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     

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.     

Computational study of shock wave focusing in a log-spiral duct

The mechanism of shock wave focusing in a two-dimensional log-spiral duct has been investigated here numerically using a finite volume method. This approach is based on a MUSCL TVD scheme with flux-vector splitting applied to the Euler equations. The isopycnics determined from the calculations are compared with the experimental results obtained by use of holographic interferometric photography and are found to be in excellent qualitative agreement with the experiments. The computational results clarify the details of the wave interactions very near to the focus. In particular, phenomena such as the formation of secondary shock waves prior to the implosion, their interaction with the reflected shock and the formation of vortices after the implosion have been examined.     

The formation of a secondary shock wave behind a shock wave diffracting at a convex corner

This paper deals with the formation of a secondary shock wave behind the shock wave diffracting at a two-dimensional convex corner for incident shock Mach numbers ranging from 1.03 to 1.74 in air. Experiments were carried out using a 60 mm 150 mm shock tube equipped with holographic interferometry. The threshold incident shock wave Mach number () at which a secondary shock wave appeared was found to be = 1.32 at an 81° corner and = 1.33 at a 120° corner. These secondary shock waves are formed due to the existence of a locally supersonic flow behind the diffracting shock wave. Behind the diffracting shock wave, the subsonic flow is accelerated and eventually becomes locally supersonic. A simple unsteady flow analysis revealed that for gases with specific heats ratio the threshold shock wave Mach number was = 1.346. When the value of is less than this, the vortex is formed at the corner without any discontinuous waves accompanying above the slip line. The viscosity was found to be less effective on the threshold of the secondary shock wave, although it attenuated the pressure jump at the secondary shock wave. This is well understood by the consideration of the effect of the wall friction in one-dimensional duct flows. In order to interpret the experimental results a numerical simulation using a shock adaptive unstructured grid Eulerian solver was also carried out. Received 1 May 1996 / Accepted 12 September 1996     

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.      

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     

Evolution of shock waves and the primary vortex loop discharged from a square cross-sectional tube

In this paper, a numerical and experimental investigation of the evolution of a transmitting shock wave and its associated primary vortex loop, which are discharged from the open end of a square cross-sectional tube, is described. The experiments were conducted in the square tube connected to a diaphragmless shock tube and the flowfield was visualized from the axial direction with diffusive holographic interferometry. The numerical simulations were carried out by solving the three-dimensional Euler equations with a dispersion-controlled scheme. The numerical results were displayed in the form of interferograms to compare them with experimental interferograms. Good agreement between the numerical and experimental results was obtained. More detailed numerical calculations were carried out, from which the three-dimensional transition of the shock wave configuration from an initial planar to a spherical shape and the development of the primary vortex loop from a square shaped to a three-dimensional structure were clearly observed and interpreted. Received 29 January 1998 / Accepted 22 May 1998     

Attenuation of shock waves propagating over arrayed baffle plates

The paper reports results of shock tube experiments of the attenuation of shock waves propagating over arrayed baffle plates, which is motivated to simulate shock wave attenuation created accidentally at the acoustic delay line in synchrotron radiation factory upon the rupture of a metal membrane separating the acceleration ring at high vacuum and atmospheric test chambers. Experiments were carried out, by using double exposure holographic interferometry with double path arrangement, in a 100 mm×180 mm shock tube equipped with a test section of 180 mm×1100 mm view field. Two baffle plate arrangements were tested: Oblique and staggered baffle plates; and vertical symmetric ones. Pressures were measured along the shock tube sidewall at individual compartments for shock Mach numbers ranging from 1.2 to 3.0 in air. The results were compared with a numerical simulation. The rate of shock attenuation over these baffle plates was compared for vertical and oblique baffle plates. Shock wave attenuation is more pronounced in the oblique baffle plate arrangements than in the vertical ones. PACS 47.40.Nm; 42.40.Kw Communicated by C. Needham     

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.     

Focusing of strong shocks in an elliptic cavity

Focusing of strong shock waves in a gas-filled thin chamber with an elliptic boundary is investigated theoretically and numerically. The process of reflection and convergence of cylindrical shocks generated at one of the focal points of the chamber is studied by means of Whitham's theory of geometrical shock dynamics (1957, 1959). The current calculations are based on the modified version of this theory, which takes into account the non-homogeneous flow ahead of the advancing shock, Apazidis and Lesser (1996). There are two main results of the present study indicating a qualitatively different behavior of strong shocks as compared to the linear acoustic case. (1) - the form of the reflected shock is not cylindrical and (2) - the reflected, converging shock does not focus at the geometrical second focal point of the chamber. The dependence of the form of the reflected shock and the location of its focusing point on the strength of the shock and the eccentricity of the chamber is investigated.     

Stability of converging cylindrical shock waves

An experimental and numerical study was made of converging cylindrical shock waves. The goal of the present study was to clarify the movement and instability of the converging cylindrical shock waves. Experiments were conducted in an annular shock tube of 230 mm o.d. and 210 mm i.d. connected to a cylindrical test section of 210 mm diameter. Double exposure holographic interferometry was used to visualize the converging cylindrical shock waves. Incident shock Mach numbers ranged between 1.1 and 2.0 in air. A numerical simulation was conducted using the TVD finite difference scheme. It was found in the experiments that although the initial shock wave configuration looked cylindrical, it was gradually deformed with propagation towards the center and finally showed mode-four instability. This is attributable to the existence of initial disturbances which were introduced by the struts which supported the inner tube of the annular shock tube. This trend was significant for stronger shock waves indicating that at the last stage of shock wave convergence the initial perturbations of the converging cylindrical shock wave were amplified to form the triple point of Mach reflection. The numerical results correctly predicted the experimental trend.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1990.     

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 waves in aviation security and safety

Accident investigations such as of Pan Am 103 and TWA 800 reveal the key role of shock-wave propagation in destroying the aircraft when an on-board explosion occurs. This paper surveys shock wave propagation inside an aircraft fuselage, caused either by a terrorist device or by accident, and provides some new experimental results. While aircraft-hardening research has been under way for more than a decade, no such experiments to date have used the crucial tool of high-speed optical imaging to visualize shock motion. Here, Penn State's Full-Scale Schlieren flow visualization facility yields the first shock-motion images in aviation security scenarios: 1) Explosions beneath full-size aircraft seats occupied by mannequins, 2) Explosions inside partially-filled luggage containers, and 3) Luggage-container explosions resulting in hull-holing. Both single-frame images and drum-camera movies are obtained. The implications of these results are discussed, though the overall topic must still be considered in its infancy. Received 22 July 2001 / Accepted 19 July 2002 Published online 4 November 2002 Correspondence to: G.S. Settles (e-mail: gss2@psu.edu) An abridged version of this paper was presented at the 23rd International Symposium on Shock Waves at Fort Worth, Texas, from July 22 to 27, 2001.     

An experimental and theoretical study of converging polygonal shock waves

An experimental investigation was carried out to explore the possibility of producing converging polygonal shocks in an essentially two-dimensional cavity. Previous calculations by Apazidis and Lesser (1996) suggested that such configurations could be produced by reflecting a cylindrical outgoing shock from a smoothly altered circular boundary, the alteration having n-gonal symmetry. In the experiments the outgoing shock was produced by a spark discharge which yielded shocks in the Mach number range from 1.1 to 1.7 at a radius just prior to the reflection. Polygonal shocks were observed as predicted by using a modified form of geometrical shock dynamics, derived in the above paper. In addition, the modified theory was used to calculate the results of an experiment carried out by Sturtevant and Kulkarny (1976). The results of the numerical calculations were found to be in substantial agreement with both experiments, suggesting that the modifications in geometrical shock dynamics for non-uniform flow ahead of an advancing shock are useful in the case of shock focusing. The experiment also showed that the polygonal shapes were stable in the examined range of shock Mach numbers, a result that may be of importance for a number of practical situations in which shock focusing is present. Received 9 October 2001 / Accepted 7 January 2002 – Published online 11 June 2002     

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     

Attenuation of weak shock waves along pseudo-perforated walls

In order to attenuate weak shock waves in ducts, effects of pseudo-perforated walls were investigated. Pseudo-perforated walls are defined as wall perforations having a closed cavity behind it. Shock wave diffraction and reflection created by these perforations were visualized in a shock tube by using holographic interferometer, and also by numerical simulation. Along the pseudo-perforated wall, an incident shock wave attenuates and eventually turns into a sound wave. Due to complex interactions of the incident shock wave with the perforations, the overpressure behind it becomes non-uniform and its peak value can locally exceed that behind the undisturbed incident shock wave. However, its pressure gradient monotonically decreases with the shock wave propagation. Effects of these pseudo-perforated walls on the attenuation of weak shock waves generated in high speed train tunnels were studied in a 1/250-scaled train tunnel simulator. It is concluded that in order to achieve a practically effective suppression of the tunnel sonic boom the length of the pseudo-perforation section should be sufficiently long. Received 23 June 1997 / Accepted 16 September 1997     

Focusing of Strong Shocks in an Annular Shock Tube

Focusing of strong shock waves in a gas-filled thin convergence chamber with various forms of the reflector boundary is investigated experimentally and numerically. The convergence chamber is mounted at the end of the horizontal co-axial shock tube. The construction of the convergence chamber allows the assembly of the outer chamber boundaries of various shapes. Boundaries with three different shapes have been used in the present investigation—a circle, an octagon and a smooth pentagon. The shock tube in the current study was able to produce annular shocks with the initial Mach number in the range M _s = 2.3 − 3.6. The influence of the shape of the boundary on the shape and properties of the converging and reflected shock waves in the chamber has then been investigated both experimentally and numerically. It was found that the form of the converging shock is initially governed by the shape of the reflector and the nonlinear interaction between the shape of the shock and velocity of shock propagation. Very close to the center of convergence the shock obtains a square-like form in case of a circular and octagonal reflector boundary. This is believed to stem from the instability of the converging shock front triggered by the disturbances in the flow field. The outgoing, reflected shocks were also observed to be influenced by the shape of the boundary through the flow ahead as created by the converging shocks.     

Shock waves and turbulence in a hypersonic inlet

A numerical investigation for an axisymmetric hypersonic turbulent inlet flow field of a perfect gas is presented for a three-shock configuration consisting of a biconic and a cowl. An upwind parabolized Navier-Stokes solver based on Roe's scheme is used to compute an oncoming flow Mach numberM =8, temperatureT =216 K, and pressureP =5.5293×10³ N/m². In order to assess the flow quantities, the interaction between shock and turbulence, and the inlet efficiency, three different flow calculations — laminar, turbulent with incompressible and compressible two-equationk- turbulence models — have been performed in this work.Computational results show that turbulence is markedly enhanced across an oblique shock with step-like increases in turbulence kinetic energy and dissipation rate. This enhancement is at the expense of the mean kinetic energy of the flow. Therefore, the velocity behind the shock is smaller in turbulent flow and hence the shock becomes stronger. The entropy increase through a shock is caused not only by the amplification of random molecular motion, but also by the enhancement of the chaotic turbulent flow motion. However, only the compressiblek- turbulence model can properly predict a decrease in turbulence length scale across a shock. Our numerical simulation reveals that the incompressiblek- turbulence model exaggerates the interaction between shock and turbulence with turbulence kinetic energy and dissipation rate remaining high and almost undissipated far beyond the shock region. It is shown that proper modeling of turbulence is essential for a realistic prediction of hypersonic inlet flowfield. The performed study shows that the viscous effect is not restricted in the boundary layer but extends into the main flow behind a shock wave. The loss of the available energy in the inlet performance therefore needs to be determined from the shock-turbulence interaction. The present study predicts that the inlet efficiency becomes relatively lower when turbulence is taken into account.     

Experimental investigation of the interaction of shock waves with textiles

Experimental studies have been performed to investigate the pressure amplification experienced behind a textile when exposed to a shock wave. Three textiles with different masses and air permeabilities were studied. Mach numbers for tests varied between 1.23 and 1.55. The distance between the back wall and the textile was varied between 3 and 15 mm. It was found that in most cases the presence of the textile led to a pressure amplification at the back wall. This amplification was dependent on the textile, Mach number and distance from the back wall. The processes causing the pressure amplification were identified by analysing pressure traces and contact shadowgraphs. It was found that when the incident wave impinges on the textile, a part is reflected upstream and a part is transmitted through the textile. The transmitted portion reflects back and forth in the gap between the textile and the back wall leading to a back wall pressure trace with a stepped profile. In addition, the textile moves towards the back wall causing compression waves to propagate towards the back wall. The combination of the stepped profile and the compression waves cause the pressure amplification. The contribution of each mechanism depends on the textile properties. Approximate wave diagrams have been constructed. Tests involving multiple layers of textiles are also discussed. Received 17 October 2000 / Accepted 2 February 2001