Dynamics of an oscillating turbulent jet in a confined cavity

We demonstrate how the self-sustained oscillation of a confined jet in a thin cavity can be quantitatively described by a zero-dimensional model of the delay differential equation type with two a priori predicted model constants. This model describes the three phases in self-sustained oscillations: (i) pressure driven growth of the oscillation, (ii) amplitude limitation by geometry, and (iii) delayed destruction of the recirculation zone. The two parameters of the model are the growth rate of the jet angle by a pressure imbalance and the delay time for the destruction of this pressure imbalance. We present closed relations for both model constants as a function of the jet Reynolds number Re, the inlet velocity vin , the cavity width W, and the cavity width over inlet diameter W/d and we demonstrate that these model constants do not depend on other geometric ratios. The model and the obtained model constants have been successfully validated against three dimensional large eddy simulations, and planar particle image velocimetry measurements, for 1600 < Re ? 7100 and 20 ? W/d < 50. The presented model inherently contains the transition to a non-oscillating mode for decreasing Reynolds numbers or increasing W/d-ratios and allows for the quantitative prediction of the corresponding critical Reynolds number and critical W/d.