Viscous modes within the compressible boundary-layer flow due to a broad rotating cone.pdf (577.66 kB)
Viscous modes within the compressible boundary-layer flow due to a broad rotating cone
journal contributionposted on 2016-11-14, 14:26 authored by P. D. Towers, Z. Hussain, P. T. Griffiths, S. J. Garrett
We investigate the effects of compressibility and wall cooling on the stationary, viscous (Type II) instability mode within the 3D boundary layer over rotating cones with half-angle greater than 40°. The stationary mode is characterised by zero shear stress at the wall and a triple-deck solution is presented in the isothermal case. Asymptotic solutions are obtained which describe the structure of the wavenumber and the orientation of this mode as a function of local Mach number. It is found that a stationary mode is possible only over a finite range of local Mach number. Our conclusions are entirely consistent with the results of Seddougui 1990, A nonlinear investigation of the stability models of instability of the trhee-dimensional Compresible boundary layer due to a rotating disc Q. J. Mech. Appl. Math., 43, pt. 4. It is suggested that wall cooling has a significant stabilising effect, while reducing the half-angle is marginally destabilising. Solutions are presented for air.
PDT and SJG wish to acknowledge support from the Engineering and Physical Sciences Research Council (grant EP/G061637/1). SJG and PTG wish to acknowledge support from the Royal Academy of Engineering and the Leverhulme Trust (LSRF1415/11/29).
CitationIMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications), 2016, 81 (5), pp. 940-960
Author affiliation/Organisation/COLLEGE OF SCIENCE AND ENGINEERING/Department of Mathematics
- AM (Accepted Manuscript)