Determination of flow field behind magnetogasdynamic spherical blast wave under the influence of viscosity

Abstract

A procedure has been given to determine analytica]ly the flow field behind a spherieal b]ast wave in the case of a viscous compressible f]uid under a spherica]]y symmetric magnetic field. l. IntroductionThe propagation of strong shock waves in a half space, due to surfaee explosion or impact, has becn treatcd in many lcvr of approximation. In one of these an attempt is made to account for the material strength by including a Newtonian viscosity term. This approximation seems to have been originated by S. W. YuA~ and various co-workers [1]--[4], who have further approximated the solution of the resulting equations by seeking a variety of quasisimilar solutions. In all of these solutions the viseosity coefficient is taken to be at most a function of time, but independent of space coordinates. In addition, the flow field in the half space is represented as though it were one half of a spherically symmetric flow. The predictions of this theory, for certain quantities on the symmetry axis at the shock front, ate then compared with experiment, and it is usually claimed that the agreement constitutes a validation of the model used. However, ir has been pointed out repeatedly that quantities at the shock front ate very insensitive to details of the model, and can be approximated fairly well by any number of approximations. A recent illustration of this fact is presented in a paper by BILLI~GSLEY [5], whose results show that the experimental data was incapable of resolving the differences between a wide variety of theoretical treatments, Even in the subset of quasi-similar solutions without viscosity, there are many remaining questions about the effects of the spherical-flow assumption, the neglect of non-similarities due to non-zero projectile size, and the approximations used in defining the equation of state, to mention only a few. These ate critically reviewed in a recent survey paper by RAE [6]. When a spherically symmetric magnetic field is added to this formulation along with a Newtonian viscosity term, the present paper proposes to study the composite effect of all the approximations.