Three-Dimensional, Shock-on-Shock Interaction Problem

Abstract

The unsteady, three-dimensional flowfield resulting from the interaction of a plane shock with a cone-shaped vehicle traveling supersonically is 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 then solved iteratively using MacCormack's algorithm. The computer simulation of this problem, compared with its experimental counterpart, is relatively easy to model and results in a complete description of the flowfield including the peak surface pressure. The numerical solution, with its complicated wave structure, compares favorably with the available schlieren photographs, and the predicted peak surface pressures obtained are shown to agree better with the experimental data than existing approximate theories.

Reflection of a rightward-moving oblique shock of first family over a steady oblique shock wave

“…Merritt & Aronson (1966) and Merritt & Aronson (1967) studied the head-on interaction of a flying supersonic model of a hemisphere–cylinder, right circular cylinder, 60 wedge and 9 half-angle cone. Numerical simulations for shock-on-shock interaction are given by Kutler, Sakell & Aiello (1974, 1975) and Kutler & Sakell (1975), using a second-order, shock-capturing, finite-difference approach.…”

Shock interactions in hypersonic flows outside the sonic circle in front of a blunt body

“…Following this, many researchers conducted experimental 10–14 and numerical 15–24 studies on the prediction and characterization of the shock interaction patterns. It has been noted that most of the experimental studies have been carried out in the hypersonic wind tunnels, which lack in simulating the energy content of the flow, typical of the hypersonic flight regime.…”