Internal annular wall jets: Radial flow in a stirred tank

Authors

  • Suzanne M. Kresta,

    Corresponding author
    1. Dept. of Chemical and Materials Engineering, University of Alberta, Edmonton, Alberta, Canada, T6G 2G6
    • Dept. of Chemical and Materials Engineering, University of Alberta, Edmonton, Alberta, Canada, T6G 2G6
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  • Kevin J. Bittorf,

    1. Dept. of Chemical and Materials Engineering, University of Alberta, Edmonton, Alberta, Canada, T6G 2G6
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  • David J. Wilson

    1. Dept. of Mechanical Engineering, University of Alberta, Edmonton, Alberta, Canada, T6G 26G
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Abstract

Similarity solutions are derived for internal annular wall jets and compared with experimentally determined velocity profiles at the wall of a stirred tank with radial flow. The first similarity solution considers a geometry where the thickness of the wall jet is small relative to the diameter of the cylinder and the fluid flows relative to a free stream velocity of zero. In the second solution, the free stream velocity opposes the direction of the jet flow, as is observed in the recirculating flow in a stirred tank. The internal annular wall jet model agrees very well with the flow at the wall of a stirred tank agitated with a Rushton turbine. The free stream counter flow is driven by the wall jet, and a single velocity and length scale define the self-similar velocity profiles for the flow in the jet and in the recirculating flow. Both the analytical model and experimentally observed expansion rates are linear and the maximum velocity in the jet decays as [U ∝ (z/T)−0.5], where (z/T) is the dimensionless streamwise distance. This decay can be contrasted with the faster decay [U ∝ (z/T)−1] observed in the 3-D wall jets produced by axial impellers. These results provide a basis for validating computational fluid dynamic simulations in stirred tanks and for estimating the largest length scales of turbulence in the bulk of the tank.

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