Showing papers on "Rarefaction published in 1995"

Statistical properties of shocks in Burgers turbulence. II. Tail probabilities for velocities, shock-strengths and rarefaction intervals

Abstract: This paper studies the structure of the random “sawtooth” profile corresponding to the solution of the inviscid Burgers equation with white-noise initial data. This function consists of a countable sequence of rarefaction waves separated by shocks. We are concerned here with calculating the probabilities of rare events associated with the occurrence of very large values of the normalized velocity, shock-strength and rarefaction intervals. We find that these quantities have tail probabilities of the form exp{−Cx 3},x≫1. This “cubic exponential” decay of probabilities was conjectured in the companion paper [1]. The calculations are done using a representation of the shock-strength and length of rarefaction intervals in terms of the statistics of certain conditional diffusion processes.

Rarefaction waves, solitons, and holes in a pure electron plasma

Abstract: The propagation of holes, solitons, and rarefaction waves along the axis of a magnetized pure electron plasma column is described. The time dependence of the radially averaged density perturbation produced by the nonlinear waves is measured at several locations along the plasma column for a wide range of plasma parameters. The rarefaction waves are studied by measuring the free expansion of the plasma into a vacuum. A new hydrodynamic theory is described that quantitatively predicts the free expansion measurements. The rarefaction is initially characterized by a self‐similar plasma flow, resulting in a perturbed density and velocity without a characteristic length scale. The electron solitons show a small increase in propagation speed with increasing amplitude and exhibit electron bursts. The holes show a decrease in propagation speed with increasing amplitude. Collisions between holes and solitons show that these objects pass through each other undisturbed, except for a small offset.

Optimal shock-wave systems

Abstract: Academician G. I. Petrov was among the first to investigate systems consisting of several plane inclined shocks and a closing normal shock [1]. In his studies the intensities of the inclined shocks in which the static and total pressure restoration coefficients reach maximum values were determined by numerical investigation. These shock systems were called optimal. A theoretical analysis of these systems is presented in [2, 5]. Exact analytic solutions determining the intensities in the optimal system in which there are maxima of not only the pressure restoration coefficients but also the values of the velocity head or density, as well as the angle of flow rotation in the wave, are obtained. Apart from shocks, the system include simple rarefaction and compression waves. The solutions obtained are not only theoretically meaningful but also have practical applications and can be used in the gasdynamic design of supersonic air intakes, jet technology devices, and other technical apparatus.

On the frame dependence of constitutive equations. I. Heat transfer through a rarefied gas between two rotating cylinders

Abstract: To verify the principle of material frame indifference a numerical calculation of the heat flux field in a rotating gas has been carried out based on the kinetic equation over wide ranges of gas rarefaction and angular velocity It has been confirmed that a radial gradient of the temperature causes a tangential heat flux Also, it has been found that the radial heat flux is affected by the rotation

Drag Coefficient Measurement of Spheres in a Vertical Shock Tube and Numerical Simulation

Abstract: The drag coefficient of spherical particles is measured in a vertical shock tube. The glass or nylon particles (diameter 1 or 2 mm) are initially in a free fall in air, SF6 or helium. During the measurement time, they are subjected to an upward-propagating shock wave followed by a rarefaction wave or not, and anyway by a reflected shock wave. Particle trajectories recorded with a high-speed motion picture camera are compared to analytical and simulated trajectories. The drag coefficients (0.50–0.62) obtained for this unsteady situation in a high Reynolds number range (5. × 103 · · · 1.2 × 105) are higher than the standard steady value (0.4).

Effects of tandem and colliding shock waves on the initiation of triaminotrinitrobenzene

Abstract: The shock initiation of the insensitive high‐explosive LX‐17, which contains 92.5% triaminotrinitrobenzene and 7.5% Kel‐F binder, was studied under simulated accident conditions in which two shock waves interact producing locally high pressures and temperatures. Two experimental geometries were studied using embedded manganin pressure gauges to measure the increases in pressure due to exothermic reaction at various locations as functions of time. These pressure histories were compared to ignition and growth reactive flow model calculations to determine whether a second shock compression of reacting LX‐17 caused unusually rapid reaction rates and thus more extreme hazards. One experiment used a tandem flyer plate of aluminum and steel separated by a gap to shock the LX‐17 charge, allow it to rarify, and then reshock the damaged charge to even higher pressures. These experiments revealed no significant enhancement of the LX‐17 reaction rates under this shock, rarefaction, and reshock loading. The second exp...

Macroscopic ESWL-induced cavitation: in vitro studies

Abstract: The rarefaction shock wave results in a liquid failure at the target/fluid interface. In the wake of the reflected ESWL-induced shock wave, a macroscopic cavity is generated in filtered water. The cavity implosion induces a large shock wave, divulging the bubble existence and lifetime. The existence of this shock wave is revealed by the diffraction of a He-Ne laser beam. The induced cavitation bubbles are registered by a camera, illuminated by an externally triggered stroboscope (exposure time 10 microseconds). The radius of the large cavity bubble, generated at the stone surface, is time dependent as theoretically predicted.

Analysis of unsteady wave processes in a rotating channel

Abstract: The impact of passage rotation on the gasdynamic wave processes is analyzed through a numerical simulation of ideal shock-tube flow in a closed rotating-channel containing a gas in an initial state of homentropic solid-body rotation. Relevant parameters of the problem such as wheel Mach number, hub-to-tip radius ratio, length-to-tip radius ratio, diaphragm temperature ratio, and diaphragm pressure ratio are varied. It is shown that for a fixed geometry and initial conditions, the contact interface acquires a distorted three-dimensional time-dependent orientation at non-zero wheel Mach numbers. At a fixed wheel Mach number, the level of distortion depends primarily on the density ratio across the interface and also the hub-to-tip radius ratio. The nature of the rarefaction and shock wave propagation is one-dimensional, although the acoustic waves are diffracted due to the radially varying propagation speed. Under conditions of initially homentropic solid-body rotation, a degree of similarity exists between rotating and stationary shock-tube flows. This similarity is exploited to arrive at an approximate analytical solution to the Riemann problem in a rotating shock-tube.

Asymptotic solution of shock tube flows with homogeneous condensation

Abstract: The asymptotic solution of shock tube flows with homogeneous condensation is presented for both smooth, or subcritical, flows and flows with an embedded shock wave, or supercritical flows. For subcritical flows an analytical expression, independent of the particular theory of homogeneous condensation to be employed, that determines the condensation wave front in the rarefaction wave is obtained by the asymptotic analysis of the rate equation along pathlines. The complete solution is computed by an algorithm which utilizes the classical nucleation theory and the Hertz-Knudsen droplet growth law. For supercritical flows four distinct flow regimes are distinguished along pathlines intersecting the embedded shock wave analogous to supercritical nozzle flows. The complete global solution for supercritical flows is discussed only qualitatively owing to the lack of a shock fitting technique for embedded shock waves. The results of the computations obtained by the subcritical algorithm show that most of the experimental data available exhibit supercritical flow behaviour and thereby the predicted onset conditions in general show deviations from the measured values. The causes of these deviations are reasoned by utilizing the qualitative global asymptotic solution of supercritical flows

The application of optical diagnostics to high energy electromagnetic acoustic transducers

Abstract: This thesis is concerned with the design and construction of an electromagnetic acoustic transducer (EMAT) and the characterisation of its acoustic field both conventionally, using a hydrophone and with high resolution laser illuminated schlieren techniques. During the early 80s the introduction of the EMA T along with the other types of shock wave source used for lithotripsy, revolutionised the treatment of stone disease. The process of shock wave induced destruction of calculi and the use of shock waves in other areas of medicine will be discussed, along with the causes and effects of stone disease in man. For the first time high temporal and spatial resolution schlierenimages of the shock waves and there interaction with simulation kidney stones have been recorded. The technique provides a clearer picture of the fragmentation process and may assist research into the suitability of shock wave treatment in other areas of medicine currently under investigation. Schlieren studies of the acoustic field have shown the complex structure of not only the EMA T shock wave, but also that associated with cavitation in the field. The primary source of cavitation is due to the rupture and subsequent collapse of bubbles generated in the water by the strong rarefaction phase of the shock wave. The images give evidence for the interaction of these 'primary' cavitation shocks with bubbles in the field, the collapse of some of these bubbles giving rise to additional or 'secondary' cavitation shocks. An optical lensing effect introduced by the shock has also been investigated. Objects seen through or immersed in the field of an EMAT shock wave such as cavitation, appear highly distorted, due to the strong positive and negative lensing effects associated with the changing refractive index of the compression and rarefaction cycles of the shock wave.

Experimental and Numerical Investigation of Shock Wave Attenuation in Dust-Gas Suspensions

Abstract: The attenuation of planar shock waves while propagating through dust-gas suspensions was studied experimentally and numerically. The numerical solution was conducted twice, each time using a different correlation for the dust particle drag coefficient. It was shown that when the Reynolds number is relatively high (Re > 200) the solution based on the nonstationary drag coefficient provides better agreement with experimental findings. Also studied was the post shock pressure signature; good agreement was found between experimental and numerical results until the reflected rarefaction wave, from the driver’s end wall, caught up with the transmitted shock wave in the suspension.

Explosive gasification of aluminium nitride powder and rapid condensation of ultrasupersaturated gas in the rarefaction wave front

Abstract: The fast phenomena occurring in the Mach disc front and the rarefaction wave front behind the disc formed by a cylindrical shock technique have been investigated using AIN powders with low densities, 17–26% of the theoretical bulk value. Electron microscopy on the microstructures of the recovered samples proved that a dense medium, shock compressed in the Mach disc front, was produced, accompanied by a drastic gasification in the rarefaction wave front. The resulting high-temperature high-pressure gas contained a large quantity of plasma (molecular gas cloud), that had rapidly condensed under the steep pressure, temperature and density gradients. The gas density was calculated to be about 76–84% of the theoretical density of AIN, and it was presumed that the gasification was terminated in the order of a nanosecond, while the condensation of ultra-supersaturated gas proceeded over the time range nanoseconds to microseconds. The distribution of the component particles developed from the gas suggest...

Optical distortion in the field of a lithotripter shock wave.

Abstract: The schlieren observation of cavitation phenomena produced in the tail of a lithotripter shock wave has indicated the presence of some interesting features. The images produced appear to indicate that cavitation transients in the field of a shock wave propagate nonsymmetrically; this is not the case. The apparent lack of symmetry exhibited by the primary cavitation transients is due to a complex optical lensing effect, which is brought about by the change in refractive index associated with the pressure profile of the shock wave. Objects seen through or immersed in the shock-wave field of an electromagnetic acoustic transducer, such as cavitation, appear highly distorted because of the strong positive and negative lensing effects of the compression and rarefaction cycles of the shock wave. A modification of the schlieren technique called the scale method has been used to model the distortion introduced by the shock wave and consequently explain the cavitation distortion. The technique has also been used to quantitatively analyze and partially reconstruct the lithotripter shock wave. The combination of schlieren and scale imaging gives more information about the refractive index field and therefore the shock-wave structure itself.

Structure of Deformation Waves in Porous Compressible Materials Under the Influence of Shock Waves

Abstract: Paper describes new experimental results concerning compression waves in porous compressible foams due to loading with shock waves generated in gas A shock tube of 100 x 100 mm cross-section has been used In addition to piezoelectric measurements and flow visualization, which were described elsewhere, new techniques for measuring the deformation waves in porous compressible media were developed The density distribution in the deformation wave is determined, based on photodetection of a reference grating on the side face of the foam with short exposure times The structure of the deformation wave was found to depend substantially on the permeability of the front face of the foam In particular, the deformation wave in open-pore polyurethane foam was shown to be transformed into a wave-like isolated compression wave with a rarefaction region between the compression wave and the foam surface The deformation wave in a foam with the front face covered with a thin mylar film is of a different structure, more like that expected in polyurethane if taken to behave like a pseudogas The rarefaction region disappeared The effect of pressure magnitude of the incident shock wave on the deformation wave structure was studied The dependence of the maximum compression of porous medium on impinging wave intensity was obtained Pressure distributions on the side wall of the shock tube under the foam were taken The dependence of pressure distribution on the Mach number of the incident shock wave has been studied

Evolution of weak shock waves in dense media

Abstract: Relations describing the evolution of a weak shock wave (SW) in a dense medium with account of its attenuation and “spreading” are derived. The evolution is presented as a result of superposition of two processes: propagation of a stepped weak shock wave and “pursuit” of the shock by a rarefaction wave.

Laser-Generated Shock Waves

Abstract: A low-energy, Q-switched Nd YAG laser has been used to generate shock waves in air, liquids and solids and high time- and space-resolution optical interferometry then leads to the pressure field in the breakdown zone.

Attenuation of a shock wave in organoplastic

Abstract: The attenuation of a plane shock wave in organoplastic was experimentally and numerically investigated during its interaction with an overtaking rarefaction wave. Measurements were carried out with manganin gauges, An earlier formulation model of the dynamic deformation of composites was used in calculations. A comparison of calcualted and experimental data has shown their good agreement.

Theoretical Investigation of Condensation Dynamics in Shock Tubes

Abstract: Condensation dynamics is investigated in the rarefaction wave of shock tube flows of a mixture of a condensable vapor and a carrier gas. The asymptotic solution which distinguishes the condensation zones with detailed analytical structure on pathlines for both subcritical and supercritical expansions is presented. An algorithm that utilizes the classical nucleation theory and the Hertz-Knudsen droplet growth formula is developed and the onset conditions for a mixture of water vapor in argon are presented against experimental data. A comparison of steady and unsteady nucleation rates for these data shows that nucleation time-lag effects are more important in the initial nucleation period than near maximum nucleation rates.

Refraction of a Shock Wave Through a Sinusoidal Discontinuous Interface Separating Gases of Different Densities

Abstract: An experimental and numerical study on the shock wave passage from one gas to another through a two-dimensional (2D) interface has been carried out. The curvature and intensity of the rarefaction and reflection waves have been found to determine the character of the following interface evolution. Three main regimes of the shock-induced discontinuous interface evolution are described.

Interaction of rarefaction waves with wet foam

Abstract: The interaction of rarefaction waves of different shapes with wet water foams is studied experimentally. It is found that the observed values of the pressure are greater, while the surface velocity is lower than the corresponding values predicted by the pseudogas model. The foam breakdown starts as the pressure decreases by 0.3 atm relative to the initial pressure. During downstream propagation of the rarefaction-wave leading edge the propagation velocity decreases. Using of water-based foams as effective screens for damping blast waves in different technological processes has caused considerable interest in studying wave propagation in such systems. The pressure wave dynamics in a foam have been investigated in much detail, both experimentally and theoretically [1–3]. However, the interaction of rarefaction waves with foam has practically never been studied, although it was mentioned in [4] that the unloading phase following the compression wave phase is one of the factors defining the damaging action of blast waves. Besides blast-wave damping, rarefaction wave propagation takes place if such waves are used to breakup foam in oil-producing wells [5]. Below, the interaction of rarefaction waves of different shapes with wet water foams is studied. The vertical shock tube described in detail in [3] was used in these experiments.

Condensation induced by rarefaction waves and reflected rarefaction waves

Abstract: In this paper, homogeneous condensation induced by unsteady rarefaction waves and reflected rarefaction waves in vapor-gas mixture was investigated experimentally. It is shown that the temperature of condensation onset during very fast unsteady expansion in vapor-gas mixture is much lower than that during equilibrium process in the atmosphere. It is of interest to indicate that the size of droplets approximates a constant, but the number density and the mass density of droplets change rapidly in the region of static flow.

On the Onset of Condensation in Rarefaction Waves in Shock Tubes

Abstract: The expansion of a mixture of a condensible vapor and a carrier gas in the rarefaction wave generated in a shock tube is considered. Using centered expansion wave theory the condensation zones and the onset of condensation are exhibited along pathlines from the asymptotic solution of the condensation rate equation. Consequently the condensation wave front is located accurately in the rarefaction wave of a given shock tube flow with homogeneous condensation. Results obtained for the expansion of moist air and of water vapor in nitrogen are compared with measurements and possible sources for the differences are discussed.