Simplified exhaust pipe noise radiation modelling using the Fourier PSTD method

The noise, radiated from the tailpipe of automotive exhaust ducts, is affected by the jet flow leaving the exhaust and by its surrounding geometry. The current work extends existing studies of sound radiation from a jet pipe with radiation over a rigid ground surface and relies on a numerical study. A simplified approach is used where the mean flow properties behind the tailpipe are calculated by solving the Reynolds averaged Navier-Stokes equations (RANS). The extended Fourier pseudospectral time-domain (PSTD) method is then utilized to compute the sound propagation in the tailpipe geometry by solving the linearized Euler equations (LEE). As the vorticity modes in the shear layer behind the tailpipe may turn unstable using the LEE, additional calculations with the LEE with applied high wave number dissipation and the LEE with mean flow gradient terms suppressed (LEE-GTS) are carried out. Results are validated by analytical expressions in free field and the necessity of solving the LEE rather than the LEE-GTS in the current application is shown. Finally, a calculation of tailpipe noise radiation over a ground surface is performed.