Numerical investigation and modelling of acoustically excited flow through a circular orifice backed by a hexagonal cavity

Resolved simulations of the sound-induced flow through a circular orifice with a 0.99 mm diameter are examined. The orifice is backed by a hexagonal cavity and is a local model for acoustic liners commonly used for aeroengine noise reduction. The simulation data identify the role the orifice wall boundary layers play in determining the orifice discharge coefficient which, in time-domain models, is an important indicator of nonlinearity. It is observed that when the liner behaviour is not well described by linear models, the orifice boundary layers contain secondary vorticity generated from its separation from the corner on the high-pressure side of the orifice. Quantitative comparisons of the simulation-predicted impedance match available data for incident sound of 130 dB amplitude at frequencies from 1.5 to 3.0 kHz. At amplitudes of 140–160 dB, the simulation impedance is in agreement with analytical predictions when using simulation-measured quantities, including the discharge coefficient and root-mean-square velocity through the orifice, although no experimental data for this liner exist at these conditions. The simulation data are used to develop two time-domain models for the acoustic impedance wherein the velocity profile through the orifice is modelled as the product of the fluid velocity and a presumed radial shape, $\dot {\xi } V(r)$. The models perform well, predicting the in-orifice velocity and pressure, and the impedance, except for the most nonlinear cases where it is seen that the assumed shape $V(r)$ can affect the backplate pressure predictions. These results suggest that future time-domain models that take the velocity profile into account, by modelling the boundary layer thickness and assuming a velocity profile shape, may be successful in predicting the nonlinear response of the liner.