Sensitivity Analysis for Flow Stability in a Multipassage Blade Cascade

This study investigated the flow stability and sensitivity in a linear blade cascade at relatively low Reynolds numbers. The adjoint method was incorporated into the immersed boundary method-based global stability analysis method, leading to the derivation of a structural sensitivity analysis approach in which the body forces representing the solid walls were treated as unknown quantities, and the no-slip condition was applied to close the system. The proposed method was validated and applied to analyze the sensitivity of a two-dimensional linear blade cascade. The results indicate that, in a single-passage computational domain, vortex shedding in the wake is highly sensitive to flow separation on the suction surface of the blade. Modifying the base flow of the laminar separation bubble has a great impact on flow stability. When the number of blade passages was increased, the global and adjoint modes exhibited a phase difference, although the blade stagger angles remained identical. Compared to a single-passage computational domain, the onset of unsteady vortex shedding became sensitive to the circumferential velocity perturbation in the wake, which originated from the phase differences of the vortex shedding between different blades. Additionally, the impact of blade installation errors on flow stability and sensitivity was investigated.