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Neutral stability curves of compressible Görtler flow generated by low-frequency free-stream vortical disturbances

Published online by Cambridge University Press:  15 August 2019

Samuele Viaro Open the ORCID record for Samuele Viaro [Opens in a new window]  and
Pierre Ricco Open the ORCID record for Pierre Ricco [Opens in a new window]
Samuele Viaro
Affiliation:
Department of Mechanical Engineering, The University of Sheffield, SheffieldS1 3JD, UK
Pierre Ricco*
Affiliation:
Department of Mechanical Engineering, The University of Sheffield, SheffieldS1 3JD, UK
*
†Email address for correspondence: [email protected]
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Abstract

Pre-transitional compressible boundary layers perturbed by low-frequency free-stream vortical disturbances and flowing over plates with streamwise-concave curvature are studied via matched asymptotic expansions and numerically. The Mach number, the Görtler number and the frequency of the free-stream disturbance are varied to obtain the neutral stability curves, i.e. curves in the space of the parameters that distinguish spatially growing from spatially decaying perturbations. The receptivity approach is used to calculate the evolution of Klebanoff modes, highly oblique Tollmien–Schlichting waves influenced by the concave curvature of the wall, and Görtler vortices. The Klebanoff modes always evolve from the leading edge, the Görtler vortices dominate when the influence of the curvature becomes significant and the Tollmien–Schlichting waves may precede the Görtler vortices for moderate Görtler numbers. For relatively high frequencies the triple-deck formalism allows us to confirm the numerical result of the negligible influence of the curvature on the Tollmien–Schlichting waves when the Görtler number is an order-one quantity. Experimental data for compressible Görtler flows are mapped onto our neutral-curve graphs and earlier theoretical results are compared with our predictions.

JFM classification

Aerodynamics: High-speed flow Compressible Flows: Compressible boundary layers Boundary Layers: Boundary layer receptivity
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 876 , 10 October 2019 , pp. 1146 - 1157
Copyright
© 2019 Cambridge University Press 

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