Characteristics of convective speeds of vortex structures in mixing layer

Abstract

Convective speed of a vortex structure in mixing layer is an important physical quantity for correcting aero-optics caused by the flowfield as a beam passes; however, knowledge about the dynamic characteristics of convective speed of a vortex structure in mixing layer is limited because the convective speed calculated from isentropic model, which is widely used at present, is a constant. Based on the large eddy simulation and ray tracing method, the optical path length (OPL) profile over the mixing layer flowfield as beams pass through the flowfield is calculated and compared with the instantaneous vorticity contours at the same time instant. The analysis of the relationship between the local minimum of OPL in the OPL profile and the position of vortex core shows that the point of the local minimum of OPL just corresponds to the center of the vortex core. Based on this corresponding relation, the position extraction of vortex core, which is a quantitative method of calculating the instantaneous convective speed of a vortex structures in mixing layer, is proposed and validated with the data obtained from direct geometry measurement. Using this quantitative method, the instantaneous convective speeds of vortex structures with different sizes, two vortexes in the process of vortex pairing and merging, and vortex structures in the strongly compressive flowfield are calculated quantitatively and analyzed. Our quantitative results clearly present the characteristics of convective speed of vortex structures in mixing layer as follows. 1) The instantaneous convective velocity of a single vortex structure in the mixing layer flowfield varies with time, that is the fluctuation characteristics, and the fluctuation amplitude also varies with the size of a vortex structure and the compressibility of the flowfield. Specifically, the amplitude is proportional to the size of a vortex and the compressibility of the flowfield. 2) In the process of vortex pairing and merging, the variation ranges of instantaneous convective speeds of the two vortex structures are large. Specifically, the maximum value of instantaneous convective speed is close to the speed of the high-speed layer and the minimum value of instantaneous convective speed is close to the speed of the low-speed layer, and the profile of instantaneous convective speed of each vortex structure in this process approximately shows a shape of sinusoidal curve. 3) The mean value of instantaneous convective speed of a vortex structure in mixing layer is not consistent with the theoretical convective speed of vortex structure, which is calculated from the isentropic model, and the deviation between instantaneous convective speed and theoretical convective speed varies with the size of a vortex structure and the compressibility of the flowfield. In addition, the physical reasons for explaining the characteristics of instantaneous convective speed of the vortex structures in mixing layer are also presented.