Mean velocity behaviour in the near wake of long slender cylinder with a sharp trailing edge at a high Reynolds number

ABSTRACT

A simple eddy viscosity model is applied to the governing equations to establish the behaviour of the mean velocity in the turbulent axisymmetric near wake. The near wake develops from a long slender cylinder which is kept parallel to the flow and is developing under zero streamwise pressure gradient. The upstream turbulent boundary layer on the body of revolution is fully developed. In the inner layer of the flow downstream of the trailing edge, the turbulent inner layer of the upstream boundary layer grows into the initial logarithmic layer, and as a consequence, the centreline velocity in the near wake is shown to increase logarithmically with streamwise distances for large streamwise distances. The analysis further leads to two regions of the near wake flow (the inner near wake and the outer near wake), similar to that of a fully developed turbulent boundary layer, for which the governing equations have been derived. The matching between these two regions leads to a logarithmic variation in the normal direction. Also shown is the variation of the square of the wake width which varies logarithmically with streamwise distance in the near wake. These features are validated by comparison with available experimental data.

KEYWORDS:

• Axisymmetric
• near wake
• eddy viscosity
• centreline velocity
• wake thickness

Acknowledgement

Authors acknowledge the support rendered by the Department of Mathematics and Statistical Sciences, BIUST.

Disclosure statement

No potential conflict of interest was reported by the authors.