An adjoint compressible linearised Navier-Stokes approach to model generation of Tollmien-Schlichting waves by sound
File(s)
Accepted version
Author(s)
Raposo, Henrique
Mughal, Mohammed
Ashworth, Richard
Type
Journal Article
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.
Date Issued
2019-10-25
Date Acceptance
2019-07-22
Citation
Journal of Fluid Mechanics, 2019, 877, pp.105-129
ISSN
0022-1120
Publisher
Cambridge University Press (CUP)
Start Page
105
End Page
129
Journal / Book Title
Journal of Fluid Mechanics
Volume
877
Copyright Statement
© 2019 Cambridge University Press. This paper has been accepted for publication and will appear in a revised form, subsequent to peer-review and/or editorial input by Cambridge University Press.
Sponsor
Innovate UK
Identifier
https://www.cambridge.org/core/journals/journal-of-fluid-mechanics/article/an-adjoint-compressible-linearised-navierstokes-approach-to-model-generation-of-tollmienschlichting-waves-by-sound/15254F26B6158C9BD7F8452F337B7730#fndtn-information
Grant Number
113022
Subjects
01 Mathematical Sciences
09 Engineering
Fluids & Plasmas
Notes
acceptance date 16/7/2019
Publication Status
Published online
Date Publish Online
2019-08-19