Kazuhisa Amemiya

On the Modification of the Ffowcs Williams-Hawkings Integration for Jet Noise Prediction

This paper proposes a modification on the end-cap treatment for the Ffowcs Williams and Hawkings (FW-H) equation with permeable control surface, aiming at jet-noise simulations by the use of time-accurate numerical methods. It is a known issue that a closed end cap affects the accuracy of the permeable FW-H equation, as turbulent jet flow passes through the control surface. This is essentially an outcome of the neglected volumetric quadrupole term. Based on our previous study of the quadrupole correction, evaluated at an end-cap surface for uniform mean flow, we derive a mathematical extension to nonuniform convection velocity. By introducing locally frozen assumption for convecting vortices, a modification factor is obtained as a convergent series if the deviation of convection velocity from mean flow is subsonic. The derived formulation is applied to a simple subsonic round jet at ReD = 1 × 10 and Ma = 0.9. Although the present jet-flow simulation fails in accurately reproducing mixing-layer transition behind a nozzle exit, which leads to a significant overestimate of far-field noise, our modification on the FW-H formulation suppresses the spurious noise due to closed end-cap surface, as well as a more empirical, disk averaging approach proposed by Shur et al. (2005)

Quadrupole Corrections for the Permeable-Surface Ffowcs Williams–Hawkings Equation

This paper focuses on the spurious noise of the Ffowcs Williams and Hawkings equation with a permeable integral surface, which is now commonly used in far-field noise prediction for computational a...

Quadrupole Effects in the Ffowcs Williams-Hawkings Equation Using Permeable Control Surface

Combined with time accurate compressible flow simulations, the Ffowcs Williams and Hawkings (FW-H) equation with permeable control surface becomes more common in aerospace applications, because of its inexpensive computational cost for far-field noise prediction, when only surface integral terms are retained. This paper discusses the effect of the neglected volumetric quadrupole term on the porous FW-H equation. Introducing frozen assumption for convecting vortices without any distortion or interaction which may cause aerodynamic noise, the quadrupole term can be approximated by a surface integral. By employing the derived term as quadrupole modification, the porous FW-H approach is drastically improved in the two dimensional wake behind a NACA0012 airfoil. The competence of the proposed approach in a turbulent jet noise prediction is somewhat unclear in the present particular numerical configuration, in comparison with an open control surface. Still a significant improvement is observed, compared to the standard porous FW-H approach.