A generalisation of the theory of geometrical shock dynamics

Best, John P.

doi:10.1007/bf01415902

Cited by 14 publications

(27 citation statements)

References 15 publications

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“…Indeed, for M 0 = 1.5 for example, we see that GSD does not have a solution for θ w < −113.7 • , whereas experiments show that the wall Mach number M w keeps larger than unity up to −150 • at least. The extension of the GSD model with post-shock flow effects [4] does not seem to correct this default as M w is further reduced in this case in comparison to the classical GSD form. Alternative approaches, such…”

Section: Limitation Of the Gsd Modelmentioning

confidence: 87%

“…By considering a ray tube as a channel with rigid walls, a simple law linking A to M closes the system. This relation, called A − M rule, is obtained from the 1D Euler system with varying cross-section [4]:…”

Section: Geometrical Shock Dynamics Model In a Two-dimensional Configmentioning

confidence: 99%

“…appears to work remarkably well in a large number of configurations [34,7,18]. Finally, the GSD model is composed of the geometrical system (2) and the A − M relation (4). The function λ is bounded and increasing from 4 at M = 1 to…”

Section: Geometrical Shock Dynamics Model In a Two-dimensional Configmentioning

confidence: 99%

“…This is in contradiction with experimental studies [29] showing that the diffracted shock front should still exist at the wall, even for weak shocks and at large deflection angles. Some modifications of GSD, such as its extension to post-shock flow [4], or another treatment of the wall condition [1], are able to recover the inflection point experimentally observed for strong shocks, but do not remove the limitation. The more recent Kinematic model [26,27,16], is no more efficient to remove this restriction [18].…”

Section: Introductionmentioning

confidence: 99%

“…This model is based on the decomposition of the shock front into elementary ray tubes. Assuming small changes in the ray tube area and neglecting the influence of the post-shock flow on the shock, a simple relation linking the local curvature and velocity of the front, known as the A − M rule, is obtained [4].…”

Section: Introductionmentioning

confidence: 99%

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Beyond the limitation of geometrical shock dynamics for diffraction over wedges

et al. 2019

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Geometrical Shock Dynamics (GSD) is a simplified model for nonlinear shock wave propagation for which the front evolution is governed by a local relation between the geometry of the shock and its velocity, so-called A − M rule. Numerous studies have proven the ability of the GSD model to estimate correctly the leading shock front in interaction with obstacles. Nevertheless, a solution for the problem of diffraction over a convex corner does not always exist, especially for weak shocks. To overcome this limitation, we propose an ad-hoc modification of the A−M relation for two-dimensional configurations: an extra term based on the transverse variation of the Mach number is added. This new closure is fitted against experimental observations, which ensures, by construction, a correct behaviour for expansive shocks. A Lagrangian numerical solver is developed, for which this new term is activated only on specific parts of the front. Results of this new model are compared with the original GSD model, experiments, and Eulerian simulations for several cases of increasing complexity. A noticeable improvement of the solution is observed.

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Section: Limitation Of the Gsd Modelmentioning

confidence: 87%

Section: Geometrical Shock Dynamics Model In a Two-dimensional Configmentioning

confidence: 99%

Section: Geometrical Shock Dynamics Model In a Two-dimensional Configmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Beyond the limitation of geometrical shock dynamics for diffraction over wedges

et al. 2019

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A shockwave calculation method for aluminized explosive of deep water explosion based on the Kirkwood‐Bethe model

Sheng

Hao

Liu

et al. 2023

Propellants Explo Pyrotec

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To calculate the shockwave propagation of deep water explosions for different explosives quickly and accurately, a calculation method, based on the Kirkwood-Bethe theory, was proposed. At the same time, an underwater explosion experiment of the aluminized explosive was carried out in the pressure vessel under high hydrostatic pressure. Then, the calculated results and experimental results were compared for peak pressure, impulse and energy flux density. The results indicated that the proposed method can quickly and accurately determine the shockwave propagation of deep water explosions for the aluminized explosives, with satisfactory agreement with experimental data. Using the proposed method, the shockwave of aluminized explosive under the conditions of different charge weight, different depth and different distance were calculated, the propagation laws of peak pressure, impulse and energy flux density with depth and distance were obtained. The calculation method proposed could be used to calculate shockwave propagation for any kind of explosive, if only knows the parameters of detonation and JWL equation of state.

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