CFD SIMULATION OF SOLID-LIQUID STIRRED TANKS
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Divyamaan Wadnerkar , Ranjeet P. Utikar , Mos O. Tade , Vishnu K. Pareek
1 1 1 1夏朝文物
Department of Chemical Engineering, Curtin University Perth, WA 6102 r.utikar@curtin.edu.au
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ABSTRACT Solid liquid stirred tanks are commonly ud in the minerals industry for operations like concentration, leaching, adsorption, effluent treatment, etc. Computational Fluid Dynamics (CFD) is increasingly being ud to predict the hydrodynamics and performance of the systems. Accounting for the solid-liquid interaction is critical for accurate predictions of the systems. Therefore, a careful lection of models for turbulence and drag is required. In this study, the effect of drag modelwas studied. A Eulerian-Eulerian multipha modelling approach is ud to simulate the solid suspension in stirred tanks. Multiple reference frame (MRF) approach is ud 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 obrved that high turbulence can increa the drag coefficient as high as forty times when compared with a still fluid. The drag force was modified to acc
ount for the increa 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 cas simulated. The modified drag law was found to be uful 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 ud in the field of chemical and mineral industry. The main purpo of mixing is the contact between the solid and liquid pha for facilitating mass transfer. In in industrial process 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 uful tool in analyzing the impact of the 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.,
Divyamaan Wadnerkar, Ranjeet P. Utikar, Mos O. Tade, Vishnu K. Pareek
2001, Ochieng and Lewis, 2006). Proper evaluation of interpha drag is esntial for accurate predictions using the CFD model. In this study four different drag models are analyd 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) ud Settling Velocity Model (SVM) and Multi fluid Model (MFM) approaches to analy 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 superimpod dimentation flow, whereas in MFM, momentum balances are solved for both phas. Computationally intensive MFM was found to be better than SVM, but for both the models it was necessary to take into account the increa 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 consu
ming, 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 ud 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 ud for den 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 pha 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 ud, 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 ttling by gravity is added. In the ca of a mixing process, owing to the action of shear and inertia, the particles may gregate and demix, thereby generating concentration gradients in the vesl. This shear-induced migration phenomenon can be simulated at the macroscopic scale, where the suspension is modelled as one continuous pha
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Divyamaan Wadnerkar, Ranjeet P. Utikar, Mos O. Tade, Vishnu K. Pareek
through a viscosity law (Fradette et al., 2007). However, this model shows potentially erratic behavior in clo-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 pha 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 ud for the simulation of liquid flow field in stirred tanks (2008). It was able to capture the key features of liquid pha mixing process. Panneerlvam et al. (2008) ud the Brucato drag law to simulate 7% v/v solids in liquid. MRF approach was ud 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 interpha 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 turb
ulence become increasingly important. Moreover, there is no connsus 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 assd to provide a clear understanding of the lection criterion of drag in a particular ca.
CFD MODEL Model Equations The hydrodynamic study is simulated using Eulerian-Eulerian multipha model. Each pha, in this model, is treated as an interpenetrating continuum reprented by a volume fraction at each point of the system. The Reynolds averaged mass and momentum balance equations are solved for each of the phas. The governing equations are given below: Continuity equation:
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Divyamaan Wadnerkar, Ranjeet P. Utikar, Mos O. Tade, Vishnu K. Pareek
Momentum equation:
Where q is 1 or 2 for primary or condary pha respectively, α is volume fraction, ρ is density, is the velocity vector, P is pressure and is shared by both the phas, is the stress tensor becau of vi
scosity and velocity fluctuations, g is gravity, to turbulent dissipation, force and is external force, is lift force, is force due is virtual mass
is interpha interaction force.
请勿乱扔垃圾The stress-strain tensor is due to viscosity and Reynolds stress 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
王维的送别诗is the shear viscosity,
is bulk viscosity and is the unit stress tensor.
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Equations for Turbulence k-ε mixture turbulence and k-ε disperd turbulence models are ud in the prent study. The mixture turbulence model assumes the domain as a mixture and solves for k and ε values which are common for both the phas. In the disperd turbulence model, the modified k-ε equations are solved for the continuous pha and the turbulence quantities of disperd pha are calculated using Tchen-theory correlations. It also takes the fluctuations due to t
urbulence by solving for the interpha 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 ur guide (ANSYS, 2009).
are constants. The mixture density,
and
are turbulent Prandtl numbers. are computed from the equations below:
and velocity,
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Divyamaan Wadnerkar, Ranjeet P. Utikar, Mos O. Tade, Vishnu K. Pareek
Turbulent viscosity, equations below:
and turbulence kinetic energy,
are computed from
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 analyd in this study. It is incorporated along with the momentum equation and is given as follows:
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Where drift velocity,
is given by,
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Dp and Dq are diffusivities and σpq is dispersion Prandtl number. Interpha Drag Force The drag force reprents interpha momentum transfer due to the disturbance created by each pha. 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 ud. 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 discusd. But for stirred tank systems, there should be a model that takes turbulence into account as with increasing Reynolds number and with the increa in the eddy sizes, the impact of turbulence on the drag increas. Considering this Brucato et al. (1998) propod a ne
w 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 propod by Brucato et al. is given below:
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