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.     

Shock wave trapping

This paper presents a two-dimensional investigation into the effectiveness of trapping shock and blast waves in a duct in order to enhance attenuation, by placing an array of opposing wedges in the channel. The concept of the wedge arrangement in the trap is to allow easy shock wave entry, with weak reflected shocks, into the trap, but stronger internal reflected shocks if a wave is re-emering. The internal reflections, including those of vortices shed from earlier shock passage, result in strong shock attenuation. Different wedge placements, wedge angles, and area blockages are investigated numerically, as well as experimentally for a particular case, using pressure measurement and schlieren photography. Received 4 August 1995 / Accepted 12 December 1995     

Specific features of incident and reflected blast waves

On the basis of numerical modeling specific features of shock wave reflections were analyzed. It was found, that after diaphragm rupture self-modeling pressure and velocity distributions nearby the shock front establish. But in some special cases the temperature behind the shock front can rise. This peculiarity should be taken into account when performing experiments with high reactive gaseous mixtures. The temperature on the shock front and the velocity gradient behind it are uniform in the case of strong blast wave reflections. This effect is observed in the zone with an elevated temperature profile behind the incident blast wave. The reflected triangular waves conserve a quasi-self-modeling character by pressure. Typical experiments were carried out to verify the theoretical predictions. The effects of reflected wave acceleration in the case of triangular waves and the self-similar character of the pressure profiles were observed.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.     

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。     

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.      

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.     

Numerical simulation of Mach reflections

In this paper, the “FLIC” difference method with triangular mesh is adopted to numerically simulate the regular and Mach reflections that occur when a shock wave pass around a wedge. The compuational result is compared with the shock tube experimental results of G. Ben-Dor and I. I. Glass. The comparison shows that the position, shape of shock wave and height of Mach stem all show a good agreement. Consequently, the “FLIC” difference method with triangular mesh is quite satisfactory in numerical simulation of the regular and Mach reflections.     

The reflected pressure field in the interaction of weak shock waves with a compressible foam

This paper deals with the waves that are reflected from slabs of porous compressible foam attached to a rigid wall when impacted by a weak shock wave. The interest is in establishing possible attenuation of the pressure field after a shock or blast wave has struck the surface. Foam densities from 14 to 38 kg/m³ were tested over a range of shock wave Mach numbers less than 1.4. It is shown that the initial reflected shock wave strength is accurately predicted by the pseudo-gas model of Gelfand et al. (1983), with a pressure ratio of approximately 80% of the value for reflection off a rigid wall. Evidence is presented of gas entering the foam during the early stages of the process. A second wave emerges from the foam at a later stage and is separated from the first by a region of constant velocity and pressure. This second wave is not a shock wave but a compression front of significant thickness, which emerges from the foam earlier than predicted by the pseudo-gas model. Analysis of the origin of this wave points to much more complex flows within the foam than previously assumed, particularly in an apparent decrease in average wave front speed as the foam is compressed. It is shown that the pressure ratio across both these waves taken together is slightly higher than that for reflection off a rigid wall. In some cases this compression wave train is followed by a weak expansion wave.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1990.     

Over forty years of continuous research at UTIAS on nonstationary flows and shock waves

Analytical and experimental research on non-stationary shock waves, rarefaction waves and contact surfaces has been conducted continuously at UTIAS since its inception in 1948. Some unique facilities were used to study the properties of planar, cylindrical and spherical shock waves and their interactions. Investigations were also performed on shock-wave structure and boundary layers in ionizing argon, water-vapour condensation in rarefaction waves, magnetogasdynamic flows, and the regions of regular and various types of Mach reflections of oblique shock waves. Explosively-driven implosions have been employed as drivers for projectile launchers and shock tubes, and as a means of producing industrial-type diamonds from graphite, and fusion plasmas in deuterium. The effects of sonic-boom on humans, animals and structures have also formed an important part of the investigations. More recently, interest has focussed on shock waves in dusty gases, the viscous and vibrational structure of weak spherical blast waves in air, and oblique shock-wave reflections. In all of these studies instrumentation and computational methods have played a very important role. A brief survey of this work is given herein and in more detail in the relevant references.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1990.     

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.     

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.      

Supersonic motion of bodies in a gas with shock waves

The authors consider the problem of supersonic unsteady flow of an inviscid stream containing shock waves round blunt shaped bodies. Various approaches are possible for solving this problem. The parameters in the shock layer on the axis of symmetry have been determined in [1, 2] by using one-dimensional theory. The authors of [3, 4] studied shock wave diffraction on a moving end plane and wedge, respectively, by the through calculation method. This method for studying flow around a wedge with attached shock was also used in [5]. But that study, unlike [4], used self-similar variables, and so was able to obtain a clearer picture of the interaction. The present study gives results of research into the diffraction of a plane shock wave on a body in supersonic motion with the separation of a bow shock. The solution to the problem was based on the grid characteristic method [6], which has been used successfully to solve steady and unsteady problems [7–10]. However a modification of the method was developed in order to improve the calculation of flows with internal discontinuities; this consisted of adopting the velocity of sound and entropy in place of enthalpy and pressure as the unknown thermodynamic parameters. Numerical calculations have shown how effective this procedure is in solving the present problem. The results are given for flow round bodies with spherical and flat (end plane) ends for various different values of the velocities of the bodies and the shock waves intersected by them. The collision and overtaking interactions are considered, and there is a comparison with the experimental data.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 141–147, September–October, 1984.     

A numerical study of shock wave reflections on low density foam

A continuum mixture theory is used to describe shock wave reflections on low density open-cell polyurethane foam. Numerical simulations are compared to the shock tube experiments of Skews (1991) and detailed wave fields are shown of a shock wave interacting with a layer of foam adjacent to a rigid wall boundary. These comparisons demonstrate that a continuum mixture theory describes well the shock interactions with low density foam.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.     

Reflection of a spherical blast wave from a planar surface

Numerous authors have carried out rather extensive studies in the last twenty to thirty years of the problem of the interaction of shock and blast waves with obstacles in their paths. Owing to the complexity of the problem, they assumed certain limiting cases for the shock wave interactions in which the parameters behind the shock wave were usually taken to be constants. The first wave diffraction studies involving variable parameters behind the front were presented in [1, 2], wherein a development of the theory of “short waves” (blast waves at a substantial distance from the center of an explosion) and their reflection from a planar surface was given. The theory of short waves assumes that the jump in pressure at the wave front and the region over which the parameters vary are small. The problem concerning reflection of a blast wave from a surface was also considered in [3, 4], wherein a solution in the region behind the reflected wave was obtained at initial times. The initial stage in the reflection of a blast wave from a planar, cylindrical, or spherical surface (the one-dimensional case) was studied in [5]. In this paper we investigate the interaction of a spherical blast wave, resulting from a point explosion, with a planar surface; we consider both regular and non-regular reflection stages. In solving this problem we use S. L. Godunov's finite-difference method. We obtain numerical solutions for various values of the shock strength at the instant of its encounter with the surface. We present the pressure fields in the flow regions, the pressure distribution over the surface at various instants of time, and the trajectories of the triple point. The parameter values at the front of the reflected wave are compared with results obtained from the theory of regular reflection of shock waves.     

Shock wave propagation in a branched duct

The propagation of a planar shock wave in a 90° branched duct is studied experimentally and numerically. It is shown that the interaction of the transmitted shock wave with the branching segment results in a complex, two-dimensional unsteady flow. Multiple shock wave reflections from the duct's walls cause weakening of transmitted waves and, at late times, an approach to an equilibrium, one-dimensional flow. While at most places along the branched duct walls calculated pressures are lower than that existing behind the original incident shock wave, at the branching segment's right corner, where a head on-collision between the transmitted wave and the corner is experienced, pressures that are significantly higher than those existing behind the original incident shock wave are encountered. The numerically evaluated pressures can be accepted with confidence, due to the very good agreement found between experimental and numerical results with respect to the geometry of the complex wave pattern observed inside the branched duct. Received 15 July 1996 / Accepted 20 February 1997     

A holographic interferometric study of shock wave focusing in a circular reflector

A holographic interferometric study was made of the focusing of reflected shock waves from a circular reflector. A diaphragmless shock tube was used for incident shock Mach numbers ranging from 1.03 to 1.74. Hence, the process of reflected shock wave focusing was quantitatively observed. It is found that a converging shock wave along the curved wall undergoes an unsteady evolution of mach reflection and its focusing is, therefore, subject to the evolution of the process of shock wave reflections. The collision of triple points terminates the focusing process at the geometrical focus. In order to interprete quantitatively these interferograms, a numerical simulation using an Eulerian solver combined with adaptive unstructured grids was carried out. It is found numerically that the highest density appears immediately after the triple point collision. This implies that the final stage of focusing is mainly determined by the interaction between shock waves and vortices. The interaction of finite strength shock waves, hence, prevents a curved shock wave from creating the infinite increase of density or pressure at a focal point which is otherwise predicted by the linear acoustic theory.     

Interaction Between a Slow Magnetohydrodynamic Shock Wave and a Tangential Discontinuity

The self-similar problem of the oblique interaction between a slow MHD shock wave and a tangential discontinuity is solved within the framework of the ideal magnetohydrodynamic model. The constraints on the initial parameters necessary for the existence of a regular solution are found. Various feasible wave flow patterns are found in the steady-state coordinate system moving with the line of intersection of the discontinuities. As distinct from the problems of interaction between fast shock waves and other discontinuities, when the incident shock wave is slow the state ahead of it cannot be given and must to be determined in the process of solving the problem. As an example, a flow in which the slow shock wave incident on the tangential discontinuity is generated by an ideally conducting wedge located in the flow is considered. The basic features of the developing flows are determined.     

Analytical and numerical investigations of the reflection of asymmetric nonstationary shock waves

The reflection of asymmetric nonstationary shock waves is analytically and numerically studied in this paper. An analytical approach, which is a combination of the shock dynamic and shock polar methods, is advanced to predict the reflection wave configurations. The numerical simulations are performed by the finite volume method based on the second-order MUSCL-Hancock scheme and the HLLC approximate Riemann solver, with the self-adaptive unstructured mesh. It is found that the transition between the overall regular reflection and overall Mach reflection in the asymmetric nonstationary reflection agrees with the detachment criterion, which is analogous to the reflection in pseudo-steady flows (i.e. shock reflection over a wedge). Some special reflection wave configurations, which have never been observed in steady or nonstationary shock reflections so far, are found to exist in this asymmetric reflection. Furthermore, the domains and boundaries of various overall reflection wave configurations are analytically predicted, and the effect of mis-synchronization is also discussed.     

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     

Non-reflecting boundary conditions applicable to general purpose CFD simulators

In simulations of propagating blast waves the effects of artificial reflections at open boundaries can seriously degrade the accuracy of the computations. In this paper, a boundary condition based on a local approximation by a plane traveling wave is presented. The method yields small artificial reflections at open boundaries. The derivation and the theory behind these so-called plane-wave boundary conditions are presented. The method is conceptually simple and is easy to implement in two and three dimensions. These non-reflecting boundary conditions are employed in the three-dimensional computational fluid dynamics (CFD) solver FLACS, capable of simulating gas explosions and blast-wave propagation in complex geometries. Several examples involving propagating waves in one and two dimensions, shock tube and an example of a simulation of a propagating blast wave generated by an explosion in a compressor module are shown. The numerical simulations show that artificial reflections due to the boundary conditions employed are negligible. © 1998 John Wiley & Sons, Ltd.