Stability of converging shock waves

Fong, Kenneth; Ahlborn, B.

doi:10.1063/1.862609

Cited by 26 publications

(23 citation statements)

References 6 publications

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“…14͒ or the existence of stability region in the physical parameter space. 13 We find a stabilization of the converging shock waves which contradicts Whitham's work. This assertion should be extended by varying the shock strength, the amplitude and the wavelength of the perturbation and checked experimentally.…”

Section: Stability Of Perturbed Shock Wavesmentioning

confidence: 67%

“…These results are consistent with some theoretical results. 13,14 However, since Whitham's works, 12,39 it is commonly acknowledged that converging shock waves are unstable. This instability is said weak 15 as it grows as a power of the radius rather than exponentially.…”

Section: Stability Of Perturbed Shock Wavesmentioning

confidence: 98%

“…11 Furthermore, the stability of spherical shock waves is still an issue. [12][13][14][15][16] Planar shock waves can easily be generated in conventional ͑straight section͒ shock tubes. These facilities are commonly used to study the interaction between shock waves and bubble, [17][18][19] foam or material interface.…”

Section: Introductionmentioning

confidence: 99%

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Analytical theory for planar shock focusing through perfect gas lens and shock tube experiment designs

Vandenboomgaerde

Aymard

2011

Physics of Fluids

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In this paper, we present a generalization of the gas lens technique developed by Dimotakis and Samtaney ͓"Planar shock cylindrical focusing by a perfect-gas lens," Phys. Fluids 18, 031705 ͑2006͔͒. This technique is devoted to converting a planar shock wave into a cylindrical one through a shaped interface between two gases. We revisit this theory and demonstrate that the shape of the lens is either an ellipse or a hyperbola. A simple formula for its eccentricity is analytically obtained: e = W t / W i , where W t and W i are the transmitted and incident shock wave velocities, respectively. Furthermore, our theory is valid for fast-slow and slow-fast configurations. It also allows the generation of spherical converging shock waves. We present numerical simulations that successfully validate our lens design. Finally, we use the gas lens technique in order to design shock tube experiments: shock wave and hydrodynamic instabilities are studied and discussed in convergent geometry.

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Section: Stability Of Perturbed Shock Wavesmentioning

confidence: 67%

Section: Stability Of Perturbed Shock Wavesmentioning

confidence: 98%

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Analytical theory for planar shock focusing through perfect gas lens and shock tube experiment designs

Vandenboomgaerde

Aymard

2011

Physics of Fluids

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“…3 Unfortunately, surface corrugation instabilities may occur and reduce the effectiveness of converging cylindrical and spherical shocks, causing a major reduction of the temperature and pressure values observed at the focus point. 1,[4][5][6][7] The onset of instabilities in curved converging shocks eventually prevents their applications to ICF problems.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of cylindrical converging shock waves interacting with aerodynamic obstacle arrays

Vignati

Guardone

2015

Physics of Fluids

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Cylindrical converging shock waves interacting with an array of aerodynamic obstacles are investigated numerically for diverse shock strengths and for different obstacle configurations in air in standard conditions. The considered number of obstacles N is 4, 6, 8, 16, and 24. Obstacles are lenticular airfoils with thickness-to-chord ratios t/c of 0.07, 0.14, and 0.21. The distances of the airfoil leading edge from the shock focus point rLE/rref LE are 1, 2, and 2.5, where rref LE = 7 is the dimensionless reference distance from the origin. Considered impinging shock Mach numbers Ms are 2.2, 2.7, and 3.2 at the reference distance from the origin. The reference experimental configuration (N = 8,t/c = 0.14,rLE = 7,Ms = 2.7) was proposed by Kjellander et al. ["Thermal radiation from a converging shock implosion," Phys. Fluids 22, 046102 (2010)]. Numerical results compare fairly well to available one-dimensional models for shock propagation and to available experimental results in the reference configuration. Local reflection types are in good agreement with the classical criteria for planar shock waves. The main shock reshaping patterns are identified and their dependence on the shock strength and obstacle configuration is exposed. In particular, different shock patterns are observed after the leading edge reflection, which results in polygonal shock wave with N, 2N, 3N, and 4N sides. The largest temperature peak at the origin is obtained for the 8-and the 16-obstacle configurations and for the smallest thickness to length ratio, 0.07, located at distance from the origin of 2rref LE. In terms of compression efficiency at the origin, the 16-obstacle configuration is found to perform slightly better than the reference 8-obstacle configuration-with an efficiency increase of about 2%-3%, which is well within the model accuracy-thus confirming the goodness of the obstacle arrangement proposed by Kjellander and collaborators

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“…Additional studies of converging shocks using geometrical shock dynamics have been discussed in Gardner, Book & Bernstein (1982) following the work in Fong & Ahlborn (1979). Both of these studies concentrated on the behaviour of converging cylindrical and spherical shocks subject to initial perturbations (possibly large) that took the shape of an isolated bulge.…”

Section: Introductionmentioning

confidence: 99%

On converging shock waves of spherical and polyhedral form

Schwendeman

2002

J. Fluid Mech.

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The behaviour of converging spherical shock waves is considered using Whitham's theory of geometrical shock dynamics. An analysis of converging shocks whose initial shape takes the form of regular polyhedra is presented. The analysis of this problem is motivated by the earlier work on converging cylindrical shocks discussed in Schwendeman & Whitham (1987). In that paper, exact solutions were reported for converging polygonal shocks in which the initial shape re-forms repeatedly as the shock contracts. For the polyhedral case, the analysis is performed both analytically and numerically for an equivalent problem involving shock propagation in a converging channel with triangular cross-section. It is found that a repeating sequence of shock surfaces composed of nearly planar pieces develops, although the initial planar surface does not re-form, and that the increase in strength of the shock at each iterate in the sequence follows the same behaviour as for a converging spherical shock independent of the convergence angle of the channel. In this sense, the shocks are stable and the result is analogous to that found in the two-dimensional case. A numerical study of converging spherical shocks subject to smooth initial perturbations in strength shows a strong tendency to form surfaces composed of nearly planar pieces suggesting that the stability result is fairly general.

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Stability of converging shock waves

Cited by 26 publications

References 6 publications

Analytical theory for planar shock focusing through perfect gas lens and shock tube experiment designs

Analytical theory for planar shock focusing through perfect gas lens and shock tube experiment designs

Dynamics of cylindrical converging shock waves interacting with aerodynamic obstacle arrays

On converging shock waves of spherical and polyhedral form

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