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Adjoint-based linear sensitivity of a supersonic boundary layer to steady wall blowing–suction/heating–cooling

Published online by Cambridge University Press:  05 January 2024

Arthur Poulain Open the ORCID record for Arthur Poulain [Opens in a new window] ,
Cédric Content ,
Georgios Rigas Open the ORCID record for Georgios Rigas [Opens in a new window] ,
Eric Garnier  and
Denis Sipp Open the ORCID record for Denis Sipp [Opens in a new window]
Arthur Poulain*
Affiliation:
DAAA, ONERA, Université Paris Saclay, F-92190 Meudon, France
Cédric Content
Affiliation:
DAAA, ONERA, Université Paris Saclay, F-92190 Meudon, France
Georgios Rigas
Affiliation:
Department of Aeronautics, Imperial College London, London SW7 2AZ, UK
Eric Garnier
Affiliation:
DAAA, ONERA, Université Paris Saclay, F-92190 Meudon, France
Denis Sipp
Affiliation:
DAAA, ONERA, Université Paris Saclay, F-92190 Meudon, France
*
†Email address for correspondence: arthur.poulain@onera.fr
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Abstract

For a Mach $4.5$ flat-plate adiabatic boundary layer, we study the sensitivity of the first, second Mack modes and streaks to steady wall-normal blowing/suction and wall heat flux. The global instabilities are characterised in frequency space with resolvent gains and their gradients with respect to wall-boundary conditions are derived through a Lagrangian-based method. The implementation is performed in the open-source high-order finite-volume code BROADCAST and algorithmic differentiation is used to access the high-order state derivatives of the discretised governing equations. For the second Mack mode, the resolvent optimal gain decreases when suction is applied upstream of Fedorov's mode $S$/mode $F$ synchronisation point, leading to stabilisation, and the converse when applied downstream. The largest suction gradient is in the region of branch I of mode $S$ neutral curve. For heat-flux control, strong heating at the leading edge stabilises both the first and second Mack modes, the former being more sensitive to wall-temperature control. Streaks are less sensitive to any boundary control in comparison with the Mack modes. Eventually, we show that an optimal actuator consisting of a single steady heating strip located close to the leading edge manages to damp the linear growth of all three instability mechanisms.

JFM classification

Boundary Layers: Boundary layer control Boundary Layers: Boundary layer stability Compressible Flows: Compressible boundary layers

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JFM Papers
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Journal of Fluid Mechanics , Volume 978 , 10 January 2024 , A16
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© The Author(s), 2024. Published by Cambridge University Press

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