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

A global description of the effect of the neck geometry on self-sustained oscillations of a grazing flow along a Helmholtz-like resonator has been given in a companion paper. Detailed flow measurements taken by means of hot-wire anemometry and numerical simulations based on the Euler equations for inviscid and two-dimensional compressible flows are now given. Vortex shedding is obtained in an inviscid flow simulation by considering a neckgeometry with sharp edges at which the code predicts flow separation. Although two-dimensional flow calculationsare attractive because of their computational efficiency, 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 the neck are qualitatively predicted by the model. The detailed flow information provides some insightinto the influence of the shape of the upstream edge of the neck that could not be obtained from analytical models proposed in the companion paper.