Shock jump equations for unsteady wave fronts

Abstract

First, the Rankine–Hugoniot (R–H) relations are generalized for unsteady shock wave fronts of infinitesimal risetime. The equation for particle velocity has a term of strain rate, while that for stress contains terms of strain rate and acceleration. Next, shock jump equations of general form for particle velocity, stress, and specific internal energy are derived. They involve the combined effect of strain wave form, its change with time, and the path in time of strain. The effect, as well as the terms of strain rate and acceleration in the generalized R–H equations, indicates uncertainty about the applicability of familiar R–H equations to the shock fronts. Finally, jump equations for specific strain waves are evaluated: Jumps in the three quantities are influenced greatly by the effect. If both the wave form and the path are linear, then the equations are of the same form as the R–H equations.

Removing Full-scale Testing Barriers: Energetic Material Detonation Characterization at the Laboratory Scale

“…As previously mentioned, the conservation equations developed are written for the case of a planar shock wave interaction. However, previous research has demonstrated that the radial divergence effects associated with spherical detonation waves are insignificant for shock wave curvatures that are orders-of-magnitude larger than the detonation-reaction-zone thickness (12)(13)(14)(15). Thus, the planar equations remain valid for the present explosive charge configuration.…”

“…The final equation required to close the system is an empirical relationship developed by Cooper (2) that relates the reaction products density to the energetic material pressing density, equation 15. This is chosen in place of a P − ρ Hugoniot for the reaction products as no all-energetic-material-encompassing Hugoniot exists.…”

Shock jump equations for unsteady wave fronts of finite rise time

“…͑2͒ in this case. This means that the treatment of 0 Ϫ 1 →0, which was carried out in the previous analysis, 16 is tantamount to assuming a constant velocity for c().…”

“…In the previous study, 16 however, the terms of finite rise time which ought to be included in the jump equations were eliminated, so that we could not clarify the influence of rise time. In this study, the influence of rise time on the jumps is examined.…”

“…This is possible, if we can derive three equations involving the path of strain for particle velocity, stress, and specific internal energy from the equations of conservation of mass, momentum, and energy, and then translate the resulting three equations into jump equations. In this manner Sano 16 first generalized the R-H relations for unsteady shock wave fronts of infinitesimal rise time. The equation for particle velocity has a term of strain rate, while that for stress contains terms of strain rate and acceleration.…”