### Abstract

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.

Original language | English |
---|---|

Pages (from-to) | 940-960 |

Number of pages | 21 |

Journal | IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications) |

Volume | 81 |

Issue number | 5 |

Early online date | 29 Aug 2016 |

DOIs | |

Publication status | Published - 1 Oct 2016 |

Externally published | Yes |

### Fingerprint

### Keywords

- compressible boundary-layer flow
- rotating cone
- Type II

### ASJC Scopus subject areas

- Applied Mathematics

### Cite this

*IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications)*,

*81*(5), 940-960. https://doi.org/10.1093/imamat/hxw041

**Viscous modes within the compressible boundary-layer flow due to a broad rotating cone.** / Towers, P. D.; Hussain, Z.; Griffiths, P. T.; Garrett, S. J.

Research output: Contribution to journal › Article

*IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications)*, vol. 81, no. 5, pp. 940-960. https://doi.org/10.1093/imamat/hxw041

}

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, S. J.

PY - 2016/10/1

Y1 - 2016/10/1

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.

KW - compressible boundary-layer flow

KW - rotating cone

KW - Type II

UR - http://www.scopus.com/inward/record.url?scp=84991051800&partnerID=8YFLogxK

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 -