Acoustic stability of nonadiabatic high-energy-density shocks

Abstract

As firstly predicted by D'yakov and Kontorovich (DK), an initially disturbed shock front may exhibit different asymptotic behaviours depending on the slope of the Rankine-Hugoniot curve.Adiabatic and isolated planar shocks traveling steadily through ideal gases are stable, in the sense that any perturbation on the shock front decays in time with the power t −3/2 (or t −1/2 in the strongshock limit). While some gases whose equation of state cannot be modelled as a perfect gas, as those governed by van der Waals forces, may induce constant-amplitude oscillations to the shock front in the long-time regime, fully unstable behaviours are seldom to occur due to the unlikely conditions that the equation of state must meet. In this work, it has been found that unstable conditions are might be found when the gas undergoes an endothermic or exothermic transformation behind the shock. In particular, it is reported that constant-amplitude oscillations can occur when the amount of energy release is positively-correlated to the shock strength and, if this correlation is sufficiently strong, the shock turns to be fully unstable. The opposite highly-damped oscillating regime may occur in negatively-correlated configurations. The mathematical description then adds two independent parameter to the regular adiabatic index γ and shock Mach number M 1 , namely: the total energy added/removed and its sensitivity with the shock strength. The formulation in terms of endothermic or exothermic effects is extended, but not restricted, to include effects associated to ionization, dissociation, thermal radiation, and thermonuclear transformations, so long as the time associated to these effects is much shorter time than the acoustic time.

Stability of expanding accretion shocks for an arbitrary equation of state

“…Distinguished regimes for isolated planar shocks ((a) known results) and expanding accretion shocks ((b) new findings) along the variable h. (Bates & Montgomery 2000), and magnesium (Lomonosov et al 2000;Konyukhov et al 2009); for ionizing shock waves in inert gases (Mond & Rutkevich 1994;Mond, Rutkevich & Toffin 1997); for shock waves dissociating hydrogen molecules (Bates & Montgomery 1999); for Gbar-and Tbar-pressure range shocks in solid metals, where the shell ionization affects the shapes of Hugoniot curves (Rutkevich, Zaretsky & Mond 1997;Das, Bhattacharya & Menon 2011;Wetta, Pain & Heuzé 2018); for shock fronts producing exothermic reactions, such as detonation (Huete & Vera 2019;Huete et al 2020). Other examples include EoS constructed ad-hoc specifically for analytical and numerical studies of shock instabilities: (Ni, Sugak & Fortov 1986;Konyukhov, Levashov & Likhachev 2020;Kulikovskii et al 2020).…”

Thermochemical effects on hypersonic shock waves interacting with weak turbulence

“…Along that branch, an increment (decrement) in post-shock pressure induces a decrement (increment) in post-shock density. For the parameters tested here, the value Γ in the upper branch of the Hugoniot curve is always larger than the critical values for the onset of (a) shock instabilities associated with multi-wave 66,67 and multi-valued 68,69 solutions, and (b) D'yakov-Kontorovich pseudo-instabilities associated with the spontaneous emission of sound 8,70 . Similar characteristics of the Hugoniot curve have been observed elsewhere for shocks subjected to endothermicity [71][72][73][74] .…”

“…Strong shock waves participate in a number of problems in physics, including the dynamics of high-energy interstellar medium [1][2][3][4] , the explosions of giant stars [5][6][7][8] , the fusion of matter in inertial-confinement devices [9][10][11] , and the ignition of combustible mixtures by lasers 12,13 . In addition to those, an important contemporary problem of relevance for aeronautical and astronautical engineering is the aerothermodynamics of hypersonic flight 14,15 .…”

Shock polars for ideal and non-ideal gases

“…We neglect the problem of slow relaxation to chemical equilibrium which is important in some applications, focusing only on sufficiently large length and time scales here. Nor do we consider the question of shock stability here (see Huete et al (2020) for related discussions).…”

“…Nor do we consider the question of shock stability here (see Huete et al. (2020) for related discussions).…”