Numerical Study of Time Domain Approach Applied to the Prediction of Noise Radiation From Rotating Blades

Aeroacoustic formulations in time domain are frequently used to model the aerodynamic sound of airfoils, the time data being more accessible. The formulation 1A developed by Farassat, integral solution of the Ffowcs Williams and Hawkings equation, holds great interest because of its adequacy for surfaces in arbitrary motion. The aim of this work is to study the numerical sensitivity of this model to specified parameters and the geometry used in the calculation. The numerical algorithms, spatial and time discretizations, and approximations used for far-field acoustic simulation are presented. A parametrical study of the relevant criteria is carried out based on the Isom’s and Tam’s test cases. A helicopter blade airfoil as defined by Farassat to investigate the Isom’s case is used in this work. According to Isom, the acoustic response of a dipole source with a constant aerodynamic load ρ₀c₀² is equal to the thickness noise contribution. In practice, this observation is subject to numerical errors that are not systematically well controlled. Variations of these errors depending on the time step, Mach number and the source-observer distance are studied. The analysis is then extended to the Tam’s test case. Tam test case has the advantage of providing an analytical solution for the first harmonic.