Large eddy simulation of supersonic mixing layers using a compressible filtered mass density function method

Abstract

To verify the applicability and superiority of the compressible filtered mass density function method in real supersonic mixing flows, a classical experimental subsonic-supersonic spatial mixing layer is numerically investigated. In the present method, a transport equation for the scalar filtered mass density function is solved using the Lagrangian particle solver, while the filtered mass, momentum, and energy equations are fully coupled and solved by the large eddy simulation finite difference solver. First, a parametric study of the mixing model constant controlling the scalar mixing rate is conducted in the two-dimensional case. It is found that the mixing model constant has a significant effect on the root mean square profile of the mixture fraction. The appropriate mixing model constant for this supersonic mixing layer is given by comparing the root mean square results under three different mixing model constants. These results also show that the suitable mixing model constant used in compressible flows is much larger than that used in incompressible flows. Second, three-dimensional simulations are performed to verify the current method. For comparison, a traditional large eddy simulation with the gradient diffusion model is also conducted. The results show that the scalar mixing is better predicted by the filtered mass density function method than the gradient diffusion model. In particular, the mean and root mean square mixture fraction computed by the present method are in excellent agreement with the experimental data whereas the gradient diffusion model overestimates the peak root mean square mixture fraction by about 45%.