Numerical investigations of transition between regular and Mach reflections caused by free-stream disturbances

Numerical simulations have been performed to study the influence of the free-stream disturbances on the alternation of the steady shock wave reflection configurations in the dual solution domain. Different types of disturbances have been considered. The analysis of interaction between disturbances and the incident shock wave can be substantially simplified for the localized density disturbances. It is shown that such disturbances can indeed cause the transition from regular reflection to Mach reflection and back, so that within a certain range of angles of incidence the shock wave reflection configuration can be considered as a bi-stable system. The threshold amplitude of the localized density disturbance, able to induce the transition, has been estimated theoretically. The results of numerical computations convince of higher stability of the Mach reflection in the dual solution domain compared to the regular reflection, which is in accordance with available experimental data. Received 10 May 2001 / Accepted 15 November 2001 Published online 8 July 2002     

Interaction of two Mach reflections over concave double wedges-analytical model

A simplified analytical model for solving the wave configuration resulting when two triple points join together over a concave double wedge is developed. The model equations are solved analytically. Predictions of the model are compared to experimental results and fairly good agreement is obtained. It is believed that the present model can be used to better understand complex wave interaction phenomena. Received 2 May 1995 / Accepted 18 December 1997     

甲烷-空气爆轰波传播的数值模拟

研究了甲烷-空气混合物爆轰波在二维突扩通道中传播的各种复杂行为。结果表明：爆轰波在进入突扩通道的初始阶段有局部向爆燃转变的现象；爆炸波在壁面发生马赫反射形成的高温高压区域将直接驱动自持爆轰波的重新形成。     

A shock dynamics theory based analytical solution of double Mach reflections

The shock-dynamics based governing equations of double Mach reflection (DMR) wave configurations were developed and solved. The analytical results were compared to experimental results from various sources. Very good to excellent agreement was evident.     

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     

11th international Mach reflection symposium

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.     

Experimental investigation of the influence of downstream flow conditions on Mach stem height

An experimental work on the influence of downstream flow expansion process on Mach stem height has been carried out in steady hypersonic flows. The results showed clearly for the first time that the Mach stem height does not depend on the extent of expansion fan. These results contradict recent analytical findings from which a strong influence of downstream flow conditions on Mach stem height may be expected. Received 31 August 1998/ Accepted 10 September 1998     

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.     

Numerical simulation of boundary-layer transition at Mach two

The linear and early nonlinear stages of boundary-layer transition at free-stream Mach numberM ==2.0 are investigated by direct numerical simulation of the compressible Navier-Stokes equations. Results from simulations with a large computational box and small-amplitude random initial conditions are compared with linear stability theory. The growth rates of oblique waves are reproduced correctly. Two-dimensional waves show a growth that is modulated in time, indicating the presence of an extra unstable mode which moves supersonically relative to the free stream. Further simulations are conducted to investigate the nonlinear development of two- and three-dimensional disturbances The transition due to oblique disturbance waves is the most likely cause of transition at this Mach number, and is found to lead to the development of strong streamwise vortices.     

Numerical simulation for nonstationary Mach reflection of a shock wave: A kinetic-model approach

A numerical simulation was performed for the process of formation of single Mach reflection on a wedge by solving a BGK type kinetic equation for the reduced distribution function with a finite difference scheme. The calculations were carried out for a shock Mach number 2.75 and wedge angle 25° in a monatomic gas, which corresponds to the conditions of single Mach reflection in the classical von Neumann theory. The calculations were performed for both diffuse and specular reflection of molecules at the wall surface. It is concluded that the diffuse reflection of molecules at the wall surface or the existence of the viscous or thermal layer is an essential factor for a nonstationary process at the initial stage of Mach reflection. Furthermore, the numerical results for diffuse reflection are found to simulate the experimental results very well, such as a transient process from regular reflection to Mach reflection along with shock propagation.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1990.     

Simulation of the Mach reflection in supersonic flows by the CE/SE method

This study employs the Space-Time Conservation Element and Solution Element (CE/SE) method to determine the influence of downstream flow conditions on Mach stem height. The results indicate that the Mach stem height depends on the incident shock wave angle and the distance between the trailing edge and the symmetry plane. Furthermore, it is shown that the downstream length ratio and the trailing edge angle do not affect the Mach stem height nor the Mach reflection (MR) configuration, and the Space-Time Conservation Element and Solution Element method is able to simulate the MR as well as many other numerical schemes. Communicated by K. Takayama PACS 47.40.Nm     

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.     

准定常强激波反射马赫杆突出变形准则的探讨

分析了滑移线延长线与楔面交点附近的流动特点,研究了准定常强激波反射中马赫杆的变形,建立了马赫杆突出变形消失的过渡准则,并用激波极曲线方法进行了求解。对马赫杆的变形过程进行了描述,研究了比热比、马赫数的变化对马赫杆突出变形消失条件的影响,并对突出变形消失区域与终点双马赫反射区域进行了比较。结果表明:马赫杆突出变形的消失是低比热比介质中出现的一种激波反射现象。马赫杆突出变形的消失,导致出现一种新的无射流、直马赫杆的双马赫反射结构。     

爆轰波在突扩通道中传播的数值模拟研究

建立了描述甲烷 空气混合物爆轰波传播的单步化学反应爆轰模型 ,通过数值模拟研究了在二维突扩通道中爆轰波的强度变化和各种波行为。结果表明 :爆轰波在进入突扩通道初始阶段的衍射使爆轰波局部向爆燃转变 ;爆炸波在壁面发生马赫反射形成的高温高压区域将直接诱导自持爆轰波的重新形成。     

Analysis of double-Mach-reflection wave configurations with convexly curved Mach stems

The wave configuration of a double Mach reflection (DMR) with a convexly curved Mach stem and the resulted flow fields are analyzed. An analytical model describing the formation of a with a curved Mach stem and predicting its wave configuration is proposed. The transition criterion from a with a straight Mach stem to a with a curved Mach stem is also suggested. Predictions based on the analytical model are compared to experimental results. The agreement is found to be good to excellent. Received 5 July 1996 / Accepted 18 March 1998     

Analytical solution of a flow field for weak Mach reflection over a plane surface

In this paper, we present an analytical solution for the flow field of single weak Mach reflection caused by an advancing plane shock wave over a simple wedge surface. We developed an improvement of Lighthill's linearized theory for the correction due to nonlinearity of the flow field through a singular perturbation. The expressions obtained, including the one for the triple point path, compared favorably with existing experimental, computational, and theoretical results. PACS 01.50.Kw; 47.15.Pn Communicated by K. Takayama     

A simple physical theory of weak Mach reflection over plane surfaces

It is shown that simple physical principles coupled with the inviscid shock jump relations can be applied to the problem of weak Mach reflection to the extent that the triple point path can be predicted from the incident shock Mach number , gas specific heat ratio and the inclination angle of the reflecting surface to the shock normal. Comparison with the Euler code data and with experiments show close agreement for conditions both far and close to transition and that the general shape of the reflected and Mach stem shocks follow simple curves except in the neighbourhood of the triple point. The conflict at the triple point in matching the flow deflection angles and pressures across the contact discontinuity remains. It is shown however that the simple model presented here gives a close match to the cfd and experimental overall shock and contact surface shapes although it cannot predict these or the flow properties in any detail. Received 10 May 1999 / Accepted 17 December 1999     

Conical Mach reflection of moving shock waves

Conical Mach reflections differ from those of the equivalent plane, two-dimensional Mach reflection because in axisymmetry, the disturbances generated at the reflecting surface are modified by their more rapidly increasing or decreasing area as they move towards or away from the centerline. Equations for conical Mach reflection cases have now been developed using a simplified ray-shock theory formulation based on the initial assumption that the stem is straight and normal to the wall. These are in a form that applies generally. Their simple structure provides an easy conceptual understanding of self-similarity and non-self-similarity as well as a clear mathematical approach for the development of the curved triple-point locus of the latter by integration. They provide a quick and direct solution in all cases and can easily incorporate the Mach stem curvature by progressively calculating the new ray direction. A range of cases has been considered and results are presented for converging and diverging, self-similar and non-self-similar cases.     

聚心火焰与激波相互作用的数值研究

基于带化学反应的2维轴对称Euler方程,利用带有monotonized centered(MC)限制器的波传播算法,在两端敞开的圆桶中对惰性介质的聚心激波和氢气-空气混合物的聚心火焰与激波的相互作用进行了数值模拟。数值结果表明,在惰性介质中激波在轴心的每次汇聚均可成长为马赫干,马赫干的追赶使激波得到一定程度的增强,但整体还呈下降趋势。在氢气-空气混合物中,燃烧诱导的激波,由于与火焰的反复作用,使激波在轴心处产生马赫干的频率和强度皆高于惰性介质中的情形。同时,火焰在与激波的相互作用过程中发生失稳变形,使其形状呈扁平头部的蘑菇云。     

Linearized and non‐linear acoustic/viscous splitting techniques for low Mach number flows

Computation of the acoustic disturbances generated by unsteady low‐speed flow fields including vortices and shear layers is considered. The equations governing the generation and propagation of acoustic fluctuations are derived from a two‐step acoustic/viscous splitting technique. An optimized high order dispersion–relation–preserving scheme is used for the solution of the acoustic field. The acoustic field generated by a corotating vortex pair is obtained using the above technique. The computed sound field is compared with the existing analytic solution. Results are in good agreement with the analytic solution except near the centre of the vortices where the acoustic pressure becomes singular. The governing equations for acoustic fluctuations are then linearized and solved for the same model problem. The difference between non‐linear and linearized solutions falls below the numerical error of the simulation. However, a considerable saving in CPU time usage is achieved in solving the linearized equations. The results indicate that the linearized acoustic/viscous splitting technique for the simulation of acoustic fluctuations generation and propagation by low Mach number flow fields seems to be very promising for three‐dimensional problems involving complex geometries. Copyright © 2003 John Wiley & Sons, Ltd.