Shock waves at a slow-fast gas interface

Abdel‐Fattah, Azza M.; Henderson, L. F.

doi:10.1017/s0022112078002475

Cited by 81 publications

(25 citation statements)

References 2 publications

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“…When i is a weak shock the transition criterion appears to be at, or close to the sonic point of the r shock, but when i is strong then transition occurs at the generalized ME point (Abdel-Fattah and Henderson 1978a). The refraction law is again violated ur ui…”

Section: Anomalous Refraction (Ane)mentioning

confidence: 99%

“…The material properties and {i will determine which one is present as a~ increases towards transition to an irregular system. By definition, regular refraction ends at the shock critical angle ai = ctsc (43) Both experiments (Abdel-Fattah et al 1976;Abdel-Fattah and Henderson 1978b) and numerical results (Henderson et al 1990a(Henderson et al , 1990b show that the criterion which determines this condition is at, or close to, the point where there is sonic flow downstream of the t shock. For ct, i > o~8c, the A~ -1 matrix has unreal elements so the yon Neumann theory provides no physically realistic solutions.…”

Section: Slow-fast Refraction N <mentioning

confidence: 99%

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The vector refraction law for shock waves

Henderson

1992

Shock Waves

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Abstract. The law is formulated in vector form and isshown to be a powerful principle for studying the refraction of shock waves. A variety of criteria for the onset of irregular refraction are discussed. The refraction index matrix is defined and it is shown that it arises naturally from the law. A projection matrix is also defined and it is found to be useful for operating on the vector wave impedance. It is expected that the methods described here will be useful for the numerical solution of problems in the refraction of shocks by materials with continuous changes in properties. The refraction law is violated in fast-slow refraction by the reflected wave over-running the incident shock to produce an irregular refraction which is either the anomalous type or the Mach-reflection-reffaction type. For slow-fast refraction the law is violated by the transmitted wave becoming a precursor and also over-running the incident shock. The precursor may either be a shock or an evanescent compression wave band.

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Section: Anomalous Refraction (Ane)mentioning

confidence: 99%

Section: Slow-fast Refraction N <mentioning

confidence: 99%

The vector refraction law for shock waves

Henderson

1992

Shock Waves

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“…Jahn compared the angles of refraction with the theoretical prediction of Polachek and Seeger [32] and found excellent agreement. Henderson and collaborators subsequently conducted extensive experimental, theoretical, and numerical studies for CO 2 -He, air-SF 6 , and CO 2 -CH 4 to elucidate the complex hydrodynamics and wave behavior of shock refraction (see [15,16,18,17,19,2,1,30]). More recently, Samtaney and Pullin [33] numerically investigated shock refraction at an interface with shock Mach numbers larger than 10.…”

Section: Shock Refraction Theorymentioning

confidence: 99%

“…Thus, the present investigation is limited to regular refraction. For a discussion of irregular refraction, see the work of Henderson [15,16,18,17,19] and the work with Abd-El-Fattah [2,1,30].…”

Section: Oblique Shock Refractionmentioning

confidence: 99%

Weighted Essentially Non-Oscillatory Simulations and Modeling of Complex Hydrodynamic Flows. Part 1. Regular Shock Refraction

Latini¹,

Schilling²

2005

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Shock refraction is a fundamental shock phenomenon observed when shocks interact with a material interface separating gases with different properties. Following refraction, a transmitted shock enters the second gas and a reflected wave returns back into the first gas. In the case of regular shock refraction, all of the waves meet at a single point called the triple-point, creating five different states for the two gases. Analytical methods based on shock polar analysis have been developed to determine the state of two ideal gases in each of the five refraction regions. Furthermore, shock refraction constitutes a basic example of complex hydrodynamic flows. For this reason, shock refraction is used in this report as one validation of the high-order accurate weighted essentially non-oscillatory (WENO) shock-capturing method, as implemented in the HOPE code. The algorithms used in the HOPE code are described in detail, together with its current capabilities. The following two-step validation process is adopted. First, analytical results are obtained for the normal and oblique shock refraction (with shock-interface angle β interf ace = 75• ) observed for a Ma = 1.2 shock. To validate the single-fluid and the two-fluid implementations of the WENO method, two pairs of gases, argon/xenon, having equal adiabatic exponents γ and air(acetone)/sulfur hexafluoride, having different adiabatic exponents, are considered. Both the light-to-heavy and heavy-to-light gas configurations are considered. Second, numerical simulations are performed using the fifth-order WENO method and values of the density, pressure, temperature, speed of sound, and flow velocity in each of the five refraction regions are compared with the analytical predictions obtained from shock polar analysis. In all of the cases considered, excellent agreement is found between the simulation results and the analytical predictions. The results from this investigation suggest that the WENO method is a very useful numerical method for the simulation and modeling of complex hydrodynamic flows.

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“…the refraction and distortion of the shock wave, [7][8][9][10] and the effects induced by the shock on the interface, viz. the setting in motion of the interface and the baroclinic generation of vorticity wherever the product " ؋"p is nonzero.…”

Section: Introductionmentioning

confidence: 99%

X-ray measurements of growth rates at a gas interface accelerated by shock waves

Bonazza

Sturtevant

1996

Physics of Fluids

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A new experimental technique to measure the density of a high atomic number gas at a shock-accelerated interface has been developed and demonstrated. It is based on the absorption of x rays by the high atomic number gas, and it was implemented in a vertical square shock tube. The object of the study was the turbulent entrainment and mixing of shock-accelerated air/xenon interfaces prepared by retracting a metal plate, initially separating the two gases, prior to the release of the shock wave. Interfaces of two types, quasi-sinusoidal and nominally flat, were examined. The amplitude of large wavelength ͑25-100 mm͒ perturbations on the interface, and the thickness of the interface were measured. An integral definition for the interface mean line was adopted, making it possible to study and time evolution of the individual Fourier modes of the perturbations. A new integral definition for the interface thickness was proposed, making it feasible to study for the first time the time evolution of the thickness of quasi-sinusoidal interfaces. Images of interfaces after interacting with a series of weak waves reverberating between the interface and the shock tube end wall were obtained. The perturbations are studied at the late stages of their evolution, when their amplitude is no longer small compared to their wavelength. Consequently, the measured growth rates of the modal amplitudes are smaller than those predicted by the impulsive model based on the small amplitude approximation. In the case of nominally flat interfaces, the thickness is observed to grow linearly at rates comparable to values previously reported.

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Shock waves at a slow-fast gas interface

Cited by 81 publications

References 2 publications

The vector refraction law for shock waves

The vector refraction law for shock waves

Weighted Essentially Non-Oscillatory Simulations and Modeling of Complex Hydrodynamic Flows. Part 1. Regular Shock Refraction

X-ray measurements of growth rates at a gas interface accelerated by shock waves

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