Convergence of a Spherical Multipole Expansion for Propeller Tonal Noise

We examine an observer-independent framework for the prediction and validation of hovering propeller tonal noise, based on a spherical multipole expansion. The formulation separates source and observer dependence, so that the multipole coefficients are evaluated only once, and the acoustic field can then be reconstructed at any arbitrary observer locations at negligible additional cost. The convergence of the truncated series is assessed locally in both near- and far-field regions for three rotational speeds. The results show that only a modest number of terms is required for accurate predictions and that, for the operating conditions considered here, the first two terms are already sufficient in the far field. Validation against measurements shows good agreement for the first blade-passing harmonic over the full microphone arc, with mean errors lower than 1 dB. A Monte Carlo analysis is also performed to quantify the effect of uncertainty in the aerodynamic, geometric, and operating inputs. The predicted uncertainty bands confirm both the accuracy and the robustness of the proposed formulation.