Numerical error analysis with application to transonic propeller aeroacoustics

This article investigates numerical error analysis in the aeroacoustic simulation of transonic propellers for transport aircraft. The objective of this work is double-edged: on one hand to assess consistency of noise predictions, and on the other hand to gain understanding of quadrupolar acoustic sources generated by flow discontinuities such as shock waves. The work methodology is based on the comparison of acoustic predictions, made from RANS flowfield solutions through the Ffowcs-Williams and Hawkings (FWH) method, after considering two major parameters: (1) the influence of CFD grid refinement; and (2) the extension of the flow region enclosed by porous FWH surfaces. The effective spatial convergence order is determined by focusing on the acoustic information in the flow. Richardson’s extrapolation is proposed as a method to enhance noise predictions without resorting to expensive CFD computations. It is shown that maximum Sound Pressure Levels (SPLs) for the Blade Passing Frequency (BPF) harmonics converge with the extension of the FWH surface, thereby delimiting a volume enclosing the major acoustic production terms radiating in the rotation plane. On the other hand, it is also shown that SPLs off the propeller plane are much more sensitive to background flow inhomogeneities and cannot be computed with precision using a two-step methodology. Finally, using results related to the convergence of maximum SPLs, an attempt is made to directly link the flowfield solution to volume acoustic sources through a brief analysis of Lighthill’s acoustic analogy source term.

► We investigate numerical error in the simulation of a transonic propeller.
► SPLs in the rotor plane converge with FWH surface location and grid resolution.
► Richardson’s extrapolation is successfully applied to our case.
► Off the rotor plane, the method prevents convergence with FWH surface location.
► Sound production relate to the structure of Lighthill’s source term at blade tip.