Abstract
Tank reactors with different mixers are very often used for many chemical and biological processes. For their effective use is necessary to know in details hydrodynamics and mass transfer which take place in them. For many practically important cases the experimental study of these processes is very expensive, very difficult or impossible. This is why recently mathematical modelling of the complex swirling flows in such reactors becomes an effective method for investigation of the behavior of the fluids in these reactors.
This paper presents mathematical model and numerical results for viscous swirling flow in a cylindrical tank reactor with a mixer.
The model is based on the Navier-Stokes equations in cylindrical co-ordinate system. These equations are written in terms of the stream function, vorticity and the momentum of the tangential component of the velocity. The flow is supposed to be stationary and axis-symmetric. A special attention is devoted to the correct formulation of the boundary conditions.
A numerical algorithm for studying this motion of the fluid is proposed in [6]. The grid for the discretization of the equations is nonuniform. Difference scheme of Alternating Direction Implicit Method for solving Navier-Stokes equations is used.
Numerical results for the stream function, the velocity field and the momentum of the tangential velocity for different Reynolds numbers are obtained by this numerical algorithm. The results are presented graphically. They are discussed and compared with results of other authors. It is observed a very good agreement between them.
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Zheleva, I., Lecheva, A.: Numerical algorithm for solving hydrodynamics in a chemical reactor with a mixer. In: Vulkov, L.G., Waśniewski, J., Yalamov, P. (eds.) NAA 2000. LNCS, vol. 1988, pp. 749–755. Springer, Heidelberg (2001)
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Zheleva, I., Lecheva, A. (2005). Numerical Investigation of the Viscous Flow in a Bioreactor with a Mixer. In: Li, Z., Vulkov, L., Waśniewski, J. (eds) Numerical Analysis and Its Applications. NAA 2004. Lecture Notes in Computer Science, vol 3401. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-31852-1_73
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DOI: https://doi.org/10.1007/978-3-540-31852-1_73
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-24937-5
Online ISBN: 978-3-540-31852-1
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