Evolution mechanism of vortices in a supersonic mixing layer controlled by the pulsed forcing

Abstract

Pulsed actuation is one of the most fundamental control types to study regularity of flow structures in supersonic mixing layers, which helps to predict the aero-optical effects caused by the supersonic mixing layer where the different-sized vortices dominate the flow field. However, the knowledge about the evolution mechanism of vortices in the supersonic mixing layer which is controlled by the pulsed forcing is limited. Based on the large eddy simulation (LES), the visualized flow field of a supersonic mixing layer controlled by the pulsed forcing is presented and the unique growth mechanism of the vortices in such a case is revealed clearly. The method of position extraction of the vortex core in the supersonic mixing layer, which is a quantitative technique to obtain the instantaneous location of a vortex in flow field, is employed to calculate the dynamic characteristics (e.g., instantaneous convective speed and size) of the vortices quantitatively. The pulsed forcings of different frequencies are imposed on the same supersonic mixing layer respectively, and the instantaneous convective speed and size of the vortices for each pulse frequency considered in this study are then computed. By comparing the dynamic characteristics of the vortices between cases, the evolution mechanism of the vortices in the supersonic mixing layer controlled by the pulsed forcing is revealed.as follows. 1) Growth of the vortices in the supersonic mixing layer controlled by the pulsed forcing no longer depends on the pairing nor merging between adjacent vortices, which is just the growth mechanism of vortices in a free supersonic mixing layer. Actually, the size of a vortex in the controlled supersonic mixing layer is dominated by the imposed pulse frequency, so the size of each vortex in such a flow field is approximately identical. 2) The number of vortices in the controlled supersonic mixing layer is proportional to the pulse frequency, whereas the size of vortex is inversely proportional to the pulse frequency. That is, the higher the pulse frequency, the bigger the number of vortices in the controlled flow field is and the smaller the size of every vortex. 3) The average convective speed of vortices in the controlled supersonic mixing layer gradually decreases with pulse frequency increasing because the pulsed forcing essentially drags on the movement of vortices in flow field. Finally, an equation which describes the quantitative relationship between the dynamic characteristics of a vortex and the pulsed forcing frequency is derived, that is, the product of the average convective speed of vortices in the controlled supersonic mixing layer and the imposed pulse period is approximately equal to the mean diameter of vortices in the flow field.