The reflection of weak shock waves has been reconsidered analytically using shock polars. Based on the boundary condition across the slipstream, the solutions of the three-shock theory ͑3ST͒ were classified as "standard-3ST solutions" and "nonstandard-3ST solutions." It was shown that there are two situations in the nonstandard case: A situation whereby the 3ST provides solutions of which at least one is physical and a situation when the 3ST provides a solution which is not physical, and hence a reflection having a three-shock confluence is not possible. In addition, it is shown that there are initial conditions for which the 3ST does not provide any solution. In these situations, a four-wave theory, which is also presented in this study, replaces the 3ST. It is shown that four different wave configurations can exist in the weak shock wave reflection domain, a Mach reflection, a von Neumann reflection, a ?R ͑this reflection is not named yet!͒, and a modified Guderley reflection ͑GR͒. Recall that the wave configuration that was hypothesized by Guderley ͓"Considerations of the structure of mixed subsonic-supersonic flow patterns," Air Materiel Command
Ernst Mach recorded experimentally, in the late 1870s, two different shock-wave reflection configurations and laid the foundations for one of the most exciting and active research field in an area that is generally known as Shock Wave Reflection Phenomena. The first wave reflection, a two-shock wave configuration, is known nowadays as regular reflection, RR, and the second wave reflection, a three-shock wave configuration, was named after Ernst Mach and is called nowadays Mach reflection, MR.
The jetting effect often appears in the Mach reflection of a shock and in more complicated irregular shock reflections. It also occurs in some natural phenomena, and industrially important processes. It is studied numerically using a W-modification of the second-order Godunov scheme, to integrate the system of Euler equations. It is shown that there is no correspondence between the shock reflection patterns and the occurrence of jetting. Furthermore, there are two kinds of jetting: strong which occurs when there is a branch point on the ramp surface where the streamlines divide into an upstream moving jet and a downstream moving slug; and weak which has no branch point and may occur at small and large values of the ramp angle θ w. The width of the jet for Mach and other reflections is determined by the angle of the Mach stem at the triple point (also called the Mach node or three-shock node). Strong jetting is unstable and the primary instability is in the jet itself. The contact discontinuity is also unstable, but its instability is secondary with respect to the jet instability. Two types of irregular reflection are identified in the dual-solution-domain. They are a two-node system comprising a Mach node followed by a four-shock (overtake) node; and another which seems to be intermediate between the previous system and a three-node reflection, which was first hypothesized by Ben-Dor & Glass (1979). An approximate criterion for the jetting ↔ no-jetting transition is presented. It is derived by an analysis of the system of Euler equations for a self-similar flow, and has a simple geometrical interpretation.
The flow developed behind shock wave transmitted through a screen or a perforated plat is initially highly unsteady and nonuniform. It contains multiple shock reflections and interactions with vortices shed from the open spaces of the barrier. The present paper studies experimentally and theoretically/numerically the flow and wave pattern resulted from the interaction of an incident shock wave with a few different types of barriers, all having the same porosity but different geometries. It is shown that in all investigated cases the flow downstream of the barrier can be divided into two different zones. Due immediately behind the barrier, where the flow is highly unsteady and nonuniform in the other, placed further downstream from the barrier, the flow approaches a steady and uniform state. It is also shown that most of the attenuation experienced by the transmitted shock wave occurs in the zone where the flow is highly unsteady. When solving the flow developed behind the shock wave transmitted through the barrier while ignoring energy losses (i.e., assuming the fluid to be a perfect fluid and therefore employing the Euler equation instead of the Navier-Stokes equation) leads to non-physical results in the unsteady flow zone.
Numerical simulations of a two-dimensional supersonic flow of an inviscid perfect gas over a double wedge in the Mach numbers range 5рM р9, revealed the existence of self-induced oscillations in the shock wave flow pattern in a narrow range of geometrical parameters.We consider a supersonic flow of an inviscid perfect gas over a double wedge ͑Fig. 1͒ in the range of high Mach numbers for which the shock waves are attached to the leading edges of both the first and the second wedges. The interaction of these two waves results in the formation of a complex shock wave flow pattern. Such flow fields can occur during flight of supersonic/hypersonic aircrafts or in the course of the re-entry of space shuttles. A numerical solution of this problem, in a stationary formulation, was conducted elsewhere. 1 Our recent success in discovering the existence of hysteresis processes in numerous cases of the interaction of supersonic flows with various geometries 2 motivated us to thoroughly complement these studies and check whether a hysteresis phenomenon exists in the case of a supersonic flow over a double wedge.Not only did our study reveal that there is a hysteresis, we also found out that there are self-induced oscillations in the shock wave flow pattern for various angles of inclination of the second wedge.The flow is described by the nonstationary Euler equations for an inviscid perfect diatomic gas (␥ϭ1.4). The parameters in the problem are the free stream flow Mach number, M , the ratio of the lengths of the surfaces of the double wedge, L 1 /L 2 , the angle of the first wedge, 1 , and the angle of the second wedge, 2 , or alternatively the difference between the two wedge angles, ⌬ϭ 2 Ϫ 1 .A W-modification of Godunov's scheme 3 that has second-order accuracies both in space and time was used in the calculations. The stationary solution was determined by settling of the nonstationary solution with time. Since the inclination of the first shock wave and the induced flow field behind it could be determined analytically, the size of the computational domain was reduced to include only the region of the interaction of the two shock waves ͑dashed line in Fig. 1͒. In order to damp the numerical oscillations that occur behind strong shock waves in stationary flows the following technique was employed. At each time step two independent calculations were performed using standard and diagonal stencils ͑Fig. 2͒, and their average was used at the following time step. This extension of the stencil enabled us to damp the numerical fluctuations and to avoid the need to use artificial viscosity. The investigation was performed with the following parameters: L 1 /L 2 ϭ2, M ϭ9, 1 ϭ15°, and ⌬ was changed in the course 20°→35°→20°. The goal was to check whether there is a hysteresis phenomenon. This was done by changing the value of ⌬ while keeping all the other parameters fixed. ⌬ was continuously changed during one dimensionless unit of time by 0.2°, and then five units of dimensionless time were spent to enable the solution to settle. ...
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