Repeated Mach reflections in curved converging contractions

Plane shock waves moving into area contractions undergo a complex series of reinforcing reflection processes. For ‘gradual’ contractions, these will be predominantly Mach reflections. Commonly, contractions may be either two-dimensional or axisymmetric. Considerable experimental and theoretical work is available on the Mach reflection processes for the former but little for the latter, this to a large extent being due to the formidable experimental problems associated with internal axisymmetric flow visualization. However, with either, the general case of a contraction having inward curving walls has additional complexities associated with it due to the interaction of the reflected waves with re-reflections from the opposing wall or centerline. In order to obtain a rapid assessment of the reflection pattern, a simple method has been developed here using the ray-shock theory. Computations can be carried out on microcomputers. Comparison with experiment in the two-dimensional case shows excellent agreement. A computational result is available for axisymmetry but this needs further experimental work for verification and further theoretical development.