Transmitted Shock Wave Research Articles

Experimental and numerical study of weak shock wave transmissions through minitubes

The aim of this letter is to present an original experimental technique to study weak shock wave in a minitube. Thus, we designed an apparatus that can be connected to any classical shock tube in order to characterize high speed flows induced by the shock wave transmission in minitubes. We proposed appropriated measurements based on high speed strioscopy coupled with pressure sensors. Two minitube diameters are considered: 1.020±0.010 and 0.480±0.010 mm. We realized preliminary experimental and numerical campaigns with an incident shock wave Mach number at 1.12±0.01. The generation of a microshock wave was observable in the two minitubes. For the smallest minitube, we found an attenuation of the strength of the shock wave with a decrease of 1.8% of the Mach number.

On the manifestation of Richtmyer-Meshkov instability in an inhomogeneous interstellar medium with radiative cooling

We numerically simulate the evolution of the plane two-dimensional deformations of a contact discontinuity that is impulsively accelerated by a shock wave. We take into account the effects of radiative cooling and perturbation scale lengths on the dynamics and shape of the forming density inhomogeneities. For moderately intense shocks in a stellar wind and for strong shocks from a supernova, we show that the radiative cooling processes do not affect significantly the growth rate of the initial perturbations and the total mass of the forming condensations. However, the density of the matter compressed by the transmitted shock wave increases dramatically. At the same time, the contribution from long-wavelength perturbations to the deformation of the contact surface decreases significantly. In the case of shock propagation from a supernova, the initial conditions have been found to be a factor that can affect the morphology of the shocked interstellar medium.

Shock wave interaction with cavitation bubble clusters generated in lithotripsy.

Collapse of cavitation bubbles generated in shock wave lithotripsy is essential to the comminution of kidney stones. After passage of the shock, however, if insufficient time has elapsed for the bubbles to dissolve, acoustic scattering from residual bubbles shields the stone from the next shock. Therefore, cavitation also limits the maximum firing rate. As important as collective bubble dynamics are to the efficacy of shock wave lithotripsy, behavior of the bubble clusters is among the least understood physical processes involved. A model was developed previously for the pulsation and translation of dynamically coupled spherical gas bubbles [Ilinskii et al., J. Acoust. Soc. Am. 121, 786 (2007)]. This model was augmented to account for interaction with the focused shock wave incident on the cluster at the order of the Born approximation. Diffraction of the shock wave is described by the KZK equation. The model predicts translation and coalescence of the bubbles due to transmission of the shock through the cluster. Predicted also is the acoustic wave scattered from the cluster, which in the forward direction is the leading order effect of the cluster on the transmitted shock wave. [Work supported by the ARL McKinney Fellowship in Acoustics and NIH DK070618.]

Head on collision of a planar shock wave with a dusty gas layer

The head-on collision of a planar shock wave with a dust-air suspension is studied numerically. In this study the suspension is placed inside a conduit adjacent to its rigid end-wall. It is shown that as a result of this collision two different types of transmitted shock waves are possible, depending on the strength of the incident shock wave and the dust loading ratio in the suspension. One possibility is a partially dispersed shock wave, the other is a compression wave. The flow fields resulting in these two options are investigated. It is shown that in both cases, at late times after the head-on reflection of the transmitted shock wave from the conduit end-wall a negative flow (away from the end-wall) is evident. The observed flow behavior may suggest a kind of dust particle lifting mechanism that could shed new light on the complex phenomenon of dust entrainment behind sliding shock waves.

Experimental study on transmission of an overdriven detonation wave from propane/oxygen to propane/air

Two sets of experiments were performed to achieve a strong overdriven state in a weaker mixture by propagating an overdriven detonation wave via a deflagration-to-detonation transition (DDT) process. First, preliminary experiments with a propane/oxygen mixture were used to evaluate the attenuation of the overdriven detonation wave in the DDT process. Next, experiments were performed wherein a propane/oxygen mixture was separated from a propane/air mixture by a thin diaphragm to observe the transmission of an overdriven detonation wave. Based on the characteristic relations, a simple wave intersection model was used to calculate the state of the transmitted detonation wave. The results showed that a rarefaction effect must be included to ensure that there is no overestimate of the post-transmission wave properties when the incident detonation wave is overdriven. The strength of the incident overdriven detonation wave plays an important role in the wave transmission process. The experimental results showed that a transmitted overdriven detonation wave occurs instantaneously with a strong incident overdriven detonation wave. The near-CJ state of the incident wave leads to a transmitted shock wave, and then the transition to the overdriven detonation wave occurs downstream. The attenuation process for the overdriven detonation wave decaying to a near-CJ state occurs in all tests. After the attenuation process, an unstable detonation wave was observed in most tests. This may be attributed to the increase in the cell width in the attenuation process that exceeds the detonability cell width limit.

Shock and impact reduction in moderate and strenuous landing activities

Shock reduction has been well studied in moderate activities such as walking and running. However, there is a clear lack of research concerning shock wave transmission and reduction in more strenuous landing activities. In this study, we examined the impact of shock transmission and reduction in landing activities with varied mechanical demands. Ten active males were recruited for the study. They performed five successful step-off landing trials from each of five heights: 30, 45, 60, 75, and 90 cm. Right sagittal kinematics, ground reaction forces, and acceleration were recorded simultaneously. Impact frequencies were analysed using a discrete Fast Fourier Transform and power spectral density was computed. Increased range of motion for the ankle, knee, and hip joints was observed at higher landing heights. The peaks of the vertical ground reaction force, forehead and tibial accelerations, and eccentric muscle work by lower extremity joints were increased with increased landing heights. The peak head power spectral density was severely attenuated at higher frequencies but the peak tibia power spectral density did not demonstrate this trend. Shock reduction showed increased reduction at higher frequencies, but minimal changes across five landing heights. Unlike the responses observed for walking and running, the shock reduction did not show significant improvement with elevated mechanical demands.

Improved acoustic coupling for shock wave lithotripsy

Previous in vitro studies of acoustic coupling in shock wave lithotripsy (SWL) have shown that air pockets trapped at the surface of the treatment head significantly reduce transmission of shock wave (SW) energy to the focal zone of the lithotripter, reducing the effectiveness of stone breakage. Since there are no reliable means to monitor the quality of coupling during SWL, we looked for a practical protocol to improve how coupling is achieved. In vitro studies were performed using a Dornier DoLi-50 lithotripter. LithoClear gel was used to couple the treatment head to the acoustic window of a clear acrylic test tank. Numerous methods of applying gel were tested including common sense variations of routine protocols typically used with patients. For each method the coverage of air pockets (% defects) was determined using digital imaging. Different coupling regimes were tested for effect on the breakage of gypsum model stones. The quality of acoustic coupling was affected by how the gel was handled--how it was dispensed and applied, and whether the gel was applied only to the treatment head or to both the lithotripter water cushion and the test tank (surrogate patient). Dispensing gel from a squeeze bottle for application by hand created significantly more defects than when a large volume (approximately 250 ml) of gel from the stock jug was applied as a mound to just the treatment head (26.5+/-2.7 vs. 1.2+/-0.5% defects, P<0.001). The efficiency of stone breakage was better when gel was applied from the stock jug compared to application by hand (P<0.006). Poor coupling was substantially improved by using the inflation feature of the water cushion to collapse air pockets, but this strategy was not a substitute for establishing good coupling at the outset. The quality of coupling in shock wave lithotripsy can be improved by minimizing the handling of the coupling medium. Hand application of coupling gel is clearly not the best way to prepare for lithotripsy. Better results can be obtained by delivering lithotripsy gel as a bolus to the treatment head alone, and allowing it to spread upon contact between the treatment head and the skin. These in vitro tests also suggest that the inflation feature of the lithotripter may be useful in reducing defects in coupling.

Propagation Behavior of Combustion Wave Induced by a Shock Wave Propagated into a Premixed Gas of Oxygen and Hydrogen

In this paper, experimental results were reported to investigate a behavior of combustion wave when a shock wave was transmitted into a combustible premixed gas of oxygen and hydrogen. In general, phenomena occurring in the premixed gas would be classified into four types, i.e. (a) the shock wave was just transmitted without causing ignition for the shock wave propagated with low-Mach number, (b) the gas was ignited behind the shock wave and a deflagration wave was propagated following the shock wave, (c) the deflagration wave was transited to a detonation wave behind the shock wave, (d) a detonation wave was directly initiated just behind incident shock wave having high-propagation Mach number. In this study, a shock wave produced by a detonation-driven shock tube was transmitted into a premixed gas of oxygen and hydrogen varied with an equivalence ratio, initial pressure of premixed gas and Mach number of the shock wave. As a result, the phenomena of combustion wave were classified using a cell-size of steady-propagating detonation wave. For sensitive gases having small cell-size, the detonation wave was directly initiated behind the shock wave even though the Mach number of the shock wave was relatively low. Empirical equations to evaluate a Mach number and temperature behind shock wave were obtained, which are threshold parameters to cause detonation wave behind transmitted shock wave.

Effect of a shock-absorbing pylon on transmission of heel strike forces during the gait of people with unilateral trans-tibial amputations

The primary objective was to test the hypothesis that walking with a shock-absorbing pylon (SAP) decreases the peak magnitude and frequency content of the heel-strike-initiated shock wave transmitted to the stump. The secondary hypotheses were that walking with a SAP decreases the heel-strike transient force between the ground and the foot and increases function as measured by walking velocity and subjective assessments. Seven people with unilateral trans-tibial amputations walked at self-selected speeds without and with a SAP. As the primary outcome measure, accelerometers were used mounted proximally and distally along the prosthetic pylon to measure the transmitted shock wave. Secondary measures included ground reaction forces from a force plate, a ten-minute walking test to determine walking speed and a questionnaire to evaluate gait function and subjective preference. The SAP provided no significant shock absorption as indicated by either the mean peak proximal accelerations of 3.19 g and 2.82 g (p = 0.28) without and with the SAP respectively or the mean difference between the peak proximal and distal accelerometers, 0.16 g and 0.19 g (p = 0.58). No significant change in the frequency content was found. Variances were high. There were no significant differences noted in the secondary measures. Although this study failed to identify any statistically significant effects due to the SAP, the magnitude and variance of the data will permit an accurate estimation of the appropriate sample size for future studies required to determine the efficacy of SAPs.

On mechanism of non-heating sterilization using the underwater shock wave loading and gas formation

In the field where the thermal sterilization can’t be applied, the establishment of the sterilization technology with non-heating is strongly requested. The sterilization by pressurizing is one of the sterilization technology. Especially, the underwater shock wave causes scarcely heat in pressurizing because the pressurizing time is extremely short. That is, it is thought that the underwater shock wave enables non-heating sterilization that originates only in pressure. Hence, in this research, the underwater shock wave loading caused by explosive was used for non-heating sterilization. Saccharomyces cerevisiae, one of the budding yeast was used for experiments. S. cerevisiae starts fermentation by feeding the glucose, and causes CO2 within its body. There is the great density difference between cells of S. cerevisiae and the gas, hence, the acoustic impedance is different on the underwater shock wave transmission. Therefore, a strong reflected wave is caused on the boundary of the cell and the gas, and a remarkable expansion is caused. Fermented S. cerevisiae are sterilized by this phenomenon, and showed high sterilization rates. The sterilization rate by the underwater shock wave was low for not giving the glucose, that is, S. cerevisiae that had not fermented. The sterilization rate that had been done on three conditions was as follows in the order of higher. 1) Fermenting S. cerevisiae, high pressure. 2) Fermenting S. cerevisiae, low pressure. 3) Non-fermenting S. cerevisiae, high pressure. The detonation fuse was used in this experiment. There was an interesting phenomenon, that is, the sterilization rate was high at the side of detonation beginning, and it was decreased toward the direction. It is thought that this is related to a constant angle of the shock wave caused from the detonation fuse. A corresponding result to the phenomenon was gotten by the numerical analysis between the progress of the detonation and the change of pressure.

Detonation interaction with an interface

Detonation interaction with an interface was investigated, where the interface separated a combustible from an oxidizing or inert mixture. The ethylene-oxygen combustible mixture had a fuel-rich composition to promote secondary combustion with the oxidizer in the turbulent mixing zone (TMZ) that resulted from the interaction. Sharp interfaces were created by using a nitro-cellulose membrane to separate the two mixtures. The membrane was mounted on a wood frame and inserted in the experimental test section at a 45° angle to the bulk flow direction. The membrane was destroyed by the detonation wave. The interaction resulted in a transmitted and reflected wave at a node point similar to regular shock refraction. A detonation refraction analysis was carried out to compare with the measured shock angles. It was observed that the measured angle is consistently lower than the predicted value. An uncertainty analysis revealed possible explanations for this systematic variation pointing to factors such as the incident wave curvature and the role of the nitro-cellulose diaphragm. Analysis of the TMZ and Mach stem formed from the reflection of the transmitted shock wave off the solid boundary were carried out and found to justify the size and strength of these features as a function of the test gas composition. The role of secondary combustion in the TMZ was also investigated and found to have a small influence on the wave structure.

Particle and drop dynamics in the flow behind a shock wave

The results of an investigation of the dynamics of hard particles and liquid drops in the flow behind a transmitted shock wave are presented. From the equation of motion of a particle in the shock wave, relations for the displacement, velocity and acceleration as functions of time and certain velocity-relaxation parameters taking into account the properties of the gas and the aerodynamic drag of the particles are obtained for unsteady flow around the particles at an acceleration of 103–104 m/s2. It is shown that the velocity-relaxation parameters are universal. Approaches to finding the aerodynamic drag of freely-accelerating bodies from the dynamics of their acceleration after being suddenly exposed to the flow are considered. It is established that under these conditions the drop dynamics observed can be well described in terms of the same velocity-relaxation parameters with account for linear growth of the transverse drop size. All the kinematic functions obtained are confirmed experimentally.

Shock wave attenuation by grids and orifice plates

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

1701 衝撃力を受けた構造材の力学特性変化に関する基礎研究(J22-1 衝撃破壊と安全性評価,J22 産業化および安全のための新技術)

1701 衝撃力を受けた構造材の力学特性変化に関する基礎研究(J22-1 衝撃破壊と安全性評価,J22 産業化および安全のための新技術)

ALE Godunov 법을 이용한 1 차원 압축성 이상유동 해석

Compressible two-phase flow is analyzed based on the arbitrary Lagrangian-Eulerian (ALE) formulation. For water, Tamman type stiffened equation of state is used. Numerical fluxes are calculated using the ALE two-phase Godunov scheme which assumes only that the speed of sound and pressure can be provided whenever density and internal energy are given. Effects of the approximations of a material interface speed are Investigated h method Is suggested to assign a rigid body boundary condition effectively To validate the developed code, several well-known problems are calculated and the results are compared with analytic or other numerical solutions including a single material Sod shock tube problem and a gas/water shock tube problem The code is applied to analyze the refraction and transmission of shock waves which are impacting on a water-gas interface from gas or water medium.

Protection of IFE First Wall Surfaces from Impulsive Loading by Multiple Liquid Layers

A large, vertical shock tube is used to explore the breakup and mitigation effects of liquid layers expected from the hydrodynamic shock generated in an inertial fusion reaction. Single and multiple layers of water are tested at two Mach numbers, 2.12 and 3.20. X-ray radiography techniques are used to image the breakup of the water layer resulting in a quantitative measure of the mass fraction distribution of water after shock impact. The amount of breakup is increased with the addition of multiple layers and the increased breakup decreases the end wall impulse. The speed of the transmitted shock wave can be reduced by 50% and is a weak function of the number of layers. The peak pressure at the end-wall of the shock tube is significantly increased due to the high impulsive force of the single liquid layer, however this pressure is substantially reduced when multiple layers containing the same mass of water are used.

Relationships between fore‐ and hindlimb ground reaction force and hoof deceleration patterns in trotting horses

The transmission of shockwaves following hoof impact is proposed to be one major source of stress to the limb. In the forelimb, there are indications that the period of horizontal deceleration of the hoof is related to the attenuation of shockwaves. In the hindlimb, information about the hoof deceleration has been lacking. To compare hoof deceleration patterns between the fore- and hindlimbs. Seven Standardbreds were trotted by hand over a force plate covered with sand, with triaxial accelerometers mounted on the fore and hind hooves. Variables representative of decelerations (first 2 main vertical deceleration peaks; characteristic minimum and maximum values in the craniocaudal deceleration; hoof braking time) and ground reaction forces (vertical loading rates; maximum and the following local minimum of the craniocaudal force) of the initial part of the stance phase, and the differences between individual fore- and hindlimb time and amplitude variables were used for statistical analyses. Force plate data showed significantly greater vertical loading rate (mean +/- s.d. 6.5 +/- 5.9 N/sec) and horizontal loads (190.4 +/- 110.2 N) in the forelimb than the hindlimb, but the parameters from accelerometer data showed no significant differences. No significant difference was found in the hoof deceleration, but the deceleration curves displayed a common pattern that described in detail the kinematics of the fore and hind hooves during the initial period of hoof braking. These results contribute to further knowledge about the characteristics of these potential risk factors in the development of subchondral bone damage in the horse. Further studies are required on the influence of hoof braking pattern at higher speed, different shoeing and ground surfaces with different properties.

On the efficiency of Gore-Tex layer for brain protection from shock wave damage in cranioplasty

The effectiveness of a Gore-Tex layer for protecting soft tissue from damage in shock wave therapy is investigated analytically, numerically and experimentally. Analytical considerations based on the fundamentals of wave dynamics and two-dimensional numerical simulations based on the elastodynamic equations are carried out for underwater shock wave propagation and interaction with Gore-Tex membrane models of different complexity. The results clearly demonstrate that considerable attenuation of shock waves with Gore-Tex is due to the air trapped inside the membrane. The experimental results confirm that a Gore-Tex sheet placed in the liquid reduces the transmitted shock wave peak overpressure significantly, by up to two orders of magnitude. Another experimental series reveals what kind of damage in the rat brain tissue can be caused by shock waves of different intensity.

Shock wave reflection from a wedge in a dusty gas

The present paper contains a detailed study of shock wave reflection from a wedge placed in various suspensions. In past works, the incident shock propagated initially in pure gas and the suspension started only at the leading edge of the deflecting wedge. However, in the present case the entire flow field is filled with a gas–dust suspension and the initial shock wave has steady-state structure relative to the shock front. In former studies the transmitted shock wave starts its propagation into the suspension and is reflected from the wedge at the same time. It is therefore obvious that the two unrelated processes of (2D) reflection and (1D) “transitional” relaxation occur simultaneously. In the present case the suspension behind the incident shock wave has reached steady state (i.e., it is a traveling wave) before the shock reaches the wedge leading edge. The reflection process from the deflecting wedge is studied for different dust mass loadings and different dust-particle diameter. It is shown that when the dust loading is low and the dust particle diameter is small the wave reflection pattern is similar to that observed in a similar pure gas case. In addition, an equilibrium state is reached, behind the evolved waves, very quickly. On the other hand, when the dust loading is relatively high and/or the dust particle diameter is relatively large, the observed reflection wave pattern is very different from that seen in a similar pure gas case. In such cases it takes much longer time to reach an equilibrium state behind the reflecting waves. It is also shown that the dust presence significantly affects the (gas) pressure on the wedge surface. The higher the dust loading is, the higher the pressure on the wedge surface. Suspensions composed of solid particle of different size, but having the same dust mass loading, will approach the same equilibrium pressure. However, it will take longer time to reach an equilibrium state for suspensions having large diameter particles.

Acoustical properties of gravel

Gravel is an example of a rigid-porous granular material. It is available with several mean stone sizes and hence with a range of flow resistivity. The flow resistivity of gravel varies significantly with flow velocity. Data for low- and high-amplitude impedance are presented and compared with predictions of linear and nonlinear theories based on the Johnson-Allard model for rigid-porous media. Comparisons are made also between data and predictions for shock wave reflection and transmission at single- and multiple-layer gravel surfaces including recent data obtained with laser-generated acoustic shocks. Tolerable agreement is obtained between data and predictions. It is found that a low flow resistivity gravel layer has a reflection coefficient that has a minimum as the incident pressure is increased. A layered system that offers the lowest reflection coefficient at linear sound pressures does not continue to do so as the incident pressure is increased. [Work supported by USACE ERDC BT25 program.]