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

TL;DR

This study analyzes how steady wall blowing, suction, and heating-cooling affect the stability of a hypersonic boundary layer at Mach 4.5, identifying effective control strategies to dampen instabilities using adjoint-based sensitivity analysis.

Contribution

It introduces an adjoint-based method to compute sensitivities of hypersonic boundary layer instabilities to boundary conditions, enabling optimal control design.

Findings

Suction upstream of the mode S synchronization point stabilizes the second Mack mode.

Leading-edge heating effectively stabilizes both first and second Mack modes.

A single steady heating strip near the leading edge can damp all studied instabilities.

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 conversely 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 all the instabilities together.