Computational Fluid Dynamics Modeling of Hydrodynamics of a New

Article pubs.acs.org/IECR

Computational Fluid Dynamics Modeling of Hydrodynamics of a New Type of Fixed Valve Tray Xingang Li,†,‡ Na Yang,† Yongli Sun,*,†,‡ Luhong Zhang,† Xuegang Li,† and Bin Jiang†,‡ †

School of Chemical Engineering and Technology, and ‡National Engineering Research Centre of Distillation Technology, Tianjin University, Tianjin 300072, People’s Republic of China S Supporting Information *

ABSTRACT: A three-dimensional computational fluid dynamics (CFD) model was developed to predict the hydrodynamics of a new type of fixed valve tray. The model considered gas- and liquid-flow within the Eulerian framework in which both phases were treated as interpenetrating continuum having separate transport equations. Interphase momentum transfer term was employed for describing the interfacial forces between the two phases, and the related average gas hold-up was obtained via the regression equation from experiment data. Calculations were carried out using the commercial packages ANSYS CFX 12.0. Clear liquid height, gas hold-up, and gas and liquid velocity profiles were predicted for various combinations of weir height, gas, and liquid flow rates. The predicted clear liquid height was generally in good agreement with measurement. The information predicted by the CFD model can be used in the optimal design of industrial trays.

1. INTRODUCTION Mass transfer tray column is an important type of gas−liquid contact equipment widely used in the oil refining and chemical industries, as it has features of easy maintainability, low cost, convenient feed, and side withdrawing.1−3 Fixed valve tray, one of the major research and industrial interests recently, draws more attention as a hybrid of floating valve tray and sieve tray. In industrial practice, however, the performance of the trays always suffers from a loss of separation ability due to maldistributed or abnormal flow regime, for example, liquid phase circulation, which occurs frequently on a tray.4−7 It has been long established that the prediction of distillation tray hydrodynamics is necessary for the separation efficiency and overall performance.5,6,8−10 Besides, the understanding of these two-phase hydrodynamic phenomena on trays is helpful for the fine-tuning and optimization of modern tray design.11−14 The hydrodynamics of fixed valve tray is significantly influenced by the configuration and type of the valves, and the operating conditions, which, in turn, affect the product properties.15−17 Because of progress in computer hardware and software and consequent increase of the calculation speed, the computational fluid dynamics (CFD) modeling technique becomes a powerful and effective tool for understanding the complex hydrodynamics in chemical engineering processes. It provides a theoretical basis and a computational technique for predicting the flow distribution on a tray. There have been many attempts to model tray hydrodynamics by use of CFD. Mehta et al.11 analyzed the liquid phase flow patterns on a sieve tray by solving the time-averaged equations of continuity of mass and momentum only for the liquid phase. Interactions with the vapor phase were taken account of by use of interphase momentum transfer coefficients determined from empirical correlations. Yu et al.4 and Liu et al.18 ignored the variations in the direction of gas flow along the height of the dispersion to simulate the two-phase flow behavior, and only the hydrodynamics of the liquid flow was obtained. Fischer and Quarini19 © 2013 American Chemical Society

have attempted to describe the three-dimensional transient gas−liquid hydrodynamics. An important key assumption made in the simulations of Fischer and Quarini concerns the interphase momentum exchange (drag) coefficient; these authors assumed a constant drag coefficient of 0.44, which was appropriate for uniform bubble flow. This drag coefficient is not appropriate for description of the hydrodynamics of trays operating in either the froth or the spray regimes. Krishna and van Batten20,21 estimated the interphase momentum exchange coefficient on the basis of the correlation of Bennett et al.22 for the liquid hold-up. Because the correlation of Bennett et al. overpredicted the liquid hold-up fraction in froth regime, Gesit et al.23 used the liquid hold-up correlation of Colwell,24 which worked well in the froth regime, to predict the flow patterns and hydrodynamics of a commercial-scale sieve tray. Their work pointed the way and extended the application scope of CFD for understanding the complex hydrodynamics in tray column. In this Article, a three-dimensional transient CFD model was developed within the two-phase Eulerian framework for the hydrodynamics of a new type of fixed valve tray, which was codeveloped by Tianjin University and Sinopec Engineering Inc. (SEI). The three-dimensional structure of the tray is shown in Figure 1. The detail dimensions (see Figure S1) are included in the Supporting Information. One of the distinguishing features is the streamlined hem, which contributes to better vapor flow and lower pressure drop. The ligulate holes on the valve play a role in pushing liquid forward when gas rises through them, reducing liquid surface gradient. Simulations were carried out to predict the clear liquid height for various combinations of superficial gas velocities, liquid weir loads, and Received: Revised: Accepted: Published: 379

February 3, 2013 July 31, 2013 December 2, 2013 December 2, 2013 dx.doi.org/10.1021/ie400408u | Ind. Eng. Chem. Res. 2014, 53, 379−389

Industrial & Engineering Chemistry Research

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The clear liquid height was measured by a static pressure tube (5) with graduated scale using the principle of communicating vessel. To obtain the average clear liquid height, hcl, as well as to eliminate the effects of the liquid surface gradient on the tray, five pressure tappings were arranged on the tray, and all were combined with tubes and connected to the static pressure tube.

3. CFD MODEL DEVELOPMENT 3.1. Governing Equations. The model considers gas- and liquid-flow within the Eulerian framework in which both phases are treated as interpenetrating continuum having separate transport equations. With the model focusing on the froth region of the fixed valve tray, the gas phase is taken as the disperse phase, while the liquid phase forms the continuous phase. The disperse phase of froth flow on the tray consists of gas bubbles, gas jets, and a combination thereof, and the twophase Eulerian simulation approach chosen here can work well in calculating the disperse phase. For either gas (subscript g) or liquid (subscript l) phases, the volume-averaged continuity (mass) and momentum conservation equations are shown as follows: Continuity Equations.

Figure 1. Structure of the new type of fixed valve tray.

weir height, and comparisons with measurements were made. Other hydrodynamic behaviors were revealed with the aid of velocity profiles, streamlines, and contours, and so on. The objective of this work is examining the extent to which CFD models can be used as an investigative and design tool in industrial practice.

2. EXPERIMENTAL SETUP The experimental setup for validation of CFD results is illustrated in Figure 2. Two fixed valve trays and ancillary

∂(αgρg ) ∂t

∂(αlρl ) ∂t

+ ∇·(αgρg u g) = 0

(1)

+ ∇·(αlρl ul) = 0

(2)

Momentum Equations. ∂ (αgρg u g) + ∇·(αg(ρg u g ⊗ u g) − αgμeff,g (∇u g + (∇u g)T )) ∂t = − αg∇pg + Mg,l + αgρg g

(3)

∂ (αlρl ul) + ∇·(αl(ρl ul ⊗ ul) − αlμeff,l (∇ul + (∇ul)T )) ∂t = − αl∇pl + Ml,g + αlρl g

Figure 2. Simplified diagram of the experimental setup to measure hydrodynamics of fixed valve tray: 1, air blower; 2, pitot tube; 3, micro manometer; 4, U-tube manometer; 5, static pressure tube with graduated scale; 6, weeping exit; 7, gas distributor and weepinggathered tray; 8, 9, valve tray; 10, entrainment-gathered tray; 11, gauze demister; 12, entrainment exit; 13, water outlet; 14, water storage tank; 15, water pump; 16, valve; 17, rotameter; 18, downcomer.

(4)

where ρ, u, α, and μ represent the macroscopic density, velocity, volume fraction, and viscosity, respectively, p is the pressure, M is the interphase momentum exchange between gas and liquid phases, and g is the gravitational force. The gas and liquid volume fractions, αl and αg, are related by the summation constraint:

entrainment-gathered tray and liquid distribution device were placed in a plexiglass column with an internal diameter of 600 mm. All tests were carried out with an air/water system in a countercurrent mode at atmospheric pressure under room temperature. Hydrodynamic performances of the fixed valve tray, including dry/irrigated pressure drop, entrainment, weeping, and clear liquid height, were investigated. A calibrated pitot tube (2) was used to control the gas flow rate. The gas was pumped into the column by an air blower (1) and entered the fixed valve tray through four 100 mm diameter copper tubes (7), each having a cap on top to ensure uniform outflow of gas. The superficial gas velocity Qg used in the experiments ranged from 0.4 to 1.5 m/s. The liquid from the storage tank (14) was fed to the downcomer (18) by means of a centrifugal pump (15). The liquid flow rate was measured by a calibrated rotameter (17). The liquid loads per weir length, Ql/Lw, ranged from 4.44 to 31.1 m3/(h·m). Various weir heights, hw, of 30, 50, and 80 mm were used in the experiments.

αl + αg = 1

(5)

Simultaneously, the same pressure field has been assumed for both phases: pg = pl (6) The effective viscosities of the gas and liquid phases are given, respectively, by: μeff,g = μ lam,g + μtur,g (7) μeff,l = μ lam,l + μtur,l

(8)

Interphase momentum transfer, Mg,l, occurs due to interfacial forces acting on the gas phase, due to interaction with the liquid phase. Note that interfacial forces between the two phases are equal and opposite, so the net interfacial forces sum to zero: Mg,l = −Ml,g 380

(9)

dx.doi.org/10.1021/ie400408u | Ind. Eng. Chem. Res. 2014, 53, 379−389


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⎡ ⎛ Q l ⎞0.67 ⎤ ⎥ hcl = αl ave⎢hw + C ⎜ ave ⎟ ⎢⎣ ⎝ Lw αl ⎠ ⎥⎦

Closure Relationships. To solve eqs 1−4 for velocities, pressure, and volume fractions, additional equations are indispensable to relate the interphase momentum transfer term M and the turbulent viscosities to the mean flow variables. For gas−liquid bubble flow on the tray, the interphase momentum transfer term includes drag force, virtual mass force, and lift force. As compared to drag force, the latter two forces do not affect the bubble flow greatly and can be ignored in this Article.20,21 To the gas as the disperse phase, the equation for Mg,l is: Mg,l

3 CD =− αgρl |ul − u g|(ul − u g) 4 dg

The formats assumed for the weir coefficient, C, and liquid hold-up, αgave, correlations are: C = m1 + m2 exp[ − m3hw ]

αl ave

(10)

24 , Re

Re ≪ 1

⎡ ⎛ ⎞m5⎤ ρ g ⎢ ⎟ ⎥ = exp⎢ − m4 ⎜Us ⎜ ⎟ ⎥ ρ − ρ l g ⎠ ⎦ ⎝ ⎣

(18)

(19)

A data analysis package firstOpt developed by 7D-Soft High Technology Inc. was used for experimental data regression to determine the parameter m1−5. firstOpt is adept at nonlinear regression as well as solution for complex model parameters without the need for initial values. The parameters were eventually confirmed, m1 = 0.41, m2 = 1.12, m3 = 50.86, m4 = 5.71, and m5 = 0.92. The experimental clear liquid height data were plotted versus the calculation using the new correlation in Figure 3. It can be seen that the maximum margin of error is

where CD is the dimensionless drag coefficient, which has different correlations to various dispersed multiphase flow. At low particle Reynolds numbers (the viscous regime), the drag coefficient for flow past spherical particles may be computed analytically. The result is Stokes’ law: CD =

(17)

(11)

For particle Reynolds numbers that are sufficiently large for inertial effects to dominate viscous effects (the inertial or Newton’s regime), the drag coefficient becomes independent of Reynolds number: C D = 0.44,

1000 ≤ Re ≤ 1 ∼ 2 × 105

(12) 19

which is the relation used by Fischer and Quarini. For the churn-turbulent regime of bubble column operation, Krishna et al.25 estimated the drag coefficient for a swarm of large bubbles using: CD =

4 ρl − ρg 1 gdg 2 3 ρl V slip

(13)

where Vslip is the slip velocity of the bubble swarm with respect to the liquid: Vslip = |ul − ug|

(14)

The slip between gas and liquid can be estimated from superficial gas velocity Us and the average gas hold-up fraction αgave: Vslip

Us = ave αg

Figure 3. Calculated hcl versus experimental hcl.

±10%, and the average error and standard error are 3.35% and 0.00203 m, respectively. As a result, the correlation of average gas hold-up fraction is obtained as follows:

(15)

Substituting eqs 13 and 15 into eq 10: Mg,l

⎛ αg ave ⎞2 ⎟⎟ |ul − u g|(ul − u g) = αg(ρl − ρg )g⎜⎜ ⎝ Us ⎠

αl (16)

ave

0.92 ⎤ ⎡ ⎛ ρg ⎞ ⎥ ⎢ ⎜ ⎟ = exp⎢ − 5.71 Us ⎜ ρl − ρg ⎟⎠ ⎥⎥ ⎝ ⎢⎣ ⎦

αg ave = 1 − αl ave

Interestingly, this relation is independent of bubble diameter. This obviates the need for its input that could have been difficult. For the average gas hold-up fraction on sieve tray, αgave, Bennett et al.22 and Li et al.26 proposed their own correlations. For the new type of fixed valve tray in this Article, however, no correlations of the average gas hold-up fraction were proposed in previous researches. In this work, Bennett et al.22 correlation was used with characteristic parameters as shown in eqs 17−19, to estimate the clear liquid height, which can be measured experimentally.

(20) (21)

Free Surface Model. A VOF-like method27 called the “free surface model”, which is used to allow the two phases to separate when incorporated with inhomogeneous model, provided by CFX for multiphase calculations, is introduced for the calculation of the interface between the fluids. This model is applicable to a multiphase flow situation where the phases are separated by a distinct interphase. Surface Tension Model. The “surface tension model” used in this study is based on the continuum surface force (CSF) 381



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model of Brackbill et al.,28 in which the surface tension force is considered as a volume force concentrated at the interface, rather than a surface force. For two-phase flow, the final formation for CSF is given as: FVol = σij

clearance is 40 mm. To save computational time and machine memory, only one-half of the tray was modeled due to its symmetric form. The valve holes in the tray deck were specified as gas inlet boundary, and the valves were taken as inner walls. Liquid Inlet. Liquid inlet was specified at the downcomer clearance. The velocity profile at the liquid inlet was found to have a significant effect on the liquid velocity distribution inside the domain. Mehta et al.11 recommended a uniform liquid inlet velocity profile in their single-phase modeling work. It was found to be an important recommendation and adopted in the present study.

ργi∇αi (1/2)(ρi + ρj )

(22)

Turbulence Model. In previous numerical simulations7,11,20,21,23,26 of flows in tray column, the turbulent momentum fluxes were generally represented by the standard κ−ε turbulence model, which is based on the Boussinesq isotropic eddy-viscosity concept with a linear stress−strain relationship. This model needs a good law of the wall to be precise, and to be exigent with the y++ in the mesh. Near the wall the flow is very complex when gas is present. The limitations of this type of turbulence model for the prediction of complex flows with streamline curvature, strong swirl, and vortices are well-known. In the present study, calculations were performed using an improved eddy-viscosity based turbulence model, the shearstress transport (SST) model, which accounts for the transport of the turbulent shear stress and gives highly accurate predictions of the onset and the amount of flow separation under adverse pressure gradients. The SST model is a combination of the eddy-viscosity based κ−ω turbulence model of Wilcox29 applied to the near-wall region and the standard κ−ε model applied away from the wall. The kinematic eddy-viscosity is obtained on the basis of Bradshaw’s assumption that the shear stress is linearly related to the turbulent kinetic energy in the boundary layer as: a1κ νt = max(a1ω , SF2) (23)

Ul,in =

Ql hapLw

(24)

where hap is the downcomer clearance and Lw is the weir length. The liquid volume fraction at the liquid inlet was taken to be unity, assuming that only liquid entered through the downcomer clearance. This approximation is acceptable, because the amount of gas entrainment is small and can be neglected. Gas Inlet. The same mass flow rate was assumed at each valve hole, and a uniform gas velocity profile was supposed.

Ug,in =

Qg NhAh

(25)

where Nh is the number of valve holes, and Ah is the area of a single hole. The gas-volume fraction at the inlet holes was specified to be unity. Liquid and Gas Outlets. The liquid outlet boundary was specified as average static pressure of atmospheric pressure with pressure profile blend of 0.5 over the whole outlet. This is the most commonly used option. The average constraint is applied by comparing the area weighted pressure average over the entire outlet to the specified value. The pressure profile at the outlet is shifted by this difference such that the new area weighted pressure average will be equal to the specified value. The flow direction is an implicit result of the computation. The gas was assumed to leave the domain from opening boundary with static pressure of atmospheric pressure. This is the most stable setting for a pressure specified opening because it puts a constraint on the momentum transported through the boundary condition. Wall and Symmetry Boundary Conditions. A no-slip wall boundary condition was specified for the liquid phase and a free slip wall boundary condition for the gas phase. All of the walls were assumed as smooth wall boundary, and a volume fraction contact model was used. The symmetry plane of the geometry was specified as symmetry boundary as shown in Figure 4. 3.3. Mesh Generation and Solution Algorithms. The computation domain was discretized using an unstructured mesh by means of ICEM CFD 14.0. The grids near the valves and gas inlets were refined to capture the geometry details as shown in Figure 5. The whole computation domain was represented using the mesh consisting of 1.47 × 106 cells with volumes ranging from 2.0 × 10−9 to 1.5 × 10−8 m3. Mesh independence tests were carried out to establish the effect of mesh size on the calculated results. Calculations were performed with three mesh sizes consisting of 1.06 × 106, 1.47 × 106, and 1.79 × 106 cells to examine the effect on the solutions. The velocities obtained from calculations using 1.79 × 106 cells were nearly identical to those obtained using 1.47 × 106 cells. This mesh was used in all further simulations.

where S is the invariant measure of the strain rate, F2 is a second blending function defined by Menter30 with the same limiting values as those of F1, and the constant a1 is assigned a value of 0.31. 3.2. Geometry and Boundary Conditions. The model geometry and boundaries are shown in Figure 4. The tray has a

Figure 4. Model geometry and boundary conditions.

diameter of 540 mm, a 10.51% opening area, with 10 fixed valves arranged in 120 mm triangular pitch. The weir length and height are 450 and 50 mm, respectively. The downcomer 382



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Figure 5. Illustration of the computational mesh.

Good initial guesses of the flow variables are important not only to avoid a significantly longer computational time but also in some cases to avoid divergence. Water and air at room temperature and atmospheric pressure were used as the gas and liquid phases, respectively, in the simulations. At the start of a simulation, the tray configuration shown in Figure 4 was filled with a uniform gas−liquid dispersion, with 50% gas holdup. The simulations were carried out using the commercial packages ANSYS CFX12.0 and run on a HP Z800 workstation with two Intel Xeon X5687 3600 MHz processors used in parallel and 96 Gb RAM. A high-resolution scheme was used to discretize the convection terms to reduce the numerical diffusion errors. The time increment used in the simulations was 0.001 s. To obtain converged results, the target value of the normalized residual for each variable was set to 10−5, as generally recommended in the CFX-12.0 User Manual.31 A function of clear liquid height, which was calculated as the tray spacing multiplied by the volume-averaged of the liquid-volume fraction, was wrote using CEL31 and taken as a monitor expression in the output control. During the simulation, the clear liquid height and the volume fraction of the gas phase in the gas−liquid dispersion in the system were monitored, and quasi-steady state was assumed to prevail if the value of the hold-up remained constant for a period long enough to determine the time-averaged values of the various parameters.

Figure 6. Transient clear liquid height monitored as a function of time. Us = 0.87 m/s; hw = 0.05 m; Ql/Lw = 0.00494 m3/(s·m).

Figure 7. Clear liquid height as a function of the superficial gas velocity. hw = 0.05 m; Ql/Lw = 0.00494 m3/(s·m).

4. RESULTS AND DISCUSSION 4.1. Comparison between Predicted and Measured Clear Liquid Heights. A transient simulation was deemed to have converged whenever the clear liquid height value showed no appreciable change with time. Typically, steady state was achieved in about 4 s from the start of the simulation with the indicator that the clear liquid height was changing with time in a bounded, chaotic manner as shown in Figure 6. Figure 7 plots the clear liquid height versus the superficial gas velocity with the results from CFD simulations, experiments, and Bennett et al.22 correlation as shown in eqs 17−20. The values of clear liquid heights from the CFD simulations were obtained after averaging over a sufficiently long time interval once quasi-steady state conditions were established and determining the cumulative liquid hold-up within the computational space. It is remarkable to note that both CFD simulations and Bennett et al. correlation match the experiments quite closely. Within the superficial gas velocity range of this study, clear liquid height decreases with increasing superficial gas velocity at a given weir height and liquid load. Also shown in Figures 8 and 9 are the clear liquid height with varying weir heights and liquid loads, respectively. It can be seen that the clear liquid height increases with increasing weir height at a

Figure 8. Clear liquid height as a function of the weir height. Us = 0.87 m/s; Ql/Lw = 0.00494 m3/(s·m).

given superficial gas velocity and liquid load, and also increases with increasing liquid load at a given superficial gas velocity and weir height. It is remarkable that CFD simulations in this study 383



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Figure 9. Clear liquid height as a function of the liquid load per weir length. Us = 0.87 m/s; hw = 0.05 m.

tend to underpredict clear liquid height. Krishna et al.21 found the CFD to give larger clear liquid height values of sieve tray than those from experiments. That is because the principle of communicating vessel used in this study measured the clear liquid height in real time without subtracting out the impact of the gas flow. Krishna et al. measured the clear liquid height in this way: the gas inlet and liquid inlet were simultaneously and instantly switched off, then the liquid on the tray drained to the container beneath and was measured, and the clear liquid height was determined. So they got the “pure” clear liquid height. In the present work, however, the measures were on the higher side in some degree due to the froth regime on the tray. With Ql/Lw = 0.00494 m3/(s·m), hw = 0.05 m, and varying superficial gas velocities, the clear-liquid height profiles determined from averages of the liquid volume fraction on vertical slices above the tray deck are shown in Figure 10. Unlike the “bath-tub” profile for sieve trays,20,21,23 the clear liquid heights are larger near the outlet weir, while they show no distinct increase near the liquid entrance. Liquid propulsion caused by the ligulate holes on the valves is expected to cause the distribution. Similarly, the clear liquid heights near the column wall, in Figure 10b, are observed to be even, because the gas from the valve holes nearby flows toward the wall and there are no calming zones as appeared on sieve trays.18,20 The fluctuating ranges of clear liquid heights along both z- and x-directions are bigger than those of sieve trays due to gas collision from adjacent narrow interstices between valve cap and the tray deck, so the liquid is strongly disturbed. We also noticed that the clear liquid height profile at Us = 0.5 m/s differs from the other two in the transverse direction as shown in Figure 10b. That is because at low superficial gas velocity, gas collision is not as great as that at high superficial gas velocity. 4.2. Gas and Liquid Velocity Profiles. Figure 11 presents computational gas velocity vector snapshots of the side view of the tray at different superficial gas velocities. As can be seen from Figure 11a, horizontal velocity component of the gas from adjacent interstices results in gas collision and gas circulation cells, consequently promoting the gas−liquid mixing and mass transfer. With the increase of superficial gas velocity, gas collision is intensified at horizontal direction and liquid layer thickness decreases. Besides, horizontal velocity component near the column wall contributes to eliminating calming zones

Figure 10. Clear liquid height profiles in longitudinal and transverse directions to liquid flow. Ql/Lw = 0.00494 m3/(s·m), hw = 0.05 m: (a) averaged on x−y slices; (b) averaged on y−z slices.

on the tray as mentioned above. Gas propulsion from the ligulate holes is apparent, in Figure 11c, supporting the explanation made earlier that the clear liquid heights are larger near the outlet weir, at the same time contributing to reducing the liquid surface gradient. Figure 12 presents computational liquid velocity vector snapshots of the top view at different elevations. The space from the tray deck to the top of the weir is the main mass transfer zone, where gas contacts sufficiently with liquid. Below the valve cap, as shown in Figure 12a, gas sprays from the valve holes dragging up a great amount of liquid, and other liquid bypasses the valve zones. The chaotic behavior of the tray hydrodynamics is shown in Figure 12b. Above the weir height, the top view at a height of 60 mm as shown in Figure 12c, the liquid volume fraction is small, and the gas rises toward the upper tray. Profiles of the gas-phase vertical-component velocity at different elevations in the liquid flow direction at x = 0 m are shown in Figure 13. Close to the tray deck, y = 0, there are two 384



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Figure 11. Gas velocity vector snapshots of the side view. Ql/Lw = 0.00494 m3/(s·m), hw = 0.05 m.

Figure 12. Liquid velocity vector snapshots of the top view. Us = 0.87 m/s, Ql/Lw = 0.00494 m3/(s·m), hw = 0.05 m.

bars along the curve corresponding to the two valve holes encountered in the sweeping direction, and the rest of the curve declines to zero for the wall boundary condition on the tray deck. At the heights of y = 0.03 m and y = 0.09 m, the peaks of the gas velocities appear between the two valve holes, and the rest of the curves declines greatly. The gas flow resistance from the valve caps in the vertical direction is expected to cause the decline. It is noticed that there are small peaks along the declined part of the curves, exactly right within the valve cap area. Obviously they are caused by the gas impinging in the oblique upward direction from the ligulate holes as shown in Figure 11c. With increasing height from the tray deck, the magnitude of the oscillations decreases. As soon as the weir height is crossed, the gas velocity decreases due to the increase in the cross-sectional area available for gas flow. 4.3. Gas and Liquid Streamline Profiles. Liquid- and gasphase streamline profiles, as shown in Figure 14, present additional insights into the two-phase flow behavior. The liquid

Figure 13. Gas-phase vertical-component velocity at different elevations above tray deck. Us = 0.87 m/s, Ql/Lw = 0.00494 m3/(s·m), hw = 0.05 m. 385



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phase streamlines is apparent in the direction of the liquid flow. Some gas-phase streamlines exit from the weir outlet along with liquid-phase streamlines near the weir area; the increased liquid flow velocities as liquid starts to flow out are expected to cause the more intense blending. After getting through the liquid layer, the gas flows in a straight path as it encounters no sideways push. The strong interphase contact is also reflected in the simulated gas−liquid interface profile and in the photograph taken from the experiment, presenting a honeycomb-like appearance as shown in Figure 15. The streamline profiles contribute to analyzing the effect of tray configuration on hydrodynamic performance and conducting optimizing design of tray parameters. 4.4. Snapshots of Gas Hold-Up. Figure 16 presents the gas hold-up snapshots at different time after the steady state was achieved. The chaotic behavior is apparent. Two valves with ligulate holes are encountered at z = 0. It can be seen that the liquid layer is broken at each ligulate hole by the gas sparging. The ligulate holes contribute to agitating liquid phase and improving interphase mass transfer. Figure 17 shows the gas hold-up snapshots of the top view at different heights from the tray deck. As can be seen, the gas hold-up does not vary in a monotonous way with increasing height, whereas it decreases below y = 30 mm and after that increases with increasing the height. The nonmonotonic variation is further reflected in Figure 18. The trough of gas hold-up is clearly evident. With increasing superficial gas velocity, the minimum of gas hold-up increases and the transition height decreases slightly. These observations differ from the results of sieve trays described by Getye Gesit23 and R. Krishna.21,25 The fixed valves above the tray deck and crosswise gas sparging are expected to cause the nonmonotonic variation of gas hold-up. The two-phase regime above the tray can be divided into liquid continuous region and gas continuous region. The transition of the two regions is approximately at the weir height. Below the weir height, the liquid phase dominates, and the gas phase is the dispersed phase. Likewise, the gas phase becomes a continuous phase with entrained liquid droplets above the weir height.

Figure 14. Streamline profiles of the liquid (in blue) and the gas (in red). Us = 0.87 m/s, Ql/Lw = 0.00494 m3/(s·m), hw = 0.05 m.

Figure 15. Simulated gas−liquid interface profile (left) and photograph taken from the experiment (right).

phase is agitated by the gas phase and follows wobbling paths. Because of the residence to the liquid flow, liquid circulation cells near the weir area are observed. The bending of the gas

Figure 16. Gas hold-up snapshots of the front view. Us = 0.87 m/s, Ql/Lw = 0.00494 m3/(s·m), hw = 0.05 m. 386



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Figure 17. Gas hold-up snapshots of the top view at different heights. Us = 0.87 m/s, Ql/Lw = 0.00494 m3/(s·m), hw = 0.05 m.

C = 0.41 + 1.12 exp[ − 50.86hw ] αl ave

0.92 ⎤ ⎡ ⎛ ρg ⎞ ⎥ ⎢ ⎟ = exp⎢ − 5.71⎜Us ⎜ ⎟ ⎥ ρ − ρ l g ⎠ ⎝ ⎢⎣ ⎥⎦

The maximum margin of error is ±10%, and the average error is 3.35%. Clear liquid height was predicted for various combinations of weir height, gas, and liquid flow rates. Additional insights into the gas and liquid flow behavior were gained with the aid of vector and velocity profiles, streamlines, and snapshots of gas hold-up. The information predicted by the CFD model can be used in the optimal design of industrial trays. Although the present CFD model well predicts the macroscopical parameters (e.g., clear liquid height), a thorough validation of predictions of the velocities, volume fractions, and turbulence quantities, which is lacking in the present study because of the nonexistence of data, is necessary to be able to assess critically the reliability. This is crucially dependent on the acquisition of good quality and detailed experimental data.

Figure 18. Distribution of gas hold-up along the height from the tray deck for different superficial gas velocities. Ql/Lw = 0.00494 m3/(s·m), hw = 0.05 m.

■

ASSOCIATED CONTENT

S Supporting Information *

5. CONCLUSIONS In this work, we have attempted to predict the hydrodynamics of a new type of fixed valve tray by means of CFD. A transient three-dimensional model was developed for gas- and liquid-flow within the Eulerian framework, and both phases were treated as interpenetrating continuum having separate transport equations. A new clear liquid height correlation for the tray was found by experimental data regression to close the model: ⎡ ⎛ Q l ⎞0.67 ⎤ ⎥ hcl = αl ave⎢hw + C ⎜ ave ⎟ ⎢⎣ ⎝ Lw αl ⎠ ⎥⎦

Dimensions of the new type of fixed valve tray. This material is available free of charge via the Internet at http://pubs.acs.org.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS We are grateful for the financial support from the National Basic Research Program of China (no. 2009CB219905), and

where 387



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the Program for Changjiang Scholars and Innovative Research Team in University (no. IRT0936).

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NOMENCLATURE Ah = area of a single hole (m2) m1−5 = parameters in the clear liquid height correlation CD = drag coefficient C = weir coefficient dg = diameter of gas bubble (m) g = gravitational force (9.8 m s−2) hap = downcomer clearance (m) hcl = clear liquid height (m) hw = weir height (m) Lw = weir length (m) M = interphase momentum exchange between gas and liquid phases (N m−3) Nh = number of valve holes P = pressure (N m−2) Qg = gas flow rate (m3 s−1) Ql = liquid flow rate (m3 s−1) Re = Reynolds number t = time (s) u = velocity vector (m s−1) Ug,in = inlet velocity profile of gas (m s−1) Ul,in = inlet velocity profile of liquid (m s−1) Us = superficial gas velocity (m s−1) Vslip = slip velocity between gas and liquid (m s−1) FVol = surface tension force (N) F2 = blending function in the SST model S = mean strain rate (s−1)

Greek Letters

ρ = density of phase (kg m−3) α = volume fraction of phase μ = viscosity of phase (P s−1) κ = turbulent kinetic energy (m2 s−2) ε = turbulent dissipation rate (m2 s−3) σ = surface tension coefficient (N/m) γ = surface curvature ω = specific dissipation rate, turbulence frequency νt = kinematic eddy viscosity (P s−1)

Subscripts

cl = clear liquid eff = effective g = referring to gas phase in = inlet l = referring to liquid phase lam = laminar slip = slip tur = turbulent w = weir Superscripts

ave = average

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REFERENCES

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