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An adjoint compressible linearised Navier–Stokes approach to model generation of Tollmien–Schlichting waves by sound

Published online by Cambridge University Press:  19 August 2019

Henrique Raposo Open the ORCID record for Henrique Raposo [Opens in a new window] ,
Shahid Mughal Open the ORCID record for Shahid Mughal [Opens in a new window]  and
Richard Ashworth Open the ORCID record for Richard Ashworth [Opens in a new window]
Henrique Raposo*
Affiliation:
Department of Mathematics, Imperial College London, South Kensington Campus, London SW7 2AZ, UK Central Research and Technology, Airbus, Bristol BS34 7PA, UK
Shahid Mughal
Affiliation:
Department of Mathematics, Imperial College London, South Kensington Campus, London SW7 2AZ, UK
Richard Ashworth
Affiliation:
Central Research and Technology, Airbus, Bristol BS34 7PA, UK
*
†Email address for correspondence: h.raposo17@imperial.ac.uk
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Abstract

The generation of the first-mode instability through scattering of an acoustic wave by localised surface roughness, suction or heating is studied with a time-harmonic compressible adjoint linearised Navier–Stokes (AHLNS) approach for subsonic flow conditions. High Strouhal number analytical solutions to the compressible Stokes layer problem are deduced and shown to be in better agreement with numerical solutions compared to previous works. The adjoint methodology of Hill in the context of acoustic receptivity is extended to the compressible flow regime and an alternative formulation to predict sensitivity to the angle of incidence of an acoustic wave is proposed. Good agreement of the acoustic AHLNS receptivity model is found with published direct numerical simulations and the simpler finite Reynolds number approach. Parametric investigations of the influence of the acoustic wave angle on receptivity amplitudes reveal that the linearised unsteady boundary layer equations are a valid model of the acoustic signature for a large range of acoustic wave obliqueness values, failing only where the wave is highly oblique and travels upstream. An extensive parametric study of the influence of frequency, spanwise wavenumber, local Reynolds number and free-stream Mach number over the efficiency function for the different types of wall perturbation mechanisms is undertaken.

JFM classification

Boundary Layers: Boundary layer receptivity Instability: Transition to turbulence
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 877 , 25 October 2019 , pp. 105 - 129
Copyright
© 2019 Cambridge University Press 

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