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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
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.
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- © The Author(s), 2024. Published by Cambridge University Press
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