Nonlinear dynamics of an acoustically compact orifice

This work presents a three dimensional, reduced order model of the dynamics of an acoustically compact aperture, subject to an arbitrary pressure forcing. It provides the time evolution of the velocity profile across the orifice section as function of the dynamical pressure excitation. The volume flow can be deduced therefrom, and can thus provide predictions of the fundamental frequency based orifice impedance. The representation of the nonlinear aperture flow proposed here establishes a direct mathematical relation to the fundamental equations of fluid mechanics. This offers a better understanding of the dominant physical mechanisms governing the system's dynamics and allows for good a priori estimates without supporting experiments. The model assumes that the viscosity induced rotational component of the fluid motion can be reduced to a discontinuity at the in-flow plane of the thin orifice, without significantly influencing the velocity profile. This seemingly counter intuitive assumption is motivated by previous studies from the literature and validated here with direct numerical simulations (DNS) of the aperture flow, using a compressible solver of the Navier–Stokes equations. Apart from the DNS performed for the occasion, the model predictions are also validated against well established experimental results from the literature.