CFD SIMULATION OF SOLID-LIQUID STIRRED TANKS

CFD SIMULATION OF SOLID-LIQUID STIRRED TANKS Divyamaan Wadnerkar 1, Ranjeet P. Utikar 1, Moses O. Tade 1, Vishnu K. Pareek 1 Department of Chemical Engineering, Curtin University Perth, WA 6102 r.utikar@curtin.edu.au ABSTRACT Solid liquid stirred tanks are commonly used in the minerals industry for operations like concentration, leaching, adsorption, effluent treatment, etc. Computational Fluid Dynamics (CFD) is increasingly being used to predict the hydrodynamics and performance of these systems. Accounting for the solid-liquid interaction is critical for accurate predictions of these systems. Therefore, a careful selection of models for turbulence and drag is required. In this study, the effect of drag modelwas studied. A Eulerian-Eulerian multiphase modelling approach is used to simulate the solid suspension in stirred tanks. Multiple reference frame (MRF) approach is used to simulate the impeller rotation in a fully baffled tank. Simulations are conducted using commercial CFD solver ANSYS Fluent 12.1. The CFD simulations are conducted for concentration 1% v/v and the impeller speeds above the just suspension speed. It is observed that high turbulence can increase the drag coefficient as high as forty times when compared with a still fluid. The drag force was modified to account for the increase in drag at high turbulent intensities. The modified drag is a function of particle diameter to Kolmogorov length scale ratio, which, on a volume averaged basis, was found to be around 13 in the cases simulated. The modified drag law was found to be useful to simulate the low solids holdup in stirred tanks. The predictions in terms of the velocity profiles and the solids distribution are found to be in reasonable agreement with the literature experimental data. The work provides an insight into the solid liquid flow in stirred tanks. INTRODUCTION Solid liquid mixing systems are amongst the common operations used in the field of chemical and mineral industry. The main purpose of mixing is the contact between the solid and liquid phase for facilitating mass transfer. In in industrial processes effective mixing is necessary at both micro and macro level for adequate performance. At the micro level, micromixing governs the chemical and mass transfer reactions. Micromixing is facilitated by mixing at macro level. Numerous factors such as the just suspension speed, critical suspension speed, solids distribution, etc. dictate the mixing performance. CFD has proved to be a useful tool in analyzing the impact of these factors on the flow characteristics of such systems (Fradette et al., 2007, Kasat et al., 2008, Khopkar et al., 2006, Micale et al., 2004, Micale et al., 2000, Montante et al.,

2001, Ochieng and Lewis, 2006). Proper evaluation of interphase drag is essential for accurate predictions using the CFD model. In this study four different drag models are analysed and their validity is checked by comparing the results of CFD simulations at low concentrations of solid with the experimental data available in the literature (Guha et al., 2007). LITERATURE REVIEW Micale et al. (2000) used Settling Velocity Model (SVM) and Multi fluid Model (MFM) approaches to analyse the particle distribution in stirred tanks. In SVM, it is assumed that the particles are transported as a passive scalar or molecular species but with a superimposed sedimentation flow, whereas in MFM, momentum balances are solved for both phases. Computationally intensive MFM was found to be better than SVM, but for both the models it was necessary to take into account the increase in drag with the increasing turbulence. Micale et. al. (2004) simulated the solids suspension of 9.6% and 20% volume fractions using the MFM approach and sliding grid (SG) approach using the Schillar Nauman drag model. Schillar Nauman is applicable on spherical particles in an infinite stagnant fluid and accounts for the inertial effect on the drag force acting on it. It provided satisfactory results at low impeller speed. Ochieng and Lewis (2006) simulated nickel solids loading of 1-20% w/w with impeller speeds between 200 and 700 RPM using both steady and transient simulations and found out that transient simulations, although time consuming, are better for stirred tank simulations. The initial flow field was generated using the multiple reference frame (MRF) approach and then the simulations were carried out using SG. The Gidaspow model was used for the drag factor, which is a combination of the Wen and Yu model and the Ergun equation (Ding and Gidaspow, 1990). Wen and Yu drag is appropriate for dilute systems and Ergun is used for dense packing. For the study of just suspended of solids using solids at the bottom of the tank as an initial condition, it provided satisfactory results. The suspension can also be modelled as a continuous phase using a viscosity law and the shear induced migration phenomenon generated by gradients in shear rates or concentration gradients can be captured at a macroscopic scale. For the prediction of shear-induced particle migration, the Shear Induced Migration Model (SIMM) was used, which states that, in a viscous concentrated suspension, small but non-brownian particles migrate from regions of high shear rate to regions of low shear rate, and from regions of high concentrations to regions of low concentrations in addition to which settling by gravity is added. In the case of a mixing process, owing to the action of shear and inertia, the particles may segregate and demix, thereby generating concentration gradients in the vessel. This shear-induced migration phenomenon can be simulated at the macroscopic scale, where the suspension is modelled as one continuous phase 2

through a viscosity law (Fradette et al., 2007). However, this model shows potentially erratic behavior in close-to-zero shear rate and high concentration zones. The dependency of the drag on the turbulence was numerically investigated by Khopkar at al. (2006) by conducting experiments using single phase flow through regularly arranged cylindrical objects. A relationship between the drag, particle diameter and Kolmogorov length scale was fit into the expression given by Brucato et al. (1998). They found that the drag predicted by the original Brucato drag model needs to be reduced by a factor of 10. This modified Brucato model was then used for the simulation of liquid flow field in stirred tanks (2008). It was able to capture the key features of liquid phase mixing process. Panneerselvam et al. (2008) used the Brucato drag law to simulate 7% v/v solids in liquid. MRF approach was used with Eulerian-Eulerian model. There was mismatch in the radial and tangential components of velocity at impeller plane. This discrepancy was attributed to the turbulent fluctuations that dominate the impeller region, which the model was not able to capture successfully. It is quite clear from the review that solids suspension and distribution is highly dependent on the turbulence and interphase drag in the tank. At low impeller speeds, turbulent fluctuations are less and hence do not affect the predictions much. However, at higher impeller speeds, the drag and turbulence become increasingly important. Moreover, there is no consensus on the appropriate drag for liquid-solid stirred tanks. Therefore, in this study, the impact of drag model on the flow distribution and the velocity fields is investigated. Different drag models are assessed to provide a clear understanding of the selection criterion of drag in a particular case. CFD MODEL Model Equations The hydrodynamic study is simulated using Eulerian-Eulerian multiphase model. Each phase, in this model, is treated as an interpenetrating continuum represented by a volume fraction at each point of the system. The Reynolds averaged mass and momentum balance equations are solved for each of the phases. The governing equations are given below: Continuity equation: 3

Momentum equation: Where q is 1 or 2 for primary or secondary phase respectively, α is volume fraction, ρ is density, is the velocity vector, P is pressure and is shared by both the phases, is the stress tensor because of viscosity and velocity fluctuations, g is gravity, is force due to turbulent dissipation, is external force, is lift force, is virtual mass force and is interphase interaction force. The stress-strain tensor is due to viscosity and Reynolds stresses that include the effect of turbulent fluctuations. Using the Boussinesq s eddy viscosity hypothesis the closure can be given to the above momentum transfer equation. The equation can be given as: Where is the shear viscosity, is bulk viscosity and is the unit stress tensor. Equations for Turbulence k-ε mixture turbulence and k-ε dispersed turbulence models are used in the present study. The mixture turbulence model assumes the domain as a mixture and solves for k and ε values which are common for both the phases. In the dispersed turbulence model, the modified k-ε equations are solved for the continuous phase and the turbulence quantities of dispersed phase are calculated using Tchen-theory correlations. It also takes the fluctuations due to turbulence by solving for the interphase turbulent momentum transfer. For the sake of brevity, only the equations of mixture model for turbulence are given below. Other equations can be found in the Fluent user guide (ANSYS, 2009). are constants. and are turbulent Prandtl numbers. The mixture density, and velocity, are computed from the equations below: 4

Turbulent viscosity, and turbulence kinetic energy, are computed from equations below: Turbulent Dispersion Force In the simulation of solid suspension in stirred tanks, the turbulent dispersion force is significant when the size of turbulence eddies is larger than the particle size (Kasat et al., 2008). Its significance is also highlighted in some previous studies (Ljungqvist and Rasmuson, 2001). The role of this force is also analysed in this study. It is incorporated along with the momentum equation and is given as follows: Where drift velocity, is given by, D p and D q are diffusivities and σ pq is dispersion Prandtl number. Interphase Drag Force The drag force represents interphase momentum transfer due to the disturbance created by each phase. For dilute systems and low Reynolds number, particle drag is given by Stokes law and for high Reynolds number, the Schillar Nauman Drag Model can be used. In the literature review other drag models such as Gidaspow model (Ding and Gidaspow, 1990) and Wen and Yu model (Wen and Yu, 1966) have also been discussed. But for stirred tank systems, there should be a model that takes turbulence into account as with increasing Reynolds number and with the increase in the eddy sizes, the impact of turbulence on the drag increases. Considering this Brucato et al. (1998) proposed a new drag model making drag coefficient as a function of ratio of particle diameter and Kolmogorov length scales. So, with the change in the turbulence at some local point in the system, the drag will also change. The drag coefficient proposed by Brucato et al. is given below: 5

where, K is constant with value, d P is particle diameter and is Kolmogorov length scale. Khopkar et al. (2006) performed DNS simulations for conditions closer to those in stirred tanks. Based on these simulations they obtained a modified version of Brucato drag that is more appropriate for stirred tanks. This modified drag has a constant value of 8.67 X 10-5. In this paper, the Gidaspow, Wen and Yu, Brucato and modified Brucato Drag models are assessed. METHODOLOGY AND BOUNDARY CONDITIONS Vessel geometry In the current study, a flat bottomed cylindrical tank was simulated. The dimensions used are tank diameter, T = 0.2 m and tank height, H= T. The tank has four baffles mounted on the wall of width T/10. The shaft of the impeller (of diameter = 0.01m) was concentric with the axis of the tank. A six-bladed Rushton Turbine was used as an impeller. The Rushton turbine has a diameter, D = T/3. For each blade, the length =T/12 and the height = T/15. The impeller off-bottom clearance was (C = T/3) measured from the level of the impeller disc. The fluid for the system was water (ρ = 1000 kg / m 3, µ = 0.001 Pa.s) and the solids were small glass particles of density 2550 kg / m 3 and diameter of 0.3 mm. Numerical simulations Owing to the rotationally periodic nature, half of the tank was simulated. Multiple reference frame (MRF) approach was used. A reference moving zone with dimensions r = 0.06 m and 0.03995 < z < 0.09325 was created (where z is the axial distance from the bottom). The impeller rod outside this zone was considered as a moving wall. The top of the tank was open, so it was defined as a wall of zero shear. The specularity coefficient is 0 for smooth walls and is 1 for rough walls. The walls of stirred tank were assumed to be smooth and a very small specularity coefficient of 0.008 was given to all other walls. In the initial condition of the simulation, a uniform concentration of 0.01 v/v fraction glass particles was taken in the tank. The rotation speed of the impeller was 1000 rpm that was above the speed of just-suspension of glass particles in the liquid. For modelling the turbulence, a standard k- ε mixture model was used. The model parameters were Cµ : 0.09, C 1 : 1.44, C 2 : 1.92, σ k : 1.0 and σ ε = 1.3. In few cases the standard k- ε dispersion model was also used with the turbulence Schmidt number, σ, taken as equal to 0.8. The steady state numerical solution of the system was obtained by using the commercial CFD solver ANSYS 12.1 FLUENT. In the present work, 6

Simple Pressure-Velocity coupling scheme was used along with the standard pressure discretization scheme. RESULTS AND DISCUSSION Preliminary numerical simulations In order to verify that the simulations have converged, the residuals as well as additional parameters namely turbulence dissipation over the volume and torque on the shaft were monitored. Once the residuals and additional parameters were constant, the simulation was deemed to have converged. Initial simulations were conducted to assess the effect of turbulence dispersion force. The flow field was analysed and it was found that there was negligible effect of this force in this particular case of 0.01 volume fraction. The turbulence dispersion force has higher influence at higher concentration of solids where its magnitude will be high enough to be comparable with the other forces being exerted on the secondary phase (Ljungqvist and Rasmuson, 2001). Flow Field Vectors in the domain converged solution showed similar flow field (velocity field vectors) as compared to that available in the literature (Guha et al., 2007). Figure 1 shows the velocity vectors on a center plane. All these characteristics of the flow are clearly visible in figure 1. For the Rushton turbine, an outward jet stream is formed due to the outward thrust of the impeller. This high velocity jet approaches towards the wall of the stirred tank and then splits Fig. 1: Velocity vectors of solids velocity for solid volume fraction of 0.01 and 1000 RPM into upward and downward direction. It creates an anticlockwise velocity field in the region above the impeller and a clockwise velocity field in the region below the impeller. The velocity near walls for the region above impeller is upwards and below the impeller is downwards. It is opposite when the velocity field is observed near the 7

centre. The intensity of the swirl in the region below the impeller is stronger than that above the impeller. Analysis of different drag models The simulations were run using different drag models and the results were then compared with the experimental data. The radial velocity of the solid particles at impeller plane is shown in Figure 2. Out of the four drag models wide disparity with experimental data was observed when using the Wen and Yu and the Gidaspow model. These two models predicted the highest radial velocities. The Brucato drag model slightly overpredicted the radial velocity, whereas the predictions from the modified Brucato drag were in reasonable agreement with experimental data. The solid velocities are higher at the impeller tip. As the solids approach towards wall, the velocity gradually decreases. Due to no slip condition on the wall, the velocity should gradually reach zero value at wall. But, quantitatively, there is an overprediction of the velocities in simulations in near wall region. The disparity can be attributed to lesser number of data points available for averaging in experiments. As the experiments clearly show a zero ensemble averaged value even at (r- Ri/(R-Ri) = 0.8. At low solid concentrations, Gidaspow drag model acts like Wen and Yu model and at higher concentrations it takes the form of the Ergun equation. Therefore, both Wen and Yu model and Gidaspow models predict the same result. The modified Brucato drag model accounts for the effect of solid phase on the turbulence. At higher impeller speed, Fig. 2: Radial velocity at impeller plane for 0.01 solid volume fraction and 1000 RPM. Fig. 3: Radial velocity at axial plane r/r -0.5 for 0.01 solid volume fraction and 1000 RPM. Fig. 4: Tangential velocity at axial plane r/r 0.5 for 0.01 solid volume fraction and 1000 RPM. 8

the role of turbulence in calculation of drag is vital factor, hence, the modified Brucato drag model predicts better results as compared to the other drag models. Figure 3 shows the comparison between the simulations results and experimental data for radial velocity at axial plane r/r = - 0.5. A positive radial velocity is expected in the upper zone of the impeller. A slight negative radial velocity in the zone below impeller suggests a strong flow towards the centre of the stirred tank in that region. It indicates the presence of strong clockwise currents. All the drag models could qualitatively capture this Fig. 5: Axial velocity at axial plane r/r 0.5 for flow behaviour. For the experimental data, the highest tangential velocity is observed at z/t = 0.36 ± 0.04. This compares well the simulation result of z/t = 0.34. In the lower region of the stirred tank, where the effect of turbulence is not as prominent as the upper region, the predictions from all the drag models compared well with experimental data. In the upper region, discrepancy was observed. Around the impeller zone, where, the turbulence and velocity fluctuations are higher, the Wen and Yu and Gidaspow drag models show large overprediction compared to the experimental data. On the other hand, the Brucato and modified Brucato drag show reasonable agreement. Figure 4 shows the comparison between the simulations results and experimental data for tangential velocity at axial plane r/r = -0.5. Similar trend to that observed in radial velocity is observed. The axial velocity profile is shown in Figure 5. The reversal of flow can be clearly seen. Above the impeller, the axial velocities are negative that means the flow is in downward direction. It reverses in the region below impeller. At the impeller, the axial velocity is zero and is distributed as the other two components of velocities viz. radial and tangential. All the drag models were able to capture the flow reversal qualitatively. Moreover, the predictions of all the drag models were comparable. The experiments show higher axial velocity in the lower region compared to the upper region, whereas, the simulations predicted similar velocities in the lower and upper region of the impeller. Although this phenomenon is visible in figure 1, the axial velocities shown in figure 5 fail to predict it. It is because of the bigger circular loop in the lower region of the impeller clearly seen in figure 1, which also affects the ensemble averaging of values in 9

this particular zone. At the impeller plane, the axial velocity is zero as it is distributed as the other two components of velocities. CONCLUSION AND SCOPE OF FURTHER STUDY CFD simulations of solid suspension in stirred tank were performed. The predictions of four different drag models were compared. It was observed that turbulence dispersion force had negligible effect due to a low volume fraction of solids. Axial, radial and tangential velocities were compared at different axial locations. It was observed that all four models could qualitatively capture the flow in stirred tank. The Wen and Yu and Gidaspow model showed biggest deviation from the experimental data while results form the modified Brucato drag model were in reasonable agreement for the liquid flow fields. Future study includes extending the comparison and validation studies to higher solid concentrations, where the effect of solids on the turbulence is expected to increase. REFERENCES ANSYS 2009. Fluent User Guide. ANSYS Inc., Canonsburg, PA, www. fluent. com. BRUCATO, A., GRISAFI, F. & MONTANTE, G. 1998. Particle drag coefficients in turbulent fluids. Chemical Engineering Science, 53, 3295-3314. DING, J. & GIDASPOW, D. 1990. A bubbling fluidization model using kinetic theory of granular flow. AIChE Journal, 36, 523-538. FRADETTE, L., TANGUY, P. A., BERTRAND, F. O., THIBAULT, F., RITZ, J.-B. T. & GIRAUD, E. 2007. CFD phenomenological model of solid-liquid mixing in stirred vessels. Computers & Chemical Engineering, 31, 334-345. GUHA, D., RAMACHANDRAN, P. A. & DUDUKOVIC, M. P. 2007. Flow field of suspended solids in a stirred tank reactor by Lagrangian tracking. Chemical Engineering Science, 62, 6143-6154. KASAT, G. R., KHOPKAR, A. R., RANADE, V. V. & PANDIT, A. B. 2008. CFD simulation of liquid-phase mixing in solid-liquid stirred reactor. Chemical Engineering Science, 63, 3877-3885. KHOPKAR, A. R., KASAT, G. R., PANDIT, A. B. & RANADE, V. V. 2006. Computational Fluid Dynamics Simulation of the Solid Suspension in a Stirred Slurry Reactor. Industrial & Engineering Chemistry Research, 45, 4416-4428. LJUNGQVIST, M. & RASMUSON, A. 2001. Numerical Simulation of the Two-Phase Flow in an Axially Stirred Vessel. Chemical Engineering Research and Design, 79, 533-546. MICALE, G., GRISAFI, F., RIZZUTI, L. & BRUCATO, A. 2004. CFD Simulation of Particle Suspension Height in Stirred Vessels. Chemical Engineering Research and Design, 82, 1204-1213. MICALE, G., MONTANTE, G., GRISAFI, F., BRUCATO, A. & GODFREY, J. 2000. CFD Simulation of Particle Distribution in Stirred Vessels. Chemical Engineering Research and Design, 78, 435-444. MONTANTE, G., MICALE, G., MAGELLI, F. & BRUCATO, A. 2001. Experiments and CFD Predictions of Solid Particle Distribution in a Vessel Agitated with Four Pitched Blade Turbines. Chemical Engineering Research and Design, 79, 1005-1010. OCHIENG, A. & LEWIS, A. E. 2006. CFD simulation of solids off-bottom suspension and cloud height. Hydrometallurgy, 82, 1-12. 10

PANNEERSELVAM, R., SAVITHRI, S. & SURENDER, G. D. 2008. CFD modeling of gas-liquid-solid mechanically agitated contactor. Chemical Engineering Research and Design, 86, 1331-1344 WEN, C. Y. & YU, Y. H. Year. Mechanics of Fluidization. In: Chemical Engineering Progress Symposium Series, 1966. 100-111. 11