Physical features of turbulence and vortex-flame interaction in engines are investigated by performing large eddy simulation and direct numerical simulation of compressible flows. A BI-SCALES (Boundary-Inner Smoothly Coupled, Alternating multi-Level Equations System) is proposed, which is a mathematical formulation of the system of governing equations suitable for computations of compressible flows. A numerical method based on the proposed formulation is developed. Using the method, the transition to turbulence in the compression process and the cyclic variations are examined. Then, the vortex-flame interaction is studied, mainly on the relation between the flame structure and the Kalvoritz- and turbulent Reynolds number effect. Finally, the large wrinkle simulation (LWS) of engine combusting flow is performed.
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