Mach reflection of a plane shock wave passing a mountain of 45° inclination

The transition from regular reflection (RR) to Mach reflection (MR) as a plane shock wave diffracts around a triangular mountain of 45° inclination is analysed in this paper, both by optical measurement in a shock tube and by numerical simulation the numerical method developed by Li Yingfan^[1] is of the FLIC type with triangular mesh. The dependence of the critical transition point Lk ofRR→MR on shock Mach numberM _i is analyzed and the variations of the incidence angle ω _i of the impinging shock and the reflection angle ω _r with the distanceL ^* are investigated. Our experimental and numerical results agree well with the theoretical results of Iton and Italya.     

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     

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 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.     

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.     

Analytical prediction of the wave configuration size in steady flow Mach reflections

Analitycal model for predicting the size of the Mach reflection wave configuration in steady flows has been improved (Azevedo 1989; Azevedo and Liu (1993)). Predictions based on the modified analytical model were compared to available experimental results. The agreement was found to be better than that obtained by Azevedo (1989) and Azevedo and Liu (1993). The reason for the better agreement is due to the fact that, unlike Azevedo's original model, downstream effects were not neglected in the modified model which was developed in the course of this study. Received 12 May 1996 / Accepted 15 January 1997     

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     

Re-initiation phenomenon of gaseous detonation induced by shock reflection

The two-dimensional, time-dependent, reactive Navier–Stokes equations including the effects of viscosity, thermal conduction and molecular diffusion were solved to reveal the wave evolution and chemical dynamics involved in the re-initiation process. The computation was performed for hydrogen–oxygen–argon mixtures at the low initial pressure (8.00 kPa), using detailed chemical reaction model. The results show that, the decoupled leading shock reflects on the right wall of the vertical branch. High temperature and pressure behind the reflected shock induce the generation of hot spots and local explosion. Therefore, the re-initiation of gaseous detonation occurs. In the re-initiation area, there exist very high OH concentration and no H ₂ concentration. However, in front of reflected shock, there exist relatively high H ₂ concentration and no OH radicals. Additionally, the shock–flame interaction induces RM instability. This results in the fast mixing between hot reacted gas mixture and the relatively cold unreacted gas mixture and accelerates the chemical reactions. However, the shock–flame interaction contributes much less to the re-initiation, in contrast with shock reflection. The transition of leading shock from regular reflection to Mach reflection happens during the re-initiation. The computed evolution of wave structures involved in the re-initiation is qualitatively agreeable with that from the experimental schlieren images.      

环形激波绕射、反射和聚焦流场的间断有限元模拟

采用间断有限元方法对环形激波在圆柱形激波管内绕射、反射和聚焦流场进行了数值模拟。将二维守恒方程的间断有限元方法发展到轴对称Euler方程,并对环形激波绕后台阶流动进行了数值计算。计算结果表明,采用间断有限元方法能够有效地捕捉运动激波在圆柱形激波管内传播的复杂流场结构;在聚焦点附近,数值解具有较大的梯度变化,表明该方法对间断解具有较强的捕捉能力,在聚焦点附近不会产生振荡或抹平间断现象。     

Investigation on nonequlibrium radiation and relaxation phenomena in shock tubes

The experimental results for the excited time of the nonequlibrium radiation and the ionization behind strong shock waves are presented. Using an optical multichannel analyzer, InSb infrared detectors and near-free-molecular Langmuir probes, the infrared radiation, the electron density of air and the nonequlibrium radiation spectra at different moments of the relaxation process in nitrogen test gas behind normal shock waves were obtained, respectively, in hydrogen oxygen combustion driven shock tubes. The project supported by the National Natural Science Foundation of China (19982005 and 10032050), and the National Defense Science Foundation of China (95JBA4.2ZK0402)     

Investigation of shock waves interference and associated hysteresis effect at variable-Mach-number upstream flow

Experimental investigations and numerical simulations have been performed to study the transition between steady regular and Mach reflections induced by flow Mach number variation. The experiments have been carried out in the supersonic wind tunnel SIGMA 4B, at the Institut Aérotechnique (IAT) in St Cyr L'Ecole, France. Symmetric and asymmetric arrangements of wedges have been tested. No significant hysteresis phenomenon has been detected experimentally. However, this phenomenon has been revealed by numerical computations obtained by solving the Navier-Stokes equations.Received: 9 October 2001, Accepted: 11 October 2002, Published online: 21 February 2003     

Numerical simulation of shock wave propagation in microchannels using continuum and kinetic approaches

Numerical simulations of shock wave propagation in microchannels and microtubes (viscous shock tube problem) have been performed using three different approaches: the Navier–Stokes equations with the velocity slip and temperature jump boundary conditions, the statistical Direct Simulation Monte Carlo method for the Boltzmann equation, and the model kinetic Bhatnagar–Gross–Krook equation with the Shakhov equilibrium distribution function. Effects of flow rarefaction and dissipation are investigated and the results obtained with different approaches are compared. A parametric study of the problem for different Knudsen numbers and initial shock strengths is carried out using the Navier–Stokes computations.      

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     

Three-dimensional propagation of the transmitted shock wave in a square cross-sectional chamber

An investigation into the three-dimensional propagation of the transmitted shock wave in a square cross-section chamber was described in this paper, and the work was carried out numerically by solving the Euler equations with a dispersion-controlled scheme. Computational images were constructed from the density distribution of the transmitted shock wave discharging from the open end of the square shock tube and compared directly with holographic interferograms available for CFD validation. Two cases of the transmitted shock wave propagating at different Mach numbers in the same geometry were simulated. A special shock reflection system near the corner of the square cross-section chamber was observed, consisting of four shock waves: the transmitted shock wave, two reflection shock waves and a Mach stem. A contact surface may appear in the four-shock system when the transmitted shock wave becomes stronger. Both the secondary shock wave and the primary vortex loop are three-dimensional in the present case due to the non-uniform flow expansion behind the transmitted shock.PACS: 43.40.Nm     

Conical Mach reflection of moving shock waves, Part 2: Physical and CFD experimentation

Analytical consideration of Mach reflections over cones using the ray-shock theory showed that they differ from those of the two-dimensional Mach reflection over wedges. Conical configurations include both self-similar and non-self-similar cases. However, even when self-similar, the conical configurations exhibit triple-point locus trajectory angles with values which, for any given reflection angle, differ from those of self-similar, wedge cases. Additionally, within the range of possible conical configurations, different values of self-similar triple-point locus angles exist for any given reflection angle depending on the geometry of the particular reflection process. While the ray-shock theory, as discussed in a previous paper on this research, provides a useful guide and a means of readily identifying these variations, verification using both shock tube and numerical simulations is required and is now available. Results of experimentation for both self-similar and non-self-similar axisym metric cases using these techniques are reported here and comparisons are made with the previous analysis. These support the calculations of the ray-shock theory over much of the reflection angle, Mach number range as well as highlighting some limitations of the theory. Received 15 October 1996 / Accepted 14 April 1997     

Comparison of kinetic and continuum approaches for simulation of shock wave/boundary layer interaction

The present paper, which is a collaboration between three different research groups, analyzes the efficiency of various numerical approaches to describe the complex problem of shock wave/boundary layer interaction. Computations were carried out based on a kinetic approach (Direct Simulation Monte Carlo method) and on two continuum approaches (Navier-Stokes equations and quasigasdynamic equations), which are validated by comparison with experimental results obtained in the R5Ch blowdown Hypersonic Wind Tunnel in ONERA. The influence of the slip boundary conditions for two continuum approaches are also studied. The results obtained by all models display the good prediction of the main structure of the flow and the levels of the flux coefficients are very close to those measured. The implementation of the slip boundary condition for the continuum approaches improves the agreement with the experimental data. Received 12 July 2001 / Accepted 24 May 2002 /Published online 4 December 2002 Correspondence to: D. Zeitoun (e-mail: David.Zeitoun@polytech.univ-mrs.fr) An abridged version of this paper was presented at the 23rd Int. Symposium on Shock Waves at Fort Worth, Texas, from July 22 to 27, 2001     

铅飞层中斜冲击波对碰马赫反射行为实验研究

采用线阵多普勒光纤探针测速技术(Doppler pins system,DPS)和高速光电分幅相机照相两种精密诊断技术,对铅飞层中斜冲击波对碰后的反射行为进行了观测。获得了飞层对碰部位速度-时间历史曲线和凸起形貌演化图像,给出了凸起轮廓发展演化过程、压力分布等实验数据和信息。结合冲击波反射理论,对铅飞层对碰区动力学现象进行了分析和解释,证实铅飞层中斜冲击波对碰后发生了马赫反射。     

Interaction of a shock with a sphere suspended in a vertical shock tube

Shock wave interaction with a sphere is one of the benchmark tests in shock dynamics. However, unlike wind tunnel experiments, unsteady drag force on a sphere installed in a shock tube have not been measured quantitatively. This paper presents an experimental and numerical study of the unsteady drag force acting on a 80 mm diameter sphere which was vertically suspended in a 300 mm x 300 mm vertical shock tube and loaded with a planar shock wave of M _s = 1.22 in air. The drag force history on the sphere was measured by an accelerometer installed in it. Accelerometer output signals were subjected to deconvolution data processing, producing a drag history comparable to that obtained by solving numerically the Navier-Stokes equations. A good agreement was obtained between the measured and computed drag force histories. In order to interpret the interaction of shock wave over the sphere, high speed video recordings and double exposure holographic interferometric observations were also conducted. It was found that the maximum drag force appeared not at the time instant when the shock arrived at the equator of the sphere, but at some earlier time before the transition of the reflected shock wave from regular to Mach reflection took place. A negative value of the drag force was observed, even though for a very short duration of time, when the Mach stem of the transmitted shock wave relfected and focused at the rear stagnation point of the sphere.Received: 31 March 2003, Accepted: 7 July 2003, Published online: 2 September 2003     

Formation of a jet and vortices behind a shock wave reflected from a concave body

A jet and vortices have been observed when a plane shock wave reflects from a concave body in a shock tube. If the cavity is deep enough then two reflected shocks appear near its edges. Air, carbon tetrafluoride (CF) and dichlorodifluoromethane (CClF) were chosen as test gases. The flow was visualized with the aid of a conventional shadow technique. Pressure measurements at the body surface were also obtained. Numerical studies have been conducted using a two-dimensional inviscid model. There is a good qualitative agreement between the experimental and numerical results. Received 8 February 1996 / Accepted 30 June 1997     

The discovery of the Mach reflection effect and its demonstration in an auditorium

This paper examines the historical background leading to the discovery of the Mach reflection effect and applies original documents from Mach's residue which are kept in the archives of the Ernst-Mach-Institut in Freiburg. Two experimental setups for the generation and demonstration of the Mach reflection effect, incorporating an overhead projector, are described: (a) Mach's historic mechanical shock wave reflection and interaction experiments with soot covered glass plates, performed in 1875. The Mach triple points sharply erase the soot which results in a residual picture of funnel-shaped V-formations. The head-on collision of two shock waves is marked as a narrow line of piled-up soot. (b) CalTech's hydraulic jump reflection experiments in a shallow ripple tank, performed during World War II. Regular reflection and its transition into a Mach reflection wave. Using a slightly inclined tank and providing a shoreline in the middle of the tank, Mach stem propagation slows down to zero when hitting the shore line and, therefore, can be observed live without the use of a slow motion technique.Visiting graduate student on an IAESTE grantThe International Mach Reflection Symposia have been held in Victoria, BC, Canada (1981); Sydney, Australia (1982); Freiburg, FRG and Melbourne, Australia (1983); Tokyo and Sendai, Japan (1984); Menlo Park, CA, USA (1985); Beer Sheva, Israel (1986); Albuquerque, USA (1987) and Toronto, Canada (1988)This article was processed using Springer-Verlag T_EX Shock Waves macro package 1990.