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     

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     

Shock wave attenuation by grids and orifice plates

The interaction of weak shock waves with porous barriers of different geometries and porosities is examined. Installing a barrier inside the shock tube test section will cause the development of the following wave pattern upon a head-on collision between the incident shock wave and the barrier: a reflected shock from the barrier and a transmitted shock propagating towards the shock tube end wall. Once the transmitted shock wave reaches the end wall it is reflected back towards the barrier. This is the beginning of multiple reflections between the barrier and the end wall. This full cycle of shock reflections/interactions resulting from the incident shock wave collision with the barrier can be studied in a single shock tube test. A one-dimensional (1D), inviscid flow model was proposed for simulating the flow resulting from the initial collision of the incident shock wave with the barrier. Fairly good agreement is found between experimental findings and simulations based on a 1D flow model. Based on obtained numerical and experimental findings an optimal design procedure for shock wave attenuator is suggested. The suggested attenuator may ensure the safety of the shelter’s ventilation systems.     

Shock wave attenuation in partially confined channels

An approximate analytical solution is presented for the attenuation of planar shock waves in channels with perforated walls. The problem is considered as quasi-one-dimensional. Good agreement is found between the theoretical results and available experimental data regarding the rate of shock wave attenuation within the range of initial shock Mach numbers between 1.1 and 4 and perforation ratios between 4.5 × 10^–3 and 0.53. A correlation for the discharge coefficient of a single hole perforation is presented which gives quantitatively good agreement with particular experimental observations.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.     

On shock wave propagation in a branched channel with particles

The problem of wave propagation in a dust–air mixture inside a branched channel has not been studied widely in literature, even though this topic has many important applications especially in process safety (dust explosions). In this paper, a shock wave interaction with a cloud of solid particles, and the further behaviour of both gas and particulate phases were studied using numerical techniques. The geometry mimicked a real channel where bends or branches are common. Two numerical approaches were used: Eulerian–Eulerian and Eulerian–Lagrangian. Using Eulerian-Lagrangian simulation, it was possible to include the effects of particle–particle and particle–wall collisions in a realistic and direct manner. Results are mainly shown as snap-shots of particle positions during the simulations and statistics for the particle displacement. The results show that collisions significantly influence the process of particle cloud formation. PACS47.40.Nm, 02.60.Cb, 47.55.kf     

Shock wave interaction with a cloud of particles

The present paper is devoted to experimental and theoretical investigation of the shock wave (SW) propagation in a mixture of gas and solid particles in the presence of explicit boundaries of the two-phase region (cloud of particles). The effect of the qualitative change in the supersonic flow behind the SW in a cloud of particles within the range of the volume concentration of the disperse phase 0.1-3% is experimentally shown and theoretically grounded. Received 15 April 1996 / Accepted 3 June 1996     

Shock wave induced phase transition in \alpha-FePO_4

Shock wave induced response of the berlinite form of FePO has been investigated up to 8.5 GPa. The X-ray diffraction measurements on the shock recovered samples reveal transition to the mixture of an amorphous phase and an orthorhombic phase around 5 GPa. The proportion of the amorphous material in the recovered sample is found to decrease at higher pressure. The results are interpreted in terms of a three-level free energy diagram for the crystal to amorphous transitions. Received 26 May 1997 / Accepted 1 September 1997     

Reinitiation process of detonation wave behind a slit-plate

The propagation phenomenon of a detonation wave is particularly interesting, because the detonation wave is composed of a 3D shock wave system accompanied by a reaction front. Thus, the passage of a detonation wave draws cellular patterns on a soot-covered plate. The pressure and temperature behind the detonation wave are extremely high and may cause serious damages around the wave. Therefore, it is of great significance from a safety-engineering point of view to decay the detonation wave with a short distance from the origin. In the present study, experiments using high-speed schlieren photography are conducted in order to investigate the behaviors of the detonation wave diffracting from two slits. The detonation wave produced in a stoichiometric mixture of hydrogen and oxygen is propagated through the slits, and the behaviors behind the slit-plate are investigated experimentally. When a detonation wave diffracts from the slits, a shock wave is decoupled with a reaction front. Since the two shock waves propagate from the slits interact with each other at the center behind the plate, the detonation wave is reinitiated by generating a hot-spot sufficient to cause local explosions. Furthermore, it is clarified that the shock wave reflected from a tube-wall is also capable of reinitiating the detonation wave. The reinitiation distance of the detonation wave from the slit-plate is correlated using a number of cells emerged from each slit.      

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     

Shock wave deformation in shock-vortex interactions

An initially planar shock wave can undergo significant distortion to its shape along with changes in its strength during the period of its interaction with a compressible vortex. This phenomenon is studied by numerically simulating the shock wave-vortex interaction with a high resolution shock-capturing scheme. Incident shock waves of various Mach numbers are made to interact with a compressible vortex and the dependence of the shock wave distortion on the strength of the incident shock wave is studied in detail. It is known that the type of complex shock structure formed in the later stages of a compressible vortex-shock wave interaction is dependent on the Mach number of the incident shock wave. A simple physical model based on the principle of shock wave reflection is proposed to explain this complex shock structure formation and its dependence on the relative strengths of the interacting vortex and shock wave. Received July 28, 1997 / Accepted November 17, 1997     

Shock wave interaction with cellular materials

The equations governing the head-on collision of a planar shock wave with a cellular material and a numerical scheme for solving the set of the governing equations were outlined. In addition, the condition for the transmitted compression waves to transform into a shock wave, inside the cellular material was introduced. It was proved analytically that a cellular material cannot be used as a means of reducing the pressure load acting on the end-wall of the shock tube. In subsequent papers, the interaction of planar shock waves with specific cellular materials, e.g., foams and honeycombs will be described in detail.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.     

Shock wave driven microparticles for pharmaceutical applications

Ablation created by a Q-switched Nd:Yttrium Aluminum Garnet (Nd:YAG) laser beam focusing on a thin aluminum foil surface spontaneously generates a shock wave that propagates through the foil and deforms it at a high speed. This high-speed foil deformation can project dry micro- particles deposited on the anterior surface of the foil at high speeds such that the particles have sufficient momentum to penetrate soft targets. We used this method of particle acceleration to develop a drug delivery device to deliver DNA/drug coated microparticles into soft human-body targets for pharmaceutical applications. The device physics has been studied by observing the process of particle acceleration using a high-speed video camera in a shadowgraph system. Though the initial rate of foil deformation is over 5 km/s, the observed particle velocities are in the range of 900–400 m/s over a distance of 1.5–10 mm from the launch pad. The device has been tested by delivering microparticles into liver tissues of experimental rats and artificial soft human-body targets, modeled using gelatin. The penetration depths observed in the experimental targets are quite encouraging to develop a future clinical therapeutic device for treatments such as gene therapy, treatment of cancer and tumor cells, epidermal and mucosal immunizations etc.      

Air shock wave interaction with an obstacle covered by porous material

The interaction between an air shock wave and a rigid wall covered by a porous screen is investigated numerically and experimentally. A mathematical two velocity with two stress tensors model is used for studying the wave processes in saturated porous media. The process of reflection of a step-type wave from a rigid wall covered with a porous layer is considered, the effect of the porous medium and wave parameters on the reflection is analyzed, and the numerical results are compared with the experimental data.Received: 30 July 2002, Accepted: 24 December 2002, Published online: 27 May 2003     

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     

Shock wave interaction with porous plates

Previous detailed studies of the interaction of a shock wave with a perforated sheet considered the impact of a shock wave on a plate with regularly spaced slits giving area blockages of 60 and 67%, at various angles of incidence, and resulting in both regular and Mach reflection. The current work extends this study to a much wider variety of plate geometries. Blockage ratios of 20, 25, 33, 50, and 67 and inclinations of 45, 60, 75, and 90° to the shock wave were tested. Four different thicknesses of plate were tested at the same frontal blockage in order to assess the effects of gap guidance. Tests were conducted at two shock Mach numbers of 1.36 and 1.51 (inverse pressure ratios of 0.4 and 0.5). It is found that secondary reflected and transmitted waves appear due to the complex interactions within the grid gaps, and that the vortex pattern which is generated under the plate is also complex due to these interactions. The angle of the reflected shock, measured relative to the plate, decreases with plate blockage and the angle of inflow to the plate reduces with increasing blockage. By analysing the flow on the underside of the plate the pseudo-steady flow assumption is found to be a reasonable approximation. Both the pressure difference and the stagnation pressure loss across the plate are evaluated. It is found that over the range tested the plate thickness has a minimal effect.     

Shock wave propagation into a surface depression

An aircraft travelling at supersonic speeds close to the ground generates a bow wave which is reflected off the ground surface. If a valley is traversed a complex reflection pattern will be generated. Similar patterns will evolve with a plane wave traversing a depression on a surface or structure. To simulate the process a planar shock wave, generated in a shock tube, is moved over several notched wedge configurations. Schlieren photographs were produced to assist in identifying the resulting complex three-dimensional wave structures and then verified and extended by three- dimensional computations. The valley geometries investigated are rectangular, triangular, parabolic and conical with a number of valley floor inclinations. The main features are extracted in surface models to demonstrate the complexity of the flow, and in particular in the case where the reflection is regular on the ground plane and Mach reflection in the valley.      

Shock wave structure in a mixture of gas,vapour and droplets

The structure of the relaxation zone behind a shock wave of moderate strength in a mixture of gas, vapour and droplets is analysed. A model is presented for shock induced evaporation, which is based on wet-bulb equilibrium and on the absence of relative motion between droplets and gas. Experimental and numerical data on heterogeneous condensation induced by an unsteady rarefaction wave and on re-evaporation due to shock wave passage are reported for a mixture of water vapour, nitrogen gas and condensation nuclei. Pressure, temperature, saturation ratio and droplet size are experimentally obtained and are very well predicted by a numerical simulation based on the non-linear quasisteady wet-bulb model for phase transition, as well for the expansion wave as for the shock wave. During expansion, droplet number density decays much faster than predicted, which is not yet satisfactorily explained. Shock induced droplet evaporation is studied for post-shock saturation ratios ranging from 5×10^–3 to 0.2, corresponding to shock Mach numbers of 1.2 to 1.9. The evaporation times are well predicted by the theoretical model. No evidence is found for droplet break-up for Weber numbers up to 13, and droplet radii of the order of 1m.On leave at Institute of Fluid Science, Shock Wave Research Center, Tohoku University, Sendai 980, JapanThis article was processed using Springer-Verlag T_EX Shock Waves macro package 1.0 and the AMS fonts, developed by the American Mathematical Society.     

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     

Detonation Initiation by Shock Reflection from an Orifice Plate

Results from an experimental investigation of the interaction of a “non-ideal” shock wave and a single obstacle are reported. The shock wave is produced ahead of an accelerated flame in a 14 cm inner-diameter tube partially filled with orifice plates. The shock wave interacts with a single larger blockage orifice plate placed 15–45 cm after the last orifice plate in the flame acceleration section of the tube. Experiments were performed with stoichiometric ethylene–oxygen mixtures with varying amounts of nitrogen dilution at atmospheric pressure and temperature. The critical nitrogen dilution was found for detonation initiation. It is shown that detonation initiation occurs if the chemical induction time based on the reflected shock state is shorter than the time required for an acoustic wave to traverse the orifice plate upstream surface, from the inner to the outer diameter. The similarity between the present results and those obtained from previous investigators looking at detonation initiation by ideal shock reflection produced in a shock tube indicates that the phenomenon is not sensitive to the detailed structure of the shock front but only on the average shock strength.This paper is based on work that was presented at the 20th International Colloquium on the Dynamics of Explosions and Reactive Systems, Montreal, Canada, July 31–August 5, 2005.     

Simulation of blast wave propagation over a cylinder

A numerical study of the interaction of plane blast waves with a cylinder is presented. Computations are carried out for various blast-wave durations and comparisons are obtained with the corresponding results of planar shock-wave. Both inviscid and viscous results based on the solution of the Euler and Navier-Stokes equations are presented. The equations are solved by an adaptive-grid method and a second-order Godunov scheme. The shock wave diffraction over the cylinder is investigated by means of various contour plots, as well as, pressure and skin-friction histories. The study reveals that the blast-wave duration significantly influences the unsteady flow over the cylinder. The differences between the viscous and inviscid results are also discussed. Received 2 March 1996 / Accepted 28 February 1997