Numerical Study Of Compressible Mixing Layer With BGK Scheme

The study of compressible mixing layer is very important for either theoretical researches or engineering applications. In present research the new developed gas-kinetic BGK scheme is simplified and applied in the numerical simulation of spatial developing planar compressible mixing layers. The equal density and pressure of free streams are chosen to study the effect of compressibility on the mixing layer.In present study the calculation of the time slope term in the BGK scheme including the non-equilibrium state effect is simplified based on the conservation of mass, momentum and energy in particle collision. Numerical tests show that the simplification not only keeps the advantages of the old one but also makes it simpler and more efficient.In the results of eight 2D simulation cases with convective Mach number ranged from 0.2 to 1.0 the mean velocities and the thickness growth rates are in good agreement with experimental results, but the turbulent fluctuation intensities are larger. With present broadband spectrum forcing added on the inflow there still exist large vortex pairing processes in the mixing layer with high convective Mach numbers, although the rolls up of large vortex need much longer spatial developing distance.The improved scheme is expanded to 3D form and applied in the spatial developing mixing layers with convective Mach numbers 0.4, 0.8 and 1.2 respectively. The numerical results show that the flow-field structures and main features of the compressible mixing layer including the distribution of mean velocity, turbulent fluctuation intensities, Reynolds stress and growth rates agree well with experimental and other numerical results. There are shocklets in the mixing layer with convective Mach number 1.2. The statistic quantities exhibit good similarity behavior as well as in present 2D simulations. With increasing convective Mach number the streamwise fluctuation intensity varies little but the transverse and spanwise intensity along with the thickness growth rate decrease. The ratio between the Reynolds stress and the turbulence energy in the inner regime of the mixing layer keeps almost constant.The strong deviation and intermittence of the velocity and pressure fluctuations are found in the outer region about 3~4 times of the momentum thickness away from the mixing layer center, which are consistent with those observed experimentally.With increasing convective Mach number the skewness and flatness factors increase a little, and the peak positions move outwards. The spanwise velocity does not show distinct deviation, but its intermittence seems stronger. On the contrary, in the results of 2D simulations, the peak positions of the skewness and flatness are nearly 5 and 1.5 times of the momentum thickness away from the layer center respectively, and the compressibility decreases the former peak values. Present 2D results also show that the deviation and intermittence are due to the pairing of large vortex. The spectrum analysis reveals that the effect of compressibility is stronger on large scales than on small scales.The distribution of each term of the transport equations in 3D mixing layers shows agreement with other temporal developing numerical results. With increasing compressibility the value of each term and the effect of the pressure diffusion decrease except for the pressure-dilataion term. But the results of 2D simulations show that the pressure fluctuation plays a more and more important role.Present study reveals the good property of the gas-kinetic BGK scheme in the simulation of compressible flows that ensures its wide applications.