Adjoint-based aeroacoustic shape optimization using lattice Boltzmann method for suppressing cavity tones at low Mach numbers

Controlling cavity tones is important in applications such as aircraft landing gears, automobile sunroofs, and train bogies. In this study, aeroacoustic shape optimization was performed using the lattice Boltzmann method (LBM) and the unsteady adjoint method to develop an innovative passive control technique for suppressing cavity tones at low Mach numbers. The adjoint-based aeroacoustic optimization establishes a direct link between far-field aerodynamic sounds and shape parameters, enabling efficient aerodynamic design to suppress sound generation. This study focused on a rectangular cavity with a length-to-depth ratio of 2.0 and a laminar upstream boundary layer. The Reynolds number, based on the cavity length, was 1.0×10⁴, and the maximum freestream Mach number was 0.15. Assuming the flow under these conditions to be two-dimensional, the LBM simulations were conducted in two dimensions. Optimizing the shape near the trailing edge of the cavity resulted in a protrusion-like shape on the rear wall of the cavity. Both simulation and experimental results indicated that the optimized shape significantly suppressed sound radiation, demonstrating the effectiveness of the adjoint-based optimization method for addressing aeroacoustic problems. Furthermore, the simulation results revealed that recirculation within the cavity played a crucial role in shear layer oscillations. This insight guided a novel passive control strategy aimed at mitigating recirculation using a simpler control device featuring a rectangular protrusion. The simulations demonstrated that this simplified protrusion could completely stabilize the free shear layer over the cavity, proving more effective at suppressing cavity tones than conventional ramping approaches.