Response characteristics of inflow-stimulated Kelvin-Helmholtz vortex in compressible shear layer

Abstract

By numerically solving the Navier-Stokes equations, the response characteristics of inflow-stimulated Kelvin-Helmholtz vortex in compressible shear layer arestudied. The mixing characteristics and the unique growth mechanism of the vortex structure are clearly revealed. By employing the index of vorticity thickness, the mixing properties are quantitatively analyzed. Based on the flow visualization results, the spatial size and the structure angle of the flow coherent structure are investigated by utilizing spatial correlation analysis. The evolution mechanism of the vortex structure in supersonic mixing layer induced by inlet forcing is revealed by analyzing the dynamical performances of the flow structure under different frequency disturbances. The numerical results show that with low forcing frequency at <i>f</i> = 5 kHz, the mixing efficiency is remarkably increased in the near-field of the flow. Whereas, in the far-field downstream the flow, the size of the structure reaches saturation state and the vortex passage frequency is locked, which causes the vorticity thickness to stabilize from 12mm to 14mm. Meanwhile, in a free mixing layer, the pairing and merging process occur in the flow field to promote the growth of the vortex structure, while in mixing layer with inlet forcing, the growth mechanism is that the vortex core engulfs a string of vortices induced by Kelvin-Helmholtz instability. The process of engulfment contributes much to the growth of the vortex structure. The analysis of spatial correlation distribution shows that in the area where engulfment occurs, the contour line shows the property of long and narrow ellipse instead of full ellipse and the structure in the area possesses the characteristics of intense rotation and inclination. Besides, with high inlet forcing frequency at <i>f</i> = 20 kHz, the size of the vortices becomes full in the near-field, and the vorticity thickness stabilizes between 3mm and 4 mm downstream the flow field. Meanwhile, the size of the vortex in controlled supersonic mixing layer is dominated by the imposed high-frequency forcing. An equation describing the quantitative relationship between the vortex characteristics and the imposed forcing frequency is derived, that is, the size of the uniform distribution vortex is approximately equal to the ratio of the value of convective velocity to inlet forcing frequency.