Resolvent-Sensitivity-Based Optimization of Wall Temperature for Quiet Hypersonic Wind-Tunnel Nozzle Design

The reliability of hypersonic ground testing is critically limited by high levels of acoustic noise radiated from turbulent boundary layers developing along the nozzle walls. Extending the operational envelope of quiet facilities requires maintaining laminar flow by mitigating the growth of convective instabilities such as Görtler vortices and Mack modes. Addressing the limitations of local stability theories in capturing strong nonparallel effects within complex nozzle geometries, this study introduces a resolvent-sensitivity-based optimization strategy to delay transition. A weakly nonlinear formalism is employed to derive the exact sensitivity of the optimal resolvent gain with respect to steady wall temperature distribution. The derived sensitivity gradients are validated, demonstrating a robust linear regime even for significant gain reductions. Subsequently, the gradients are integrated into a constrained optimization loop using B-spline parameterization to ensure physically realizable control profiles. Results identify a robust control strategy characterized by throat heating followed by downstream cooling, which simultaneously dampens the amplification of all dominant instability mechanisms, achieving up to a 47% reduction in peak [Formula: see text]-factors. Depending on the freestream disturbance environment, this multimode mitigation effectively delays the predicted transition onset (estimated here via empirical [Formula: see text] criteria) by 7–25% of the controlled nozzle length. This approach not only delays transition but also aligns with existing roughness control practices, establishing resolvent sensitivity-based optimization as an efficient design tool for the aerodynamic design of next-generation quiet facilities.