Sensitivity analysis and uncertainty quantification for the ffowcs williams-hawkings equation

Abstract

The acoustic propagation stage of a computational aeroacoustic analysis has been in- vestigated for possible sources of uncertainty and sensitivity. The acoustic propagation is realized through an acoustic prediction module that is fundamentally based on the Ffowcs Williams-Hawkings equation. Non-intrusive polynomial chaos expansion methods are used, along with a direct sensitivity analysis based on Sobol indices. Three analytical test cases are chosen in order to isolate the acoustic propagation stage from the noise source identification stage. In an analysis of a theoretical helicopter blade, it is identified that the mean flow Mach number and blade tip Mach number are significant contributors to noise uncertainty. As the advancing blade tip Mach number approaches the transonic and supersonic flow regimes, these uncertainties are amplified. The source of the uncertainty is mainly attributed to the blade tip Mach number at low mean flow Mach numbers, however as the mean flow Mach number increases, the contribution of the mean flow Mach number to the uncertainty significantly increases. © 2017, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved