/ locate /cep

FD simulation of hydrodynamics of valve tray

in Gang Lia,b, De Xin Liuc,d, Shi Min Xua,b,∗, Hong Lia

School of Chemical Engineering and Technology, TianJin University, Tianjin 300072, ChinaNational Engineering Research Center for Distillation Technology, TianJin University, Tianjin 300072, ChinaChina Textile Industrial Engineering Institute, Beijing 100037, ChinaChina Textile and Chemical Fiber Engineering CORP., Beijing 100037, China

r t i c l e i n f o

rticle history:eceived 25 April 2007eceived in revised form 18 February 2008

a b s t r a c t

A transient computational fluid dynamics (CFD) model was developed to predict the hydraulics of a fullopen valve tray. The model studied the three-dimensional two-phase flow of gas and liquid in the Eule-rian framework. Based on the clear liquid height measured on a full open valve tray, a new correlation

ccepted 1 March 2008vailable online 15 March 2008

eywords:omputational fluid dynamics (CFD)alve tray

of liquid hold-up was developed, and the interphase momentum transfer term was calculated. Severalsimulations were carried out for a rectangular full open valve tray with varying characters of system. TheCFD simulations reflect chaotic tray hydrodynamics. The predicted results were in good agreement withthe experimental data.

© 2008 Elsevier B.V. All rights reserved.

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dvphmtQgociKhcc

iquid hold-uplear liquid height

. Introduction

The valve trays are widely used as phase-contacting devicesn distillation, absorption columns. The description of the hydro-ynamics of valve trays is of great importance in industrialractice. Based on the hydrodynamics of valve trays, the sepa-ation efficiency and overall tray performance will be predicted,or a given set of operating conditions, tray geometry and sys-em properties. Hydrodynamics of valve trays was reported by

any open literatures [1–5]. In general, published literature corre-ations for tray hydrodynamics were largely empirical. An impassehat hindered the further improvement of these devises is theoor understanding of the complex behaviors of the two-phaseows and operating conditions inside the tray for given geome-ry.

In recent years, there are considerable academic and industrialnterests in the use of computational fluid dynamics (CFD) to modelwo-phase flows in some chemical engineering equipments. Theolume-of-fluid (VOF) technique can be used for a prior determi-

ation of multiphase flow on structure packing. Szulczewska et al.6] simulated gas–liquid counter-current flow in a plate-type struc-ured packing. Gu et al. [7] developed a two-phase flow CFD modelsing the VOF method to predict the hydrodynamics of falling film

∗ Corresponding author at: School of Chemical Engineering and Technology, Tian-in University, Tianjin 300072, China. Tel.: +86 22 27404701; fax: +86 22 27404705.

E-mail address: xusm2002@163.com (S.M. Xu).

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iud

255-2701/$ – see front matter © 2008 Elsevier B.V. All rights reserved.oi:10.1016/j.cep.2008.03.001

ow on structured packing. Ataki et al. [8] simulated the liquid flowtructure on a structured packing element and liquid redistributiont the node of structure packing with the VOF model.

There are many attempts so far to simulate sieve tray hydro-ynamics using CFD. Yu et al. [9] and Liu et al. [10] ignored theariations in the direction of gas flow along the height of the dis-ersion to simulate the two-phase flow behavior, and only theydrodynamics of the liquid flow was obtained. The interphaseomentum exchange (drag) coefficient was required to model

he hydrodynamics of multiphase flow on sieve tray. Fischer anduarini [11] attempted to describe the three-dimensional transientas–liquid hydrodynamics, by assuming a constant drag coefficientf 0.44, which was appropriate for uniform bubbly flow. This dragoefficient was not appropriate for description of the hydrodynam-cs of sieve trays operating in either the froth or spray regimes.rishna et al. [12] and van Batten and Krishna [13] described theydrodynamics of sieve trays by estimating a new drag coeffi-ient correlation for a swarm of large bubbles on the basis of theorrelation of Bennett et al. [14] for the liquid hold-up. Becausehe correlation of Bennett et al. over-predicted the liquid hold-upraction in froth regime, Gesit et al. [15] used the liquid hold-uporrelation of Colwell [16], which worked well in the froth regime,o predict the flow patterns and hydraulics of a commercial-scale

ieve tray.

At present, CFD is becoming a powerful research and design tooln chemical engineering. But there are not any reports about sim-lating the hydrodynamics of valve trays by using CFD. The majorifficulty for this is that valve floats as valve hole gas velocity chang-

1 ing and Processing 48 (2009) 145–151

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46 X.G. Li et al. / Chemical Engineer

ng. When the velocity of gas passing through the valve hole is largerhan a certain value-the critical valve hole velocity, the valve is fullpen. It means that valve lifts with the maximum extent and itoes not float. In this condition, CFD can be used to simulate theydrodynamics of valve trays.

In this paper, a three-dimensional transient CFD model waseveloped within the two-phase Euler framework for hydrodynam-

cs of a rectangular full open valve tray. For the rise of a swarm ofarge bubbles in the gas–liquid bubbly flow on full open valve tray,n appropriate liquid hold-up correlation was required to calculatehe interphase momentum exchange coefficient by correlation ofrishna et al. Therefore, at first, a new correlation of liquid hold-upf full open valve tray was developed based on the experimentallear liquid height. Then, simulations were carried out with vary-ng superficial gas velocity, liquid weir loads and weir heights whenalves are full open. The objective of this work was to examine thextent to which CFD models can be used as an investigative andesign tool in industrial practice.

. Experimental

The experimental set-up was shown in Fig. 1, and a big hole sieveray (12) was installed to confirm gas uniform distribution. Thealve tray geometry used in the experiments was shown in Fig. 2,nd there were 14 standard V1 Glitsch valves (diameter = 48 mm,ole diameter = 38 mm, triangular pitch = 100 mm, lift = 8 mm and

ractional hole area on tray = 0.067).A calibrated Pitot tube (10) was used to measure the gas flow

ate, and the superficial gas velocity, Us, used in the experimentsanged from 0.65 to 1.1 m/s to ensure valve full open. The liq-id flow rate was controlled by a calibrated liquid flowmeter (4),nd the liquid loads per weir length, QL/W, ranged from 0.0032 to.0039 m3/(s m). Various weir height, hW of 40, 50, 60 mm weresed in the experiments.

To measure the clear liquid height, hcl, the liquid on the trayas allowed to drain to the tray beneath. For the air–water sys-

em used in the experiments, the clear liquid height was deductedynamic head measured at five different positions. One limb of

ig. 1. Simplified diagram of the experimental set-up to measure hydrodynamicsf rectangular valve tray. 1, valve tray; 2, storage tank for liquid; 3, liquid pump; 4,iquid flowmeter; 5, downcomer; 6, weir (exchangeable); 7, liquid filled stainlessube; 8, liquid outlet; 9, gas supply; 10, Pitot tube; 11, valves; 12, sieve tray.

hes

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itIt

wm

M

ig. 2. The rectangular valve tray used in the experiment (unit: mm). The holerea = 0.0156 m2, fraction hole area to bubbling area = 8.86%.

ach manometer was mounted flush with the tray floor and thether was connected to the manifold which was connected to their space above the liquid on the tray.

. CFD model development

The model considered the gas and liquid phases as interpen-trating continuum having separate transport equations in theulerian framework. Within simulations, the gas phase was treateds the disperse phase, and the liquid phase was taken as the con-inuous phase. The disperse phase of gas–liquid bubbly flows onhe valve tray consisted of gas bubbles, gas jets and a combinationhereof, and the two phases Eulerian simulation approach chosenere can work well in calculation the disperse phase. The transportquations of gas (subscript G) and liquid (subscript L) phases werehown as follow.

G + ˛L = 1 (1)

∂(˛G�G)∂t

+ ∇ · (˛G�GVG) = 0 (2)

∂(˛L�L)∂t

+ ∇ · (˛L�LVL) = 0 (3)

∂

∂t(˛G�GVG) + ∇ · (˛G(�GVGVG))

= −˛G∇pG − MG + ∇ · (˛G�eff,G(∇VG + (∇VG)T)) (4)

∂

∂t(˛L�LVL) + ∇ · (˛L(�LVLVL))

= −˛L∇pL + ML + ∇ · (˛L�eff,L(∇VL + (∇VL)T)) (5)

The same pressure field was assumed for both phases, whichs pG = pL. MG and ML in above equations are momentum transfererm of the gas and liquid phase, and equal the sum of forces on it.n our simulation, they include the interphase momentum transfererms and per phase momentum transfer term.

For continued gas flow in valves, MG is only affected by theeight of valve and liquid on valve, and there is not any interphaseomentum transfer, and the equation is

G = mvalveg + �L(hcl − hvalve)Avalveg (6)

ng and Processing 48 (2009) 145–151 147

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X.G. Li et al. / Chemical Engineeri

here hcl is the clear liquid height computed by Eq. (13) developeds follow, and hvalve is the height of valve.

For gas–liquid bubbly flows out of valve in experiment, the inter-hase momentum transfer term includes drag force, virtual massorce and lift force. According to Krishna et al. [12] and van Batennd Krishna [13], the other forces compared to drag force, do notffect the bubbly flows greatly and can be ignored in this paper. Tohe gas as the disperse phase in bubbly flow, the equation for MG is

G = MGL = 34

CD

dG˛G�L|VG − VL|(VG − VL) (7)

here CD is the interphase momentum transfer (drag) coefficient.or the rise of a swarm of large bubbles in the churn turbulentegime, Krishna et al. [12] estimated the drag coefficient as

D = 43

�L − �G

�LgdG

1

V2slip

(8)

here Vslip is the slip velocity of the bubble swarm with respect tohe liquid, and is shown as

slip = Us

˛averageG

(9)

ubstituting Eqs. (9) and (8) into Eq. (7)

GL = ˛G(�L − �G)g(˛average

G )2

U2s

|VG − VL|(VG − VL) (10)

One advantage of using Eq. (10) as interphase momentumxchange term lies in that the bubble size does not need to be spec-fied. For the average liquid hold-up fraction, ˛average

G on the valverays, a new correlation would be regressed based on experimentalata as follow.

Turbulence was taken into account for the mixture phase,ncluding continuous phase and the dispersed gas phase. The wellnown single-phase standard k − ε turbulence model was appliedo model the turbulence phenomena of the gas–liquid flow, usingtandard single-phase parameters C� = 0.09, C1ε = 1.44, C2ε = 1.92,k = 1 and �ε = 103. A whole tray was modeled, as shown in Fig. 3.ne of the geometry modeling problems was to specify the detail

eometry of valves, and a method was used to overcome this prob-em that the valves were considered as columns. The top face ofolumn was cover of valve, and the foot face was hole and a part ofray. Except the top and foot faces, other faces of column were useds interior faces of solution domain and all phases can pass through

Fig. 3. The calculation space and boundaries in CFD simulation.

U

u

3

bar

3

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gtg

Fig. 4. The grid map of CFD simulation.

hem. In the x-, y- and z-direction, grid cells of 5 mm size were cho-en. But at the round of valves, GAMBIT (the tool of making grids ofLUENT) automatic changed the grid size to 5 mm × 5 mm × 4 mmo cover the all valves by two complete cells. The total number ofnstructured cells within the computational space was 419,300,nd they were shown in Fig. 4.

To solve the equations of continuity and momentum for thewo-fluid mixture, appropriate boundary conditions for each phasehould be specified at all inside and external boundaries of theimulated domain.

.1. Liquid inlet

For our experimental rectangular valve tray, a uniform liquidnlet velocity profile was recommended.

L,in = QL

hapLW(11)

Only liquid entered through the downcomer clearance, so theiquid-volume fraction was taken as unity.

.2. Gas inlet

The gas inlet holes of the model were captured by cell faces, anduniform gas velocity was supposed.

G,in = QG

NhAhole(12)

The gas-volume fraction at the inlet holes was specified to benity.

.3. Liquid and gas outlet

The liquid- and gas-outlet boundaries were specified as pressureoundaries with volume fraction specifications. The specificationsssumed that only liquid or gas leaves the simulation geometry,espectively.

.4. Wall

All wall for two phases were specified as no-slip wall boundary.A commercial CFD package FLUENT was used to solve the equa-

ions of continuity and momentum for the two-fluid mixture. Thisackage is a finite volume solver, and all variables are evaluated athe cell center. The pressure–velocity coupling was obtained usinghe phase coupled SIMPLE algorithm. A fully implicit backward dif-

erencing scheme was used for the time integration.

At ambient pressure conditions, air and water were used as theas and liquid phases, respectively. At the start of a simulation,he tray configuration shown in Fig. 3 was filled with a uniformas–liquid dispersion (50% liquid hold-up) except space in the

148 X.G. Li et al. / Chemical Engineering and Processing 48 (2009) 145–151

Fv

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�

Based on the experimental data, the correlation was devel-

ig. 5. Transient simulation convergence as indicated by a plot of clear liquid heights. time.

alves, which was full of gas phase. The time increment used inhe simulations was 0.001 s. During the simulation the clear liquideight in the simulation system was monitored, and quasi-steadytate was assumed to prevail if the value of the clear liquid heightemained constant for an enough long period. Typically, steadytate is achieved in about 15 s from the start of the simulations,s shown in Fig. 5.

. Results and discussion

In this paper, an average liquid hold-up correlation of full open

alve was developed. Like sieve tray, the clear liquid height of valveray is mainly affected by the superficial gas velocity, liquid loadnd weir height. If a new correlation of clear liquid height on fullpen valve tray is obtained, and the liquid hold-up, which is �e in

oaev

Fig. 7. Snapshots of the front view of the simulations at a superficial gas velocity, Us

ig. 6. Calculated values of clear liquid height, hcl, using new correlation comparedgainst experiment hcl.

q. (13) [14], is found.

cl = �e

[hW + C

(QL

�e

)2/3]

(13)

The format assumed for the C and �e correlation are

= a1 + a2 exp[−a3hW] (14)

e = exp

[−a4Us

(√�G

�L − �G

)a5](15)

ped and the undetermined parameters (a1–5) were confirmed,1 = 0.012, a2 = 0.034, a3 = 110, a4 = 1.44 and a5 = 0.74. In Fig. 6, thexperimental clear liquid height data was plotted vs. the calculatedalue using the new correlation. The average error was 1.4%, and the

= 0.64 m/s; weir height hW = 0.05 m; liquid weir load QL/W = 0.0032 m3/(s m).

X.G. Li et al. / Chemical Engineering and Processing 48 (2009) 145–151 149

ty, Us

md

�

tw

ofdN

itaig

ct

h

Fig. 8. Snapshots of the top view of the simulations at a superficial gas veloci

ean error was 4.7%. The coefficient which minimize the standardeviation gave the following equations for �e,

e = exp

[−1.44Us

(√�G

�L − �G

)0.74]

(16)

Based on correlation of liquid hold-up, several simulations aboutwo-phase hydrodynamics of full open valve tray were carried outith varying simulation configures.

Figs. 7 and 8 present snapshots of the front view and top view

f the computation results. The chaotic behavior can be seen fromront and top views. The two-phase region above the tray can beivided into liquid continuous region and gas continuous region.ear the tray, gas is dispersed by the continued liquid after thrust-

Fig. 9. Clear liquid height as a function of the superficial gas velocity.

�

el

= 0.64 m/s; weir height hW = 0.05 m; liquid weir load QL/W = 0.0032 m3/(s m).

ng out valves, and liquid hold-up decreases as height increases. Atransient of two regions, there has no clear interface between gasnd liquid phase. In the gas continuous region, the liquid dimin-shes rapidly, leaving most space of the tray to be filled with theas.

To validate the simulation results against the experimental data,lear liquid height was computed, and compared with experimen-al data, and the Dhulesia correlation [4] shown as follow:

cl = 0.42� 1/3h2/3W (17)

QL/W√(

�L)

=Us �G

(18)

Clear liquid height is defined as the height of liquid that wouldxist on the tray in the absence of vapor flow. After a sufficientlyong time interval once quasi-steady state condition was estab-

Fig. 10. Clear liquid height as a function of the liquid weir load.

150 X.G. Li et al. / Chemical Engineering an

Fig. 11. Clear liquid height as a function of the weir height.

lm

hstsisw

ls

irt[cp

etvtoAofl

pgrpep

5

aticcthohcif

�

Fig. 12. Gas V velocity profiles at different elevations above tray, y = 0 m.

ished, the clear liquid height was calculated as the tray spacingultiplied by the volume average of the liquid-volume fraction.Figs. 9–11 show the comparison of the predicted clear liquid

eight by CFD simulations and experimental data with varyinguperficial gas velocity, liquid weir loads and weir height, respec-ively. The predicted clear liquid height decreases with increasing

uperficial gas velocity at a given liquid flow rate and weir heightn Fig. 9, and it increases with increasing liquid flow rate at a givenuperficial gas velocity and weir height in Fig. 10, and it decreasesith increasing weir height at a given superficial gas velocity and

Fig. 13. Liquid U velocity profiles at different elevations above tray, x = 0 m.

Ctetri

A

N0n

A

AA

d Processing 48 (2009) 145–151

iquid flow rate in Fig. 11. Clear liquid heights predicted by CFDimulations have the same changing trends as experimental data.

A major advantage of the extension to the two-phase modelings the availability of the gas phase and liquid phase flow profilesespectively, which is needed in simulating the interphase massransfer, and calculating the Murphree tray efficiency. Rahimi et al.17] predicted the Murphree point efficiencies and tray efficien-ies of sieve tray based on gas–liquid two-phase hydrodynamicserformance by CFD.

Profiles of the gas-phase vertical-component velocity on differ-nt height elevations are shown in Fig. 12. Closed to the tray floor,he maximum values of oscillations correspond to the location ofalve holes, and there are two holes encountered in sweeping fromhe liquid inlet to the liquid outlet at y = 0 m. The magnitude of thesescillations decreases with increasing heights above the tray floor.s soon as the weir height is crossed, the gas velocity decreaseswing to the increase in the cross-sectional area available for gasow.

Fig. 13 illuminates profiles of the liquid phase transverse com-onent velocity on different height sections. Unlike profiles of theas phase vertical velocity, the minimum values of oscillations cor-espond to the location of valve holes. The reason is that the liquidhase is affected by high speed gas thrusting out valves, and is accel-rated between valves. As height increases, the interval of liquidhase transverse component velocity reduces.

. Conclusions

In this paper, we have tried to predict the flow hydraulics offull open valve tray by the means of CFD. A three-dimensional

wo-phase CFD model was developed in the Eulerian framework,n which gas and liquid phases were treated as interpenetratingontinuous phases, and the model was solved by FLUENT. The dragoefficient correlation of Krishna et al. for momentum interaction ofwo-phase flow was incorporated into the model, but since thereas no appropriated correlation of liquid hold-up fraction on fullpen valve tray for CFD, to overcome this problem, clear liquideight on full open valve tray was measured. A new correlation oflear liquid height on full open valve tray was found based on exper-mental data. As a parameter in the correlation, the liquid hold-upraction �e was obtained as

e = exp

[−1.44Us

(�G

�L − �G

)0.74]

Based on this equation, the closed model was developed. TheFD model was used to predict clear liquid for various combina-ions of gas and liquid rates, and weir height. The simulation resultsxhibit some known features of the two-phase flow field in valverays and are in good agreement with the experimental results. Theesults of this work show that CFD can be used as a powerful tooln the design and analysis of industrial trays.

cknowledgements

The authors wish to acknowledge financial support by theatural Science Key Foundation of Tianjin China (project no.7JCZDJC02600) and the assistance of the staff in the National Engi-eering Research Center for Distillation Technology (China).

ppendix A. Notation

hole area of hole (m2)valve area of valve (m2)

ng an

CdghhhLMNpQQRtUVVWxyz

G˛��

ScdGL

R

[

[

[

[

[

[15] G. Gesit, K. Nandakumar, K.T. Chuang, CFD modeling of flow patterns and

X.G. Li et al. / Chemical Engineeri

D drag coefficientG diameter of gas bubble (m)

acceleration due to gravity (9.81 m/s2)ap downcomer clearance (m)cl clear liquid height (m)W weir height (m)W weir length (m)

interphase momentum exchange term (N/m3)h number of holes

pressure (Pa)G gas flow rate across tray (m3/s)L liquid flow rate across tray (m3/s)e Reynolds number

time (s)s superficial gas velocity (m/s)

velocity vector (m/s)slip slip velocity between gas and liquid (m/s)

weir length (m)coordinate (m)coordinate (m)coordinate (m)

reek lettersvolume fraction of phaseviscosity of phase (Pa s)density of phase (kg/m3)

ubscripts

l clear liquidisp dispersion

referring to gas phasereferring to gas phase

[

[

d Processing 48 (2009) 145–151 151

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13] J.M. van Baten, R. Krishna, Modelling sieve tray hydraulics using computationalfluid dynamics, Chem. Eng. J. 77 (2000) 143–151.

14] D.L. Bennett, R. Agrawal, P.J. Cook, New pressure drop correlation for sieve traydistillation columns, AIChE J. 29 (1983) 434–442.

hydraulics of commercial-scale sieve trays, AIChE J. 49 (2003) 910–924.16] C.L. Colwell, Clear liquid height and forth density on sieve trays, Ind. Eng. Chem.

Proc. Des. Dev. 20 (1979) 298–299.17] R. Rahimi, M.R. Rahimi, F. Shahraki, M. Zivdar, Efficiencies of sieve tray distilla-

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