TY - JOUR
T1 - Viscous modes within the compressible boundary-layer flow due to a broad rotating cone
AU - Towers, P. D.
AU - Hussain, Z.
AU - Griffiths, P. T.
AU - Garrett, Stephen
PY - 2016/10
Y1 - 2016/10
N2 - 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.
AB - 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.
UR - https://academic.oup.com/imamat/article-abstract/81/5/940/2198354?redirectedFrom=fulltext&login=false
U2 - 10.1093/imamat/hxw041
DO - 10.1093/imamat/hxw041
M3 - Article
VL - 81
SP - 940
EP - 960
JO - IMA Journal of Applied Mathematics
JF - IMA Journal of Applied Mathematics
SN - 0272-4960
IS - 5
ER -