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An extension of the ‘Malkus hypothesis’ to the turbulent base flow of blunt sections

Published online by Cambridge University Press:  21 April 2006

William S. Vorus  and
Liyong Chen
William S. Vorus
Affiliation:
Department of Naval Architecture and Marine Engineering, The University of Michigan, Ann Arbor, MI 48109-2145, USA
Liyong Chen
Affiliation:
Department of Naval Architecture and Marine Engineering, The University of Michigan, Ann Arbor, MI 48109-2145, USA
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Abstract

This work develops and demonstrates an approximate theory for the mean turbulent near-wake of cylindrical bodies with blunt after edges. A closed free-streamline model is used to relate base pressure to the separation-streamline length. The additional relationship between base pressure and streamline length required for closure is an extension of the maximum dissipation hypothesis of Malkus, which was originally proposed for the turbulent-channel-flow problem. In the current application, the Malkus hypothesis leads to maximization of the rate of change of mean kinetic energy along the separation-cavity streamline.

The theory is implemented in terms of a linearized closed free-streamline theory of thin blunt-based symmetric sections, which was actually developed as an application to supercavitation, rather than separation. The calculations performed compare quite well with experimental measurements of mean base pressures and section drag. However, the linearizing assumptions on section-cavity slenderness and base-pressure magnitude are not so well preserved in the calculated results. Numerical analysis in terms of a nonlinear closed free-streamline model is a possible recourse. However, an important class of problems where the assumptions required in applying the linear theory may be better represented by the prevailing physics is the superseparation of thin lifting foils. This would appear to be the immediately most fruitful direction for the work, as a very mature theory of linearized supercavitation of thin lifting foils is available for providing the required free-streamline model.

Even though the formulation contains the effects of turbulent dissipation, the intricacies of the wake turbulence are avoided in achieving the solution. The lumped mean turbulent transfer rate per unit length of the mean dividing streamline is quantified, and defined in terms of the turbulence variables. Because of this, it is suggested that the theory may prove useful as a tool for studying wake turbulence characteristics.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 184 , November 1987 , pp. 551 - 569
Copyright
© 1987 Cambridge University Press

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