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 trapping

This paper presents a two-dimensional investigation into the effectiveness of trapping shock and blast waves in a duct in order to enhance attenuation, by placing an array of opposing wedges in the channel. The concept of the wedge arrangement in the trap is to allow easy shock wave entry, with weak reflected shocks, into the trap, but stronger internal reflected shocks if a wave is re-emering. The internal reflections, including those of vortices shed from earlier shock passage, result in strong shock attenuation. Different wedge placements, wedge angles, and area blockages are investigated numerically, as well as experimentally for a particular case, using pressure measurement and schlieren photography. Received 4 August 1995 / Accepted 12 December 1995     

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 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     

Critical reactions for the hydrazine vapor detonations

A detailed kinetic model devoted to the hydrazine vapor detonation has been built. It consists of 33 reversible reactions and 13 species. A reduced kinetic model has been proposed by using the Principal Component Analysis of matrix F (PCAF) method as implemented in KINALC. It is constituted of 26 reactions and 11 species. This model has been shown to be valid over a pressure range of 0.1 to 10 atm. However, the predictions of the models are significantly affected by changes in the enthalpy of formation of NH. With the help of the full kinetic model, a value of A, the proportionality factor in the ZND model between the induction distance in the detonation wave and the detonation cell size, of has been derived if one considers that the collision efficiency of NH on the thermal decomposition of hydrazine is equal to the one of N. The value of A for pure hydrazine detonation is shown to be strongly dependent on the value of the collision efficiency of NH. Received 24 December 2000 / Accepted 11 April 2001     

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-induced phase transformation and vortex instabilities in shock loaded titanium alloys

Spall-tests of four kinds of high-strength titanium alloys (VT-6, VT-14, VT-20 and VT-23) have been performed by using a two-channel velocity interferometer for recording free surface velocity profiles and a SEM-technique for microstructure investigations of post-shocked specimens. Screw rotational structures in the spall zone are thought to be responsible for the more effective shock-wave energy scattering during spallation. Free surface velocity profiles display forward and reverse phase transitions in the all alloys under investigation. The threshold stress for the forward and reverse phase transitions turns out to be practically independent of the chemical and phase compositions of specimens, and monotonously increases with strain rate. Received 7 February 1999 / Accepted 3 November 1999     

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.      

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 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.     

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.     

A preparation method of functionally graded materials with phase transition under shock loading

The propagation of phase boundary in a material undergoing shock induced irreversible phase transition is studied theoretically using a model based on simple-mixture rule. It is found that along with the decay of the phase boundary, a functionally graded material (FGM) forms in the mixed-phase region. Such FGMs are composed of parent phase and product phase, and the composition and physical properties are changing continuously without apparent macro-interfaces. The effect of stress boundary conditions on formation of the FGM is investigated in detail with a numerical method. The possibility of producing FGMs with impact method is proposed and the limit of this method is discussed.     

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     

On the structure of the Hugoniot relation for a shock-induced martensitic phase transition

The Hugoniot curve relates the pressure and volume behind a shock wave, with the temperature having been eliminated. This paper studies the Hugoniot curve behind a propagating sharp interface between two material phases for a solid in which an impact-induced phase transition has taken place. For a solid capable of existing in only one phase, compressive impact produces a shock wave moving into material, say, at rest in an unstressed state at the ambient temperature. If the specimen can exist in either of two material phases, sufficiently severe impact may produce a disturbance with a two-wave structure: a shock wave in the low-pressure phase of the material, followed by a phase boundary separating the low- and high-pressure phases. We use a theory of phase transitions in thermoelastic materials to construct the Hugoniot curve behind the phase boundary in this two-wave circumstance. The kinetic relation controlling the evolution of the phase transition is an essential ingredient in this process.      

Martensitic phase transition involving dislocations

A model of solid–solid phase transition involving dislocations in crystals is proposed within the nonlinear continuum dislocation theory (CDT). The co-existence of phases having piecewise constant plastic slip in laminates is possible for the two-well free energy density. The jumps of the plastic slip across the phase interfaces determine the surface dislocation densities at those incoherent boundaries. The number of phase interfaces should be determined by comparing the energy of dislocation arrays and the relaxed energy minimized among uniform plastic slips.     

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.     

Shock waves in an elliptical cavity with varying height

Transient shock waves in a confined elliptical chamber are experimentally investigated. Quantitative results of the pressure distribution are obtained for an air-filled cavity. Lower bounding surfaces of different geometrical shapes can be inserted making it possible to get chambers with varying height. An electrical discharge across a pair of electrodes inside the cavity gives rise to the shock waves. Double pulsed holographic interferometry is used to study the propagation and focusing process of the waves. The results are quantitatively evaluated by using the method of two-reference-beam holography. The angular pressure distribution behind the converging wave front is presented for different geometries of an air-filled cavity. The pressure distribution is non-homogeneous but symmetric along the wave front. The pressure level is higher for the geometry where the height of the chamber decreases with the radial distance from the outgoing focus and lower for increasing height of the chamber. In addition, shock waves in a water-filled cavity are studied. In this case qualitative results are obtained. Received 3 November 1996 / Accepted 5 January 1997