HP Labs Technical Reports
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Evaluation of Laminar Mixing in Stirred Tanks using a Discrete Time Particle Mapping Procedure
Harvey, Albert D.; West, David H.; Tufillaro, Nicholas B.
Keyword(s): flow field; stirred tank; mixing; Poincare map; advection equation; mixing efficiency
Abstract: While much progress has been made in computing the flow field in stirred tanks, the flow field alone does not really give any direct information about a very important characteristic of the design, namely the mixing time. Efficient and accurate computational tools are needed to compute mixing time and to identify isolated mixing regions. In this paper we attempt to address both of these needs by developing a discrete-time model of the flow in a stirred tank based on a numerical approximation of the Poincare map. We start by computing the 3D flow field. Next we integrate the advection equation for more than 10(superscript 4) passive particles through one period of the flow. A mapping is defined between each particles' initial and final radial and axial coordinates, and the elapsed time for each particle trajectory. The time evolution for tracer particles can then be continued for arbitrarily long times by iterating the map. This mapping procedure is demonstrated on four different impeller stirred tank configurations. It is shown that the error in the mapping procedure can be made to be less than the error in the time integratiion scheme at a significantly reduced computational effort. Furthermore, as a quantitative aid in evaluating the mixing efficiency, we compute a mixing time which is defined as the time needed for a particle to travel a prescribed distance from its starting location.
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