Shock wave refraction enhancing conditions on an extended interface

Abstract

We determined the law of shock wave refraction for a class of extended interfaces with continuously variable gradients. When the interface is extended or when the gas parameters vary fast enough, the interface cannot be considered as sharp or smooth and the existing calculation methods cannot be applied. The expressions we derived are general enough to cover all three types of the interface and are valid for any law of continuously varying parameters. We apply the equations to the case of exponentially increasing temperature on the boundary and compare the results for all three types of interfaces. We have demonstrated that the type of interface can increase or inhibit the shock wave refraction. Our findings can be helpful in understanding the results obtained in energy deposition experiments as well as for controlling the shock-plasma interaction in other settings.

A Shock Wave Instability Induced on a Periodically Disturbed Interface With Plasma

“…As seen in (12)(13)(14), the common dependence of the parameters t 0i , t λ , and t γ on the same factor 2 Ak ≈ χ establishes the similarity law with respect to the curvature in this non-uniform case too. To visualize this conclusion, numerical simulations of the instability development were run for a set of different parameters A and λ but their ratio kept the same.…”

“…toward or off their symmetry axes. The Mach number components along the normal to the interface M 1n and M 2n are defined through the corresponding velocity components [7] and their ratio accounts for the losses due to the shock reflections off the interface [13]. In the equations below, the interaction time…”

The cumulative energy effect for improved ignition timing

“…Then the Mach number ratio will also take some intermediate values which can be estimated using the relations derived in the paper. 18 For the whole range of possible Mach number ratios, the results for shock front shape and its location will be somewhere between two limiting curves in the pairs presented in Fig. 7.…”

“…To set its lower limit, the calculations were performed for a sharp (step-wise) boundary, when the refraction effect is weaker. 18 In this case, energy losses due to shock wave reflection off the interface occur [51][52][53] and the ratio of the normal components of the Mach numbers M 2n /M 1n will be less than the unit. 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 .…”

“…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.…”