Tonal noise optimization of propeller using a steady adjoint method

This paper presents an efficient optimization framework for reducing tonal noise generated by an isolated propeller, targeting applications in urban air mobility. The approach couples the Ffowcs-Williams-Hawkings (FWH) acoustic analogy with the Reynolds-averaged Navier-Stokes (RANS) equations, solved via the open-source su2 solver in a rotating reference frame (RRF). This steady formulation circumvents the need for unsteady simulations, enabling significant computational savings. Acoustic pressure fluctuations are propagated to the far field using the FWH formulation, and the tonal sound pressure level perceived by multiple observers serves as the objective function for optimization. A discrete adjoint solver, constructed via algorithmic differentiation, is employed to compute the sensitivities of the coupled RANS-FWH approach. The resulting sensitivity map provides detailed insights into the noise-generation mechanisms and serves as an effective gradient for driving automatic shape optimization. The proposed methodology inherently targets steady noise components: thickness noise and steady loading. Nevertheless, in the presented forward flight test case, the tonal noise predicted using RRF closely matches that from a time-resolved simulation, confirming the suitability of the approach for tonal noise optimization. The optimization yields a 3-dB reduction in upstream SPL while preserving the required thrust level. Furthermore, the optimizer consistently identifies the blade tip as a critical region.