Reflection of a strong shock wave from a sphere and a cylinder

Abstract

We examine the flow on the axis in the vicinity of the stagnation point for reflection of a strong plane shock wave (with uniform parameters behind the wave) from a sphere and a circular cylinder whose generators are parallel to the incident wave front.

The small parameter method [1, 2] is used to obtain, in closed form, relations which define the time variation of the velocity profile, pressure, enthalpy, and reflected shock wave standoff.

As the time t → ∞, these relations reduce to the known formulas [3, 4] which define the steady flow on the axis for the flow behind the incident shock wave about a body, if account is taken of the leading terms containing the small parameter.

The solution is extended to the case in which account for equilibrium dissociation and ionization is necessary.

Comparison of the results with measurement [5] of the reflected shock wave distance from a sphere, as a function of time, shows satisfactory agreement.