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.     

A weak shock wave reflection over wedges

When a weak shock wave reflects from wedges its reflection pattern does not appear to be a simple Mach reflection. This reflection pattern is known to be von Neumann Mach reflection in which a Mach stem can not necessarily be straight. In this paper the local change of the Mach stem curvature was experimentally and numerically investigated. A distinct triple point, at which the curvature becomes infinite as appears in a simple Mach reflection, was not observed but the Mach stem curvature became a maximum between foot of the Mach stem and a point, P₁, at which an incident shock met with a reflected shock. Maximum curvature point P₂ and P₁ do not coincide for small wedge angles and tend to merge over a certain wedge angle. Experimental results agreed with numerical results. The trajectory angle of P₂ was found to be expressed well by Whitham's shock-shock angle.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.     

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.     

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.     

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.     

Droplet break-up through an oblique shock wave

The interaction of a two-phase flow with a wedge where a stationary shock wave is initially settled is studied in a two-dimensional configuration. Before the introduction of the dispersed phase, the flow around the wedge is a supersonic one phase flow such as an attached stationary shock wave is present. Then, the dispersed phase is introduced upstream the initial position of the stationary shock wave. The purpose of this study is to point out two-phase and droplets break-up effects on the oblique shock wave. The two-dimensional equations are solved by a TVD scheme where fluxes are computed by using Riemann solver for the gas phase equations and also for the dispersed phase equations wich is an original approach due to the authors (Saurel et al. 1994). In addition to drag forces and heat and mass transfers, the process of droplets fragmentation based on the particle oscillation is considered. Accepted April 28, 1995     

Shock wave reflection over wedges: a benchmark test for CFD and experiments

In the Shock Wave Journal Vol. 2, No. 4 a benchmark test for shock wave reflection over wedges was announced. International scientists who are interested in shock wave research were invited to participate. The benchmark test aimed at comparison of various advanced numerical schemes as well as experimental results. During the last three years more than twenty results, including both CFD and experiments, were collected from all over the world. Efforts contributed by these scientists made the present benchmark test reach to a standard of the state of the art of the computational fluid dynamics applied to the shock wave research. However, it was regrettable not to publish all the results collected due to limitation on the available page number. Received 5 November 1994 / Accepted 9 September 1996     

Focusing of a shock wave in a rarefied gas A numerical study

The process of focusing of a shock wave in a rarefied noble gas is investigated by a numerical solution of the corresponding two dimensional initial–boundary value problem for the Boltzmann equation. The numerical method is based on the splitting algorithm in which the collision integral is computed by a Monte Carlo quadrature, and the free flow equation is solved by a finite volume method. We analyse the development of the shock wave which reflects from a suitably shaped reflector, and we study influence of various factors, involved in the mathematical model of the problem, on the process of focusing. In particular, we investigate the pressure amplification factor and its dependence on the strength of the shock and on the accommodation coefficient appearing in the Maxwell boundary condition modelling the gas-surface interaction. Moreover, we study the dependence of the shock focusing phenomenon on the shape of the reflector, and on the Mach number of the incoming shock. Received 25 May 1998 / Accepted 4 January 2000     

Shock wave diffraction by a square cavity filled with dusty gas

A simple two-dimensional square cavity model is used to study shock attenuating effects of dust suspension in air. The GRP scheme for compressible flows was extended to simulate the fluid dynamics of dilute dust suspensions, employing the conventional two-phase approximation. A planar shock of constant intensity propagated in pure air over flat ground and diffracted into a square cavity filled with a dusty quiescent suspension. Shock intensities were and , dust loading ratios were and , and particle diameters were and {\rm \mu}$m. It was found that the diffraction patterns in the cavity were decisively attenuated by the dust suspension, particularly for the higher loading ratio. The particle size has a pronounced effect on the flow and wave pattern developed inside the cavity. Wall pressure histories were recorded for each of the three cavity walls, showing a clear attenuating effect of the dust suspension. Received 15 November 1999 / Accepted 25 October 2000     

Some aspects of streamwise vortex behavior during oblique shock wave/vortex interaction

An experimental study of the flowfield generated by the interaction of a streamwise vortex having a strong wake-type axial Mach number profile and a two-dimensional oblique shock wave was conducted in a Mach 2.49 flow. The experiments were aimed at investigating the dynamics of supersonic vortex distortion and to study downstream behavior of a streamwise vortex during a strong shock wave/vortex encounter. The experiments involved positioning an oblique shock generator in the form of a two-dimensional wedge downstream of a semi-span, vortex generator wing section so that the wing-tip vortex interacted with the otherwise planar oblique shock wave. Planar laser sheet visualizations of the flowfield indicated an expansion of the vortex core in crossing a spherically blunt-nose shock front. The maximum vortex core diameter occurred at a distance of 12.7 mm downstream of the wedge leading edge where the vortex had a core diameter of more than double its undisturbed value. At distances further downstream the vortex core diameter remained nearly constant, while it appeared to become more diffused at distances far from the wedge leading edge. Measurements of vortex trajectory revealed that the vortex convected in the freestream direction immediately downstream of the bulged-forward shock structure, while it traveled parallel to the wedge surface at distances further downstream. The turbulent distorted vortex structure which formed as a result of the interaction, was found to be sensitive to downstream disturbances in a manner consistent with incompressible vortex breakdown. Physical arguments are presented to relate behavior of streamwise vortices during oblique and normal shock wave interactions. Received 7 September 1996 / Accepted 10 February 1998     

Experimental and numerical studies of underwater shock wave attenuation

The attenuation of an underwater shock wave by a thin porous layer is studied both experimentally and numerically. The shock waves are generated by exploding 10 mg silver azide pellets and the pressures at different distances from the explosion center are measured. Measurements are also carried out with a gauze layer placed between the explosion source and the pressure gauge. The results with and without the gauze layer are compared evaluating the shock wave attenuation. Numerical simulations of the phenomenon are also carried out for a simple wave attenuation model. The results are compared with the experimental data. Despite the simple mathematical model of wave attenuation, the agreement between the experimental and numerical results is reasonable.Received: 22 October 2002, Accepted: 17 June 2003, Published online: 5 August 2003PACS: 47.11.+j, 47.40.Nm, 47.55.Mh     

Reconsideration of pseudo-steady shock wave reflections and the transition criteria between them

The shock wave reflection phenomenon in pseudosteady flows was reconsidered by replacing the Law-Glass assumption by models accounting for the interaction of the shock wave reflection and the shock induced flow deflection processes. As a result, the analytical predictions of the location of the kink of a transitional-Mach reflection and the second triple point of a double-Mach reflection improved tremendously. It has also been proven that based on gas dynamic considerations a triple-Mach reflection wave configuration is physically impossible. In addition, the transition lines between the various reflection configurations were also found to better agree with the experimental results when they were calculated using the proposed models.     

Three-dimensional shock wave reflection over a corner of two intersecting wedges

This paper presents an experimental and numerical investigation of three-dimensional shock wave reflections over a corner of two wedges intersecting perpendicularly in a shock tube. Experiments were conducted in a diaphragmless shock tube equipped with double-exposure diffuse holographic interferometry in which the time interval between the first and second exposure was set to be . This arrangement clearly visualized complex configurations of three-dimensional shock wave reflections. A numerical study was also carried out for interpreting these holographic interferometric observations by using the Weighted Average Flux (WAF) method to solve the three-dimensional unsteady compressible Euler equations. It was found that along the line of the intersection of these two wedges, two Mach stems intersected each other resulting in the formation of a Mach stem which leaned forward. Received 30 June 1996 / Accepted 6 October 1996     

A comparison of four recent numerical schemes giving high resolution of shock wave and concentrated vortex

ＡＣＯＭＰＡＲＩＳＯＮＯＦＦＯＵＲＲＥＣＥＮＴＮＵＭＥＲＩＣＡＬＳＣＨＥＭＥＳＧＩＶｉＮＧＨＩＧＨＲＥＳＯＬＵＴＩＯＮＯＦＳＨＯＣＫＷＡＶＥＡＮＤＣＯＮＣＥＮＴＲＡＴＥＤＶＯＲＴＥＸＨｕａｎｇＤｕｎ（黄敦）（Ｄｅｐａｒｔ．ｏｆＭａｔｈ．ＰｅｋｉｎｇＵ...     

爆轰波在楔面上反射数值分析

应用基元反应模型和频散可控耗散格式(DCD)对氢氧爆轰波在楔面反射进行了数值模拟,计算中氢氧混合物的化学反应采用了8种组分20个反应方程式,在处理化学反应引起的刚性问题时采用了时间算子分裂的方法,模拟了爆轰波在楔面反射由马赫反射向规则反射转变的过程,得到了反射转变临界角,同时考虑了初始压力和组分的影响,并和实验及理论分析结果进行了比较,结果是令人满意的。     

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     

Reflection of shock wave from a compression corner in a particle-laden gas region

We investigated in this paper the progression of a shock-wave reflected from a compression corner in a particle-laden gas medium using a TVD class numerical technique and a MacCormack scheme. For a gas-only flow, the numerical results agreed well with the existing experimental data, suggesting that the gas phase is correctively solved. The effect of particle size and mass fraction ratio is investigated for a dilute gas-particle flow. It has been shown that the shock-wave diffraction and the flow configuration after the shock can become remarkably different from the gas-only flow depending on the particle parameters. Relaxation phenomenon due to the momentum drag and the heat exchange between the gas and the particle phases is explained.Graduate Student of Korea Advanced Institute of Science and TechnologyThis article was processed using Springer-Verlag T_EX Shock Waves macro package 1990.     

A study of shock wave interaction with a rotating cylinder

Shock wave reflection over a rotating circular cylinder is numerically and experimentally investigated. It is shown that the transition from the regular reflection to the Mach reflection is promoted on the cylinder surface which rotates in the same direction of the incident shock motion, whereas it is retarded on the surface that rotates to the reverse direction. Numerical calculations solving the Navier-Stokes equations using extremely fine grids also reveal that the reflected shock transition from RR MR is either advanced or retarded depending on whether or not the surface motion favors the incident shock wave. The interpretation of viscous effects on the reflected shock transition is given by the dimensional analysis and from the viewpoint of signal propagation.Received: 24 April 2002, Accepted: 16 August 2002, Published online: 25 March 2003     

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 non-equilibrium multiscale simulation of shock wave propagation

A novel non-equilibrium multiscale dynamics (NEMSD) is proposed to simulate non-equilibrium thermal–mechanical processes. The model couples coarse-grain thermodynamics with a fine scale molecular dynamics. A Distributed Nośe-Hoover Thermostat Network is used, which regulates the temperature in each coarse scale Voronoi cell according to the finite element (FE) nodal temperature. The atoms in each element-cell, namely Voronoi cell-ensemble, are assumed to be in a local equilibrium state within one coarse scale time step. The change of FE nodal temperature provides a source of random forces, which drive the system out of equilibrium. The proposed NEMSD can successfully simulate shock wave propagation in a cubic lattice.