Stability of E-H type regular shock refraction

2018 ◽  
Vol 59 (11) ◽  
pp. 111504
Author(s):  
Dian Hu ◽  
Wancheng Sheng
Keyword(s):  
Shock Refraction

scholarly journals Regular shock refraction at an oblique planar density interface in magnetohydrodynamics

2005 ◽  
Vol 522 ◽  
pp. 179-214 ◽  
Author(s):  
V. WHEATLEY ◽  
D. I. PULLIN ◽  
R. SAMTANEY
Keyword(s):  
Density Interface ◽  
Shock Refraction

scholarly journals One Dimensional Shock Refraction at a Plasma-cold Gas Interface

1973 ◽  
Vol 28 (10) ◽  
pp. 1668-1675
Author(s):  
J. Gerofi ◽  
H. K. Messerle
Keyword(s):  
Plasma Temperature ◽  
Region Of Interest ◽  
Initial Pressure ◽  
Step Function ◽  
Initial Plasma ◽  
Function Discontinuity ◽  
Definition Of ◽  
Shock Refraction ◽  
Weak Shocks ◽  
Cold Gas

Refraction and reflection of a shockwave at a plasma/cold gas interface has been studied using an R.F. preheated section in an electrothermal shock tube. The gas used in the experiment was Argon at initial pressures from 10 to 30 Torr, with initial temperature of 9000 K.A detailed numerical analysis of the refraction event has been undertaken using a method that does not require definition of an effective γ. Methods that do use such a γ are not accurate, except for very weak shocks. Because of short ionization times it has been possible to assume equilibrium behind the various shock waves. Calculations suggest that in the region of interest, reflected and refracted shock velocities depend primarily on initial shock velocity, slightly on initial plasma temperature and very weakly on initial pressure. The analysis covers initial temperatures of 6000 to 12 000 K and initial pressures of 10 to 50 Torr.Calculations and experimental results are presented. These show that a step function discontinuity is a good approximation to the nature of the plasma cold gas interface in this situation.

scholarly journals Shock refraction from classical gas to relativistic plasma environments

2010 ◽  
Vol 6 (S274) ◽  
pp. 441-444
Author(s):  
Rony Keppens ◽  
Peter Delmont ◽  
Zakaria Meliani
Keyword(s):  
Shock Waves ◽  
Strong Shock ◽  
Magnetized Plasma ◽  
Riemann Solver ◽  
Classical Gas ◽  
Relativistic Flow ◽  
Interstellar Material ◽  
Shock Refraction ◽  
Strong Shock Waves ◽  
Astrophysical Research

AbstractThe interaction of (strong) shock waves with localized density changes is of particular relevance to laboratory as well as astrophysical research. Shock tubes have been intensively studied in the lab for decades and much has been learned about shocks impinging on sudden density contrasts. In astrophysics, modern observations vividly demonstrate how (even relativistic) winds or jets show complex refraction patterns as they encounter denser interstellar material.In this contribution, we highlight recent insights into shock refraction patterns, starting from classical up to relativistic hydro and extended to magnetohydrodynamic scenarios. Combining analytical predictions for shock refraction patterns exploiting Riemann solver methodologies, we confront numerical, analytical and (historic) laboratory insights. Using parallel, grid-adaptive simulations, we demonstrate the fate of Richtmyer-Meshkov instabilities when going from gaseous to magnetized plasma scenarios. The simulations invoke idealized configurations closely resembling lab analogues, while extending them to relativistic flow regimes.

scholarly journals On the interaction of a planar shock with an polygon

2015 ◽  
Vol 773 ◽  
pp. 366-394 ◽  
Author(s):  
Xisheng Luo ◽  
Minghu Wang ◽  
Ting Si ◽  
Zhigang Zhai
Keyword(s):  
High Speed ◽  
Soap Film ◽  
Von Neumann ◽  
Interface Characteristics ◽  
Planar Shock ◽  
Wave Patterns ◽  
Formation Method ◽  
Planar Shock Wave ◽  
Triple Points ◽  
Shock Refraction

The interaction of a planar shock wave ($M\approx 1.2$) with an $\text{SF}_{6}$ polygonal inhomogeneity surrounded by air is experimentally investigated. Six polygons including a square, two types of rectangle, two types of triangle, and a diamond are generated by the soap film technique developed in our previous work, in which thin pins are used as angular vertexes to avoid the pressure singularities caused by the surface tension. The evolutions of the shock-accelerated $\text{SF}_{6}$ polygons are captured by a high-speed schlieren system from which wave systems and the interface characteristics can be clearly identified. Both regular and irregular refraction phenomena are observed outside the volume, and more complex wave patterns, including transmitted shock, refracted shock, Mach stem and the interactions between them, are found inside the volume. Two typical irregular refraction phenomena (free precursor refraction, FPR, and free precursor von Neumann refraction, FNR) are observed and analysed, and the transition from FPR to FNR is found, providing the experimental evidence for the transition between different wave patterns numerically found in the literature. Combined with our previous work (Zhai et al., J. Fluid Mech., vol. 757, 2014, pp. 800–816), the reciprocal transitions between FPR and FNR are experimentally confirmed. The velocities and trajectories of the triple points are further measured and it is found that the motions of the triple points are self-similar or pseudo-stationary. Besides the shock dynamics phenomena, the evolutions of these shocked heavy polygonal volumes, which are quite different from the light ones, are captured and found to be closely related to their initial shapes. Specifically, for square and rectangular geometries, the different width–height ratios result in different behaviours of shock–shock interaction inside the volume, and subsequently different features for the outward jet and the interface. Quantitatively, the time-variations of the interface scales, such as the width and the normalized displacements of the edges, are obtained and compared with those from previous work. The comparison illustrates the superiority of the interface formation method and the significant effect of the initial interface shape on the interface features. Furthermore, the characteristics of the vortex core, including the velocity and vortex spacing, are experimentally measured, and the vortex velocity is compared with those from some circulation models to check the validity of the models. The results in the present work enrich understanding of the shock refraction phenomenon and the database of research into Richtmyer–Meshkov instability (RMI).

Shock-bubble interactions: Features of divergent shock-refraction geometry observed in experiments and simulations

2008 ◽  
Vol 20 (3) ◽  
pp. 036101 ◽  
Author(s):  
Devesh Ranjan ◽  
John H. J. Niederhaus ◽  
Jason G. Oakley ◽  
Mark H. Anderson ◽  
Riccardo Bonazza ◽  
...  
Keyword(s):  
Bubble Interactions ◽  
Shock Refraction

scholarly journals Stability of the E–H type regular shock refraction

2013 ◽  
Vol 254 (8) ◽  
pp. 3146-3199 ◽  
Author(s):  
Shuxing Chen ◽  
Dian Hu ◽  
Beixiang Fang
Keyword(s):  
Shock Refraction

The non-linear refraction of shock waves by upstream disturbances in steady supersonic flow

1970 ◽  
Vol 43 (1) ◽  
pp. 1-33 ◽  
Author(s):  
Sheldon Weinbaum ◽  
Arnold Goldburg
Keyword(s):  
Shock Wave ◽  
Shock Waves ◽  
Interaction Parameter ◽  
Wave Interaction ◽  
Oblique Shock ◽  
Rational Approach ◽  
Oblique Shock Wave ◽  
Local Ratio ◽  
Non Linear ◽  
Shock Refraction

The general problem studied is the propagation of an oblique shock wave through a two-dimensional, steady, non-uniform oncoming flow. A higher-order theory is developed to treat the refraction of the incident oblique shock wave by irrotational or rotational disturbances of arbitrary amplitude provided the flow is supersonic behind the shock. A unique feature of the analysis is the formulation of the flow equations on the downstream side of the shock wave. It is shown that the cumulative effect of the downstream wave interactions on the propagation of the shock wave can be accounted for exactly by a single parameter Φ, the local ratio of the pressure gradients along the Mach wave characteristic directions at the rear of the shock front. The general shock refraction problem is then reduced to a single non-linear differential equation for the local shock turning angle θ as a function of upstream conditions and an unknown wave interaction parameter Φ. To lowest order in the expansion variable θΦ, this equation is equivalent to Whitham's (1958) approximate characteristic rule for the propagation of shock waves in non-uniform flow. While some further insight into the accuracy of Whitham's rule does emerge, the theory is not a selfcontained rational approach, since some knowledge of the wave interaction parameter Φ must be assumed. Analytical and numerical solutions to the basic shock refraction relation are presented for a broad range of flows in which the principal interaction occurs with disturbances generated upstream of the shock. These solutions include the passage of a weak oblique shock wave through: a supersonic shear layer, a converging or diverging flow, a pure pressure disturbance, Prandtl–-Meyer expansions of the same and opposite family, an isentropic non-simple wave region, and a constant pressure rotational flow. The comparison between analytic and numerical results is very satisfactory.

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