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A comparative study of high resolution schemes for solving population balances in crystallization

MPG-Autoren
http://pubman.mpdl.mpg.de/cone/persons/resource/persons86438

Qamar,  S.
Physical and Chemical Foundations of Process Engineering, Max Planck Institute for Dynamics of Complex Technical Systems, Max Planck Society;
COMSATS Institute of Information Technology, Dep. of Mathematics, Islamabad, Pakistan;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons86282

Elsner,  M. P.
Physical and Chemical Foundations of Process Engineering, Max Planck Institute for Dynamics of Complex Technical Systems, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons86141

Angelov,  I.
Systems and Control Theory, Max Planck Institute for Dynamics of Complex Technical Systems, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons86477

Seidel-Morgenstern,  A.
Physical and Chemical Foundations of Process Engineering, Max Planck Institute for Dynamics of Complex Technical Systems, Max Planck Society;
Otto-von-Guericke-Universität Magdeburg, External Organizations;

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Zitation

Qamar, S., Elsner, M. P., Angelov, I., Warnecke, G., & Seidel-Morgenstern, A. (2006). A comparative study of high resolution schemes for solving population balances in crystallization. Computers and Chemical Engineering, 30(6-7), 1119-1131. doi:10.1016/j.compchemeng.2006.02.012.


Zitierlink: http://hdl.handle.net/11858/00-001M-0000-0013-9ACE-A
Zusammenfassung
This article demonstrates the applicability and usefulness of high resolution finite volume schemes for the solution of population balance equations (PBEs) in crystallization processes. The population balance equation is considered to be a statement of continuity. It tracks the change in particle size distribution as particles are born, die, grow or leave a given control volume. In the population balance models, the one independent variable represents the time, the other(s) are “property coordinate(s)”, e.g. the particle size in the present case. They typically describe the temporal evolution of the number density functions and have been used to model various processes. These include crystallization, polymerization, emulsion and cell dynamics. The high resolution schemes were originally developed for compressible fluid dynamics. The schemes resolve sharp peaks and shock discontinuities on coarse girds, as well as avoid numerical diffusion and numerical dispersion. The schemes are derived for general purposes and can be applied to any hyperbolic model. Here, we test the schemes on the one-dimensional population balance models with nucleation and growth. The article mainly concentrates on the re-derivation of a high resolution scheme of Koren (Koren, B. (1993). A robust upwind discretization method for advection, diffusion and source terms. In C. B. Vreugdenhill, & B. Koren (Eds.), Numerical methods for advection–diffusion problems, Braunschweig: Vieweg Verlag, pp. 117–138 [vol. 45 of notes on numerical fluid mechanics, chapter 5]) which is then compared with other high resolution finite volume schemes. The numerical test cases reported in this paper show clear advantages of high resolutions schemes for the solution of population balances. ©2006 Elsevier Ltd. All rights reserved [accessed 2013 November 27th]