On the Receptivity Problem for Goertler Vortices: Vortex Motions Induced by Wall Roughness
Abstract
The receptivity problem for Goertler vortices induced by wall roughness is investigated. The roughness is modelled by small amplitude perturbations to the curved wall over which the flow takes place. Linear theory can be used for small perturbations. The roughness will vary in the spanwise direction on the boundary layer length scale, whilst in the flow direction the corresponding variation is on the length scale over which the wall curvature varies. In fact the latter condition can be relaxed to allow for a faster stream wise roughness variation so long as the variation does not become as fast as that in the spanwise direction. The function which describes the roughness is assumed to be such that its spanwise and streamwise dependencies can be separated; this will enable the use of Fourier or Laplace transforms where appropriate. The cases of isolated and distributed roughness elements are investigated and the coupling coefficient which relates the amplitude of the forcing and the induced vortex amplitude is found asymptotically in the small wavelength limit. This coefficient is exponentially small in the latter limit so that it is unlikely that this mode can be stimulated directly by wall roughness. The situation at 0(1) wavelengths is quite different and this is investigated numerically for different forcing functions. An isolated roughness element induces a vortex field which grows within a wedge at a finite distance downstream of the element. Immediately downstream of the obstacle the disturbed flow produced by the element decays in amplitude. The receptivity problem at larger Goertler numbers appropriate to relatively large wall curvature is discussed in detail. (JHD)
Document Details
- Document Type
- Technical Report
- Publication Date
- May 01, 1990
- Accession Number
- ADA227155
Entities
People
- James P. Denier
- Philip Hall
- Sharon Seddougui