Plate thickness effect on orifice impedance with nonlinear acoustic/grazing flow interaction

This paper presents a theoretical study of the acoustic properties of a small rectangular orifice in a plate of finite thickness, in the presence of both grazing flow and high-intensity sound wave. The present investigation has three basic objectives. The first is to study the plate thickness effect on acoustic properties of the orifice. The second is to study the interaction of high-intensity sound with grazing flow. The third objective is to present flow details around the orifice. On the assumption of large aspect ratio, a 2D discrete vortex method is employed to provide the near field unsteady flow simulation results that are then substituted into a spanwise-averaged 3D Green function integral formula to develop a quasi-3D model. Depending on this strategy, the nonlinear acoustic impedance of the orifice is calculated from the average flow velocity through the orifice. The reactance of the orifice increases markedly with the increase of the plate thickness, and the reactance results of the finite-thickness plate are apparently larger than the one of the zero-thickness plate. The calculated resistance reveals that the acoustic property of the orifice undergoes a transition from linear to nonlinear, as the sound pressure amplitude increases; the grazing flow velocity has influence on the transition SPL, resulting from the interaction. More detailed analyses of the effects of the grazing flow and the incident sound wave on the acoustic properties of the orifice are carried out. The vortex shedding process at the orifice edge and the evolution of the shed vortex sheet are simulated, the simulation results exhibit the major features of the vortex sheet, such as the rolling up nature and the "flapping" motion of the shear layer over the orifice.