Flows in stirred tanks

In these model equations it is assumed that turbulence is isotropic, i.e. it has no favoured direction. The k-e model frequently offers a good compromise between computational economy and accuracy of the solution. It has been used successfully to model stirred tanks under turbulent conditions (Ranade, 1997). Manninen and Syrjanen (1998) modelled turbulent flow in stirred tanks and tested and compared different turbulence models. They found that the standard k-e model predicted the experimentally measured flow pattern best. 

Manninen, M. and Syrjanen, I., 1998. Modelling turbulent flow in stirred tanks. CFX Update, 16, 10-11. 

On the analogy of simulating the process of adding blobs of a miscible liquid, two-phase flow in stirred tanks in a RANS context may be treated in two ways Euler-Lagrange or Euler-Euler, with the second, dispersed phase treated according to a Lagrangian approach and from a Eulerian point of view, respectively. 

Figure 19.1 Examples of nonideal flow in stirred-tank and packed-bed vessels...

Kresta, S. M., and Wood, P. E., Prediction of the three-dimensional turbulent flow in stirred tanks. AIChE. J. 37(3), 448 (1991). 

Ranade and Tayalia (2000) validated the snapshot approach by considering a two-dimensional case of rotating flows. Application of this approach to simulating complex, three-dimensional flows in stirred tank reactors is discussed below. The next section will discuss application of this approach to cases relevant to reactor engineering. 

Many of the situations encountered by reactor engineers involve (refer to Table 10.1) contact with more than one phase in a stirred tank. It is, therefore, essential to examine whether CFD models can simulate complex multiphase flows in stirred tanks. Here the case of gas-liquid flows in a stirred tank is considered. Similar methodology can be applied to simulate other two-phase or multiphase flows in stirred vessels. The computational snapshot approach discussed previously has been extended to simulate gas-liquid flows (see Ranade et al., 2001c for more details). A two-fluid model was used to simulate gas-liquid flow in a stirred vessel the model equations and boundary conditions are listed below. 

In general, it may be concluded that the computational snapshot approach or other equivalent, state of the art CFD models can capture the key features of flow in stirred tank reactors and can be used to make either quantitative (for single-phase or pseudo-homogeneous applications) or semi-quantitative (for complex, multiphase applications) predictions. Possible applications to reactor engineering are discussed below. 

Lane, G.L., Schwarz, M.P. and Evans, G.M. (1999), CFD simulation of gas-liquid flow in stirred tank, 3rd Int. Symp. on Mixing in Industrial Processes, Japan. 

Placek J., Tavlarides L.L., Turbulent Flow in Stirred Tanks. Part I Turbulent Flow in the Turbine Impeller Region, AIChE J. 31 (1985) 7, p. 1113-1120... 

By far the most widely employed models for turbulent reactive flows in stirred tanks are based on the Reynolds averaged Navier Stokes (RANS) equation. This is a moment equation containing quantities that are averaged over the whole wave spectra, as explained in sect 1.2.7. 

Murthy JY, Mathur SR, Choudhury D (1994) CFD Simulation of Flows in Stirred Tank Reactors Using a Sliding Mesh Technique. ICHEME Symposium Series, No. 136, pp. 341-348. Eight European Conference on Mixing, Cambridge (ISBN 0852953291)... 

Measurements have been made of turbulence structure by a number of workers using laser-Doppler methods and using hot-film anemometry Application of computational fluid dynamics to turbulent flow in stirred tanks is developing rapidly and involves using assumptions inherent in Kolmogoroff s theory and turbulence measurements to supply boundary conditions. 

Modeling and Simulation of Gas-Liquid Flow in Stirred Tank Reactors. 24... 

In spite of improved hard- and software, which have greatly expanded the tools available for simulating fluid flow in stirred tank reactors, a number of unsolved problems and open questions still exist. 

Aubin J, Fletcher DF, Xueieb C. (2004) Modelling turbulent flow in stirred tanks with CFD the influence of the modelling approach, turbulence model and numerical scheme. Thermal Fluid Sd., 28 431 5. 

Lane GL, Schwarz MP, Evans GM. (2004) Numerical modeling of gas-liquid flow in stirred tanks. Chem. Eng. Sci., 60 2203-2214. 

BOUNDARY CONDITIONS REQUIRED FOR THE CFD SIMULATION OF FLOWS IN STIRRED TANKS... 

Accurate CFD (computational fluid dynamic) simulation of the flow in stirred tanks requires correct specification of both the geometry and the physical conditions of the flow. While specification of the geometry, the gridding, and the solution algorithm is relatively straightforward, some other issues remain difficult. The most challenging problem is definition of a physically accurate, computationally tractable impeller or impeller model which incorporates the effect of the tank geometry. This... 

At present, the simulation of flow in stirred tanks requires particular attention to accurate treatment of the impeller. The rotating impeller is difficult to simulate directly in the context of a stationary CFD domain. Even with the introduction of sliding mesh techniques which allow the impeller to rotate in a fixed tank, and thus reproduce the trailing vortices behind the impeller blades [13,23]), only 5 to 10 rotations of the impeller have been reported [13]). Laroche reported that 16 sliding mesh steps, for 90° of tank simulation, took over 10 hours on a Cray [23]. Since the (time varying) bulk flows of interest take of the order of 50 rotations to become established, and the process results of interest may span 10,000 rotations (60 rpm for 3 hours on an industrial scale), this approach is still impractical for the typical user. 

The rest of this chapter is devoted to examining the physical and numerical issues underlying CFD simulations of flow in stirred tanks. Under physical issues, the general issues of turbulence modeling and degree of swirl are addressed first. The comments in these sections can be applied to any flow field. The specific stirred tank flow field depends on the tank geometry, the boundary conditions at the edges of the computational domain, and the impeller model. These issues are discussed in detail. Many of the numerical issues which were the focus of early CFD research... 

Smith, G. W., L. L. Tavlarides and J. Placek, Turbulent flow in stirred tanks scale-up computations for vessel hydrodynamics, Chem. Eng. Comm., 93, 49-73 (1990). 

Rammohan AR, Kemoim A, Al-Dahhan MH, Dudukovic MP A Lagrangian description of flows in stirred tanks via computer-automated radioactive particle tracking (CARPT), Chem Eng Sci 56 2629-2639, 2001a. http //dx.doi.org/10.1016/S0009-2509(00)00537-6. 

In turbulent flow in stirred tanks, the overall circulation a) is usually the slowest process. The breaking down of eddies (b and c) proceeds faster the smaller the eddies become, and the diffusion within the smallest eddies d) is often the fastest process. The smallest eddies are usually smaller than 0.1 nun, so that the diffusion times are generally much smaller than 1 s (see p. 65). When the agitation rate is increased, die overall circulation and the bresddng down processes are enhanced, and at the same time the size of the smallest eddies is reduced, so that the diffusion process is also promoted. 

Conclusions and recommendations for laminar mixing The equations presented in sections 4.2.3.1 and 4.23.2 give only a rough indication of the flow and mixing phenomena in laminar flow in stirred tanks (of Newtonian liquids). There are as yet no theories that are generally applicable to this type of mixing problems. There are several reasons for this ... 

In section 5.2.3 various models for describing reaction and diffusion, in laminar flow in stirred tanks, were presented. Here two of these models will be presented in more detail. 

In spite of the success of CFD simulations for the multiphase turbulent fluid flow in stirred-tank bioreactors (see Section 3.4), their application to coupled material balance equations in case of more complicated reaction networks is still limited by the required computing power. Even in case of successful approaches for model reduction, the number of compounds necessary for reliable portrayal of cellular dynamics in response to spatial variation of extracellular compounds may be still too large. An interesting method to overcome these numerical difficulties is the general hybrid multizonal/CFD [27-36], which gave momentum to the application of CFD modeling for bioreactors. 

Manikowski, M., S. Bodemeia-, A. Ltibbert, W. Bujalski, and A. W. Nienow (1994). Measurement of gas and liquid flows in stirred tank reactors with multiple agitators. Can. J. Chem. Eng., 72, 769-781. 

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