Three-dimensional, shock-on-shock interaction problem

摘要

The unsteady, three-dimensional flow field resulting from the interaction of a plane shock with a cone-shaped vehicle traveling supersonically was determined using a second-order, shock-capturing, finite-difference approach. The time-dependent, inviscid gas dynamic equations are transformed to include the self-similar property of the flow, to align various coordinate surfaces with known shock waves, and to cluster points in the vicinity of the intersection of the transmitted incident shock and the surface of the vehicle. The governing partial differential equations in conservation-law form are solved iteratively using MacCormack's algorithm. The computer simulation of this problem, compared with its experimental counterpart, is easy to model and results in a complete description of the flow field including the peak surface pressure. The numerical solution with its complicated wave structure compares favorably with available schlieren photographs, and the predicted peak surface pressures obtained are shown to agree better with the experimental data than existing approximate theories.