Simulation and modeling of compressible turbulent mixing layer
Samadi Vaghefi, Seyed Navid
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Direct numerical simulations (DNS) of compressible turbulent mixing layer are performed for subsonic to supersonic Mach numbers. Each simulation achieves the self-similar state and it is shown that the turbulent statistics during this state agree well with previous numerical and experimental works. The DNS data is used to extract the physics of compressible turbulence and to perform a priori analysis for subgrid scale (SGS) closures. The flow dynamics in proximity of the turbulent/non-turbulent interface (TNTI), separating the turbulent and the irrotational regions, is analyzed using the DNS data. This interface is detected by using a certain threshold for the vorticity norm. The conditional flow statistics based on the normal distance from the TNTI are compared for different convective Mach numbers. It is shown that the thickness of the interface layer is approximately one Taylor length scale for both incompressible and compressible mixing layers, and the flow dynamics in this layer differs from deep inside the turbulent region. Various terms in the transport equations for total kinetic energy, turbulent kinetic energy, and vorticity are examined in order to better understand the transport mechanisms across the TNTI in compressible flows. The DNS data is also employed to analyze the local flow topology in compressible mixing layers using the invariants of the velocity gradient tensor. The topological and dissipating behaviors of the flow are analyzed in two different regions: near the TNTI, and inside the turbulent region. It is found that the distribution of various flow topologies in regions close to the TNTI differs from inside the turbulent region, and in these regions the most probable topologies are non-focal. The occurrence probability of different flow topologies conditioned by the dilatation level is presented and it is shown that the structures in the locally compressed regions tend to have stable topologies while in locally expanded regions the unstable topologies are prevalent. In order to better understand the behavior of different flow topologies, the probability distributions of vorticity norm, dissipation, and rate of stretching are analyzed in incompressible, compressed and expanded regions. The DNS data is also used to perform a priori analysis for subgrid scale (SGS) viscous and scalar closures. Several models for each closure are tested and effects of filter width, compressibility level, and Schmidt number on their performance are studied. A new model for SGS viscous dissipation is proposed based on the scaling of SGS kinetic energy. The proposed model yields the best prediction of SGS viscous dissipation among the considered models for filter widths corresponding to the inertial range. For the range of Mach numbers and Schmidt numbers studied in this work, the SGS scalar dissipation model based on proportionality of turbulent time scale and scalar mixing time scale produces the best results in the filter widths corresponding to the inertial subrange. For both viscous and scalar SGS dissipation models, two dynamic approaches are used to compute the model coefficient. It is shown that if the dynamic procedure based on global equilibrium of dissipation and production is employed, more accurate results are generated compared to the conventional dynamic method based on test-filtering.