Development of dynamic perturbations in initial stage of a point explosion in a thermally conducting gas

Abstract

The one-dimensional perturbations originating in a cold homogeneous gas (T₁ = 0, ϱ₁ = const) by the instantaneous release of finite energy at the origin of the coordinates are considered. The starting equations are compiled for a gas in which the heat-transfer mechanism is simulated by a nonlinear thermal conductivity with coefficient λ ∼ Tⁿ. Transformation of the equations to the dimensionless form by the introduction of “natural” variable allows the simplest path for investigating the process as a whole to be shown by means of the method of perturbations. The initial approximation corresponds to the well-known solution for a thermal wave [1], while subsequent approximations describe the joint development of both, thermal and dynamic perturbations. An investigation of the properties of the solutions and an example of the calculation of the first two approximations (without taking account of the starting approximation) for the case of a point spherical explosion with n = 5 gives a representation of the formation of the shock wave.