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Shock wave research covers important inderdisciplinary areas which range from basic topics on gasdynamics, combustion and detonation, physico-chemistry of high temperature gases, plasma physics, astro and geophysics, materials science, astronautics and space technology to medical and industrial applications. This book includes 202 papers presented at the 18th the International Symposium on Shock Waves which describe the research frontier of shock wave phenopmena and 14 plenary lectures which show the state of the art of various fields of shock wave research. This proceedings is a unique collection of most important and updated shock wave research.



Plenary lectures


Shock tube application: High enthalpy European wind tunnels

High enthalpy wind tunnels which are used in Europe for the development of new hypersonic vehicles are described. Also included are three new tunnels which will be in operation shortly. More details are given for one piston tunnel (Longshot at VKI in Brussels, Belgium) and two shock tunnels (C2 at Vernon, France and TH2 at Aachen, Germany). A key problem is the knowledge of the test section flow. A technique has been developed to rely only on the measured test section data for the determination of Stanton numbers and pressure coefficients.

H. Grönig

Research issues of concern: Scientific and medical

Extracorporeal shock wave lithotripsy has now been applied for human stone therapy for over a decade. Aside from the fact that we know that this is an effective modality to fragment stones, what do we really know about these high energy shock waves? Clearly, many questions exist. The answers to these questions are of differing interests to both the medical and basic scientific communities. It is the purpose of this paper to explore some basic questions regarding lithotripsy expressed in terms of relative concern to both medicine and science.

L. B. Kandel

Vorticity in shock-accelerated density-stratified interfaces: Deposition and “intermediate” time evolution of coherent structures

The results of two dimensional direct numerical simulations of inviscid shock-accelerated density-stratified interfaces are presented. We emphasize and quantify intermediate-time evolution of coherent vortex structures. Our numerical experiments model laboratory shock tube experiments in which a planar shock (M = 4.0) interacts with an inclined interface separating fluids of different density or acoustic impedance. Two generic interfacial classes are considered, where the shock passes from: heavy-to-light gas (“slow /fast”, or s/f in terms of sound speeds); and a light-to-heavy gas (“fast/slow”, or f/s). The initial impulsive interaction between the shock and the interface results mainly in vorticity layers being deposited along the interface. Strong (M = 4.0) shocks generate more secondary interacting shock structures and vortex layers. For proper cases, early-time validation is obtained by comparing with shock polar analyses. The importance of secondary baroclinic effects in both cases is emphasized. In addition to shock-interface interaction, we discuss one shock-cylinder f/s interactions. The direct numerical simulations of the time-dependent Euler equations were performed using a second-order Godunov scheme.

N. J. Zabusky, R. Samtaney, X. Yang, I-L. Chern

Modern shock-capturing schemes

This paper discusses some of the strategies employed for shock-capturing calculations, especially of highly compressible transient flows. In most such cases, the cost of achieving given resolution can be reduced by an order of magnitude or more by employing a grid that adapts dynamically to the evolving solution. Such a grid implies a need for data structures that are not of the simple matrix type. Advantages and disadvantages of unstructured and partly structured meshes are discussed, as well as some of the requirements for flow algorithms able to perform well on such grids.

P. L. Roe

Effects of focused shock waves on biological tissues: Cavitation in the prefocal region and the fluid flow in the focal region

In order to elucidate the mechanism of shock wave injury in biological tissues, the mechanical damage of aluminum foils and the hyperechoic region, in the focal zone were studied. The shock waves were produced by a specially designed piezo-ceramic (overhead and water-bag type) generator. For focus localization an ultrasonic sector probe was used. On aluminum foils numerous pits were observed circumferentially around the central major deformity. The pits were formed not only in the focal region but also in the pre-focal region. The hyperechoic region, which appeared as a cloudy area on an ultrasound screen in the focal region, moved and disappeared after more than 5 sec. The numerical simulation indicated that the maximum flow speed reached 30 meter per second, and the direction of the flow was both axial and radial.The results indicate that, in addition to the tensile and compression stress, a cavitation phenomenon which induces pits and fluid flow in the focal region should also be considered in the mechanism of biological tissue injury caused by focused shock waves.

M. Kuwahara, N. Ioritani, T. Saito, S. Hoshi, S. Shirai, K. Taguchi, S. Orikasa, T. Obara, K. Takayama, S. Aida

Shock tube studies of combustion chemistry

A historical review of shock-tube studies of the chemical reactions involved in gas-phase combustion is given. Limitations of shock tube technology as applied in combustion studies are discussed, including effects of wall boundary layers, non-steady wave motion due to reaction exothermicity, incomplete knowledge of chemical compositions, and unsatisfactory accounting for experimental data scatter. Possible improvements of experimental and interpretive methods are presented.

W. C. Gardiner

Studies in shock waves, liquid impact, jets and cavitation

Shock waves in liquids play a fundamental role in problems of liquid impact, high speed liquid jet emergence, and shock induced cavity collapse. Key problems that relate to all these areas occur in the liquid impact situation. Thus the article concentrates on shock development and detachment conditions arising in liquid impact. High speed photographic evidence is presented and a gel simulation technique is used to form shapes such as wedges, disks and cavities. Accurate asymptotic expressions, convenient for calculation, are presented for critical pressure and angles in shock escape. The paper closes with a comments on jet emergence and shock induced cavity collapse and some comments on the state of outstanding important problems.

M. Lesser, J. Field

The shock tube technique applied to study aerosol rate processes

Aerosols are gas-particle suspensions characterized by two features: the size of the particles is very small and the volume fraction of the particle phase is extremely low. Aerosols can undergo different rate processes causing changes of the particle and/or of the gas properties. In the present case a shock tube is used as an isothermal-isobaric reactor, in which aerosol rate processes can be started by the step-like temperature and the fluid velocity increase. Examples are heterogeneous oxidation reactions at the surface of carbonaceous particles, evaporation of solid or liquid aerosol particles, or fluid flow induced disintegration of agglomerated solid primary particles. All these aerosol rate processes were studied behind shock waves in the form of relaxation processes. Rate parameters were determined from light scattering or spectroscopic measurements as will be shown in the paper.

P. Roth

Shock-interface interaction: Current research on the Richtmyer-Meshkov problem

In the last decade, the extension of the Rayleigh-Taylor instability problem to impulsive accelerations has generated much interest. The topic under study is that of the evolution of a slightly perturbed fluid interface towards a fully turbulent mixed region. Shock tubes are the natural experimental tool for furthering our understanding of the phenomena involved. They have been used by several researchers to probe, with an array of diagnostics, the mixed region which develops when an incident shock and subsequent reflected compression or expansion waves traverse a material interface. In most of the experimental techniques used so far, the turbulent region has been observed through the wall boundary layers. In such experiments care needs to be taken to separate the signature of these layers from that of the mixed region. Methods used to generate the interface also affect the phenomenon observed, so that experimental results are still the object of some controversy. Newer techniques strive to overcome these problems.In parallel with the experimental work, a number of researchers have attacked the problem computationally, first with two dimensional and now with three dimensional simulations. Good agreement is found among the numerical results, but they seem to differ from the observations by a significant amount. Possible causes for the discrepancies include the cross talk between mixed region and boundary layer, which is seldom included in the computations, and the initial conditions at the interface. While the Rayleigh-Taylor instability has been shown to tend asymptotically to a fully turbulent regime that is independent of initial conditions, numerical simulations and experiments indicate that the effect of initial conditions on the Richtmyer-Meshkov instability is more significant. This bodes ill for the numerous attempts which have been made to develop predictive models to describe the evolution of the mixed region with low order simulations. Nonetheless much effort has been expended along these lines, and has yielded some degree of success.

V. Rupert

Wave problems in high-speed railway tunnels

When a high-speed railway train enters a tunnel, a compression wave is generated and propagates along the tunnel. The compression wave is reflected back at the exit and an impulsive wave is emitted outward. This paper deals with some subjects concerning the waves of railway train-tunnel systems, i.e., an entry compression wave, the attenuation of the compression wave propagating along the tunnel, and the generation of an impulsive wave at the exit portal of the tunnel, focusing our attention to the alleviation of the impulsive noises from the tunnel exit.

K. Matsuo, T. Aoki

The use of high velocity launchers for scientific and engineering studies

Shock wave techniques have been used for decades to study the dynamic states of matter in temperature and pressure regimes inaccessible by other methods. These techniques have been employed in a wide variety of scientific and commercial applications. A principal scientific objective has been to determine high-pressure equations of state (EOS) to ultra-high pressures; pressures of a few TPa have been reported for several materials. Most recently, these methods have been used for studies of thermophysical properties under shock compression, including phase transition kinetics, and mechanical properties, such as the high-pressure yield strength. In this paper, a brief discussion of recent developments in high velocity launchers is given. Advances in techniques for subjecting materials to a wide range of loading conditions are presented, including selected illustrations of shockwave measurements to Mbar pressures.

J. R. Asay, L. C. Chhabildas, M. D. Furnish

Mach reflection research - paradox and progress

The failure of the two-shock theory to adequately describe the conditions at which transition from regular to Mach reflection occurs, and of the three-shock theory to describe the Mach reflection of shocks with a strength less than about Mach 1.5 are described and discussed. The failures occur when the assumptions used in the theories are not fulfilled. It is suggested that the particle velocities behind the reflected and Mach stem shocks in the region of the triple point may, as a result of the curvature of these shocks, have transverse components. A revised three-shock solution is discussed, together with modifications of the Mach reflection phenomenon in truly unsteady configurations and for very strong incident shocks.

J. M. Dewey

Phase changes in solids during shock loading and unloading

Polymorphic phase transformations have been found in many substances by shock compression. The transition pressures observed by dynamic and static compression are generally in good agreement, provided that the kinetics of phase changes, such as those which are displacive or electronic in origin, is sufficiently fast to be completed within the short time interval of a shock process. Molecular dynamical calculations of rutile under uniaxial stress showed that the phase transition to high pressure fluorite phase could be completed within a few picoseconds, much shorter than the shock rise time within the shock front. The fact that the phase transition pressures of rutile single crystals depends on the shock loading directions can also be explained, given the uniaxial nature of the plane shock loading within the shock front. On the other hand, there are also many examples in which the recovered materials cannot be considered as due to the shock-induced high pressure phase itself, but metastably formed during the unloading process. To apply the shock wave technique for materials synthesis, the importance of the knowledge on the shock-induced phase transformations as well as pressure-temperature history of shock process is mentioned.

Y. Syono, K. Kusaba, T. Atou, K. Fukuoka

Explosive volcanism in Japan and the United States: Gaining an understanding by shock tube experiments

On 15 July, 1888, Bandai Volcano in central Japan erupted explosively in a style which, in many aspects, was imitated by Mount. St. Helens nearly 100 years later. The episode began with a violent earthquake, and there was a major debris avalanche and many large explosions that resulted in the death of 461 people. The last and largest explosion was directed laterally across the landscape. The eruption and its aftermath were extremely well documented in the press, by scientists and by eye witnesses. We present some of the early photographs and paintings of the eruption of Bandai-San. The eruption of Mount. St. Helens on 18 May, 1980, documented with modern observational methods, caused a revolution in the understanding of explosive volcanism, and so led to a more detailed understanding of the eruption of Bandai Volcano. The information gathered a century ago serves now as an important resource.Physical processes which cause the destructiveness of explosive eruptions include the energetic fragmentation of liquid magma into fire ash particles and ejection of the particles and liberated gases through the vent at supersonic speed. It is possible to study these processes at laboratory scale by using shock tube techniques. Impulsive, highly accelerating flows, in which the greater effect of earth’s gravity under full scale conditions plays little role, can be generated by rapidly depressurizing volatile liquids or pressurized beds of solid particles. One experiment of each type is described. In the first, superheated refrigerants are used to simulate gas-rich magma, and the explosive vaporization that results (‘evaporation wave’) is studied as a model of magma fragmentation. In the second, it is shown that accelerating dense dusty gases are inherently unstable to density perturbations, and that the resulting flow experience density fluctuations of order 1000. Implications regarding the interpretation of volcanological deposits and blast effects are described.

B. Sturtevant, H. Glicken, L. Hill, A. V. Anilkumar

Shock wave structure, propagation and interaction


Vorticity produced by shock wave diffraction

Numerical simulations with a monotonicity preserving flow solver have been performed to study shock diffraction phenomena and shock wave generated vorticity. The computations were performed using the conservative Finite Element Method-Flux Corrected Transport (FEM-FCT) scheme, which has been shown to have an excellent predictive capability for various compressible flows with both strong and weak shocks. Adaptive unstructured methodology based on adapting to high density and entropy gradients was used in conjunction with a conservative shock-capturing scheme to adequately resolve storng and weak flowfield gradients. The chief interest was therefore, a topic of vortices (original paper:the formation of vorticity) arising from shock wave propagation over a sharp corner and the high accuracy and resolution of the interacting compressible wave features. Numerical simulations were compared with previous experimental results and exhibited remarkably good agreement in terms of compressible wave propagation, as well as vorticity development and transport. The computations also allowed insight to the fundamental fluid dynamics, spencifically shock diffraction, vortex convection and shock-vortex interactions.

S. Sivier, J. Baum, E. Loth, R. Löhner

Simulation of shock and vortex interactions

Numerical simulations of the interaction of a shock with either a single vortex or a vortex pair are used to investigate the resulting shock structure and the production of acoustic waves. The results include the interaction of a shock (M=1.5) with a strong vortex which has a peak velocity equal to the velocity of the fluid behind the shock. The simulations show that at early times, the distortion of a shock by a strong vortex can be predicted using a simple linear model. In addition, a quadrupolar wave propagates upstream as predicted by linearized theories. At later times, the interaction of the diffracted and refracted portions of the shock produces connected reflected shock structures. For the strong shock, the reflected shock structure merges with the quadrupolar wave to produce the asymmetric acoustic wave observed in experiment.

J. L. Ellzey, J. M. Picone, E. S. Oran

Shock interactions with a dense-gas wall layer

Described here are experiments and calculations of the interaction of a planar shock with a dense-gas layer located on the floor of the shock tube test section. The shock front deposited vorticity in the layer by the baroclinic mechanism. The wall shear layer was unstable and rapidly evolved into a turbulent boundary layer with a wide spectrum of mixing scales. Density effects dominated the dynamics in the wall region.

A. L. Kuhl, H. Reichenbach, R. E. Ferguson

Formation of shock waves in transient base flow

The formation of shock waves behind a symmetrical body was studied in a shock tube. Three models of different afterbody shape were examined: a step, flare and boattail. The initial pressure ratio was set to 200 and optical measurements were made. It is shown that in all cases the reflected shock merges with the secondary shock and develops into the recompression shock. However, in the intermediate stage the recompression shock is unstable and asymmetric with respect to the centerline.

N. Saida, Y. Hashiba, T. Ozeki

Nonstationary interaction of strongly radiating ionizing shock wave with a thermal layer

The computation study was made of a propagation of strongly radiating and ionizing shock wave in a plane channel. The heating of the channel walls and the adjacent gas by the precursor radiation is included. This heating leads to transverse stratification of the media ahead of shock and results to emergence of γ-condition on the wave front. The nonstationary flow fields were found and the local and integral radiation characteristics of shock heated gas were calculated, which agreed with experimental data.

S. I. Bochkarev, A. Kh. Mnatsakanyan, V. E. Pasternak, M. B. Zhelezniak

Interaction of blast waves from a pair of exploding wires

This paper reports the results of our experiments on the interaction of a pair of cylindrical blast waves in air, which were generated by exploding wires. The interaction process for the head on collision of the blast waves was investigated. The experimental data includes schlieren photographs of the wave interactions, their radii, shock Mach number, and pressure, versus time, as well as various cross plots and data on the shock regular/irregular interaction transition condition.

F. Higashino, L. F. Henderson, F. Shimizu

High pressure treatment of iron by conically converging shock waves in a cylindrical capsule

A capsule, consisting of an inner iron rod as a sample and an outer 2024 aluminum alloy cylinder, was shock-treated. An iron flyer plate, 3.2 mm thick, was impinged on the capsules at an impact velocity of 2.2 km/s. The shock velocity in the cylinder is higher than that in the rod. This led to the formation of a Mach disk. The recovered sample was examined with an optical microscope. It was found that the grain size of the recovered sample is much smaller than that of a starting one. This means that the phase transition was induced by the propagation of shock waves. The recovered rod consisted of several regions, characterized by the respective metallographic features. These microstructures reflect shock compression history in the iron rod. In the cylindrical capsule, it was concluded that shock waves converge and interact to form the Mach disk in the iron rod.

K. Dan, H. Tamura, H. Kunishige, A. B. Sawaoka, T. Mori

Dynamics and structure of pressure jumps in non-Riemann gas dynamics

The paper considers the problem of pressure wave generation in a gap of two co-axial tubes under the effect of shock wave propagating in the central tube filled in, particularly, with gas. The existence of “transonic situation” is revealed when the shock wave can overtake the pressure jump generated by it in a gap, i.e. run away from it. The result of such overtaking is the jump “break”. Such situation can never take place in Riemann gas dynamics.

L. P. Smirnova, I. R. Shreiber

Discrepancies between theory and experiment for shock reflection

It was discovered that by using redesigned experimental models some discrepancies between theory and experiment found by previous investigators for strong pseudo-stationary flow could be eliminated. Also the von Neumann paradox for strong shocks could be adequately resolved by comparison with BGK code numerical computations of the experiments.

R. J. Virgona, L. F. Henderson, H. Honma, D. Q. Xu

Shock wave loading on a rubber rod: Experimental investigation

The head on collision of a planar shock wave with a rubber rod was investigated both analytically and experimentally. In view of the experimental limitations the agreement between the theory and experiments could be considered as good.

G. Ben-Dor, O. Igra, M. Mond, G. Mozor, H. Reichenbach

Shock wave attenuation in channels with perforated walls

An approximate analytical solution is presented of the problem on planar shock wave attenuation in channels with perforated walls. It is found on the basis of comparison between the theoretical results and available experimental data that the solution predicts satisfactory the rate of shock wave attenuation within the range of initial shock Mach numbers between 1.3 and 4 and perforation ratios between 0.07 and 0.53.

S. M. Frolov, B. E. Gelfand

Oscillations of circular shock waves with upstream disturbance

Both the oscillation state and mode of the disturbed circular shock waves by upstream nonuniformity of the velocity were investigated experimentally. Steady wake behind circular cylinders which were set up at the entrance of the nozzle. The free and forced oscillations of the shock wave mainly consist of mode 0 including other weak modes, which shows the strong influence of the wake of the upstream cylinder. The wake separates the circular shock wave into some pieces and makes their oscillation independent from each other. The resonance of forced oscillation is also weaker, and the shock wave is more stable than in the case without upstream disturbances.

M. K. Park, S. Oshima, R. Yamane

Three dimensional flow structure behind a shock wave discharged from a rectangular cross section shock tube

The structure and behavior of the vortex ring and the secondary shock wave generated behind a shock wave discharged from an open ended rectangular cross section shock tube were investigated experimentally and numerically. For the visualization, double exposure diffuse holographic interferometry was introduced to this phenomenon in addition to double exposure holographic interferometry which had been used previously. For the numerical simulation the TVD finite difference scheme was used. These results indicated that the vortex ring structure which was generated from the shock tube exit was distorted and the secondary shock wave was a complex three dimensional shape.

A. Abe, M. Watanabe, K. Suzuki

A code-based study of the pseudo-steady shock reflection process

Numerical calculations of the shock wave reflection at plane inclined walls (wedges) were performed applying the Code SHARC. The parametrical study made for incident shock Mach numbers of 1.37 and 2.55 covered a wedge angle range from 40° to 57°. The aim of the present paper is to compare experimentally determined reflection factors with numerical data as well as with predictions of the von Neumann theory. The numerical data confirm the experimental ones; the theory does it partially. Analyzing the numerically obtained spatial distribution of the pressure close to the wedge surface and for wedge angles near the transition angles indications for transition from regular (RR) to irregular reflection (IR) could be found.

W. Heilig, A. van Netten

Shock wave reflection, diffraction, refraction and focusing


Single-Mach and double-Mach reflection — its representation in Ernst Mach’s historical soot method

In 1875 Ernst Mach discovered the effect of irregular interaction of shock waves, the so-called single Mach reflection (SMR), which for symmetric geometry is characterized by two triple points. He recorded their two trajectories on a soot-covered glass plate. Appearing as two mirror-symmetric V-brancries, they form the well-known Mach soot funnel. Combining this soot method with the schlieren technique facilitates the interpretation of soot-recorded interaction phenomena as well as allows to resolve the soot removal mechanism in time. Increasing the dynamic recording range of the soot layer in terms of reflected shock pressures even renders visualization of double-Mach reflection (DMR) which, in the case of symmetric shock interaction, is characterized by a second concentric, external 0“double-Mach funnel”. At transition of DMR=> SMR it merges into the ordinary “single-Mach funnel”.

P. Krehl

Observations of the initial stages of the Mach reflection process

The initial stages of single, complex and double Mach reflection of incident shocks with Mach numbers of approximately 1.38 and 2.65 have been observed on wedges with angles ranging from 23° to 48°. At the smaller wedge angles no delay in the initiation of Mach reflection could be observed, to within ± 200 mean free paths of the ambient gas (γ). At larger wedge angles close to those for transition between regular and Mach reflection, both single and double Mach reflection were delayed by distances in the order of 10,000 γ. In the case of double Mach reflection, the reflection appeared to pass in sequence from regular to single, to complex and finally to double Mach reflection. Beyond distances in the order of 100,000 γ, the Mach reflections had become self similar and the trajectories of the triple points intersected the leading edge of the wedge.

J. M. Dewey, A. A. van Netten

Repeated Mach reflections in curved converging contractions

Plane shock waves moving into area contractions undergo a complex series of reinforcing reflection processes. For ‘gradual’ contractions, these will be predominantly Mach reflections. Commonly, contractions may be either two-dimensional or axisymmetric. Considerable experimental and theoretical work is available on the Mach reflection processes for the former but little for the latter, this to a large extent being due to the formidable experimental problems associated with internal axisymmetric flow visualization. However, with either, the general case of a contraction having inward curving walls has additional complexities associated with it due to the interaction of the reflected waves with re-reflections from the opposing wall or centerline. In order to obtain a rapid assessment of the reflection pattern, a simple method has been developed here using the ray-shock theory. Computations can be carried out on microcomputers. Comparison with experiment in the two-dimensional case shows excellent agreement. A computational result is available for axisymmetry but this needs further experimental work for verification and further theoretical development.

R. D. Archer, B. E. Milton

Unsteady behavior of Mach reflection over a particulate layer

Abstract Results of oblique shock reflection over a particulate layer are reported. A variable parameter was the reflecting wedge angle. Other parameters such as an incident shock Mach number and a mean diameter of particles deposited on the wedge were fixed at 1.41 and 30mm, respectively. The wave structure is compared with that for a two-dimensional rough surface model, and their qualitative resemblance reveals that, although the structure is more complicated than the two-dimensional case, the physical phenomenon which plays an essential part (sink effect) is the same in both cases. It is clearly ascertained that the behavior of the triple point is unsteady and self-similarity of wave structure no longer holds.

S. Kobayashi, T. Adachi, T. Suzuki

Shock diffraction over a flat plate

As part of the development of a new second-order hydrodynamic computer code, a series of calculations was run to check out the behavior of the differencing scheme in a variety of environments. The calculation reported here is the diffraction phase of a Mach 1.7 square shock wave interacting with a flat plate 7cm thick by 28cm in length. Forces on the plate are calculated and an inviscid drag coefficient is determined and compared with wind tunnel data. Comparisons are made with photographic data from a one-tenth scale shock tube experiment.

C. E. Needham, D. F. Dawson, J. E. Crepeau

Three-dimensional diffraction of shock wave

This paper describes an experimental and numerical study of the shock wave diffraction at the exit of axisymmetric and square cross-sectional channels. The flow was visualized by a shadowgraph and a laser interferometer with a narrow reference beam. The intesity of the shock wave diffracted backwards was measured by means of piezoelectric presssure transducers. In the axisymmetrical case the diffracted wave moves more slowly than that one in the plane case, and its intensity falls faster. It was revealed that different propagation velocities of the diffracted shock wave at the exit of the square cross-sectional channel results in a 45 degree turn of the picture of the normal view of the 3-dimensional shock diffraction.

S. B. Bazarov, T. V. Bazhenova, O. V. Bulat, V. V. Golub, A. M. Shulmeister

Diffraction of weak shock waves by barriers

The diffraction of weak shock waves (M <1.2) around a wall is studied in experiments with scale models. Measurements were performed for a model of a screen and a dike-shaped wall. The flow field around the models was visualized with a shearing interferometer; the pressure was also measured with piezo-resistive transducers. The experimental pressure distribution is compared with calculations based on the linear-acoustic formalism of Oberhettinger. The theory gives a good description of the diffraction phase, but shows strong deviations after the reflection of the diffracted shock on the floor. Therefore, the linear-acoustic theory can not be used to calculate the attenuation of shock waves by a wall.

E. A. Bakkum, J. Weerheijm, H. J. Pasman

Bifurcation of a reflected shock wave in a shock tube

The problem of shock bifurcation observed for a reflected shock interacting with a boundary layer is investigated both experimentally and numerically. The process has been visualized by means of color schlieren photographs that clearly show the characteristic wave pattern. Accompanying pressure measurements hint at the three-dimensional character of the wave system. In a numerical scheme based on the Euler equations the problem has been simulated giving good agreement between the calculated and the observed wave configuration.

H. Kleine, V. N. Lyakhov, L. G. Gvozdeva, H. Grönig

Nonstationary reflection of dispersed waves in carbon dioxide

Experimental and numerical results of weak oblique shock reflections from ramp surfaces are given in carbon dioxide. The results are shown for several combinations of the shock Mach number M s and ramp angle θ :M s , θ) = (1.027, 30°), (1.027, 20°), (1.047, 10°), (1.070, 20°) and (1.133, 30°). The maximum density just behind the stem shock increases with distance as the wave proceeds along the ramp surface, and approaches a finite value far downstream. This nonstationary phenomenon is attributed to the finite thickness of dispersed shock waves. The relaxation distance of the maximum density is defined from its exponential behaviour and found to depend mainly on the ramp angle rather than the incident shock Mach number.

H. Honma, M. Itabashi, H. Maekawa, T. Usui

The propagation and stability of converging cylindrical shocks in narrow cylindrical chambers

A theoretical and experimental analysis of boundary layer effects on the propagation law of converging cylindrical shock waves in narrow cylindrical chambers is presented. Experimentally, the pressure attenuations due to the boundary layers were isolated from those due to area contraction by splitting the converging shock into two sections. The pressure variations were determined by means of miniature pressure transducers placed at different locations along the converging shock path. The tests were carried out for cylindrical chamber widths of 2.5, 1.3, 0.6 and 0.33 mm and for converging shock Mach numbers of 1.57 and 2. Flow visualization near the geometric center was obtained by means of spark schlieren and shadowgraph systems. For the 0.6 mm gap, the results show that the exponent n in the relation M = CR-n varies from the value of 0.215 for the largest gap (2.5mm) used, to 0.185 due to boundary layers and eventually to 0.165 due to both boundary layers and area contraction. The results also show that just before collapse, the shock becomes elliptic in shape which leads to the formation of two pairs of vortices propagating in a direction perpendicular to the major axis of the converging shock.

R. A. Neemeh

The enhancement of shock wave loads by means of porous media

The enhancement of shock wave loads on the end-wall of a shock tube owing to its coating by a porous medium was investigated numerically. The results indicate that the pressure acting on the shock tube end-wall can be amplified significantly.

G. Ben-Dor, G. Mazor, G. Cederbaum, O. Igra, S. Sorek

Anomalous refraction of shock waves

We present the results of our numerical work on anomalous shock refraction at air/C02 and air/SF6 interfaces. The numerical method was a second-order multi-fluid Godunov code. The results indicate that anomalous refraction is not one phenomena but a group of them, and their natures depend on whether the wave impedance increases or decreases during refraction.

L. F. Henderson, E. G. Puckett, P. Colella

Control of pressure distribution in shock generators with elliptic and parabolic cross-sections

Theoretical investigation of liquid shock generating devices with elliptically and parabolically shaped chambers is presented. A device of such kind with an elliptic geometry has been previously fabricated and tested experimentally. Experimental observations confirmed the results of earlier theoretical analysis of the problem, showing that shock waves produced by an electric discharge at one of the foci of the elliptic chamber will converge at the second focus after the reflection from the cavity wall. In the present paper a previous two-dimensional model is extended to account for the height variation in the chamber. Expression for the pressure distribution behind the converging wave front is obtained and a relation between the shape of the upper bounding surface of the chamber and pressure distribution behind the converging wave front is investigated. It is shown that a desired pressure distribution may be obtained by an appropriate choice of the upper surface of the chamber.

N. Apazidis

Formation of the shock reflection on a wedge

The formation of shock reflection close to the leading edge of a wedge is investigated. Varying the wedge angle, a regular reflection or a Mach reflection can be obtained. To get a good resolution of the reflection process, measurements are performed under rarefied gas conditons. The observed flow field is definitely unsteady. The measuring method and the data reduction have to satisfy these requirements. The results are represented by the density distribution in the flow field at different time steps.

J. Fuchs, B. Schmidt

Shock dynamic description of reflected shock waves

An application of the shock dynamic equations for a moving gas to regular reflection over a wedge is made. First of all, a description of the formation of reflected shock in RR and the corresponding relations are presented. Secondly, a comparison is made between sound theory and shock dynamics for moving gas, the behaviour of the first disturbance point propagating on the reflected shock, and the corresponding transition criteria. Thirdly, an improved relation is given for the disturbance propagating on a reflected shock, which is a simple, useful way for us to calculate the reflected shock.

Z.-Y. Han

A method to reduce the pressure wave intensity caused by a shock wave radiated from a duct

Modern trains, such as the Shinkansen (Superexpress train in Japan) or TGV (France), pass through long tunnels at such high speed that a pressure or weak shock wave generated by the nose of a train causes a huge booming sound at the exit of the tunnel. The intensity of the noise increases with the speed of train and with the length of the tunnel. This noise is becoming to be one of the bottlenecks to increase the capacity of transportation. This report deals with a method to control a shock wave traveling in a rectangular duct to simulate a tunnel. A density gradient decreasing from the bottom wall of the tunnel toward the top, is created in the gas just before the exit of the duct so that the direction of shock wave propagation will be bent toward the bottom where the density is the highest. The behavior of the pressure wave is investigated by both computer simulation and experiments using a model duct, and a simple method is tried for absorbing the higher pressure wave at the bottom surface of the model duct.

K. Wakai, K. Yamada, S. Shimizu, T. Matsukawa

Rayleigh-Taylor instability generated by rarefaction waves: Comparison with Richtmyer-Meshkov instability

Acceleration induced by rarefaction waves can destabilize a contact surface between fluids of different dinsity. This instability causes irregularities on the contact surface to grow. The growth can persist long after the rarefaction wave has passed, leading to significant enhancement of mixing. This rarefaction-driven Rayleigh-Taylor instability is studied numerically and compared with the analogous Richtmyer-Meshkov instability.

C. Li, D. L. Book

Experimental investigation of Richtmyer-Meshkov turbulent mixing in shock tube

The experimental investigation of the turbulent mixing induced by the Richtmyer-Meshkov instability has been undertaken in a shock tube. Results show that the turbulent mixing zone thickness evolution seems to obey a tα -power law where the average value of a is 0.45 for an incident shock Mach number Ms,i about 4; 0.65 for Ms,i ≈ 2; and 0.85 for Ms,i≈1.3. As previously pointed out, we confirm that effect of boundary layers is a decrease of the growth rate of the turbulent mixing zone thickness.

L. Houas, I. Chemouni, A. Touat

Richtmyer-Meshkov instability of shocked gaseous interfaces

The instability of shocked and reshocked perturbed interface between gases of different densities is analyzed by comparing flow visualization from 2-D and 3-D shock tube experiments with 2-D numerical simulations and theory. The shadowgraphs and calculations show similar large scales of mixing by fluid interpenetration induced by the Richtmyer-Meshkhov instability. In 2-D, experimental instability growth following acceleration by the initial shock is less than calculated by linear theory or simulated. The 3-D experiments are approximately simulated by 2-D calculations with an increased initial amplitude of the interface. The kinetic energy of the interpenetrating velocity field from the simulations are also compared to a theoretical estimate derived from the linear theory.

R. F. Benjamin, D. Besnard, J.-F. Haas

X-ray densitometry of shock-excited Richtmyer-Meshkov instability at an air-xenon interface

Experiments were performed in a vertical, square shock tube to study the development of the Richtmyer-Meshkov instability excited by the interaction of a shock wave with an air/xenon interface. The objective is to measure the mixing that occurs at the interface due to the instability. New flow visualization and densitometry techniques based on X-ray absorption by the xenon have been developed. Continuous interfaces between the gases are prepared by initially separating the gases with a metal plate which is retracted out of the tube prior to the release of the shock wave. Depending on the time elapsed between the end of plate retraction and shock arrival, the interface can be either quasisinusoidally or randomly perturbed. An X-ray 50 ns long flash is projected through the flow and a 20 × 25 cm X-ray negative is exposed at each run. The negatives are digitized and mean xenon-density profiles across the interfaces are generated by image processing methods developed specially for this purpose. The amplitude of the perturbations, the thickness of the diffuse interfaces and the growth rates of these two quantities are measured from the density profiles.

R. Bonazza, B. Sturtevant

Shock dynamics method for focusing of reflected blast waves

The nonlinear focusing of a cylindrical blast wave reflected from a solid concave wall is investigated numerically by a modified CCW method. The results are compared with experimental data from exploding wire experiments and with numerical simulations obtained by a finite difference PLM scheme (Higashino et al. 1987). The agreement of the present method with the PLM results as well as with the measurement is satisfactory, however, the CPU time is 90% less than that required for the PLM simulation.

R. Holl, F. Higashino, I. Sakamoto

Focusing of shock waves reflected from an axisymmetrically parabolic wall

Computational and experimental studies of shock wave reflection from an axisymmetrically parabolic wall were conducted. The numerical results showed that a high temperature region was achieved by the reflection. In order to verify the results of the numerical calculations, experiments were carried out in a shock tube with argon as the test gas at an incident shock Mach number of 3. The emission intensity profiles were measured to confirm the existence of high temperature region. Measured emission showed the existence of strong radiation at the time and location which were predicted by numerical results. The measured pressure profiles at the side wall of the shock tube almost agreed with numerical results. The experimental results supported the numerical predictions of the existence of a high temperature region.

H. Kishige, K. Teshima, M. Nishida

Experimental and numerical studies of blast wave focusing in water

An aspect of blast wave focusing in water is observed in detail by the schlieren method and the whole process from generation to focusing of the wave is clarified. In the next place are a numerical simulation is performed regarding the two-dimensional focusing of blast waves generated by a spark discharge or a wire explosion in water. Numerical results are shown as bird’s eye views of pressure distribution and computer schlieren diagrams. These diagrams are found to correspond to Schlieren pictures obtained optically.

K. Isuzugawa, M. Horiuchi

The possibility of shock wave focusing to a pre-set space region with the elements of diffraction quasioptics

The results of a numerical experiment on the focusing of a plane shock wave into a “ring” by elements of diffraction quasioptics “transfered” from electromagnetic applications to fluid mechanics are presented. The possibility of nonlinear shock focusing with such elements to an arbitrary space region is shown where the acoustic approximation does not apply.

V. F. Minin, I. V. Minin, O. V. Minin

Irregular interaction of two shock waves

A primary study was made of an irregular shock-on-shock interaction problem. The elementary theory of five-shock collision system was formulated. The interaction of planar shock with a supersonic blunt body was numerically computed.

V. P. Goloviznin, I. V. Krasovskaya

Turbulent mixing induced by Richtmyer-Meshkov instability

Turbulent mixing development, induced by shock wave passage through the interface, has been studied on the basis of two semi-empirical models. The process of transition from randam initial perturbations to turbulence is a rather complicated one, but proceeds in a finite time. Here it is assumed that the shock wave passage through the initial zone of “roughness” leads to the instantaneous development of mixing. An expression for the turbulent kinetic energy, transfered by shock wave, has been derived. The value of this energy is determined by a non-dimensional parameter which is equivalent to the Richardson number. The analytical solution describing the turbulent kinetic energy decay and the change of mixing zone width in time has been obtained. The analytical form of the solutions allows to compare the models with the existing experimental results. Comparison of the theoretical results with Zaitzev’s experimental data is given for the impulsive acceleration.

V. Ye. Neuvazhayev

Study of the second type instability of shock heated Xe-plasma in the flow behind shock front

The rate of development of the second type instability in shock heated Xe-plasma (M = 10∼16) as a function of shock strength gas pressure, and microimpurity content of molecular gases was determined. The evolution of flow relaxation region was recorded. It was shown that the ionization relaxation time as well as the maximum level of the plasma emission varies within wide limits at each cycle of instability development.

G. K. Tumakaev, Z. A. Stepanova, P. V. Grigoriev

Shock waves in condensed matter


Explosive shock synthesis of polycrystalline diamond powders

Research and development for manufacturing micro polycrystalline diamond powders by use of explosives has been carried out. At first, basic research was conducted by a plane shock compression method using a flyer plate. The sample material, which is a mixture of carbon and copper powders, was shock compressed at pressures of 30 to 60 GPa. Under the best conditon of shock pressure and temperature, the conversion yield from graphite to diamond amounted to more than 60%. Next, cylindrical compression methods have been developed in order to treat a large amount of smaple compared with the plane method. It was found that an increase of shock duration time, which needs a much larger size of explosive charge, gave a good conversion yield. An explosion chamber which has a firing capability of a 100 kg-explosive without any damage was constructed. Many tests with large charge shots have been conducted without any environmental problems.

S. Fujihara, K. Narita, Y. Saito, K. Tatsumoto, S. Fujiwara, M. Yoshida, K. Aoki, Y. Kakudate, S. Usuba, H. Yamawaki

Shock wave processes in porous elastoplastic materials

There exist a few different approaches for the description of shock propagation in porous media. These studies may be divided into three groups; layered models, homogeneous approximation, heterogeneous models. Each of these approaches has its advantages and disadvantages. In the present paper, a new mathematical model is proposed and applied to the problems of piston motion and the rebound of a porous striker from a rigid obstacle. Further, the explanation of the effect of “cold layer” formation by shock compaction of powders, and the separation of powders in the presence of weak shock waves is presented.

V. F. Fomin, S. P. Kiselev

Nonlinear wave propagation and shock wave formation in quasi-brittle materials

Fracture of quasi-brittle materials such as concrete, rocks by impact, ceramics and calculi is known to occur due to the formation and development of microcracks. Microcracks reduce the macroscopic value of Young’s modulus of the material and hence reduce the wave speed when the dynamic problem is considered. By applying the continuum model for microcracking, nonlinear wave propagation is analyzed numerically for an infinite plate made of granite. The plate is subjected to an impact compressive stress at one surface. Another surface of the plate is assumed to be stress free. It is shown that the process forming the shock wave progresses near the stress-free surface by the occurrence of microcracks according to the tensile strain caused by the wave reflection.

M. Saka, S. Ohba, H. Abe

X-ray diffraction line broadening Fourier analysis of a dynamic loaded metal matrix composite obtained by liquid infiltration

The crystallite size, the residual lattice strains, the components of Gaussian and Cauchy functions of the line profiles obtained by Fourier analysis of X-diffraction lines, are correlated for a better knowledge of mechanical properties of an ultra light weight metal matrix composite after high and low velocity impact loadings. An explosively accelerated flying plate compresses the samples with the same thickness but different impact areas. Two deformation directions are analyzed with respect to the main whisker orientation: one along the main alignment of the whiskers and the other perpendicular to it. The results are discussed taking into account the effects of the high velocity impact loadings on the dislocation generation and relocation mechanisms in different crystallographic directions.

C. Patuelli, M. Zaffagnini

Sub-nanosecond X-ray diffraction from laser-shocked crystals

We have used single-shot sub-nanosecond x-ray diffraction to directly measure lattice parameters of crystals during the passage of laser-driven shock waves. Changes in the interatomic spacings can be measured with a temporal resolution better than 50 ps. We have studied shock-launching in single crystals and have directly measured dynamic tension during shock-breakout from a rear surface. In separate experiments we have directly observed the onset of shock-induced plasticity by diffracting from planes running perpendicular to the shock front. In addition to the single crystal work we have recently demonstrated that we can record x-ray powder patterns with sub-nanosecond exposure times; and are now in a position to laser-shock polycrystalline material simultaneously with the x-ray flash. The technique promises to be useful in the study of many fundamental problems in shock wave physics, including the behaviour of materials at the lattice level during plastic deformation and shock-induced polymorphic phase transitions.

J. S. Wark, N. C. Woolsey, W. J. Blyth, R. R. Whitlock

Planetary fluids at high shock pressures and temperatures

High pressures and temperatures in the deep interiors of the giant planets are accessed in the laboratory by shock compression of liquid specimens using a two-stage light-gas gun. Measurements of properties of dense fluids comprising these planets are described and discussed.

W. J. Nellis, A. C. Mitchell, N. C. Holmes, P. C. McCandless

Shock metamorphism in artificial impact craters

Shock metamorphism has been investigated in artificial impact craters of gabbroic anorthositic and granitic target rocks. Shocked quartz grains with irregularly wavy extinction are found at crater walls and eject a, and show the largest values of density in the fine aggregates of eject a. When shock loaded by a steel projectile, a larger density of shocked quartz has been obtained in target rock of gabbroic anorthosite with smaller homogeneous grains, than in granite rock with larger irregular grains. There are two types of shocked quartz; 1) shocked quartz formed by direct transformation from high-pressure silica, and 2) fine shocked quartz crystallized by chemical change mainly from feldspar composition under the vapour condition of the impact event. The closed system of the experimental chamber produced easily shocked cristobalite high-temperature type silica, but no stishovite high-pressure type. Chemical change of feldspar composition can be proved also by the anomalous composition of low-KNa-Ca elements revealed by electron microprobe data. Shock pressures of shocked quartz are estimated by a regression equation for the density-deviation of shocked quartz from the Charlevoix impact structure.

Y. Miura, K. Takayama, T. Kato, N. Kawashima, A. Yamori

Computation of the collision of a large asteroid with the primordial earth

The results of calculations of the collision of a large asteroid with primordial Earth are presented. In these calculations primordial Earth is assumed to be a uniform sphere except that a radial variation of density is taken into account. Gravity is considered to be the only force keeping the planet intact. The asteroid is assumed to be a body of uniform density and with a certain incoming velocity. The so called “free particle method” was used for numerical solution of the problem. The shock wave position, area of total destruction, variation of the outer shape, distribution of surface velocity, variation of the pressures the shock front, acceleration of the surface elements, and surface uplift were all calculated for a few different energy levels.

K. Jach, P. Wolański

Computer studies of the dynamic strength of ceramics

Using a new constitutive model, computer studies were performed concerning the dynamic yield strength of six ceramics, SiC, TiB2, A1N, two types of B4C, and partially stabilized zirconia. The relative importance of the Bauschinger effect and the thermomechanical variables, strain, strain rate, pressure, and temperature is demonstrated in determining the time response of ceramics to high-strain-rate deformation. The constitutive model is easy to implement in a hydrodynamic computer code and successfully reproduces a variety of data for these materials.

D. J. Steinberg

Shock-induced conductivity waves at metal-metal, metal-semiconductor transitions and in high porous nickel foam

The electrical properties of metals show strong variations under shock wave action (metal-semiconductor, metal-metal and metal-vapor transitions). The thin foil method of conductivity measurement (Keeler 1974) is unavailable for materials with an internal structure (metallic foams, powders, conductive compacts etc.), because of the large time of the current relaxation in thick samples made of such materials. The essential point of measurements is the consideration of the transient electrodynamic processes in a sample. Conceptually this problem is very close to the analysis of the non-stationary electrodynamics of the shock-induced waves of the conductivity in initially unconducting materials (Bichenkov et al. 1989).

E. I. Bichenkov, S. D. Gilev, A. M. Trubachev

On the modeling of reactive shock synthesis of materials

High pressure shock wave processing is said to hold promise for synthesis of new materials or materials with unique microstructures. In this paper several key issues are reviewed that are critical in the numerical modeling of shock-induced chemical reactions in inorganic powder mixtures. A simple model that is thought to represent a variety of powder mixtures is illustrated using plane shock propagation in a mixture of diamond, Si, and graphite.

Y. Horie, M. Hwang, S. You

Surface phenomena of shock-loaded metallic samples

The evidence and the understanding of the predominant physical mechanisms which control the surface phenomena induced by shock wave reflection on a metallic sample free surface, require a comprehensive experimental approach. Optical shadowgraphy with a high speed framing camera associated with an electronic flash, 600 kV X-ray transmission analysis and the Laser Doppler Interferometry (LDI) thin foil method have been developed in our laboratory. Shock loading of samples has been carried out with a 60 mm in diameter powder gun providing a pressure range from 5 to 40 GPa or with explosive generators providing a pressure range between 40 GPa and 60 GPa. These experimental studies are mainly concerned by the matter ejection from the free surface and the bulk microspalling of the sample near the free surface. These two surface phenomena essentially depend on sample melting in release and also on other parameters such as the incident shock level, the nature and the thickness of the sample and the rugosity of the free surface.

P. Chapron, P. Elias

Hugoniot-measurement study of the stabilized zirconia single crystal

Hugoniot-measurement experiments of the Y2O3-doped (9.6 mol%) stabilized zirconia in the pressure range up to 120 GPa were performed by using single crystals to study cubic directly the yielding property, phase transition and their crystal-axis effects to shock propagation. The Hugoniot parameters were measured by means of the inclined-mirror method combined with a powder gun and a two-stage light gas gun in the impact velocity range of 1.2-3.6 km/s. The Hugoniot-elastic limits (HEL) parallel to (100) and (110) axes showed large difference. Above the HEL’s, the Hugoniot data parallel to (100) and (110) axes converged each other, and showed large relief to an isotropic compression state. In addition, this material transformed to the high pressure phase up to 70 GPa.

T. Mashimo, M. Kodama, K. Kusaba, K. Fukuoka, Y. Syono

Hugoniots of eight meteorites

Shock wave data have been obtained for the first time for the following meteorites (chondrites in particular): Wellman (H5), Gilgoin Station (H5), Gladstone (H6), Arapahoe (L5), Farmington (L5), Kunashak (L6), Bruderheim (L6) and Leedey (L6). Utilizing a single-stage powder gun, the experimental pressure range is from 0.8 to 28 GPa. Shock wave velocities in the specimens were measured by means of the electric pin-contactor method. The data for the shock wave velocity-particle velocity of chondrites are rather scattered due to the thinness of the specimen (≃ 2 mm). On the other hand, the data for the pressure(P)-particle velocity(u) of H and L chondrites are spread in bands of certain widths. For H chondrites:P = 21.2u, ΔP =1.5 GPa and for L chondrites:P = 17.8u, ΔP = 3.0 GPa where P and u are measured in GPa and km/s respectively and ΔP is the width of the band. The Hugoniots for the chondrites are calculated from the Hugoniots of the constituents. Discrepancy between the calculated and experimental data exists but good agreement is obtained when corrections are made for porosity.

K. Kani, Y. Matsushima, T. Matsui

Grüneisen equation of state for solids and solution of the Riemann problem

Equation of state for solids in terms of the specific internal energy, entropy, and specific volume has been discussed starting from the Grüneisen assumption. Thermal variables, like specific heat or temperature can be expressed by specific volume and entropy. The square of the acoustic impedance along an isentrope is expressed as a polynomial of a function X, which is the solution of the differential equation for isentropic pressure. In this case, the form of the Riemann integral has been obtained explicitly. The solution of the Riemann problem has been calculated for the case of aluminum.

K. Nagayama, T. Murakami

Shock wave codes at Sandia National Laboratories

Sandia National Laboratories is very active in developing multi-dimensional, multi-material shock wave physics codes. One example is the state-of-the-art, three-dimensional Eulerian code CTH which is used at numerous government and university sites. CTH is being ported to both Single Instruction Multiple Data (SIMD) and Multiple Instruction Multiple Data (MIMD) massively parallel computers. The next-generation arbitrary-Lagrangian-Eulerian code RHALE is under development. This paper will discuss these codes. CTH is an Eulerian code for modelling multi-dimensional, multi-material, large deformation, strong shock physics. Finite-volume numerical schemes are used with one-dimensional, two-dimensional and three-dimensional meshes. CTH has models for elastic-plastic materials, porous materials, high explosive detonation, fracture, and energy deposition. Several analytic equations of state are available including ideal gasses, Jones-Wilkins-Lee high explosive reaction products, Mie-Griineisen solids, and sophisticated multi-phase models that are valid for a very broad range of densities and temperatures. Tabular equations of state are also available. Second-order accurate advection schemes are used to minimize the dispersion found in Eulerian codes. Very large three-dimensional calculations may be run efficiently on a CRAY supercomputer because the code is highly vectorized and the data bases reside on the Solid State Disk (SSD). Data bases larger than one hundred million words are commonly used. Sophisticated color post-processing software was developed to aid in interpreting the results. Much of CTH has been ported to both SIMD and MIMD massively parallel computers. The two-dimensional version is running three times faster than a single CPU CRAY/YMP on the 16k node SIMD Connection Machine and five times faster on the 1024 node nCUBE2 MIMD computer. Both of the massively parallel computers can be expanded by a factor of four to eight yielding a system an order of magnitude faster than a CRAY. The next-generation, three-dimensional arbitrary-Lagrangian-Eulerian code RHALE is under development. Finite element techniques are used to integrate the physics through time. The mesh will move with the material (Lagrangian mesh) until the distortion becomes excessive and then the nodes are automatically repositioned to smooth the mesh and improve the accuracy (Eulerian mesh). Node motion occurs only where the distortion is excessive. This results in a code with the best features of both Lagrangian and Eulerian codes. Arbitrary-connectivity meshes are used to generate very complicated and sophisticated meshes. However, this dramatically increases the complexity of the Eulerian algorithms.

J. M. McGlaun

Explosive powder compaction with a water pressure medium

Shock pressures of 10 to 20 GPa were obtained by utilizing underwater-shock waves generated by explosive detonation in a new assembly which was developed for the compaction of difficult-to-consolidate powders. The advantage of this assembly was the ease of the convergence, reflection and focusing of the underwater-shock wave. Simplicity and economy were also advantages over other shock compaction techniques. Crack-free compacts of silicon nitride (Si3N4) powders with 98% or more of relative density were produced without additives by the assembly. It is concluded that this process is effective for producing high density compacts of difficult-to-consolidate powders. However, the hardness of as-compacted Si3N4 was about 150 Hv. The mechanical properties of the compacts were improved by post sintering treatment. The average hardness and fracture toughness values of the specimen sintered at 1973 K were 3000 Hv and 4.0 MPam1/2, respectively. Microstructural aspects of the resulting compact are also described.

A. Chiba, R. Tomoshige, M. Nishida, K. Imamura, M. Fujita

Equation of state of H2O under ultra-high pressure

The equation of state (EOS) and metallization of ice in a recently proposed ultra-high-pressure phase (anti-fluorite structure) have been studied from first principles by using the local-density approximation. The calculated EOS is in good agreement with the quantum statistical model above 0.7 TPa. It is shown that a pressure-induced insulator-metal transition takes place at P=1.76 TPa with V=2.50 cm3/mol. The metallization pressure is 2.5 times higher than that estimated by the classical Herzfeld theory and it is much higher than the pressures at the core-ice layer boundary of Uranus and Neptune.

J. Hama, K. Suito

Shock waves in dusty gases and multiphase media


Condensation and evaporation relaxation induced by non-linear waves

New 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 quasi-steady wet-bulb model for phase transition by Gyarmathy(1982). During expansion, droplet number density decays much faster than predicted, which is attributed to the growth of a thermal boundary layer. Shock induced droplet evaporation is studied for post-shock saturation ratios ranging from 5.10-3 to 0.2. Again the characteristic droplet evaporation time is well described by Gyarmathy’s model.

H. J. Smolders, C. J. G. M. de Kok, M. E. H. van Dongen

Propagation of a reactive wave in a bubbly liquid

Experiments have been performed to elucidate on the structure of self-sustained reactive waves (SSRW) in bubbly liquids. The initial bubble dimension does not affect the wave velocity, but it changes its structure. This seems to suggest that although the wave structure is dependent on bubble dynamics, its velocity is governed by averaged fluid properties. The existence or not, of a fundamental length scale (such as critical tube diameter) could not be resolved in the present study. As such, these waves have nothing in common with classical CJ detonations in a reactive gas, whose speed is driven by equilibrium thermodynamics only. The SSRW is governed by the nonequilibrium dynamics of bubbly liquids.

T. Scarinci, X. Bassin, J. H. S. Lee, D. L. Frost

Comparative measurements of film condensation on the side and end walls of a shock tube

The non-equilibrium process of film condensation of a superheated gas on the walls of a shock tube behind a shock wave is investigated experimentally. The supersaturation of condensable gas relative to the wall temperature is the driving force for the condensation. The main goal of the investigation is the measurement of film thicknesses on the end wall as well as on the side wall of a shock tube as a function of the supersaturation and of the mole fraction of non-condensable gas. The thicknesses of the films formed by condensed vapour on walls of a shock tube are detected interferometrically.

T. Teske, F. Obermeier

Shock tube study of the drag coefficient of a sphere in a nonstationary flow

A shock tube facility was used for inducing relatively high acceleration on small spheres laid on the shock tube floor. The acceleration resulted from the drag force imposed by the post shock wave flow. Using double exposure holography, the sphere trajectory could be constructed accurately. Based upon such trajectories, the sphere drag coefficient was evaluated for a relatively wide range of Reynolds numbers (6000≤ Re ≤ 101000). It was found that the value obtained for the sphere drag coefficient were significantly larger than those obtained in a similar steady flow case.

O. Igra, K. Takayama

Shock interaction with a dust layer

Results of a shock tube study of unsteady particle laden flows developing just behind shock propagating over a dust layer are presented in this paper. Laser light extinction method is employed for measurement of dust mass concentration behind the moving shock front. For two shock Mach numbers 1.92 and 2.48 for which measurements are performed, it is found that duct concentration at different heights from the shock tube floor for different times from arrival of the shock can be expressed in form of an exponential law.

P. Manjunath, J. Kurian

Shock compression of a polyvinylchloride based elastomer and polyvinylchloride

Shock compression of a polyvinychloride based elastomer, commercially known as Isodamp, to 7.8 GPa, shows evidence for an onset of glass transition around 3.5 GPa. The values of pressure derivatives of bulk modulus of Isodamp below and above the transition pressure are 9.36 and 2.21, respectively.

D. P. Dandekar

Gas dynamic and physical behaviour of compressible porous foams struck by a weak shock wave

A detailed set of experiments has been conducted on the interaction of a Mach 1.4 shock wave with porous compressible foams of densities 32.5 and 35 kg/m3. It is shown that the velocity of the front face of the foam is approximately the same as the gas velocity behind the first reflected wave (55 m/s). A well defined wave propagating through the skeleton material at some 90 m/s is detected, whereas the leading edge of the gas disturbance moves at approximately 200 m/s. It is concluded that the frequently made assumption that the foam/air combination behaves as a homogeneous material is innapropriate, in that the existence of two distinct waves is established. The wave in the gas within the foam becomes less steep with time, as noted by other workers, and is consistent with a pressure drop resulting from the gas been forced through the foam skeleton. Furthermore it is shown that a contact surface emerges from the foam as it approaches the position of maximum compression, in contrast to the usual assumption that there is no flow across the interface. The motion of this surface follows that of the gas in front of the foam. A wave diagram is presented consistent with the above results.

B. W. Skews, M. D. Atkins, M. W. Seitz

Three-dimensional effects in the study of shock wave loading of porous compressible foams

Three-dimensional effects during the loading and relaxing phases of a compressible porous foam have been qualitatively examined. The physical collapse of the foam skeleton was visualized using high speed photographs. The photographs clearly show the effects of wall friction drag and the effects of a wall gap. The front foam face profiles, being concave during the compression and convex during the relaxation phase, show the limitations of schlieren photography (silhouette view of the foam). The three-dimensional gas flow field adjacent to the foam front face was visualized using both schlieren photography and a fine tracer powder. Using these techniques, edge leakage at the foam front edges and a contact front that emerges from the centre of the foam were identified. All the findings show that the one-dimensional assumptions used to analyze test results may need revision.

M. W. Seitz, B. W. Skews

Numerical investigation of dusty gas shock wave propagation along a variable cross-section channel

The propagation of dusty gas shock waves in a variable cross section channel is investigated. In this paper, the two-continuum model and one-dimensional approximation are employed for the unsteady flow problem of dilute gas-particle suspensions. The governing equations of two-phase flows are numerically solved by a GRP scheme. Using this finite difference method, the pressure history behind the shock front and the profiles of density, temperature and velocity for the gas and particle phases are calculated. The behavior of dusty gas shock waves propagating along divergent and convergent tubes are given. The effects of dust particles on the shock wave propagation are discussed in detail.

B. Y. Wang, Q. S. Wu

Gun propellant break-up effects on transient combustion processes

A two-dimensional interior ballistics computer code has been developed to solve the viscous two-phase flow in a combustion chamber of a gun tube during the ignition phase beginning with primer discharge and ending with projectile motion. The motivations are to achieve a better understanding of the physical processes occuring during this phase and to predict overpressures which can occur under certain ignition conditions and configurations of loading. Calculations are presented for axisymmetric two-phase flow in a model combustion chamber assuming grain fracture or not. Predicted results indicate that grain fracture due to high compaction may generate substantial local pressure peaks along the combustion chamber. In extreme cases of severe grain fracture, the result is a catastrophic overpressure which can explain structural gun-damage and spontaneous deflagration-to-detonation transition.

B. Porterie, J. C. Loraud, M. Larini, R. Saurel

Wave dynamics of bubbly liquids mathematical models and numerical simulation

Propagation of pressure waves in a bubbly liquid is investigated numerically taking into account the internal phenomena inside the bubble. Governing equations for the bubbly liquid are formulated with emphasis on the radial and transverse motion and volumetric change, is developed. Numerical results under several conditions reveal that the radial motion of the bubbles, which is affected by the internal phenomena, such as thermal conduction through the bubble wall, have significant influence on the relaxation phenomena behind the shock wave and also behind the rarefaction wave in the bubbly liquid.

Y. Matsumoto, M. Kameda, F. Takemura, H. Ohashi, A. Ivandaev

Convergence of pressure wave in a liquid

Convergence of an impulsive pressure wave in a liquid is investigated numerically. The pressure wave is generated by an impulsive movement of a spherical daiphragm. In this simulation, propagation of very short pulse wave (wave length of about 6 mm) is calculated almost without damping by using high-order accurate finite different schemes and the result reveals that the pressure wave converges at the focal point, and the expansion wave generated from the edge of the diaphragm produces a negative pressure region following the compression wave.

F. Takemura, Y. Matsumoto, H. Ohashi

Shock wave reflection in a gas-vapor mixture with condensation

The experimental investigation on Mach reflection of shock waves propagating through a fog was carried out. The fog was generated by the adiabatic expansion of a water vapor and air mixture by using a double diaphragm type of shock tube. Growth of the droplets was measured by an optical method based on Mie scattering. Mach reflection from an inclined flat surface was observed by means of shadowgraph method. As a light source, a nano pulse light was used. The results obtained by the scattering measurements show that a relaxation region was formed behind the shock front. Shadowgraphs of Mach reflection have been obtained when the inclination angle of the flat surface was 20 degrees and the initial relative humidity of the mixture was changed from 50% to 90%.

H. Hirahara, M. Kawahashi

Enhanced mixing from shock-generated turbulence in dusty air

Rapid, localized deposition of energy in air accompanies the propagation of laser beams, lightening bolts, and charged-particle beams. Unless the beam and the ionized channel in which it propagates are perfectly symmetric, uniform, and coaxial, there is misalignment between pressure gradients generated by the shocks associated with the energy deposition and the density gradients induced by the rapid expansion of the heated beam channel. This results in persistent vorticity rapidly cascading into turbulence. This shock-generated turbulence mixes cold gas from outside the channel with the beam-heated gas, quenching and broadening the channel much faster than thermal conductivity would suggest. This “anomalous thermal conduction,” which in lightening bolts accounts for much of the Earth’s nitrogen fixation, was first observed without explanation in experiments (Grieg et al. 1985). It was subsequently explained theoretically and simulated computationally in a number of two-dimensional cases (Picone et al. 1981, Picone and Boris 1983, 1988). Recent experiments at Livermore, discussed in (Hubbard 1990) with very uniform symmetric beams in clean gas, however, showed markedly less turbulence than earlier experiments, suggesting that possibly the purity of the propagation gas may have been a factor. This paper reports 2-D and 3-D simulations including the enhanced turbulence arising from dust particles exploded by the beam in air.

P. Boris, J. Boris, R. Hubbard, E. Oran, S. Slinker

Interaction of two bubbles near a free surface

Two bubbles are simultaneously generated in a line perpendicular to a free surface by focusing two Q-switched ruby laser beams into tap water. The dynamic behavior of the induced bubbles is investigated by means of high-speed photography. It is found that the period of the motion of the upper bubble becomes longer than that of a single bubble near a free surface as the mutual distance between two bubbles becomes shorter. If the two bubbles are much different in size, we observed counterjet formation, bubble splitting and interpenetration.

T. Kodama, Y. Tomita, K. Sato, A. Shima

Numerical simulation of shock wave interaction with powder layers

A new microscopic mechanism of interaction between incident and traveling shock waves and a thin powder layer consisting of randomly packed solid particles is studied numerically.Particles contact each other at a finite number of points and then deformation of the powder layer occurs mainly due to compaction. Interphase drag as well as interphase heat transfer is explained according to the case of a contactless dispersed mixture. Moreover, Saffman’s lift force is considered in order to describe the entrainment and dispersion of particles from a powder layer behind a shock wave when the shock wave travels through the powder layer.

H. Sakakita, A. K. Hayashi, A. I. Ivandaev

Moderate shock wave propagation in a vapour-liquid slug flow

Experimental results on the shock wave dynamics of a vapour-liquid slug flow are reported. Experiments were carried out in a vertical and inclined 8 mm i.d. tube with Freon-11 as test liquid. Essential pecularities of wave evolution in the slug flow were found together with common phenomena revealed earlier for the bubble structure of a vapour-liquid flow. The shock wave structure here also differs much from that for a gas-liquid slug flow. High-speed filming together with pressure history recording show, for waves strong enough (ΔP0/P0 > 1.2) that practically complete collapse of slugs occurs already at the first compression phase and a comb-wise wave with high-pressure pulses forms. Each pulse corresponds to the collapse of the next slug. The first one coincides with the complete condensation wave front, moving with a velocity close to the calculated steady value.

B. G. Pokusaev, N. A. Pribaturin, E. S. Vasserman

Hypersonic flows and shock waves


Plume effects at hypersonic speeds

A 7° semi-angle blunted cone has been tested at a Mach number of 8.2 in an intermittent hypersonic wind tunnel. The Reynolds number based on cone base-diameter was 2.8×105. The heat transfer rate distribution was measured along the cones surface and schlieren pictures were taken of the whole flow field.Initially the plume was simulated by a solid disc at the rear of the cone but subsequently some tests were made using a radial jet of air, or foreign gas, in place of the disc.With no disc, the flow was attached over the entire forward surface of the cones and the measured heat transfer rates indicated a wholly laminar boundary layer. Fitting a disc causes the flow to separate and, as the disc diameter is increased, so the separation point rapidly moves forward, leading to an extensive separated shear layer with re-attachment at the rim of the disc. The flow was laminar at separation but the separated shear layer rapidly underwent transition to the turbulent state. The heat transfer beneath the laminar region was reduced but, following transition, rose rapidly to substantially exceed the laminar value over the rest of the conical surface.Thus, under the given test conditions at M =8.2, the simulated plume could cause extensive separation, early transition of the shear layer and an increase in total heat transfer to the cone surface.

J. L. Stollery, N. P. B. Sperinck, P. Atcliffe

Two dimensional numerical simulation of the Marseille university free piston shock tunnel-TCM2

A numerical analysis of the hypersonic free piston shock tunnel under construction in Marseille is presented. Since the few wind tunnels of this type actually operational (Australia) suffer performance losses when compared to expected data given by analytical theory (Stalker 1967), an axisymmetric numerical simulation is performed by a finite volume method which allows to emphasize the unsteady phenomena which restrict the expected performances. Taking into account these effects, it is possible to obtain simulations of the complete wind tunnel with initial conditions allowing to realize high enthalpy flows characteristic of the reentry phase of the HERMES European Shuttle.

Y. Burtschell, R. Brun, D. Zeitoun

An overview of Ames experimental aerothermodynamics

This paper reviews the recent experimental research activities on aerothermodynamics within NASA Ames Research Center. The activities included in this review are those in (1) the electric arc-driven shock tubes, (2) the combustion-driven shock tube, (3) the ballistic ranges, and (4) the arc-jet wind tunnel facilities. The paper is a collection and collation of the papers published previously in the open literature on the activities in these facilities. The paper highlights the contributions made by each facility in the high temperature real-gas flow regimes.

C. Park

Performance considerations in the operation of free-piston driven hypersonic test facilities

There are two fundamental limitations to useful test time in a free-piston driven shock tunnel. One is the contamination of the test flow by driver gas (a limitation in all shock tunnels). The second is the ability to maintain a nearly constant stagnation pressure in the gas driving the nozzle flow. However, practical experience has shown that it is possible to manipulate the operating variables of a tunnel of a given design so as to trade off these two phenomena and obtain the optimum conditions for particular experimental requirements. While contamination remains an absolute limit to performance, both experimental results and theoretical investigations have shown that the requirement for “constant” pressure can be relaxed. With appropriate treatment of data, valid and useful tests can be carried out in a falling (or rising) pressure regime.

D. M. Jenkins, R. J. Stalker, W. R. B. Morrison

Performance data of the new free-piston shock tunnel T5 at GALCIT

A new free piston shock tunnel has been constructed at the Graduate Aeronautical Laboratories at Caltec. Compression tube length is 30 m and diameter 300 mm. Shock tube length is 12 m and diameter 90 mm. Piston mass is 150 kg and maximum diaphragm burst pressure is 130 MPa. Special features of this facility are that the pressure in the driver gas is monitered throughout the compression process until well after diaphragm rupture, and that the diaphragm burst pressure can be measured dynamically. An analysis of initial performance data including transient behavior of the flow over models is presented.

H. Hornung, B. Sturtevant, J. Bélanger, S. Sanderson, M. Brouillette, M. Jenkins

Shock tube validation experiments for the simulation of ram-accelerator-related combustion and gasdynamic problems

This paper presents the work done at the ISL for validating the shock tube as a useful tool for simulating ram-accelerator-related combustion and gasdynamic phenomena. We were able to show that, with a specially devised expansion shock tube, an explosive gas mixture can be accelerated to a superdetonative velocity without autoignition. By reducing the driver length, a test flow of decreasing velocity was generated enabling the observation of all three detonative regimes of interest namely super-, trans- and subdetonative in only one experiment. Pressure measurements in a combustion test chamber provided the ignition conditions for different gas mixtures and varying flow geometry. An unexpected sharp onset of the ignition was found. The experiments in the shock tube will be able to support and optimize the operation of two ram accelerator facilities, a small and a large one that are presently being built at the ISL.

J. Srulijes, G. Smeets, F. Seiler, A. George, G. Mathieu, R. Resweber

Hugoniot analysis of the ram accelerator

The thermodynamic properties of a combustible propellant gas, after it has been processed by a ram accelerator propulsive mode, are related by a “ram accelerator Hugoniot” expression. These end states are determined from the 1-D conservation equations in a manner similar to that used for detonation waves, but with the addition of a force term in the momentum equation. Establishment of a region of potentially accessible thermodynamic end states that are consistent with ram accelerator operation at and above the Chapman-Jouguet detonation speed indicates that there are no fundamental constraints on accelerating projectiles over a wide range of Mach numbers in a single propellant mixture. Interpreting experimental data in the context of a genetalized ram accelerator process leads to relatively simple propulsive models which can predict the projectile acceleration of any propulsive mode. The projectile velocity and acceleration histories determined by the Hugoniot analysis for the thermally choked ram accelerator mode are in excellent agreement with experiments.

C. Knowlen, A. P. Bruckner

Initiation of combustion in the thermally choked ram accelerator

The methodology for initiating stable combustion in a ram accelerator operating in the thermally choked mode is presented in this paper. The ram accelerator is a high velocity ramjet-in-tube projectile launcher whose principle of operation is similar to that of an airbreathing ramjet. The subcaliber projectile travels supersonically through a stationary tube filled with a premixed combustible gas mixture. In the thermally choked propulsion mode subsonic combustion takes place behind the base of the projectile and leads to thermal choking, which stabilizes a normal shock system on the projectile, thus producing forward thrust. Projectiles with masses in the 45-90 g range have been accelerated to velocities up to 2650 m/sec in a 38 mm bore, 16 m long accelerator tube. Operation of the ram accelerator is started by injecting the projectile into the accelerator tube at velocities in the 700 - 1300 m/sec range by means of a conventional gas gun. A specially designed obturator, which seals the bore of the gun during this initial acceleration, enters the ram accelerator together with the projectile. The interaction of the obturator with the propellant gas ignites the gas mixture and establishes stable combustion behind the projectile.

A. P. Bruckner, E. A. Burnham, C. Knowlen, A. Hertzberg, D. W. Bogdanoff

Three-dimensional structure of pseudo-shock waves in a rectangular duct

The three-dimensional structure of a pseudo-shock wave in a straight square duct was investigated using a 2 color 4 beam LDV and a color schlieren method. The Mach number just upstream of the pseudo-shock wave was 1.83, the Reynolds number was 6.8xl04, and the confinement parameters were about 0.2 for the upper and side walls. It was shown that the structure of the pseudo-shock wave depends on the characteristics of the wall boundary layer and that the formation of the second shock is due to the variation of the displacement thickness of the boundary layer (aerodynamic nozzle) in the pseudo-shock wave.

H. Sugiyama, T. Arai, N. Uno, T. Takahashi

Spectroscopic study of high-Mach-number air shock layers generated by a ballistic range

Spectroscopic studies on high-Mach-number air shock layers generated by a ballistic range have been conducted. Using a spectrograph and a highly-sensitive film system, spectrograms of the shock layer at flight velocities higher than 3 km/sec were taken. These photographic data were transformed into numerical data using a digital data-processing system composed of a CCD camera and an image processor. In the wavelength range from 350 nm to 440 nm, several band spectra of N2 and CN were observed. In order to investigate the contributions of the respective species on the radiative emission, a high-speed shuttering system using an image intensifier, along with highly-sensitive film, has been set-up.

A. Sasoh, X. Chang, M. Henmi, T. Fujiwara

Applications of liquid crystal surface thermography to hypersonic flow

The use of surface coatings of microencapsulated liquid crystals for heat transfer measurements in two short running time (0.02 ~ Is) hypersonic flow facilities is discussed. Techniques are described from which both qualitative surface flow-fields and quantitative heat transfer data may be obtained. Calibration techniques suitable for application to short duration aerothermody-namic testing are described. Applications of the techniques to the study of a variety of hypersonic flow problems are presented. These include heat transfer investigations in several hypersonic flows involving shock/boundary layer interactions, a study of the effect of sweep on boundary layer transition and an experimental assessment of the heat transfer distribution on complex shapes typical of aerospace plane configurations.

R. A. East

Applications of infrared measurement technique in hypersonic facilities

For the design of thermal protection systems for future space vehicles it is necessary to localize and quantify the thermal loads due to convective surface heating. This paper presents tunnel experiments which demonstrate how surface heating due to interaction phenomena have been visualized and measured by infrared thermovision. An impinging shock wave on a laminar boundary layer of a flat plate and an axial corner configuration under 20° angle of attack were studied in a 60 em hypersonic blow down facility of DLR Cologne at Mach number 8.7 for laminar flow conditions. In addition to the shock interaction study the capability of the infrared technique as diagnostic tool for short duration measurements was tested in the shock tunnel TH2 at the Stoßwellenlabor RWTH Aachen.

A. Henckels, A. F. Kreins, F. Maurer

A laser induced fluorescence system for the high enthalpy shock tunnel (HEG) in Göttingen

It is planned to use the LIF technique to examine the gas flows around models located in the test section of the high enthalpy shock tunnel (HEG) in Göttingen, at present nearing the end of construction. The technique will be used to measure concentrations of NO (in 2D) and O atoms (ID) and to obtain a measure of an NO internal temperature. A complex automated apparatus consisting of two lasers and image capturing systems has been constructed and is described here. This system is at present undergoing tests in a heated cell, and will be further tested in other wind/shock tunnels before its installation at HEG in early 1992. Preliminary test results from the heated cell are presented - a spectral analysis of NO and a temperature determination. The role of quenching in applying the LIF technique to HEG gas flows (which are not in chemical equilibrium) is discussed. An ongoing study in the shock tube laboratory of the University of G#x00F6;ttingen addresses this problem; quenching of NO is being examined behind a shock wave. Results for quenching with argon are presented here.

P. Andresen, W. H. Beck, G. Eitelberg, H. Hippler, T. J. McIntyre, A. Riedl, T. Seelemann, J. Troe

Aerodynamic heating phenomenon in three dimensional shock wave/turbulent boundary layer interaction induced by sweptback fins in hypersonic flows

The detailed structure of aerodynamic heating phenomena in three-dimensional shock wave/turbulent boundary layer interaction induced by sweptback blunt and sharp fins in hypersonic flows is investigated carefully in order to study the effects of the shape and sweep angle of the leading edge of the fin on aerodynamic heating phenomena on the body. A new method of measuring heat flux developed by the present authors is used, and is based on a new type of thin-film heat transfer gauge with high spatial resolution and fast response.Heat transfer experiments were performed Mach number 4, wall temperature ratio Tw/T0 of 0.65 an Reynolds number of 1.2 × 107. Sweptback blunt fins with semi-circular leading edge and sweptback sharp fins with wedge angle of 30° in the plane normal to the leading edge were used for the present experiments. Sweep angles are 0°, 15°, 30° and 45°, with the fins placed normal to the flat plate model. The flow fields are visualized by oil flow and detailed surface pressure and surface heat flux distributions in the interaction regions for various sweep angles were measured. The results that the effects of the shape and sweep angle of the leading edge on aerodynamic heating load are quite significant.

S. Aso, S. Nakao, S. Maekawa, M. Hayashi

Studies of radiative emission from the simulated shock layer of the Huygens probe

An investigation has been conducted to determine the radiative heating of the Huygens probe. The shock tube facility at Stanford University was used to generate plasma behind strong shocks, which simulates the flow field around the probe. Spectroscopic thchnigues have been used to measure thermophysical quantities of the plasma in the shock tube. A numerical code has been developed using a three temperature model in order to generate one dimensional flow field solutions for comparison with these experimental data. Based on this analysis, the radiative heat transfer at the stagnation point of the prove was approximated.

C. S. Park, D. Bershader

The high enthalpy shock tunnel in Göttingen (HEG)

The current status of the new free piston shock tunnel being built in Göttingen is described. The facility is nearing completion with all major components on site and assembled. HEG represents a considerable scale up on existing facilities of this type and consideration of the energies involved must be taken in all aspects of the design. Described are the layout of the facility, calculations of the driving conditions including piston trajectories, expectations for the shock tube flow and calculations for the nozzle flow.

W. H. Beck, G. Eitelberg, T. J. McIntyre, J. P. Baird, J. Lacey, H. Simon

Vibrational and rotational temperature measurements in a shock tube

Vibrational and rotational temperatures in nitrogen test gas relaxing behind a normal shock are measured using the emission spectra of N2+ (1-) and N2(2+) band systems in an electric-arc driven shock tube, at a shock velocity of 6.2 km/sec. The results are compared with similar data obtained by AVCO-Everett Research Laboratory during the 1960s. The vibrational and rotational temperatures in the equilibrium region obtained in the present experiment agreed with those of AVCO, but those in the nonequilibrium region are greatly different fron the AVCO results. The measured rotational temperature seems to be in nonequilibrium with the translational temperature, contradicting the two-temperature model widely used in CFD. Also, the relaxation rates for both N2+ and N2 molecules seem to be of the same order.

S. P. Sharma

Chemical and thermal processes on hypersonic shock layer

When a spacecraft reenters the earth’s atmosphere, a high post-shock translational temperature causes thermal and chemical nonequilibrium phenomena. These are extremely important in treating such a htpersonic shock layer. Here, a chemical and thermal nonequilibrium two-temperature model is used. For thermal nonequilibrium, we have used Park’s two-temperature model; T trans = T rot , T vib = T electron . For chemical nonequilibrium, the following 11 chemical species are taken into account: O2, N2, N,O, NO, O2+,N2+,N+,O+, NO+ and e-. The problem is solved on a spherically blunt cone by numerical methods, for flight Mach numbers 25,30 and 35 at altitude 70km.

T. Murayama, A. Sasoh, T. Fujiwara

Acoustic waves in shock tunnels and expansion tubes

It is shown that disturbances in shock and expansion tubes can be modelled as lateral acoustic waves. The ratio of sound speed across the driver-test gas interface is shown to govern the quantity of noise in the test gas. Frequency “focusing” which is fundamental to centred unsteady expansions is discussed and displayed in centreline pitot pressure measurements.

A. Paull, R. J. Stalker

Shock wave/turbulent boundary layer interactions induced by gaseous secondary flows injected into supersonic flow through slot and circular nozzles

The complex flowfields induced by a gaseous secondary flow injected into a supersonic flow have been studied experimentally. A gaseous nitrogen jet is injected normally into the external flow through slotted and circular nozzles mounted on a flat plate model. Experiments are conducted under the following conditions: the free stream Mach number of 3.8, total pressure of 1.2 MPa, the Reynolds number of 2.0 × 107. In the flowfields, the widths of the slotted nozzles and the pressure ratio Pc/P0(Pc: total pressure of secondary flow, P0 : total pressure of free stream) are used as primary parameters. In the interacting flow, barrel shock waves and Mach disk are observed clearly. As the total pressure ratio or the thickness of the nozzle is increased, the separation region, the extent of the interaction region, the extent of the interaction region and of their shock structures become significantly large.

S. Aso, S. Okuyama, Y. Ando

A numerical analysis for radiation profile behind strong shock waves about 10 km/s in low-density air

The double-peak characteristic of radiation intensity behind shock waves above 10 km/s in a low-density air are studied by carrying out a numerical analysis for one-dimensional, steady hypersonic flows with nonequilibrium chemical reactions. The gas model is based on 11 gas species, 3 temperatures and 47 chemical reactions. The radiation model includes all possible types of emissions from bound-bound, free-bound and free-free transitions. The result indicates that the double-peak characteristic of the radiation profile can be attributed to the increase of the radiation intensity of the atomic line spectra and the continuum spectra from the free-bound and free-free transitions in the near equilibrium region far downstream of the shock front

H. Iizuka, H. Honma

Computation of chemical nonequilibrium nozzle flow of air in high-enthalpy shock tunnels

A high enthalpy flow can be produced by using a shock tunnel such as the Stalker tube. Because of the high enthalpy, the gas is as well as ionized dissociated. Although the flow is assumed equilibrium at the stagnation condition, in a convergent-divergent nozzle it is usually chemically nonequilibrium because the chemical reaction rate is slower than the characteristics time of the flow. In the present paper a chemical nonequilibrium nozzle flow in high enthalpy shock tunnels is discussed. The distributions of temperature, pressure, velocity and mass fractions are presented.

M. Mitsuda, T. Kurosaka

Radiative heat transfer from non-equilibrium high-enthalpy shock layers

Numerical calculation of radiative heat transfer from non-equilibrium, high-enthalpy shock layers generated around a blunt body has been performed. At Mach numbers from 25 to 35, the radiative heat transfer is mainly caused by strong radiative emission in a thermally and chemically non-equilibrium layer generated immediately behind the shock wave. Accordingly, as upstream Mach number increases, the intensity of the radiative emission sharply increases, resulting in sharp increase in the radiative heat transfer. In this study, the thickness of the strong emission layer is almost independent of the nose radius. Hence, the radiative heat transfer is almost unchanged with the radius.

A. Sasoh, X. Chang, T. Murayama, T. Fujiwara
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