High Resolution Simulation of Laminar and Transitional Flows in a Mixing Vessel
Rice, Matthew Jason
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The present work seeks to fully investigate, describe and characterize the distinct flow regimes existing within a mixing vessel at various rotational speeds. This investigation is computational in nature and simulates the flow within a baffled tank containing a Rushton turbine of the standard configuration. For a Re based on impeller diameter and blade rotational speed (Re â ¡ Ï ND2/Î¼) the following flow regimes were identified and investigated in detail: Reverse/reciprocating flows at very low Re (<10); stalled flows at low Re (â 10); laminar pumping flow for higher Re and transitional pumping flow (10 squared < Re <10 to the 4th). For the three Re numbers 1, 10 and 28, it was found that for the higher Re number (28), the flow exhibited the familiar outward pumping action associated with radial impellers under turbulent flow conditions. However, as the Re number decreases, the net radial flow during one impeller revolution was reduced and for the lowest Re number a reciprocating motion with negligible net pumping was observed. In order to elucidate the physical mechanism responsible for the observed flow pattern at low Re, the forces acting on a fluid element in the radial direction were analyzed. Based on this analysis, a simplified quasi-analytic model of the flow was developed that gives a satisfactory qualitative, as well as quantitative representation of the flow at very low Re. Investigation of the transitional flow regime (Re â 3000) includes a compilation and characterization of ensemble and turbulent quantities such as the Reynolds stress components, dissipation length Î· and time scales Ï , as well a detailed investigation of the near-impeller flow and trailing vortex. Calculation and compilation of all terms in the turbulent kinetic energy transport equation was performed (including generation and the illusive turbulent pressure work). Specifically, the most important transport mechanism was turbulent convection/diffusion from the impeller disk-plane/trailing vortex region. Mean flow transport of turbulent kinetic energy was primarily towards the impeller disk-plane and radially outward from the trailing vortex region. The turbulent pressure work was found to partially counteract turbulent convection. Turbulent dissipation followed by turbulent viscous work were found to be the least important mechanism responsible for turbulent transport with both terms being maximized within the vortex region and at the disk-plane down-stream from the vortices.
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