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AbstractComputational fluid dynamics (CFD) provides a method for investigating the highly complex fluid flowin mechanically stirred tanks. Although there are quite a number of papers in the literature describing CFDmethods for modelling stirred tanks, most only consider single-phase flow. However, multiphase mixturesoccur very frequently in the process industries, and these are more complex situations for which modellingis not as well developed. This paper reports on progress in developing CFD simulations of gas–liquidmixing in a baffled stirred tank. 31248
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The model is three-dimensional and the impeller region is explicitly in-cluded using a Multiple Frames of Reference method to account for the relative movement between im-peller and baffles. Fluid flow is calculated with a turbulent two-fluid model using a finite-volume method.Several alternative treatments of the multiphase equations are possible, including various expressions fordrag and dispersion forces, and a number of these have been tested. Variation in bubble size due to co-alescence and break-up is also modelled. The CFD simulation method has been used to model a gas-sparged tank equipped with a Rushton turbine, and simulation results are compared with experimentaldata. Results to date show the correct pattern of gas distribution and the correct trends in local bubble sizein the tank. Further work is needed to improve the quantitative agreement with experimental data. 2002Elsevier Science Inc. All rights reserved.Keywords: CFD; Mixing; Stirred vessel; Gas dispersion; Bubble break-up; Coalescence1. IntroductionComputational fluid dynamics (CFD) is becoming an increasingly useful tool in analysis of thehighly complex fluid flow in mechanically stirred tanks. There are a number of papers published to date (e.g. [1–3]) which present simulation methods for stirred tanks. However, most simulationsreported in the literature deal with just single-phase liquid flow, whereas applications in theprocess industries often involve gas–liquid, solid–liquid, or three-phase mixtures, and hencemodelling methods need to be extended to deal with multiphase flows. This paper describesprogress in developing a simulation method for gas–liquid contacting in stirred tanks. It is in-tended that the model should be able to predict characteristics such as gas holdup, interfacial area,mass transfer rate and reaction rates. Such a model would have applications in design and op-timisation of a wide range of gas–liquid processes carried out in stirred vessels.A number of simulations of gas–liquid dispersion in stirred tanks have been presented in theliterature thus far, and although some degree of success is reported, several significant limitationsare apparent. For example, in several cases the model is axisymmetric, which is perhaps not veryrealistic [4–6], although three-dimensional simulations have also been carried out, notably byBakker [1]. In several cases accuracy is probably limited by low grid resolution (e.g. [7]). Aconstant bubble size is often assumed, although Bakker’s method [1] allows for bubble coales-cence. Another limitation common to all published methods is that the impeller is not directlysimulated, but is instead modelled, for example using experimentally determined impellerboundary conditions, in which case valid measurements must always be available. Also, suchmethods do not provide information about the flow in the impeller region.Work is being undertaken to develop improved modelling methods for gas–liquid flow instirred tanks. To make the method as independent as possible of experimental data, the impeller isexplicitly included in the simulation.
Emphasis is also given to obtaining the most efficient meansof computation of such a complex flow, to determining the most appropriate models for the gas–liquid interaction, and predicting gas bubble sizes and interfacial area.2. Modelling the impellerLiterature on CFD modelling of baffled stirred tanks demonstrates a range of modellingmethods, one of the main variations being in the treatment of the impeller–baffle interaction,where a significant modelling problem arises since there is no single frame of reference for carryingout computations. In some cases an empirical model is provided for the impeller, as in gas–liquidsimulations reported thus far (e.g. [1,5]). However, several methods are reported for single-phaseflow which treat the impeller region explicitly and these might possibly be extended to two-phaseflow. The Sliding Mesh method has been widely used in recent years [3]. This is a time-dependentmethod where the section of the grid surrounding the impeller is allowed to rotate stepwise, andthe flow field is recalculated for each step. This method is therefore very computationally in-tensive, and computational requirements become excessive for two-phase flow. An alternative method is theMultiple Frames of Reference method, where flow is calculated bypiding the tank into two domains each with its own frame of reference. In the impeller regionflow is calculated in a rotating frame of reference where the impeller appears stationary, while inthe bulk of the tank a stationary frame of reference is used, a correction in the velocities beingmade at the interface between the two zones. Thus, a steady-state calculation can be carried out.For single-phase flow, the method has previously been shown [2,8] to provide a saving in com-puter time of a factor of about 10, while providing a degree of accuracy similar to the SlidingMesh method. Therefore, to permit more efficient computation, this method has been adoptedhere and extended to two-phase flow.3. Equations for two-phase flowGas–liquid flow is modelled using a two-fluid approach where the gas and liquid are describedas interpenetrating continua and equations for conservation of mass and momentum are solvedfor each phase. However, since the flow is turbulent, the equations are solved in an averaged formrequiring a turbulence model for closure.
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