Decay Of Shock Waves Research Articles

Growth and decay of shock and acceleration waves in a traffic flow model with relaxation

The usual Ficken-based constitutive relation for traffic flux is replaced with one based on the Maxwell–Cattaneo model. The resulting flux law, which now takes into account the reaction time of driver and vehicle, results in a second-order, hyperbolic generalization of Burgers’ equation as the PDE governing the traffic density. An analytical study of this equation is presented with an emphasis on shock and related kinematic wave phenomena. Specifically, the exact traveling wave solution (TWS) is derived and it is shown that shock formation is possible only if the diffusivity is non-vanishing. Using singular surface theory, exact amplitude expressions for both shock and acceleration waves are obtained and their temporal evolution determined. The exact upper bound of the reaction time parameter is established and connections between singular surface and TWS results are noted.

Improved target stability using picket pulses to increase and shape the ablator adiabat

Hydrodynamic simulations have shown that a picket pulse preceding the main target drive pulse in a direct-drive inertial confinement fusion implosion can reduce both the ablation-interface Rayleigh–Taylor (RT) seed and growth rate by increasing the adiabat (ratio of the plasma pressure to the Fermi-degenerate pressure) while maintaining the low adiabat in the inner-fuel layer for optimal target compression and a minimal drive energy for ignition. Experiments with planar and spherical targets have been carried out on the OMEGA [T. R. Boehly, D. L. Brown, R. S. Craxton, R. L. Keck, J. P. Knauer, J. H. Kelly, T. J. Kessler, S. A. Kumpan, S. J. Loucks, S. A. Letzring, F. J. Marshall, R. L. McCrory, S. F. B. Morse, W. Seka, J. M. Soures, and C. P. Verdon, Opt. Commun. 133, 495 (1997)] laser system, showing that the RT growth of nonuniformities was reduced by picket-pulse laser illumination. Adiabat shaping in spherical targets has been investigated with two types of picket pulses—a “decaying shock wave” and a “relaxation” picket. Planar growth measurements using a wide, intense picket to raise the adiabat of a CH foil showed that the growth of short-wavelength perturbations was reduced, and even stabilized, by adjusting the intensity of the picket. Planar imprint experiments showed the expected reduction of imprinting when a picket pulse is used. The data show that the imprint level was reduced when a picket was added and for short wavelengths was as effective as one-dimensional (1D), 1.5 Å smoothing by spectral dispersion. A series of implosion experiments with a 130 ps wide picket pulse showed a clear improvement in the performance of direct-drive implosions when the picket pulse was added to the drive pulse. Results from relaxation-picket implosions show larger yields from fusion reactions when the picket drive was used. These adiabat-shaping concepts make the likelihood of achieving ignition with direct-drive implosions on the National Ignition Facility [W. S. Hogan et al., Nucl. Fusion 41, 567 (2001)] significantly more probable.

Propagation and Decay of Shock Waves in Turbofan Engine Inlets

Numerical experiments are carried out to investigate the tone noise radiated from a turbofan engine inlet under conditions at which the relative flow past the rotor tip is supersonic. Under these conditions, the inlet tone noise is generated by the upstream-propagating rotor-locked shock wave field. The spatial evolution of this shock system is studied numerically for flows through two basic hard-walled configurations: a slender nacelle with large throat area and a thick nacelle with reduced throat area. With the flight Mach number set to 0.25, the spatial evolution of the acoustic power through the two inlets reveals that the reduced throat area inlet provides superior attenuation. This is attributed to the greater mean flow acceleration through its throat and is qualitatively in accord with one-dimensional theory, which shows that shock dissipation is enhanced at high Mach numbers. The insertion of a uniform extension upstream of the fan is shown to yield greater attenuation for the inlet with large throat area, while the acoustic performance of the reduced throat area inlet is degraded. This occurs because the interaction of the nacelle and spinner potential fields is weakened, resulting in a lower throat Mach number. The effect of forward flight on the acoustic power radiated from the two inlets is also investigated by examining a simulated static condition. It is shown that the slender nacelle radiates significantly less power at the static condition than in flight, whereas the power levels at the two conditions are comparable for the thick nacelle. The reason for this behavior is revealed to be a drastic overspeed near the leading edge of the slender nacelle, which occurs to a lesser degree in the case of the thick inlet. This has implications for ground acoustic testing of aircraft engines, which are discussed.

Analysis of Gas Flow Evolution and Shock Wave Decay in Detonation Thermal Spraying Systems

The reactive Euler equations with variable gas properties are solved in both axisymmetric and plane two-dimensional flows to analyze the gas flow evolution, shock wave decay, and shock reflections in pulsed detonation thermal spraying (PDTS) systems. The gas phase governing equations are numerically solved using a high-resolution shock capturing numerical method. Expansion-compression waves are formed upon external gas expansion and persist for a long time (on the time scale of a PDTS cycle) with wide fluctuations in the gas velocity and temperature. The results show that the reflected shock wave from the substrate dies out extremely fast that micron-sized particles used in PDTS do not encounter these transients. The external shock wave decay is also analyzed for different reactive mixtures and flow geometries and is related to the truncation of the computational domain and the implementation of numerical boundary conditions at the open end boundaries.

Ion acceleration in a solitary wave by an intense picosecond laser pulse.

Acceleration of ions in a solitary wave produced by shock-wave decay in a plasma slab irradiated by an intense picosecond laser pulse is studied via particle-in-cell simulation. Instead of exponential distribution as in known mechanisms of ion acceleration from the target surface, these ions accelerated forwardly form a bunch with relatively low energy spread. The bunch is shown to be a solitary wave moving over expanding plasma; its velocity can exceed the maximal velocity of ions accelerated forward from the rear side of the target.

Efficiency of ablation loading and the limiting destruction depthof material irradiated by a high-power laser pulse

The problems of calculating the energy of a substance encompassed by a shock wave (the ablation loadingefficiency) and determining the limiting destruction depth of asolid irradiated by a plasma-producing laser beam of intensityvarying in a broad range from 108 to 1014 W cm-2 are analytically solved. The limiting destruction depth of material iscalculated. This depth is a total thickness of the substancelayers evaporated and melted during the laser pulse and of amelted substance layer behind the front of a shock wave decaying in a target after the pulse end. For laser pulses withintensities above ~ 1011— 1012 W cm-2 and duration 20 —100 ns, the material destruction depth caused by the action ofthe decaying shock wave substantially exceeds the depth ofevaporation and melting of material during irradiation by thelaser pulse.

Laser shock experiments with nanoseconds pulses: a new tool for the reproduction of shock defects in olivine

Laser shock experiments with olivine have been carried out in order to test the capability of this new experimental approach to produce known shock defects in olivine. To determine the shock conditions, numerical simulations of experiments have been undertaken, indicating the generation of a rapidly decaying shock wave with an initial pressure of 60 GPa and a duration of 5 ns. The pressure prevailed thus distinctly shorter than in conventional shock experiments with explosives or light gas guns (0.1–1 μs). Despite this shorter pressure pulse in our laser experiment, TEM revealed that a high density of dislocations and planar fractures was activated in olivine up to a depth of 30 μm. A drastic decrease of dislocation and fracture densities observed deeper in the sample is attributed to the decay of the shock wave. The dislocation systems and the orientations of planar fractures in our experiment are identical to those found in naturally shocked olivine. The TEM observations indicate furthermore that fractures in olivine are the sources of dislocations and that the stress field around fractures determines which slip system is activated. Our study demonstrates that laser shock experiments are not only a powerful new tool in the reproduction of shock defects but also an indispensable tool to understand better the role of time in impact processes and the formation mechanisms of shock defects.

Collisional Disruption of Ice by High-Velocity Impact

High-velocity impact among icy planetesimals is a physical phenomenon important to the planetary evolution process in the outer Solar System. In order to study this phenomenon, impact experiments on water ice were made by using a two-stage light gas gun installed in a cold room (−10°C) to clarify the elementary processes of collisional disruption and to study the reaccumulation and the escape conditions of the impact fragments. Cubic ice targets ranging in size from 15 to 100 mm were impacted by a nylon projectile of 7 mg with an impact velocity ( v i) from 2.3 to 4.7 km/s. The corresponding mass ratio of the projectile to the target ( m p/ M t) ranged from 10 −3 to 10 −6, which is two orders of magnitude lower than that used in previous studies (Arakawa et al. 1995, Icarus 118, 341–354). As a result, we obtained data on elementary processes such as attenuation of the shock wave and fragmentation dynamics. We found that the shock pressure attenuates in the ice target according to the relation of P∝( L p/ r 2, irrespective of the mass ratio between 10 −3 and 10 −5, where L p is the projectile size and r is a propagation distance. The largest fragment mass ( m l) normalized by the original target mass has a good relationship to a nondimensional impact stress ( P I, NDIS) defined as the ratio of the antipodal pressure to the material strength. This relationship is described as m l/ M t ∝ P I −1.7 for a wide range of impact conditions (50 m/s< v i<4 km/s and 10 −1< m l/ M t<10 −6), and shows the utility of NDIS. Using a measured shock wave decay constant of 2, the reaccumulation and the escape conditions of icy bodies in high-velocity collisions were estimated. As a result, it was clarified that a rubble pile could be formed when large icy bodies (radius>20 km) reaccumulated. On the other hand, when smaller icy bodies (radius<2 km) disrupted catastrophically, all fragments escaped and a rubble pile was never formed.

Experimental study of laser-driven shock waves in stainless steels

Two industrial stainless steels were investigated under laser-shock loading in plasma confined regime with water at nearly 10 GW/cm2 irradiance, driving to stress loadings close to 7 GPa—20 ns at the surface of the targets. A velocimetry interferometer system for any reflector was used to measure shock wave decay and estimate, through the determination of elastic precursors, the dynamic yield strengths at strain rates approaching 106 s−1. Some 50%–100% increases could be found between dynamic yield strengths and static plastic flow limits at 10−3 s−1. Different behaviors were noticed: on AISI 316L Austenitic steel, elastic precursors were shown to have constant values, whatever the propagation depths, whereas on a Martensitic X12CrNiMo12-2-2 steel, precursor attenuations in depth were evidenced. Concerning the application of laser-shock waves to reinforce surfaces, the determination of Hugoniot elastic limits was shown to be useful to predict the plastified depths and the general evolution of plastic deformations in-depth. For instance, comparisons between shock wave profiles and in-depth residual stress fields were shown to give accurate correlations. Lastly, the propagation of laser-shock waves in work-hardened layers was also investigated, which allowed to point out some stress amplitude increases behind 316L foils in the case of a material saturated with defects (shot peening at very high coverage rate).

Influence of Baffle Plate Geometry on Decay of Shock Waves Propagating in a Beamline.

Dependency of geometries of baffle plates in a shock tube on the decay of shock waves was investigated to find an optimal design for acoustic delay lines (ADLs) in beamlines of a synchrotron radiation facility. Fabricating a thin orifice, a coned baffle plate, a diverging tube and a converging tube as a model of the ADL, we performed pressure measurement with piezo-pressure transducers by using a dedicated shock tube and two-dimensional flow visualization around the model by means of Schlieren photography. According to the results of pressure measurements, a theory of one-dimensional steady flow employed generally is not available for the coned baffle. The decay ratios defined by the strength of incident and transmitted shock waves clearly differ among the four types of the ADL models, although all of the models have the same aperture. These results suggest that non-steady phenomena observed by the Schlieren photography, such as shock wave reflection and diffraction, viscous flow behind shock waves, may be involved in shock wave decay through baffle plates.

Numerical simulation of a porous cooling effect observed when a hypersonic stream of viscous gas with a decaying shock wave flows round a wall

The concept of porous cooling observed when a hypersonic stream of viscous gas with a decaying shock wave flows round a wall is substantiated by means of a finite-difference solution of the Reynolds equations, closed by using a two-parameter dissipative turbulence model.

One-Dimensional Numerical Simulation of Shock Wave Propagation Induced by Vacuum Accidents in a Beamline.

A simulation for shock wave propagation in a vacuum tube has been conducted from the viewpoint of protection from vacuum accidents in beamlines of a synchrotron radiation facility. Inserted devices in beamlines such as absorbers, slits, masks and beryllium windows were replaced with orifices installed in a shock tube as a simulation model. One-dimensional Euler's equations with friction terms were used for estimating the effects on shock wave decay as well as the effects of friction along a tube on shock attenuation. The results indicated that the entrance diameter of the shock tube was an important parameter for determining the strength of shock waves generated by the expansion of gases at the tube entrance and that the friction effects were too large to delay the arrival time of shock waves at the end of a long tube. Moreover, shock wave propagation in a long beamline model based on the MR beamline in the National Laboratory for High Energy Physics was simulated for designing adequate protection from vacuum accidents. The present simulation provides necessary information for the design of a protection system for vacuum accidents in other facilities.

Nanoscale shock wave generation by photodissociation of impurities in solids: A molecular dynamics study

The dynamics of shock wave generation, propagation, and decay in an Ar lattice following photodissociation of an I2 impurity are studied using molecular dynamics simulation. A two-dimensional model is treated to allow the modeling of shock wave propagation over larger distances than easily accessible in full three-dimensional calculations. The shock waves are created on atomic length scales by binary collisions between the nascent photofragments and adjacent lattice atoms, and propagate long distances through the crystal in a highly directed, quasi-one-dimensional manner. As a consequence of the I/Ar mass ratio, the I fragments undergo multiple collisions with the adjacent Ar atoms situated along the I–I bond axis, generating pulse trains of shock waves, each with a characteristic initial energy, velocity, and decay rate. The dynamics of the system are interpreted using a simple one-dimensional hard sphere model.

Modeling of dynamic compression of porous iron

A relation closing the model of a porous medium, which is based on the Maxwell representation of the irreversible strain mechanism, has been obtained. This model takes into account the effect of grain (particle) size on dynamic compression. To specify the model, use is made of the experimental data on uniform compression of specimen of porous iron. The shock adiabats have been calculated. The obtained results are compared with the data of independent experiments. The evolution of compression pulses of finite duration which propagate over a porous half-space is analyzed. The grain size is shown to affect the shock wave processes in a porous medium. It has been established that it is possible to estimate the stress (pressure) in a decaying shock wave by the known mass velocity and shock adiabat.

Design of an Inert Material Type Plane Wave Generator

AbstractA simple model calculation, a hydrodynamic code simulation and experimental verifications are presented in this paper for the design of a plane wave generator (PWG), composed of plexiglass as the inert material and Composition‐B (Comp‐B) as the high explosive with a density of about 1.72 g/cm3. Along with the design concept of the PWG, a simple model, based on the steady state detonation and decaying shock wave theory is proposed to calculate the time difference. Calculation results of this model are in good agreement with those of the experiment.The experimental verifications are done with the aid of a Hamamatsu streak camera, taking the so‐called “time difference” as a measure of the quality of a plexiglass PWG. The smaller the time difference, the better the PWG which will generate a wave approaching a plane wave.A hydrodynamic computer code (2DL) is used to study the inert material type PWG. The results agree with experiment and with the simple model.From our study we have the following conclusions: The time difference is less than 0.04 microseconds; For the generation of a plane wave, a PWG of height 30 mm requires a base angle of 25°, and a PWG of height 20 mm requires a base angle of 30°; It is expected that the model will be applicable to other heights and base angles.

Decay of shock waves in a dusty-gas shock tube

A numerical study is performed for the unsteady nonequilibrium flow of a gas-particle mixture in a shock tube, where a semi-empirical formula for a single particle is assumed to calculate the drag and heat transfer rate of the particle cloud. To simulate actual flows of the mixture in which the size of the particles is distributed over a finite range, the motion of the particles is analyzed by dividing them into several groups according to their different diameters. It is shown that the particles of diameter larger than the average value cause a significant delay in the relaxation of the gas-particle flow. Good agreement is obtained between the numerical and the experimental results of the decrease in the shock propagation velocity, except for strong shock waves transmitted into dusty gas with a high loading ratio.

Shock wave decay and spall strength in laser-matter interaction

A new experimental method was developed in order to estimate the decay of the laser-generated shock waves and the dynamic spall pressure. Experiments were performed on aluminum, copper, and unidirectional carbon fiber epoxy composites with impact strain rates of the order of 107 s−1. The following values for dynamic spall pressure and pressure gradient were obtained (to an accuracy of a factor of two): aluminum [25 kb (kb=kilobars), 60 kb/mm]; copper (20 kb, 180 kb/mm); carbon fiber epoxy composite (0.3 kb, 15 kb/mm) perpendicular to the fiber direction; and (7 kb, 100 kb/mm) when the impact is parallel to the fiber direction.

The evolution laws of dilatational spherical and cylindrical weak nonlinear shock waves in elastic non-conductors

The theory of singular surfaces yields a set of coupled evolution equations for the shock amplitude and the amplitudes of the higher order discontinuities which accompany the shock. To solve these equations, we use perturbation methods with a perturbation parameter ε characterising the initial shock amplitude. It is shown that for decaying shock waves, if the accompanying second order discontinuity is of order one, the straightforward perturbation procedure yields uniformly valid solutions, but if the accompanying second order discontinuity is of order ε, the method of multiple scales is needed in order to render the perturbation solutions uniformly valid with respect to the distance of travel. We also construct shock wave solutions from modulated simple wave solutions which are obtained with the aid ofHunter & Keller's “Weakly Nonlinear Geometrical Optics” method. The two approaches give exactly the same results within their common range of validity. The explicit evolution laws thus obtained enable us to see clearly how weak nonlinear curved shock waves are attenuated because of the effects of geometry and material nonlinearity, and on what length scale these effects are most pronounced.

Energy transport in aluminum targets irradiated by a 263-nm laser

Emission from the rear side of 263-nm laser irradiated thin foil targets shows the temporal profile of rear surface heating by several processes with different energy transport mechanisms. Formation and decay of shock waves are observed by varying target thickness. Propagation of a thermal conduction wave is clearly separated from the shock propagation.

Uniformly valid analytical solution to the problem of a decaying shock wave

An explicit representation of an analytical solution to the problem of decay of a plane shock wave of arbitrary strength is proposed. The solution satisfies the basic equations exactly. The approximation lies in the (approximate) satisfaction of two of the Rankine-Hugoniot conditions. The error incurred is shown to be very small even for strong shocks. This solution analyses the interaction of a shock of arbitrary strength with a centred simple wave overtaking it, and describes a complete history of decay with a remarkable accuracy even for strong shocks. For a weak shock, the limiting law of motion obtained from the solution is shown to be in complete agreement with the Friedrichs theory. The propagation law of the non-uniform shock wave is determined, and the equations for shock and particle paths in the (x, t)-plane are obtained. The analytic solution presented here is uniformly valid for the entire flow field behind the decaying shock wave.