Optimization of pulsed jets in crossflow

We use direct numerical simulation to study the mixing behaviour of pulsed jets in crossflow. The pulse is a square wave and the simulations consider several jet velocity ratios and pulse conditions. Our objective is to study the effects of pulsing and to explain the wide range of optimal pulsing conditions found in experimental studies of the problem. The central theme is that pulsing generates vortex rings; the effect of pulsing on transverse jets can therefore be explained by the behaviour of vortex rings in crossflow. Sau & Mahesh (J. Fluid Mech., vol. 604, 2008, pp. 389-409) show that vortex rings in crossflow exhibit three distinct flow regimes depending on stroke and ring velocity ratios. The simulations of pulsed transverse jets in this paper show that at high velocity ratios, optimal pulse conditions correspond to the transition of the vortex rings produced by pulsing between the different regimes. At low velocity ratios, optimal pulsing conditions are related to the natural time scale on which hairpin vortices form. An optimal curve in the space of stroke and velocity ratios is presented. Data from various experiments are interpreted in terms of the properties of the equivalent vortex rings and shown to collapse on the optimal curve. The proposed regime map allows the effects of experimental parameters such as pulse frequency, duty cycle, modulation and pulse energy all to be predicted by determining their effect on the equivalent stroke and velocity ratios.