CFD gas-liquid simulation of oriented valve tray

Yufeng Ma,Lijun Ji,Jiexu Zhang,Kui Chen,Bin Wu,Yanyang Wu,Jiawen Zhu

School of Chemical Engineering,East China University of Science and Technology,Shanghai 200237,China

Keywords:CFD simulation Oriented valve tray Gas-liquid flow Volume fraction correlation

ABSTRACT Computational fluid dynamics(CFD)has recently emerged as an effective toolforthe investigation ofthe hydraulic parameters and ef ficiency of tray towers.The computation domain was established for two types of oriented valves within a tray and meshed into two parts with different grid types and sizes.The volume fraction correlation concerning inter-phase momentum transfer source was fitted based on experimental data,and built in UDF for simulation.The flow pattern of oriented valve tray under different operating conditions was simulated under Eulerian-Eulerian framework with realizable k-ε model.The predicted liquid height from CFD simulation was in good agreement with the results of pressure drop and volume fraction correlations.Meanwhile,the velocity distribution and volume fraction of the two phases were demonstrated and analyzed,which are useful in design and analysis of the column trays.

1.Introduction

Float valve tray has been extensively applied in distillation,absorption,desorption and stripping processes.Compared with conventional float valve tray,oriented float valve tray has a better performance in many aspects.First,due to restraints of oriented valve caps,the gas and liquid are perpendicularly contacted,which effectively reduces the back-mixing and increases the ef ficiency oftray.Second,the guiding hole above the cover of each oriented valve offers the gas driving forces to the liquid flow which reduces the difference of liquid level along the flow direction[1].Moreover,its flexible con figuration makes the larger opening fraction possible,good for improving processing capacity.Last but not least,the oriented float valve does not rotate,resulting in no physical deterioration.

Nevertheless,the speci fic flow state on oriented valve tray hasn't been studied or determined intensively.For a certain separation process,the flow pattern of trays plays an important role,since the hydraulics of the gas and liquid phases on tray can affect the separation ef ficiency and overalltray performance.Especially,the liquid circulation or the reverse flowatthe side regions has been arisen much attention as it causes serious reduction of the Murphree tray ef ficiency[2].Generally,experimental method has been used to obtain first-hand investigation of tray flow state,however,it suffers from poor reproducibility and high cost.Therefore,computational fluid dynamic(CFD)with advantages of simplicity,accuracy and ef ficiency,has become attractive in the research of many separation processes,such as distillation,absorption,and crystallization[3-5].

CFD simulation can provide a realistic picture of the flows and the results have been used to improve separator ef ficiency[6,7].Considering both the resistance and bubbling effect,Liu et al.[3]proposed a two-dimensional two-equation model and simulated the liquid flow pattern on sieve tray.The simulation result was in good agreement with the experimental data measured by the hot- film anemometry.By simultaneously solving CFD control equations and mass transfer equations,Wang et al.[8]obtained the velocity,concentration pro files on each tray as well as the overall tray ef ficiency,their study demonstrated that the application of CFD as a tool for the theory-based distillation design and performance analysis is feasible and dependable.Adopting hypothesis single-phase flow model,Liu et al.[9]inspected the in fluence of liquid flow rate and weir to diameter ratio on flow state,and proved that the two methods can effectively help us achieve optimization of flow state on tray.Some advances about CFD simulation of packed column have been achieved,too[10-12].

This work was aimed to establish a precise CFD model to investigate the flow pattern oforiented valve tray and distribution of flow field,and finally giving a comprehensive instruction to other kinds of float valve tray design.Based on experimental data of oriented valve tray and other correlations,a precise volume fraction correlation was established and applied in CFD to investigate the flow pattern on oriented valve tray.The results of CFD simulation,volume fraction correlation and pressure drop correlation of liquid layer were compared,which were in good agreement and the availability of volume fraction correlation in CFD simulation was veri fied.The liquid fraction variation along height,and the liquid X-velocity distribution along radial direction and axial direction were analyzed,and it showed that inclined valves resisted the liquid flow forward,leading to reverse flow and increasing the height difference of clear liquid,which would provide an available instruction to valve tray design.

2.CFD Models

2.1.Flow model

Two models,i.e.the Euler-Lagrange approach and the Euler-Euler approach,have been employed to investigate gas-liquid two-phase flow.In the Euler-Lagrange approach,the continuous fluid phase is modeled by solving the time-averaged Navier-Stokes equations,and the dispersed phase is simulated by tracking a large number of particles through flow field,based on Newton's second law.Implementation of the Euler-Lagrange leads to the Discrete Phase Model(DPM).DPM works well for certain flow regimes where discrete phase is less than 12%volume fraction.The Euler-Euler approach regards multiple phases as continuous phases interacting with each other.Since the volume of one phase cannot be occupied by the other phases,phase volume fractions are assumed to be continuous function of space and time,and their sum is equal to 1.Comparing the two approaches,the Euler-Euler approach was considered more suitable for simulating gas-liquid two-phase flow on the column trays[6,13,14].

The Euler-Euler approach was applied to study an oriented valve tray system with realize k-ε model.The finite volume method with an upwind difference scheme was adopted forthe discretization ofconvective terms[15].

2.1.1.Basic mathematical model

In this Eulerian multiphase model,the phases are considered as the interpenetrating continua.For either gas or liquid phase in the twophase dispersion on the tray,the volume-averaged mass and momentum conservation equations are given by

MG,Lworks as the momentumtransfer term,and itis equalto the sum of forces between two phases[16].

Atthe same time,the same pressure field was shared by both phases.At any spatial location,gas fraction and liquid fraction sum up to 1.

2.1.2.Turbulence equations

Since the presence of dispersed phase could affect turbulence in the continuous phase,the situation on tray becomes quite complex due to the coupling between continuous and dispersed phases.Hence,as closure models for momentum equations,turbulence equations are introduced for simulating turbulence behavior.

The effective viscosity in Eqs.(3)and(4)could be expressed as

The turbulent viscosity is predicted by using the k-ε turbulent equations,and the turbulent viscosity is as follows:

In the turbulence equations,the realizable k-ε turbulence equations are veri fied to be accurate and time-saving,superiorto standard k-ε and RNG k-ε models.Realizable k-ε turbulence equations are as follows:

Gkis the generation by turbulent kinetic energy of average velocity gradient;Gb,generation by turbulent kinetic energy of buoyancy force;and YM,in fluence ofcompressible turbulence in flation on dissipation rate.C1ε,C1,C3ε,C2,σk,and σεcan be taken as 1.44,1.9,0.09,1.9,1.0,and 1.2,respectively,with

2.1.3.The fitting of gas phase volume fraction correlation

Drag force,virtual mass force and lift force were relevant to the total MG,L.The friction between bubble and liquid is the essence ofdrag force.It has been proved that virtual mass force exerts little in fluence on simulation result[17]and most researchers af firm that the lift force can be neglected[15],since they do not contribute signi ficantly in obtaining better flow.So the virtual mass force and lift force were neglected in the simulation.

In terms of the drag force,among several models of drag force coefficient CD[17-22],it has been proved that only the model proposed by Krishna et al.[22]is more suitable for tray column,because the model is based on bubble cluster instead of one single bubble,which is more consistent with the actual situation.

According to the clear liquid height model by Colwell[23],

Eqs.(13)and(14),with different corresponding parameter values,were compiled into UDF by predecessors in our simulation.

2.2.Mesh generation

As the other researchers did,by virtue of symmetry in physics,only halfofa tray was modeled to save computationaltime and some simplifications were applied for convenient meshing.With pre-processor GAMBIT 2.4,the physical model corresponding to real experimental equipment was built and then meshed with hybrid grids,unstructured grid(5 mm)close to tray deck,and structured grid(12 mm)far from tray deck.The use of hybrid grids can not only guarantee the accuracy but also save computing time and memory[25-27].When meshing,the face of vertical hole over valve on valve face was allowed to make gas come outfromthe guiding hole to push the liquid forward effectively.After being checked in GAMBIT,the mesh quality between 0 and 0.8 accounts for 99.96%(the worse,the closer to 1),which is superior to 99.6%[26],and the only worst grid is 0.93,all the other grids are below 0.9,outshining 226 grids(0.13%)above 0.9 in[26].

The whole computational domain and layout of valve was demonstrated in Fig.1.

Fig.1.Computation domain.

The length and height of all valves are 72 mm and 15 mm,respectively.The width of rectangular valve is 25 mm,and that of trapezoidal valve is 32 mm(baseline)and 25 mm(topline).Each hole on valve has a trapezoidal cross-section with topline of 16 mm,baseline of 22 mm and height of 4 mm.Adjacent valves have interval of 55 mm in Y-direction,90 mm in X-direction.The structural dimensions of tray were obtained by measuring the actual experimental tray which had been used for investigating tray ef ficiency by Zhao et al.[28].

2.3.Boundary condition

2.3.1.Liquid and gas and inlet

A uniform liquid inlet velocity and gas inlet pro file was adopted.

Assume that only liquid entered through the downcomer clearance,since the amountofgas entrainmentwas small.The gas volume fraction at the inlet holes was speci fied to be unity.

2.3.2.Gas and liquid outlet

The liquid and gas outlet boundaries were set as pressure boundaries,and itwas assumed thatonly liquid or gas could leave the flow geometry respectively[16,29].

2.3.3.Wall and symmetry boundary conditions

The walls were de fined as no-slip wall,and the standard wall functions were used near wall regions[16,25-27,29-31].The normal velocity was zero and the gradients of other variables in the transverse coordinate directions were taken to be zero.

For gas and liquid,the following equations were suitable:

3.Results and Discussion

3.1.Average liquid volume fraction correlation

The flow,volume fraction and turbulence equations were solved.All discretization schemes of variables were First Order Upwind and the way of pressure and velocity coupling was SIMPLE algorithm[31].The part close to deck was adapted to a region full of liquid and the upper filled with gas,since during simulation,initialization with the adaption region was more bene ficial to convergence.

The simulation process without UDF(only designated air bubble diameter)was dif ficult to converge and no distinct clear liquid layer was formed.With the experimental data of the oriented valve tray column by Zhang[32],Eqs.(13)and(14)were fitted,and the parameter values were obtained as a1=1.475,a2=1.385,a3=0.216,a4=21.542,and a5=1.0687.Then,

With the above two equations,the simulation succeeded in quickly converging,and the apparent clear liquid layer was demonstrated.

3.2.Clear liquid height

During the simulation,the clear liquid volume fraction was monitored,and quasi-steady state was assumed to prevail if the clear liquid height remained constant for a period long enough.As shown in Fig.2,the time step was set as 0.001 s and the steady state was achieved approximately in 2.0 s after the start of simulation,less than 4.0 s[16].The liquid volume fraction about 0.1625 means the clear liquid height was almost steady at 0.065 m.

Fig.2.Clear liquid height monitored as a function of time.

At given F0factor and weir height in Fig.3,the changing tendency with liquid load of CFD simulation was in accordance with pressure drop correlation[33]and the volume fraction correlation,and the clear liquid height increased with liquid flow.

Fig.3.Clear liquid height results of CFD simulation.

Clear liquid height correlations proposed by Zhu et al.[33]are

Clear liquid height hclwere calculated with either Eqs.(12),(21)and(22)of this paper,or Eqs.(23)and(24)of Zhu et al.[33],respectively.

The two calculations were compared with hclfrom CFD simulation.At lower liquid load,the results of hclfrom CFD simulation were closer to that calculated with correlations of this paper,and at higher liquid load hclcalculated under pressure drop correlations were less deviated from hclwith CFD simulation.Along with liquid load changing,the average relative errors between CFD simulation and experimental results were 4.4%,10.0%,22.1%,23.8%,and 43.6%,respectively for Refs.[16,34,13,29,22].In Fig.3,the range of present relative error was averaged to be 15.5%.Therefore,the three parameters were relatively in good agreement and from distribution of relative errors,they decreased along with the increasing of liquid load,which was in agreement with Refs.[13,29,34].

The simulation results of the clear liquid layer ata given F0factor,hwand QL/LWwas showed in Fig.4(the flow from left to right),and the height difference was also demonstrated,like the real experimental phenomenon.The two-phase flow chaotic behavior can be seen from Figs.4 and 5(the snapshots of the top view of the computation).At the part close to deck,liquid as continuous phase dominates the flow pattern.With the increasing of vertical height,the percentage of gas increased,and the gas gradually became continuous phase,no clear interface between gas and liquid phase was shown.

3.3.Velocity vector details

Fig.6 illustrated the liquid velocity vector and effects of oriented holes on liquid flow.Near the bottom of tray,the liquid was drawn toward the center and was dragged up vertically by gas,but close to weir,the velocity of liquid was up-inclined.This was because the gasliquid interaction in the vicinity of valves was drastic,delivering momentum to upper liquid and the gas from valves directly threw liquid up,which in fluenced liquid direction remarkably.The liquid disengaged itself from the gas stream and fell down to the sides,resulting in circulation near the liquid inlet.Due to the gravity,water has the downward velocity in upper space,where gas has an upward velocity,as reported in the literature[26,27,34,35].

Fig.7 shows the variation of average liquid fraction in the vertical direction.The height of foam layer was de fined as the height at which the average liquid hold-up was below 10%[16].According to this,we can read out the height of foam layer was 130 mm.From Fig.7,at the height of valve cap(Z=15 mm),a rising point of liquid hold-up appeared,which demonstrated the existence of dead zone to gas flow.

The liquid flow above tray was mainly divided into three regions:arc back flow region(1 in Fig.8a),main flow region,and outlet back flow region(3 in Fig.8a).The area of arc back flow region was close to half of whole arc region,which was superior to that in dividing wall column[36].For the main flow region,the liquid X-velocity was presented to be the plug flow,but reverse flow existed at several spots(4 in Fig.8a)which was resulted from the resistance of oriented float valve wall and the reinforced gas-liquid interaction.Due to the existence of two inclined valves at point 2 in Fig.8a,the gas coming out from their sides obstructing liquid forward flow,an obvious reverse flow appeared.Comparing the plane of Z=5 mm(a)and Z=16 mm(b),we found that at tray center,relative higher liquid X-velocity 0.43-2.24 m·s-1(red and yellow velocity vectors)appeared on Z=16 mm(Fig.8b)and reverse liquid velocity was reduced at the arc back flow region and outlet back flow region.The fraction of nodes with negative X-component of liquid velocity declined from 31.8%to 17.7%,because each valve was 15 mm high and with guiding hole above it from which gas transferred momentum to liquid,making liquid velocity increase.

4.Conclusions

A new correlation of gas hold-up was built based on experimental data.The parameters in Eqs.(13)and(14)were a1=1.475,a2=1.385,a3=0.216,a4=21.542,and a5=1.0687.

Fig.4.Snapshots of the front view of liquid fraction distribution at Y=35 mm with liquid height changing demonstrated.

The simulation results based on Eqs.(13)and(14)showed the existence of back-mixing and the transient variation of clear liquid height.The calculated clear liquid height changing along with liquid load by CFD was compared with pressure drop correlation of liquid layer and volume fraction correlation,and they were observed in good agreement.Owing to guiding holes,relative higher liquid X-velocity of 0.43-2.24 m·s-1showed up on Z=16 mm,and reverse liquid velocity was reduced at the arc back flow region and outlet back flow region.The percentage of nodes with negative X-component of liquid velocity decreased from 31.8%to 17.7%.Inclined valves resisted the liquid flow forward,leading to the decrease of reverse flow and increase in the fluctuation of clear liquid height.The study of this work lays the foundation for further research on optimizing the tray design with CFD methods.

Fig.5.Snapshots of the top view of liquid fraction distribution,Z=5 mm.

Fig.6.Snapshots of the liquid velocity vector at Y=80 mm.

Fig.7.Average liquid fraction at different elevations.

Fig.8.Top view of liquid X-velocity pro file at Z=5 mm and Z=16 mm.

Nomenclature

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