Helmholtz-Like Resonator Self-Sustained Oscillations, Part 2: Detailed Flow Measurements and Numerical Simulations

Abstract

A global description of the effect of the neck geometry on self-sustained oscillations of a grazing e ow along a Helmholtz-like resonator has been given in a companion paper. Detailed e ow measurements taken by means of hot-wire anemometry and numerical simulations based on the Euler equations for inviscid and two-dimensional compressible e ows are now given. Vortex shedding is obtained in an inviscid e ow simulation by considering a neck geometry with sharp edgesat which the code predictse ow separation. Although two-dimensional e owcalculations are attractive because of their computational efe ciency, they are not able to represent the three-dimensional acoustical radiation from the resonator into free space without special frequency-dependent boundary condition treatments. Frequency-independent time-domain boundary conditions are considered. In view of the crudeness of this approximation, the agreement between theory and experiments is quite fair. The effects of changes in the geometry of theneck are qualitatively predicted by the model. The detailed e owinformation provides someinsight into the ine uence of the shape of the upstream edge of the neck that could not be obtained from analytical models proposed in the companion paper.