Density distribution characteristics of fluid inside vortex in supersonic mixing layer

Abstract

Based on the large eddy simulation, the boundary of a vortex and the coordinates of its core are both obtained by using the Lagrangian coherent structure method and the location extraction method of the vortex core, and thus the method of representing fluid density inside a vortex is proposed. The density distribution characteristics of fluid inside the vortex in a supersonic mixing layer are revealed by analyzing the changes in density of the fluid inside a vortex under different conditions (e.g. spatial size of the vortex, compressibility of the supersonic mixing layer, and merging process of the two paired vortices) as follows. For the weak and medium compressive supersonic mixing layers, the density distribution of the fluid inside a vortex is symmetrical about both the flow direction (<i>x</i>-axis) and longitudinal direction (<i>y</i>-axis), the fluid density at the vortex core is lowest while it is highest at the vortex boundary, and fluid density increases monotonically and nearly uniformly along the ray connecting the vortex core and the vortex boundary. For the strongly compressible supersonic mixing layer, however, the density distribution of the fluid inside the vortex is no longer symmetrical about any flow direction and moreover it shows the fluctuation characteristics of fluid density distribution. With the increase of the spatial size of a vortex and the compressibility of a supersonic mixing layer, the fluid density at the vortex core decreases (the maximum reduction is about 31%–56%) while it changes about 6%–27% at the vortex boundary. In the merging process of two adjacent vortices, the variation of fluid density in the two vortices is slight, which shows that the merging process is probably of a peer-to-peer combination of fluid inside the two adjacent vortices. Considering the practical engineering applications, the density distribution characteristics of fluid inside the vortex in the supersonic mixing layer with different inflow densities of its upper and lower layers are also investigated, and the results show that the density distribution of the fluid inside a vortex is symmetrical about the longitudinal direction (<i>y</i>-axis), but not the flow direction (<i>x</i>-axis). It is also found that the density distribution near the vortex boundary is determined by the inflow density there, so a good strategy of reducing the aero-optical effects caused by the supersonic mixing layer is that the difference in density between the upper and lower layers should be as small as possible.