Investigation of supersonic turbulent flows over a sphere by fully resolved direct numerical simulation

In this work, a fully resolved direct numerical simulation study of the interaction between supersonic turbulent flow and inertial particle is carried out. For the compressible flow, an eighth-order bandwidth optimization weighted essentially nonoscillatory scheme is used for shock capturing, and the central finite difference scheme is used for the spatial discretization of diffusion terms. The three-dimensional ghost zone immersed boundary method is adopted for solid-fluid interface identification. These numerical schemes are integrated in a direct numerical simulation solver, and its validation is demonstrated by comparing to several benchmark cases. Such a developed method is then used to attack the problem of an upstream supersonic turbulent flow over a spherical particle. Three cases with different inflow turbulence intensities are studied. It is shown that with the turbulence intensity increasing the drag force coefficient presents a smaller relative increase compared to the incompressible situation. Analysis of the bow shock-turbulence interaction is also reported. Similar to the normal shock-turbulence interaction, both the Kolmogorov and Taylor scales decrease after being compressed by the shock. Moreover, both the streamwise and transverse Reynolds stresses have a peak at the shock position. These results indicate the significance of taking the effects of shock into consideration when modeling the modulation of a solid particle to the compressible turbulence.