Effects of a Single-pulse Energy Deposition on Steady Shock Wave Reflection

The effects of energy deposition in the free stream on steady regular and Mach shock wave reflections are studied numerically. A short-duration laser pulse is focused upstream of the incident shock waves. It causes formation of the expanding blast wave and the residual hot-spot interacting in a complex way with the steady shock wave reflection. It was found that the laser energy addition in the free stream may force the transition from regular to Mach reflection in the dual solution domain. In contrast to previously reported numerical results, the transition from Mach to regular reflection has not been reproduced in our refined computations since the Mach reflection is restored after the flow perturbation.     

Transition between regular and Mach reflection of shock waves: new numerical and experimental results

New numerical and experimental results on the transition between regular and Mach reflections of steady shock waves are presented. The influence of flow three-dimensionality on transition between steady regular and Mach reflection has been studied in detail both numerically and experimentally. Characteristic features of 3D shock wave configuration, such as peripheral Mach reflection, non-monotonous Mach stem variation in transverse direction, the existence of combined Mach-regular-peripheral Mach shock wave configuration, have been found in the numerical simulations. The application of laser sheet imaging technique in streamwise direction allowed us to confirm all the details of shock wave configuration in the experiments. Close agreement of the numerical and experimental data on Mach stem heights is shown. Received 23 November 2000 / Accepted 25 April 2001     

Numerical confirmation of the hysteresis phenomenon in the regular to the Mach reflection transition in steady flows

Numerical calculations based on the Navier-Stokes equations are carried out to investigate the reflection of shock waves over straight reflecting surfaces in steady flows. The results for a flow Mach number of M₀=4.96 confirm the recent experimental findings of Chpoun et al. (1995) concerning the transition from regular to Mach reflection. Numerical calculations as well as experimental results show a hysteresis phenomenon during this transition and the regular reflection is found to be stable in the dual-solution domain in which theoretically both regular and Mach reflection wave configurations are possible.     

Stability and analogy of shock wave reflection in steady flow

Numerical simulations have been performed to investigate the stability of shock wave reflection in supersonic steady flow. Wall deflection control has been applied just downstream of the reflection point in the regular reflection configuration. The results provide the magnitude of the disturbance required to cause transition from one configuration to the other throughout the range of incident shock angle. An argument focusing on the subsonic region generated behind the Mach stem in the Mach reflection configuration explains the mechanism of the transition. Numerical results show that both regular and Mach reflections are possible in the dual-solution domain, and also indicate the presence of the hysteresis effect. The transition processes and the stability of the possible states are shown to be described consistently by an analogy based on the potential energy of a particle on a surface. The necessity of more sophisticated experimental investigations is emphasized to verify the argument about the stability of shock reflections and proposed analogy. Received 17 March 1997 / Accepted 26 February 1998     

Diffuse holographic interferometric observation of shock wave reflection from a skewed wedge

The pattern of shock wave reflection over a wedge is, in general, either a regular reflection or a Mach reflection, depending on wedge angles, shock wave Mach numbers, and specific heat ratios of gases. However, regular and Mach reflections can coexist, in particular, over a three-dimensional wedge surface, whose inclination angles locally vary normal to the direction of shock propagation. This paper reports a result of diffuse double exposure holographic interferometric observations of shock wave reflections over a skewed wedge surface placed in a 100 × 180 mm shock tube. The wedge consists of a straight generating line whose local inclination angle varies continuously from 30° to 60°. Painting its surface with fluorescent spray paint and irradiating its surface with a collimated object beam at a time interval of a few microseconds, we succeeded in visualizing three-dimensional shock reflection over the skewed wedge surface. Experiments were performed at shock Mach numbers, 1.55, 2.02, and 2.53 in air. From reconstructed holographic images, we estimated critical transition angles at these shock wave Mach numbers and found that these were very close to those over straight wedges. This is attributable to the flow three-dimensionality.      

A numerical study of oblique shock wave reflections over wedges in an ideal quantum gas

The various oblique shock wave reflection patterns generated by a moving incident shock on a planar wedge using an ideal quantum gas model are numerically studied using a novel high resolution quantum kinetic flux splitting scheme. With different incident shock Mach numbers and wedge angles as flow parameters, four different types of reflection patterns, namely, the regular reflection, simple Mach reflection, complex Mach reflection and the double Mach reflection as in the classical gas can be classified and observed. Both Bose–Einstein and Fermi–Dirac gases are considered.      

Investigation of the hysteresis phenomena in steady shock reflection using kinetic and continuum methods

The problem of transition of planar shock waves over straight wedges in steady flows from regular to Mach reflection and back was numerically studied by the DSMC method for solving the Boltzmann equation and finite difference method with FCT algorithm for solving the Euler equations. It is shown that the transition from regular to Mach reflection takes place in accordance with detachment criterion while the opposite transition occurs at smaller angles. The hysteresis effect was observed at increasing and decreasing shock wave angle. Received September 1, 1995 / Accepted November 20, 1995     

Three-dimensional effects on regular reflection in steady supersonic flows

The reflection of shock waves between two symmetrical wedges is investigated for the case of three-dimensional flows. Oblique shadowgraphs at various optical angles of yaw and pitch were used to examine the nature of fully three-dimensional flows, with wedge aspect ratios as low as 0.25 being considered. These images were used to construct surface models of the overall flow field for various reflection patterns and aspect ratios, which provides a visual indication of the flow field shape. For a Mach number of 3.1, and suitable wedge angles, the flow field with regular reflection on the tunnel centreline and Mach reflection further out is examined. The point of transition from regular reflection to the peripheral Mach surfaces is identified for various wedge angles and aspect ratios. It is shown that the transition points move outwards from the central plane as the aspect ratio decreases. This shows that three-dimensional flows favor regular reflection, because of the increasing curvature of the incident shock as the wedge becomes narrower, causing a decrease in the local angle of incidence. The height of the Mach stem is shown to be highly dependent on the geometry of the test wedge models. The Mach stem height decreases with aspect ratio due to the three-dimensional relieving effect, where the increase in lateral flow relieves the pressure over the surfaces of the wedges. Experimental evidence of the existence of the strong oblique shock solution in steady flows is presented.Received: 7 July 2003, Revised: 20 October 2003, Accepted: 6 November 2003, Published online: 10 February 2004PACS: 47.40.Nm Correspondence to: B.W. Skews     

激波在不同三角楔面内传播特性的数值研究

激波在收缩管内的反射与聚焦会形成高温高压区,点燃可燃混合气并诱导爆轰,因此对爆轰发动机的点火具有重要意义。本文基于二维N-S方程,结合五阶WENO格式,对马赫数为6的正激波在三角形楔面内的反射与聚焦现象进行了数值研究。结果表明,楔面顶角的变化对激波的反射类型以及聚焦均有明显的影响:随着顶角的增加,激波的反射类型从马赫反射向过渡马赫反射和双马赫反射转变,且壁面上的前向射流更加明显;三波点第一次碰撞产生的高温高压区足够满足可燃混合气体的点火条件,且其温度与压力值随顶角的增加而增大;当激波在楔面上发生临界双马赫反射时,温度与压力达到最大;当顶角增加到一定值时,激波在楔面反射转变为常规反射,不会产生激波对碰,因而没有高温高压区。     

Least energy as a criterion for transition between regular and Mach reflection

A new criterion is suggested to define the point of transition between regular and Mach reflection. The suggested criterion is based on the natural tendency of a physical system to minimize its energy. The increases of the specific energy behind the reflected shock of a regular reflection and behind the Mach stem of a Mach reflection are calculated. It is hypothesized that the type of reflection that will occur is that which produces the smaller change of specific energy. The transition angles predicted using this criterion show better agreement with experimental results than those predicted using the detachment criterion for incident shock waves with Mach numbers between 1.1 and 2.0.This article was processed using Springer-Verlag TEX Shock Waves macro package     

Theoretical considerations on shock reflections and their implications on the evaluation of air intake performance

Many theoretical studies have shown the existence of a hysteresis effect in the solution of oblique shock reflections. In fact, a wide domain of free-stream Mach number and shock angle values exists where regular reflection and Mach reflection are both possible solutions for the same flow conditions. Part of this domain overlaps the typical operating conditions of supersonic air intakes, and therefore it is of practical interest to obtain a deeper understanding of the theoretical problem. Indeed, although both solutions are theoretically possible, they yield very different flowfields and consequently large discrepancies in the evaluation of the air intake performance. Numerical solutions for steady configurations have been carried out and compared with the flow evolution obtained for time-dependent cases. The results have confirmed numerically the existence of the multiple solution domain where hysteresis takes place in time-dependent simulations. The analysis of the physical and numerical problems encountered has provided indications for a correct simulation in practical applications. Received 10 August 1999 / Accepted 6 October 2000     

Existence criteria for reflection configurations in shock–vortex interactions

The length scale criteria is widely accepted as an explanation for transition and hence existence of different shock wave reflection configurations in pseudo-steady flows. However, there has not been any attempt to validate this criteria using information obtained from a time-dependent numerical simulation. A high resolution time-dependent numerical simulation in pseudo-steady flow is carried out in the present work. Time-dependent numerical data is used to calculate flow features in a laboratory frame of reference to verify validity of the length scale criteria for existence of different shock wave reflection configurations in pseudo-steady flow. This analysis is then extended to the study of unsteady shock wave reflection configurations in shock–vortex interactions. It is shown that the existence of regular reflection (RR) and Mach reflection (MR) configurations in an unsteady flowfield resulting from shock–vortex interactions can also be explained locally based on limiting conditions similar to that prescribed by the length scale criteria for pseudo-steady flow.

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Normal shock interaction with a yawed wedge moving at supersonic speed

In this article, the interaction of a normal shock with a yawed wedge moving at supersonic speed has been considered. The vorticity distribution of a particle over the diffracted shock wave for various combinations of yawed angles, Mach number of the shock wave and Mach number of the moving wedge have been obtained. Further triple point angle χ in Mach reflection has been calculated for the various parameters.      

Oblique reflection of shock waves from rigid porous materials

A study to determine the general gas dynamic behaviour associated with the impact of a shock wave on a porous wedge has been undertaken. A number of interesting features are noted. The pattern of wave reflection is shown to be significantly affected by the inflow of gas into the wedge. This has the effect of reducing the triple point trajectory angle for cases of Mach reflection and for strongly reducing the reflection angle in regular reflection. The permeability of the wedge has a significant effect on the strength of the reflected wave and in some cases this wave can be attenuated to the extent that it is almost eradicated. Pressure measurements taken under the wedge are characterized by oscillations which are of similar shape, for a given wedge, over a range of shock wave Mach numbers. It is shown that the wave transmitted into the wedge is attenuated to varying degrees depending on the material properties, and that for weak incident waves the mean propagation velocity can be less than the sound speed in the pore fluid. Photographs taken using a specially constructed wedge which allows the transmitted wave to be visualised, show that the transmitted wave is nearly plane.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1.0 and the AMS fonts, developed by the American Mathematical Society.     

Steady shock wave reflections in thermochemical nonequilibrium flows

The shock wave reflection phenomena in hypersonic steady air flows, including thermochemical nonequilibrium effects, are investigated. The main objectives are to study the influence of these effects on the two shock wave reflections (regular and Mach reflections), on the Mach stem height and on the hysteresis behavior. The air computations are performed using a multi-block MUSCL-TVD finite-volume scheme. The computational results with and without thermochemical effects in the air mixture flow at an upstream Mach number equal to 7 are compared. The comparison reveals a strong dependence of the transition angles, of the height and location of the Mach stem on the physical modeling of the gas flow. Received 17 February 2000 / Accepted 30 August 2000     

The reflection of a shock wave over a cone

An investigation was made of the reflection of planar shock waves from cones. 86 cones, the half apex angle of which varied from 10° to 52° at every 0.5°, were installed in a 60 mm×150 mm diaphragmless shock tube equipped with holographic interferometry. The diaphragmless shock tube had a high degree of reproducibility with which the scatter of shock wave Mach number was within ±0.25% for shock wave Mach number ranging from 1.16 to approximately 2.0. The reflection of shock waves over cones was visualized using double exposure holographic interferometry. Whitham's geometrical shock wave dynamics was used to analyse the motion of Mach stems over cones. It is found that for relatively smaller apex angles of cones trajectory angles of resulting irregular reflections coincide with the so-called glancing incidence angles and their Mach stems appear to be continuously curved from its intersection point with the incident shock wave, which shows the chractericstic of von Neumann reflection. The domain of the existence of the von Neumann reflection was analytically obtained and was found to be broadened much more widely than that of two-dimensional reflections of shock waves over wedges.     

Regular versus Mach reflection for converging polygonal shocks

The onset of Mach reflection or regular reflection at the vertices of a converging polygonal shock wave was investigated experimentally in a horizontal annular shock tube. The converging shock waves were visualized by schlieren optics. Two different types of polygonal shock convergence patterns were observed. We compared the behavior during the focusing process for triangular and square-shaped shocks. It is shown that once a triangular shaped shock is formed, the corners in the converging shock will undergo regular reflection and consequently the shape will remain unaltered during the focusing process. A square-shaped shock suffers Mach reflections at the corners and hence a reconfiguring process takes place; the converging shock wave alternates between a square and an octagon formation during the focusing process.      

Changes in the type of the shock-wave structure in high-velocity flows

Physical aspects of nonuniqueness of shock-wave structures in supersonic and hypersonic flows are considered. Thermodynamic conditions determining the dual solution domains are analyzed, and the boundaries of the transition from Mach to regular reflection are examined.Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 2, pp. 23–32, March–April, 2005.     

Numerical simulations of shock wave reflection phenomena in non-stationary flows using regularized smoothed particle hydrodynamics (RSPH)

In this paper we wish to demonstrate to what extent the numerical method regularized smoothed particle hydrodynamics (RSPH) is capable of modelling shocks and shock reflection patterns in a satisfactory manner. The use of SPH based methods to model shock wave problems has been relatively sparse, both due to historical reasons, as the method was originally developed for studies of astrophysical gas dynamics, but also due to the fact that boundary treatment in Lagrangian methods may be a difficult task. The boundary conditions have therefore been given special attention in this paper. Results presented for one quasi-stationary and three non-stationary flow tests reveal a high degree of similarity, when compared to published numerical and experimental data. The difference is found to be below 5, in the case where experimental data was found tabulated. The transition from regular reflection (RR) to Mach reflection (MR) and the opposite transition from MR to RR are studied. The results are found to be in close agreement with the results obtained from various empirical and semi-empirical formulas published in the literature. A convergence test shows a convergence rate slightly steeper than linear, comparable to what is found for other numerical methods when shocks are involved.     

Aspect ratio effects in wind tunnel studies of shock wave reflection transition

The transverse wave patterns and flow fields around double wedge experimental arrangements in supersonic facilities for the study of transition from regular to Mach reflection are examined. Guidelines for the minimum inlet aspect ratio to be used are determined in order to ensure that the reflection point is protected from side influences. A preliminary visualization study of the reflection of the wave systems from two wedges of small aspect ratio, has shown the appearance of a new feature in the transition from regular to Mach reflection, that of a dynamic flow distortion, which is presumed to arise due to three-dimensional adjustments in pressure. It occurs in the vicinity of the 2-dimensional mechanical equilibrium point. Oblique shadowgraph images are used to help visualize the flow system. Received 10 December 1996 / Accepted 24 March 1997