A comparison between off and on-body control surfaces for the FW-H equation: Application to a non-compact landing gear wheel

Abstract

This work is a contribution to the ongoing debate about the role of quadrupoles in low Mach number flows, studied through the use of solid and permeable surface Ffowcs-Williams & Hawkings (FW-H) integrals for landing gear numerical noise predictions. It rests upon the key idea that the dominance of surface sources over volume sources can only be guaranteed when the compact-source condition is met. We propose here to express this property as a condition on the smallness of the product between the Mach and Strouhal numbers, or formally as MSt < 1. We consider a canonical isolated wheel, that basically consists in a shallow circular cavity inscribed in a coin-like cylinder, thus presenting few different length scales, as compared to a full landing gear assembly. Zonal Detached Eddy Simulations are performed on several gradually refined grids to assess the grid convergence of the numerical result. In particular, important computational effort is put into the accurate resolution of acoustic waves up to Strouhal numbers such that MSt > 1. Overall, determining the real significance of quadrupoles was challenging as numerical errors or misleading effects such as near-field terms, surface discretization, or source domain truncation biased the initial permeable surface results. Even when these sources of bias are removed, non-negligible differences are found between the solid and permeable noise spectra at non-compact St values, while both formulations are equivalent at lower Strouhal numbers. The analysis of these differences is extended to the determination of their impact on frequency-domain noise maps obtained with the DAMAS algorithm fed with far-field signals computed with both FW-H approaches. A tentative interpretation of the wheel noise sources is finally proposed, highlighting the dominant role of the scattering of aerodynamic sources by the cavity downstream edge at low Strouhal numbers, while wake sources dominate at higher Strouhal numbers.

Computationally efficient, frequency-domain quadrupole corrections for the Ffowcs Williams and Hawkings equation

“…The proposed correction terms were shown to be effective in a jet noise computation, as well as in the noise prediction for a low-Mach blunt-body flow. 12 As a frequency-domain approach, Lockard and Casper 7 derived correction terms for the convective FW-H equation in the form of an infinite series. However, for M > 0.5, the series was shown to be divergent.…”