Effect of shock-generated turbulence on the Hugoniot jump conditions

Abstract

Interaction of a shock wave with preshock random density nonuniformities is known to generate turbulence in the postshock flow. The turbulent motion, in turn, modifies the shock jump conditions. As first detected in the simulations by Hazak et al. [Phys. Plasmas 5, 4357 (1998)], shock compression of a deuterium-filled foam is less than that predicted for a uniform medium of the same average density. Exact analytical small-amplitude theory of this shock undercompression effect is reported, and explicit formulas for the turbulent corrections to the strong-shock Hugoniot jump conditions are presented.

Effect of equivalence ratio fluctuations on planar detonation discontinuities

“…In particular, changes are expected in the jump conditions given the averaged downstream magnitudes with respect to the case of uniform mixtures with the same averaged upstream properties (Lele 1992). As a direct consequence, the averaged propagation speed of the detonation wave will also be affected, as previously noted for inert shocks (Hazak et al 1998;Velikovich et al 2012).…”

“…The goal of this section is to predict these changes and to provide analytical expressions, which are similar to those reported in Velikovich et al (2012) in terms of the parameters characterizing the detonation front. Then, the non-uniformity parameter…”

Analytical linear theory for the interaction of a planar shock wave with a two- or three-dimensional random isotropic acoustic wave field

“…In order to solve the wave equation (20) and the linearized RH [Eqs. (22) and (23)], we use the Laplace transform over the variable r. We define the Laplace transform of any quantity φ:…”

“…We use the variable q defined by s = sinh q, and then the wave equation (20) together with Eq. (21) can be rewritten as…”

“…Nevertheless, a complete and general study of the downstream quantities as functions of the fluid compressibility and shock strength could not be presented in those works. Quite recently, linear theoretical models for the interaction of a shock wave with an isentropic vorticity field [17] and with an isotropic density field [18][19][20] have been reported, where such an extensive study of the downstream quantities (turbulent kinetic energy, acoustic flux, vorticity, density) was done. Exact analytical expressions for arbitrary values of the shock Mach number and fluid compressibility were obtained for the quantities of interest behind the shock in terms of elementary functions, completing the work started more than 50 years ago.…”