Compressibility effects on the transition to turbulence in a spatially developing plane free shear layer

摘要

The compressibility effects on the transition to turbulence in a spatially developing, compressible plane free shear layer are investigated via direct numerical simulation using a high-order discontinuous spectral element method for three different convective Mach numbers of 0.3, 0.5, and 0.7. The location of the laminar-turbulent transition zone is predicted by the analyses of vorticities, Reynolds stresses, and the turbulent dissipation rate. In the turbulence transition and self-similar turbulence regions, the effects of compressibility on the flow properties, such as the velocity autocorrelation function, integral time scale, momentum thickness, Reynolds stress, and turbulent kinetic energy budget, are investigated. The compressibility effects on the onset and length of the turbulence transition zone are studied based on the analyses of such flow properties. The mean velocity, momentum thickness, and Reynolds stress profiles compare well with published experimental data. Vorticity contours and iso-surface of the second invariant of velocity gradient tensor identify the characteristic of flow structures. The two-point correlation functions of velocity components, the one-dimensional (1D) spanwise energy spectrum, and the balance of the turbulent kinetic energy transport equation validate the domain size and resolution of the adopted grid for turbulence simulation. An increase in the convective Mach number leads to a reduction in the sizes of the largest-scale structures, resulting in a significant decrease in Reynolds stresses and turbulence production. The onset of turbulence transition and the location where the transition completes shift downstream, while the length of the transition zone increases with increasing convective Mach number.