DSMC approach to nonstationary Mach reflection of strong incoming shock waves using a smoothing technique

The direct simulation Monte Carlo (DSMC) method is applied to simulation of nonstationary Mach reflection of strong shock waves. Normally the DSMC method is very time consuming in solving unsteady flow field problems especially for high Mach numbers, because of the necessity of iterative calculations to eliminate the inherent statistical fluctuation caused by a finite sample size. A central weighted smoothing technique is introduced to process the DSMC results, so that the iteration time can be significantly reduced. In spite of some relaxations of the shock wave structure, the smoothing technique is verified to be useful to estima te the flow fields qualitatively and even quantitatively by using a relatively small sample size. The comparison between the present approach and the kineticmodel approach (Xu et al. 1991a, 1991b) on the application to unsteady rarefied flow fields was also carried out.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.     

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     

Class of two-dimensional nonstationary flows with shock waves

A numerical investigation was made of a two-dimensional plane-parallel nonsteady motion resulting from the decay of an arbitrary discontinuity on the boundaries of several neighboring angular regions filled by gases in different states.     

Double Mach reflection of strong shock waves

The Mach reflection of shock waves in those cases in which the gas ideality condition is satisfied with high accuracy is well-known. The effects associated with the excitation of the internal degrees of freedom for the molecules lead to a qualitative change in the reflection pattern. The present study is an extension of [1, 2], devoted to the study of the Mach reflection of shock waves from a wedge under conditions in which the physical and chemical transformations in the gas heated by the shock wave play a significant role.     

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.     

Shear-layer instability in the Mach reflection of shock waves

The Kelvin–Helmholtz instability (KHI) is an instability that takes the form of repeating wave-like structures which forms on a shear layer where two adjacent fluids are moving at a relative velocity to one another. Such a shear layer forms in the Mach reflection of shock waves. This work focuses on experimentally visualising the presence of the KHI in Mach reflection as well as its evolution. Experimentation was performed at shock Mach numbers of 1.34, 1.46 and 1.61. Plane test pieces and parabolic profiled pieces followed by a plane section having wedge angles of 30 \(^\circ \) and 38 \(^\circ \) were tested. Flow field visualisation was performed with a schlieren optical system. The KHI was best visualised with the camera-side knife edge perpendicular to the shear layer (i.e. the axis of sensitivity along the length of the shear layer). The structure and growth of the instability were readily identified. The KHI forms more readily with increasing Mach number and wedge angle. Second-order Euler, and Navier–Stokes numerical simulations of the flow field were also conducted. It was found that the Euler and laminar Navier–Stokes solvers achieved very similar results, both producing the KHI, but at a much less developed state than the experimental cases. The k \(-\epsilon \) solver, however, did not produce the instability.     

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。     

Numerical investigations of shock waves in gas-particle mixtures

The propagation of shock waves in gas-particle mixtures in one- and two-dimensional geometries is numerically investigated. Two schemes for approximating conservation laws for particles, which are collectively treated as a continuum medium, are compared and discussed. Different models of the drag coefficient and Nusselt number, directly affecting the interaction between the gas and particle phases, are used for obtaining shock profiles, and the results are compared. The oblique shock reflections at a solid wedge in a gas-particle mixture are simulated. The results demonstrate that the reflection pattern changes as the shock propagates along the wedge, revealing strong non-selfsimilarity of the phenomenon.Received: 22 May 2003, Accepted: 28 August 2003, Published online: 12 November 2003 Correspondence to:T. Saito     

Analytical,numerical and experimental investigations of architectural sandwich panels

Architectural sandwich panels with thin-walled cold-formed steel facings and rigid foamed insulating core are becoming more and more popular as enclosures for system buildings. In this paper, the structural behavior, including flexural stresses/deflections, flexural wrinkling, axial stability, thermal stresses and vibration, is presented, summarizing more than a decade of research. Methods used are analytical (boundaryvalued approaches), numerical (finite-strip, finite-layer, finite prism approaches) and experimental (full-scale testings). Key equations are formulated, and results by different methods are compared.     

Effect of the adiabatic exponent on the reflection of shock waves

The effect of the adiabatic exponent on certain features of shock-wave reflection is analyzed with particular reference to the nature of the dependence of the critical angle on the incident wave intensity. The latter is shown to increase with increasing shock-wave intensity. Limit cases of weak shock waves at any arbitrary adiabatic exponent and of strong shock waves with the adiabatic exponent equal to unity are analytically investigated. Results of calculations of the critical angle for various adiabatic exponents throughout the possible range of incident wave intensities are presented.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, Vol. 11, No. 1, pp. 62–66, January–February, 1970.     

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.     

Plane nonstationary self-similar gas flow with energy liberation in shock waves

Two plane nonstationary, self-similar problems occurring with energy supply in shock waves are examined in a linear formulation; the pressure distributions in the perturbed flow domains are obtained. Results and methods used extensively in the theory of diffraction of shock waves [1–3] are employed in this paper.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 164–167, July–August, 1978.In conclusion, the author is grateful to M. N. Kogan for supervising the research, and also to A. I. Golubinskii and V. P. Kolgan for useful comments and valuable discussion.     

Interferometric measurement of density in nonstationary shock wave reflection flow and comparison with CFD

We present density measurements from the application of interferometry and Fourier transform fringe analysis to the problem of nonstationary shock wave reflection over a semicircular cylinder and compare our experimental measurements to theoretical results from a CFD simulation of the same problem. The experimental results demonstrate our ability to resolve detailed structure in this complex shock wave reflection problem, allowing visualization of multiple shocks in the vicinity of the triple point, plus visualization of the shear layer and an associated vortical structure. Comparison between CFD and experiment show significant discrepancies with experiment producing a double Mach Reflection when CFD predicts a transitional Mach reflection.Received: 12 November 2003, Accepted: 21 October 2004, Published online: 31 March 2005[/PUBLISHED]PACS: 47.40.-x, 42.40.Kw     

Theory of anomalous modes of regular reflection of shock waves

It is well known [1, 2] from numerical calculations of the reflection of a shock wave for a diatomic gass that in some cases regular reflection is accompanied by higher pressures than the pressure of normal reflection (anomalous modes of regular reflection). A theory explaining this phenomenon is presented in this paper. It is shown that if the adiabatic exponent is larger than some critical value, then for any shock wave intensity there exists a finite range of angles of incidence for which anomalous reflection modes occur. If the adiabatic exponent is smaller than this critical value, anomalous reflection occurs only for shock waves whose intensity is smaller than some characteristic value dependent on the adiabatic exponent. Explicit formulas are obtained which relate the angle and pressure of reflection of a shock wave to the initial parameters of the problem.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 117–125, September–October, 1973.The author thanks V. A. Belokon' for stimulating discussions.     

Mach reflection of weak shock waves from a rigid wall

On the basis of experimental observations and theoretical analysis of flow structure in the neighborhood of the triple point, it is shown that one should reject the condition for equality of the angle of deflection of flows passing through the Mach front and the two other fronts and replace it with some supplementary condition. The system of consistency equations in the indicated region is closed by an equation which is obtained under the assumption of the extremality of the deflection angle of a flow passing through the incident and reflected fronts. Calculations of the pressure drops behind the shock fronts agree with experimental data in this case.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 26–33, September–October, 1973.The authors thank S. A. Khristianovich for consideration of the work and advice.     

Geometrical investigation of the regular reflection of shock waves from a wall

By means of a geometrical approach it has been possible to find a new connection between the geometrical characteristics of an oblique shock wave. The obtained expressions are used to establish some features of the reflection process.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 182–185, September–October, 1980.I am very grateful to V. P. Stulov for discussion and valuable advice.     

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.     

Experimental investigations of the interaction of shock waves in soils containing obstacles

A model of water-saturated soil as an ideal liquid has already been proposed [1], Experimental investigations of shock waves [2] have shown that for small stresses in water-saturated soil features of a solid plastic body begin to manifest themselves. As regards its properties the soil approximates to the model proposed in [3].The results of tests on the interaction of a plane shock wave in the soil with a moving obstacle are given below. As a development of papers [2,4, 5] an approximate solution is given for the problem of the interaction of waves with an obstacle. At high pressures the ground is regarded as nonlinearly elastic, and at low pressures as a plastic medium. A similar approach may be applied to water-saturated and nonsaturated soils when the wave is a shock wave. Experimental values of the parameters of motion of the obstacle are compared with the results of calculation.The authors are grateful to S. D. Mizyakin for participating in the tests.     

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.