Axisymmetric Flow Past a Slender Body of Finite Length
The axisymmetric laminar boundary layer on a finite slender body of revolution whose radius scales with the boundary-layer thickness is studied theoretically with the aim of establishing the flow properties near the trailing tip of the body. It is found that, in contrast to the case of two-dimensional flow, the axisymmetric boundary layer does not simply set up an arbitrary velocity profile at the onset of the trailing tip: instead it develops a rather involved and interesting multilayer structure dependent on the trailing-tip shape, which we take to be of the form (1-x)^n. Because of the unusual nature of the boundary layer at the onset of the trailing tip, we expect that the viscous-inviscid interaction, which comes into play within a short length scale near the tip, is also of a rather novel form. The interaction length scale depends significantly on the range of the index n of the body shape. It is concluded that interactive cases for body shapes with 1/4 < n < 1/3 might be studied next in future work, since for n in this range the wall layer thickness and the body radius are comparable in size and so the interactive flow is not quasi-planar.
Proceedings of the Royal Society of London Series A
- Pub Date:
- July 1985