Shock Wave in Condensed Matter Generated by Impulsive Load

Anisimov, S. I.; Kravchenko, V. A.

doi:10.1515/zna-1985-0104

Cited by 8 publications

(5 citation statements)

References 3 publications

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“…o 0 8 D B S 2 g 8 n N P G 8 / o j Y y j u 5 p m q A f 8 l E k h 1 J w s q N 2 T 1 l 0 w P v l i l t 1 F 2 K r x s t N B X I 1 + u X P λ/(v s ∆t) = 1 − M 2 2 /M 2 as the dimensionless characteristic frequency, in agreement with (45). Note that different normalization yields λ/(c 2 ∆t) = 1 − M 2 2 .…”

Section: B Transverse Acoustic Modessupporting

confidence: 78%

“…Canonical shock problems in gas dynamics, such as Guderley-type converging shock, impulsive-loading, or the popular blast wave problem [43][44][45][46] , can be formulated in absence of temporal and spatial scales through the combination of the inviscid Euler equations and the Rankine-Hugoniot (RH) equations at the shock, provided that additional boundary and initial conditions do not involve spatio-temporal scales. In that case, the possibility of writing a solution in terms of self-similar variables only relies on properties of EoS.…”

Section: Introductionmentioning

confidence: 99%

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The stability of expanding reactive shocks in a van der Waals fluid

2022

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Despite the extensive literature accumulated since the pioneering works of D'yakov and Kontorovich in the 1950s, the stability of steady shocks is still an open question when realistic boundary conditions are accounted. The consideration of a supporting mechanism, which is indeed a necessary condition for shock steadiness, modifies the perturbation shock dynamics in the unstable range. The Noh problem is a suitable example to form steady expanding shocks. This configuration is of great interest to the high-energy-density-physics community because of its direct application to inertial confinement fusion and astrophysics, for which the stagnation of a supersonically converging material via an accretion shock front is ubiquitous. In this work, we extend the generalized Noh problem, both base-flow solution and linear stability analysis, to conditions where endothermic or exothermic transformations undergo across the shock. Within the spontaneous acoustic emission conditions found for a van der Waals gas [J. W. Bates and D. C. Montgomery, “The D'yakov-Kontorovich instability of shock waves in real gases,” Phys. Rev. Lett. 84, 1180 (2000)], we find that cylindrical and spherical expanding shocks become literally unstable for sufficiently high mode numbers. Counterintuitively, the effect of exothermicity or endothermicity across the shock is found to be stabilizing or destabilizing, respectively.

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Section: B Transverse Acoustic Modessupporting

confidence: 78%

Section: Introductionmentioning

confidence: 99%

The stability of expanding reactive shocks in a van der Waals fluid

2022

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“…For example, self-similar profiles are displayed in figure 2 for ν = 2 (cylindrical) and ν = 3 (spherical) for three different equations of state that include: ideal gas(a), vdW gas (b) and three-terms equation for aluminum (c), whose constitutive details are provided in Appendix A. Note that the mathematical description for the EoS and the internal energy is not restricted to the reduced Mie-Grüneisen form E( p, ρ) = pf (ρ), where f (ρ) is an arbitrary positive function of density, which is a pre-requisite to construct classic self-similar solutions for blast-wave, impulsive-loading, converging-shock and classic Noh problems (Anisimov & Kravchenko 1985;Sedov 1993;Axford 2000;Giron et al 2020). For example, used a reduced form of the vdW EoS to meet the reduced Mie-Grüneisen form and, therefore, find a self-similar solution for the spherical implosion problems, and Ramsey, Boyd & Burnett (2017) demonstrated that there is no classic Noh solution for spherical and cylindrical geometry with an EoS for which the internal energy is not simply proportional to the pressure.…”

Section: Problem Formulationmentioning

confidence: 99%

“…Self-similar solutions describing the stagnation phase after the shock convergence or the cavity collapse (Guderley 1942;Hunter 1960;Stanyukovich 1960;Lazarus 1981;Zababakhin & Zababakhin 1988;Zel'dovich & Raizer 2002) do not satisfy this requirement. The class of non-ideal EoS permitting these self-similar solutions (Anisimov & Kravchenko 1985;Sedov 1993;Axford 2000;Ramsey et al 2018;Giron, Ramsey & Baty 2020) is narrow, not including most non-ideal EoS of interest. The family of generalized Noh solutions, on the other hand, fits the above requirement.…”

Section: Introductionmentioning

confidence: 99%

Stability of expanding accretion shocks for an arbitrary equation of state

et al. 2021

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We present a theoretical stability analysis for an expanding accretion shock that does not involve a rarefaction wave behind it. The dispersion equation that determines the eigenvalues of the problem and the explicit formulae for the corresponding eigenfunction profiles are presented for an arbitrary equation of state and finite-strength shocks. For spherically and cylindrically expanding steady shock waves, we demonstrate the possibility of instability in a literal sense, a power-law growth of shock-front perturbations with time, in the range of $h_c< h<1+2 {\mathcal {M}}_2$ , where $h$ is the D'yakov-Kontorovich parameter, $h_c$ is its critical value corresponding to the onset of the instability and ${\mathcal {M}}_2$ is the downstream Mach number. Shock divergence is a stabilizing factor and, therefore, instability is found for high angular mode numbers. As the parameter $h$ increases from $h_c$ to $1+2 {\mathcal {M}}_2$ , the instability power index grows from zero to infinity. This result contrasts with the classic theory applicable to planar isolated shocks, which predicts spontaneous acoustic emission associated with constant-amplitude oscillations of the perturbed shock in the range $h_c< h<1+2 {\mathcal {M}}_2$ . Examples are given for three different equations of state: ideal gas, van der Waals gas and three-terms constitutive equation for simple metals.

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“…The Mie-Grüneisen EoS [27,28] p e , 5 ( ) r = G after an approximation, it can be written as [29] constant.…”

Section: Basic Equations and Boundary Conditionsmentioning

confidence: 99%

Structure of shock wave in tungsten and titanium metals by using navier-stokes equation

Singh

Anand

2023

Phys. Scr.

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Using the Navier-Stokes equation, we present the structure of a one-dimensional stationary shock wave formed in condensed alloy materials such as tungsten and titanium. In this study, the shock wave structure in the mentioned materials has been analysed by deriving several important parameters such as material viscosity, the Mie-Gruneisen parameter, and Mach number (M). One of our derived results is shock thickness, which is found to be of the order of 10-6 meters. In addition, we address a number of key insights into the shock wave interaction with tungsten and titanium. It should be noted that the validity of the model discussed in this study is limited to high M values, i.e., M ≥ 2.0.

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Shock Wave in Condensed Matter Generated by Impulsive Load

Cited by 8 publications

References 3 publications

The stability of expanding reactive shocks in a van der Waals fluid

The stability of expanding reactive shocks in a van der Waals fluid

Stability of expanding accretion shocks for an arbitrary equation of state

Structure of shock wave in tungsten and titanium metals by using navier-stokes equation

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