Refractive phenomena in the shock wave dispersion with variable gradients

Abstract

In this article the refraction effects in the weak shock wave ͑SW͒ dispersion on an interface with a temperature variation between two mediums are described. In the case of a finite-gradient boundary, the effect of the SW dispersion is remarkably stronger than in the case of a step change in parameters. In the former case the vertical component of velocity for the transmitted SW ͑the refraction effect͒ must be taken into account. Results of comparative calculations based on the two-dimensional model corrected for the refraction effect show significant differences in the shapes of the dispersed SW fronts.

Shock wave refraction enhancing conditions on an extended interface

“…For a smooth boundary, 19 the coefficient b in the velocity ratio (15) is equal 1 = 2 exactly (1/R ¼ 0) since the Mach number does not change across the interface. For a sharp boundary, 21 the coefficient b is remarkably smaller than 1 = 2 since the velocity ratio (2) is dependent also on the Mach number ratio. This Mach number ratio decreases across the interface at a rate close to the square root law, making b much smaller than 1 = 2 .…”

“…We want to calculate the shape of the shock front (X i , Y i ) dispersed on a spherical interface of radius R with the coordinates (x i , y i ) as in Ref. 21…”

The cumulative energy effect for improved ignition timing

“…At this stage, the refracted shock speed and the angle of refraction can be determined with the refraction equations. 17 The second stage takes place when the refracted shock wave starts to propagate from the interface through the medium with the decreasing density. Here, the shock front coordinates and the speed as a function of time are to be determined using the relations obtained in the paper.…”

“…This was accounted in the equations that now are requiring the solution of the transcendental equation determining the Mach number for the refracted shock M 2n . 17 To explore the effect of the boundary type alone, the rest of the problem parameters were kept fixed, and only two different Mach number ratios in the equations were used. The results plotted in Fig.…”

“…16 The shock front shape can be changed from plane to curved and back, with the possibility of gaining an additional dimension. [17][18][19][20] The specific details of the gas state, such as electron kinetic, ionization/dissociation processes, radiation, atomic/molecular transitions, energy exchange processes in collisions, chemical processes, boundary effects, heat, charge (in plasma), or radiation convection, 21,22 add to the variety and complexity of the final state of the gas/plasma or the shock wave structure after the interaction.…”