A numerical study of an acoustic–hydrodynamic system exhibiting an intermittent prelude to instability

Abstract

A model problem comprising two subsytems (acoustic and hydrodynamic), both admitting unsteady flows, has been studied using numerical simulations. Simulations capture all key features observed in an experiment with a similar configuration, and reveal the differences in flow field evolution that manifest as an intermittent prelude to instability in this nonlinear system, coupling acoustic and hydrodynamic phenomena. The system consists of a uniform flow that enters a long duct and leaves through an orifice into the atmosphere. The duct supports acoustic modes, while the shear layer at the boundary of the jet emerging from the orifice can develop into a train of vortices. Over some range of inflow velocities that support a stable operation, duct acoustic modes and shear layer breakup result in aperiodic, small amplitude pressure fluctuations. As the flow rate is increased, fluctuations become essentially periodic and have much larger amplitudes. This transition from a quiescent to a (so-called) whistling state occurs over a range of flow rates and is characterized by intermittent, moderately large, aperiodic fluctuations. As in the experiment, the aperiodic time series from the quiescent state is found to be multifractal; multifractality is then lost as the flow transitions to whistling. Simulation flow fields reveal differences in the development of vortices in the bounding shear layer, and near the orifice walls, that give rise to the large changes in pressure fluctuations, as well as the intermittent behavior that precedes whistling.