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. Published under license by AIP Publishing.