Physical and Numerical Aspects of Self-Induced Shock Oscillatory Flowfields.

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Self-Induced shock oscillation is essential physics in flow filed of supersonic under-expanded jet. Although there are many simulations for the self-induced shock oscillation flow fields, there exist strong dependency of resultant frequency on schemes used. Thus each schemecalculates its frequency of the oscillation. Thus, it is verydifficult to simulate these flow fields since the real physics should reveal only type of spectrum. The purpose of the present project is to investigate the cause of this difference and to develop the accurate and suitable scheme to calculate such self-induced shock oscillation.The project has been carried out during fiscal years 1999 to 2001. In the project, four types of the flow fields have been investigated with three types of flux functions and explicit/implicit time integration schemes. Parametric studies on the effect of the grid spacing and time/space accuracy. Results show the following conclusions. Viscous effect is not strong, the inviscid transportation of the vortices is essential physics of the shock oscillation. As for the effect of the grid spacing, the large grid spacing produces large numerical damping and results non-oscillatory flow. Thus it is shown that the appropriate resolution is essential for capturing shock oscillations. Although geometry of the problem is axisymetric, threedimensional effect is shown to be important. In this project, a new numerical scheme which especially suitable to simulate unsteady shocked flows has been proposed and developed. The scheme is based and estimated on the space-time control volume in order to assure the conservation of the physical properties and geometric properties.