Steady Shock Research Articles

Relaxation layer in electro-magnetically driven strong shocks

A study on electro-magnetically driven shock in laboratory experiments is reported. The shock waves are driven by a compact pulse device at 40 km/s into a high-Z gas with 1 μg/cm3. The pulse power device with tapered electrodes can generate a quasi steady and one-dimensional shock. Ion-electron and ionization relaxation processes, based on a steady and 1-Dimensional shock condition, are calculated. Comparison of the experimental result to calculation one indicates that the shocks produced by the pulse power device have potential to observe ion-electron and ionization relaxation layer with an appropriate spatial scale.

Effect of Rotation on the Stability of a Stalled Cylindrical Shock and Its Consequences for Core‐Collapse Supernovae

A perturbative analysis is used to investigate the effect of rotation on the instability of a steady accretion shock (SASI) in a simple toy-model, in view of better understanding supernova explosions in which the collapsing core contains angular momentum. A cylindrical geometry is chosen for the sake of simplicity. Even when the centrifugal force is very small, rotation can have a strong effect on the non axisymmetric modes of SASI by increasing the growth rate of the spiral modes rotating in the same direction as the steady flow. Counter-rotating spiral modes are significantly damped, while axisymmetric modes are hardly affected by rotation. The growth rates of spiral modes have a nearly linear dependence on the specific angular momentum of the flow. The fundamental one-armed spiral mode (m=1) is favoured for small rotation rates, whereas stronger rotation rates favour the mode m=2. A WKB analysis of higher harmonics indicates that the efficiency of the advective-acoustic cycles associated to spiral modes is strongly affected by rotation in the same manner as low frequency modes, whereas the purely acoustic cycles are stable. These results suggest that the linear phase of SASI in rotating core-collapse supernovae naturally selects a spiral mode rotating in the same direction of the flow, as observed in the 3D numerical simulations of Blondin & Mezzacappa (2007). This emphasizes the need for a 3D approach of rotating core-collapse, before conclusions on the explosion mechanisms and pulsar kicks can be drawn.

Global transonic conic shock wave for the symmetrically perturbed supersonic flow past a cone

In this paper, we are concerned with the global existence and stability of a steady transonic conic shock wave for the symmetrically perturbed supersonic flow past an infinitely long conic body. The flow is assumed to be polytropic, isentropic and described by a steady potential equation. Theoretically, as indicated in [R. Courant, K.O. Friedrichs, Supersonic Flow and Shock Waves, Interscience Publishers, Inc., New York, 1948], it follows from the Rankine–Hugoniot conditions and the entropy condition that there will appear a weak shock or a strong shock attached at the vertex of the sharp cone in terms of the different pressure states at infinity behind the shock surface, which correspond to the supersonic shock and the transonic shock respectively. In the references [Shuxing Chen, Zhouping Xin, Huicheng Yin, Global shock wave for the supersonic flow past a perturbed cone, Comm. Math. Phys. 228 (2002) 47–84; Dacheng Cui, Huicheng Yin, Global conic shock wave for the steady supersonic flow past a cone: Polytropic case, preprint, 2006; Dacheng Cui, Huicheng Yin, Global conic shock wave for the steady supersonic flow past a cone: Isothermal case, Pacific J. Math. 233 (2) (2007) 257–289] and [Zhouping Xin, Huicheng Yin, Global multidimensional shock wave for the steady supersonic flow past a three-dimensional curved cone, Anal. Appl. 4 (2) (2006) 101–132], the authors have established the global existence and stability of a supersonic shock for the perturbed hypersonic incoming flow past a sharp cone when the pressure at infinity is appropriately smaller than that of the incoming flow. At present, for the supersonic symmetric incoming flow, we will study the global transonic shock problem when the pressure at infinity is appropriately large.

Failure Analysis of Reverse Shaft in the Transmission System of All-Terrain Vehicles

This paper presents a failure analysis of a reverse shaft in the transmission system of an all-terrain vehicle (ATV). The reverse shaft with splines fractured into two pieces during operation. Visual examination of the fractured surface clearly showed cracks initiated from the roots of spline teeth. To find out the cause of fracture of the shaft, a finite element analysis was carried out to predict the stress state of the shaft under steady loading and shock loading, respectively. The steady loading was produced under normal operation, while the shock loading could be generated by an abrupt change of operation such as start-up or sudden braking during working. Results of stress analysis reveal that the highest stressed area coincided with the fractured regions of the failed shaft. The maximum stress predicted under shock loading exceeded the yield strength and was believed to be the stimulant for crack initiation and propagation at this weak region. The failure analysis thus showed that the premature fatigue fracture of the shaft was caused by abnormal operation. Finally, some suggestions to enhance service durability of the transmission system of ATV are discussed.

Study of the Effect of Glow Discharges Near aM = 3 Bow Shock

This paper aims at investigating the effect of discharges generated near steady bow shocks and their possible use for localized heat deposition leading to drag reduction. We report the observation of steady discharges generated in front of a blunted model in a M = 3 supersonic flow. The test model is designed as a pair of coaxial electrodes, and set up in the ONERA R1Ch M = 3 blowdown wind tunnel. A high voltage power supply is used to generate negative discharges. A corona regime, a glow regime, and a filamentary arc regime are observed. The negative corona regime consists of Trichel pulses dissipating less than 200 mW of electrical power. The glow discharge absorbs powers up to 0.5 kW. It displays a strong light emission in the vicinity of the shock front, followed by a darker region downstream of the shock. The drag coefficient is measured and shows no measurable change when a glow discharge is switched on. To explain this and further investigate the effect of localized heat deposition at the shock front, modified Rankine-Hugoniot jump relations are computed, taking into account a volumetric heat source. This allows one to compute a fair estimate of the drag coefficient and shows that drag reduction by localized heating in the shock front is possible. However, it also shows that in our experiment, the plasma thermal power is too small to appreciably reduce the drag, possibly because of the role of the electron impact excitation of N 2 vibrations, whose fairly long relaxation time could shift downstream the effective gas heating. More generally, the model shows that power-efficient plasma-induced drag reduction requires high plasma heating efficiency.

A new framework for evaluating potential risk of back disorders due to whole body vibration and repeated mechanical shock*

A number of studies have examined the potential relationship between exposure to occupational vibration and low back pain associated with operation of vehicles. Only a handful of studies, however, have attempted to differentiate between the relative contributions of the steady state and transient mechanical shock components (the latter also being known as ‘jarring and jolting’, ‘high acceleration event’, ‘multiple shocks’ and ‘impact’) of the vibration exposure. The primary objective of this paper is to present a review of current studies that examine mechanical shock, present a case for the importance of evaluating both steady state and mechanical shock components and propose a new framework for evaluating the health effects due to occupational vibration exposure. A computerized bibliographical search of several databases was performed with special reference to the health effects of mechanical shock in relation to lower back disorders. Based on the analysis, eight experimental studies and nine epidemiological studies with relevance to exposure to ‘mechanical shock’ were identified. These studies suggested that rough vehicle rides are prevalent and that repeated exposure to mechanical shock may increase the risk of lower back pain. There is an urgent need for assessing the health effects of mechanical shocks in epidemiological studies. In particular, the new ISO 2631–5: International Organization for Standardization 2004 standard for shock exposure assessment should be evaluated with regard to musculoskeletal health effects. *The findings and conclusions in this report are those of the author(s) and do not necessarily represent the views of the National Institute for Occupational Safety and Health.

Shock wave structure in a strongly nonlinear lattice with viscous dissipation

The shock wave structure in a one-dimensional lattice (e.g., granular chain of elastic particles) with a power law dependence of force on displacement between particles (F proportional to delta(n)) with viscous dissipation is considered and compared to the corresponding long wave approximation. A dissipative term depending on the relative velocity between neighboring particles is included to investigate its influence on the shape of a steady shock. The critical viscosity coefficient p(c), defining the transition from an oscillatory to a monotonic shock profile in strongly nonlinear systems, is obtained from the long-wave approximation for arbitrary values of the exponent n. The expression for the critical viscosity is comparable to the value obtained in the numerical analysis of a discrete system with a Hertzian contact interaction (n=3/2) . The expression for p(c) in the weakly nonlinear case converges to the known equation for the critical viscosity. An initial disturbance in a discrete system approaches a stationary shock profile after traveling a short distance that is comparable to the width of the leading pulse of a stationary shock front. The shock front width is minimized when the viscosity is equal to its critical value.

Stellar wind/ISM shocks in gravitational potentials

The geometry of stellar wind bow shocks has been solved analytically in the thin shell, no gravity limit by Wilkin. We determine when, where and how gravity influences those results. In particular, we find that gravity strongly influences weak wind shocks, potentially prevents steady shocks and even pulls shocks back on to the star.

Analysis of simulation technique for steady shock waves in materials with analytical equations of state

We calculate and analyze a thermodynamic limit of a multiscale molecular dynamics based scheme that we have developed previously for simulating shock waves. We validate and characterize the performance of the former scheme for several simple cases. Using model equations of state for chemical reactions and kinetics in a gas and a condensed phase explosive, we show that detonation wave profiles computed using the computational scheme are in good agreement with the steady state wave profiles of hydrodynamic direct numerical simulations. We also characterize the stability of the technique when applied to detonation waves and describe a technique for determining the detonation shock speed.

On the CO Near‐Infrared Band and the Line‐splitting Phenomenon in the Yellow Hypergiant ρ Cassiopeiae

We report on multiepoch optical and near-infrared spectroscopy around the first-overtone rovibrational band of CO in the pulsating yellow hypergiant ρ Cas, one of the most massive stars in the Galaxy and a candidate SN II progenitor. We argue that the double cores of the CO absorption lines, which have previously been attributed to separate circumstellar shells expelled during its recurrent outbursts, result in fact from a superposition of a wide absorption line and a narrow central emission line. The CO line doubling returns over subsequent pulsation cycles, where the superposed line emission assumes its largest intensity near phases of maximum light. We find that the morphology and behavior of the CO band closely resemble the remarkable line-splitting phenomenon also observed in optical low-excitation atomic lines. Based on radiative transport calculations, we present a simplified model of the near-infrared CO emission emerging from cooler atmospheric layers in the immediate vicinity of the photosphere. We speculate that the kinetic temperature minimum in our model results from a periodic pulsation-driven shock wave. We further discuss a number of alternative explanations for the origin of the ubiquitous emission-line spectrum, possibly due to a quasi-chromosphere or a steady shock wave at the interface of a fast expanding wind and the interstellar medium. We present a number of interesting spectroscopic similarities between ρ Cas and other types of cool variable supergiants, such as the RV Tau and R CrB stars. We further propose a possibly common mechanism for the enigmatic outburst behavior of these luminous pulsating cool stars.

Reversal of magnetic field rotation in the reconnection layer due to shear flow effects

[1] We investigate the effects of shear flows on the so-called “component reconnection,” in which the guide field By ≠ 0, by solving a one-dimensional Riemann problem for magnetopause reconnection using a resistive MHD simulation. Specifically, we consider the existence of a shear flow perpendicular to the antiparallel magnetic field Bz, while a finite shear flow tangential to Bz may also be present. In the cases without a magnetosheath flow and having thus a sheared flow across the reconnection layer, two time-dependent intermediate shocks TDIS and TDIS′ are present on the magnetosheath side and the magnetospheric side, respectively, and the strength of TDIS is much stronger than that of TDIS′. Nevertheless, the existence of the shear flows modifies the structure and strength of the time-dependent intermediate shocks significantly. (1) The perpendicular shear flow Vy0 can lead to the reversal of the rotation sense of the tangential magnetic field in time-dependent intermediate shocks. The critical shear flow speeds, Vc and V′c, for the reversal of field rotations in TDIS and TDIS′, respectively, are calculated. (2) For shear flow speed Vy0 = Vc, the strong TDIS is replaced by a steady intermediate shock (IS), whereas at Vy0 = V′c an Alfven wave pulse is present in the reconnection layer. (3) The presence of tangential shear flow Vz0 alters not only the strength of TDIS and TDIS′ but also the critical speeds Vc and V′c. The critical shear flow speeds obtained from our simulation are found to agree very well with those from the ideal magnetohydrodynamics (MHD), in which the time-dependent intermediate shocks are replaced by rotational discontinuities.

ATTENUATION OF SPURIOUS OSCILLATIONS IN THE NUMERICAL CAPTURE OF SHOCK WAVES

Artificial viscosity is often expressed as a superposition of linear and quadratic terms in the first derivative of the velocity field. In trying to find a continuous solution for the hydrodynamic equations, we propose an alternative one-term artificial viscosity which is a linear form of the derivative of the specific volume. It is shown that this artificial viscosity is able to capture the profile of the steady plane shock wave, largely removing the non-physical oscillations originated by the artificial viscosity of von Neumann and Richtmyer. Analytical and numerical calculations for one-dimensional shock using both artificial viscosities are compared.

A New Smoothness Indicator for the WENO Schemes and Its Effect on the Convergence to Steady State Solutions

The convergence to steady state solutions of the Euler equations for the fifth-order weighted essentially non-oscillatory (WENO) finite difference scheme with the Lax---Friedrichs flux splitting [7, (1996) J. Comput. Phys. 126, 202---228.] is studied through systematic numerical tests. Numerical evidence indicates that this type of WENO scheme suffers from slight post-shock oscillations. Even though these oscillations are small in magnitude and do not affect the "essentially non-oscillatory" property of WENO schemes, they are indeed responsible for the numerical residue to hang at the truncation error level of the scheme instead of settling down to machine zero. We propose a new smoothness indicator for the WENO schemes in steady state calculations, which performs better near the steady shock region than the original smoothness indicator in [7, (1996) J. Comput. Phys. 126, 202---228.]. With our new smoothness indicator, the slight post-shock oscillations are either removed or significantly reduced and convergence is improved significantly. Numerical experiments show that the residue for the WENO scheme with this new smoothness indicator can converge to machine zero for one and two dimensional (2D) steady problems with strong shock waves when there are no shocks passing through the domain boundaries.

Effects of a Single-pulse Energy Deposition on Steady Shock Wave Reflection

The effects of energy deposition in the free stream on steady regular and Mach shock wave reflections are studied numerically. A short-duration laser pulse is focused upstream of the incident shock waves. It causes formation of the expanding blast wave and the residual hot-spot interacting in a complex way with the steady shock wave reflection. It was found that the laser energy addition in the free stream may force the transition from regular to Mach reflection in the dual solution domain. In contrast to previously reported numerical results, the transition from Mach to regular reflection has not been reproduced in our refined computations since the Mach reflection is restored after the flow perturbation.

Modeling plastic shocks in periodic laminates with gradient plasticity theories

Steady plastic shocks generated by planar impact on metal–polymer laminate composites are analyzed in the framework of gradient plasticity theories. The laminate material has a periodic structure with a unit cell composed of two layers of different materials. First- and second-order gradient plasticity theories are used to model the structure of steady plastic shocks. In both theories, the effect of the internal structure is accounted for at the macroscopic level by two material parameters that are dependent upon the layer's thickness and the properties of constituents. These two structure parameters are shown to be uniquely determined from experimental data. Theoretical predictions are compared with experiments for different cell sizes and for various shock intensities. In particular, the following experimental features are well-reproduced by the modeling: • the shock width is proportional to the cell size; • the magnitude of strain rate is inversely proportional to cell size and increases with the amplitude of applied stress following a power law. While these results are equally described by both the plasticity theories, the first gradient plasticity approach seems to be favored when comparing the structure of the shock front to the experimental data.

Far-Ultraviolet Spectral Images of the Cygnus Loop

We present far-ultraviolet (FUV) spectral images, measured at C IV λ1550, He II λ1640, Si IV+O IV] λ1400, and O III] λ1664, of the entire Cygnus Loop, observed with the SPEAR/FIMS instrument. The spatial distribution of FUV emission generally corresponds to a limb-brightened shell and is similar to optical, radio, and X-ray images. The features found in the present work include a carrot, diffuse interior, and breakout features, which have not been seen in previous FUV studies. Shock velocities of 140-160 km s-1 are found from the line ratio of O IV] to O III], which is insensitive not only to resonance scattering but also to elemental abundance. The estimated velocity indicates that fast shocks are widespread across the remnant. By comparing various line ratios with steady state shock models, it is also shown that resonance scattering is widespread.

Analytical modeling of the steady radiative shock

In a paper dated 2000 [1], a fully analytical theory of the radiative shock has been presented. This early model had been used to design [2] radiative shock experiments at the Laboratory for the Use of Intense Lasers (LULI) [3-5]. It became obvious from numerical simulations [6, 7] that this model had to be improved in order to accurately recover experiments. In this communication, we present a new theory in which the ionization rates in the unshocked (Ż 1 ) and shocked (Z 2 ≠ Z 1 ) material, respectively, are included. Associated changes in excitation energy are also taken into account. We study the influence of these effects on the compression and temperature in the shocked medium.

On the Hydrodynamic Interaction of Shock Waves with Interstellar Clouds. II. The Effect of Smooth Cloud Boundaries on Cloud Destruction and Cloud Turbulence

The effect of smooth cloud boundaries on the interaction of steady planar shock waves with interstellar clouds is studied using a local adaptive mesh refinement technique with an axisymmetric Godunov hydrodynamic scheme. A three-dimensional calculation is also done to confirm the two-dimensional results. We find that smooth cloud boundaries significantly affect cloud morphology and retard cloud destruction. After shock passage, a sharp density jump formsdue to velocity gradientsgeneratedinthe smooth cloud boundary.Werefer to this density jump as a‘‘slip surface’’because the velocity isshearedparalleltoits surface. Theformation of aslip surface leads tocompletecloud destruction because of the Kelvin-Helmholtz and Rayleigh-Taylor instabilities. We construct analytic models of cloud drag and vorticity generation that compare well with the numerical results. Small shreds formed by the instabilities have significant velocity dispersions of 10%‐20% of the ambient shock velocity. They could be related to the small cold H i clouds recently observed by Stanimirovic´ & Heiles. The dependence of the velocity dispersion on region size, the so-called line width‐size relation, is found to be time-dependent. In the early stages, the line width‐size relation is more or less flat because of the significant small-scale fluctuations generated by the KelvinHelmholtz instability. In the later stages, the small-scale fluctuations tend to damp, leading to a line width that increases with size. The possibility of gravitational instability triggered by shock compression is discussed. We show thatgravitationalcollapsecanbeinducedinaninitiallyuniformcloudbyaradiativeshock( �< 4/3)onlyif itisnot too strong and nonthermal motions are weak. Subject headingg hydrodynamics — ISM: clouds — shock waves — supernova remnants — turbulence

Transition scale at quasiperpendicular collisionless shocks: Full particle electromagnetic simulations

One-dimensional full particle simulations of almost perpendicular supercritical collisionless shocks over a wide Alfvén Mach number range are presented. The physical ion to electron mass ratio has been used; however, due to computer time limitations a value of the ratio of the electron plasma frequency to the electron gyrofrequency of 4 has been assumed. The shock structure in the density and magnetic field consists of a foot, formed by reflected ions, and a steeper ramp leading to an overshoot. It is shown that the shock ramp scale in units of the upstream ion inertial length is more or less constant and close to 1 over the Mach number regime investigated, i.e., up to MA≈14. Further, the convective ion gyroradius in units of the upstream ion inertial length is also constant with the Mach number when the gyroradius is evaluated with the magnetic field strength in the overshoot. Thus the shock transition also scales with the convected gyroradius. When a hyperbolic tangent function is fitted to the density profile the neglect of the overshoot essentially results, for high Mach number shocks, in a fit of the foot and not of the ramp, i.e., the shock transition scale is grossly overestimated. The simulations suggest that in a regime above the critical Mach number the nonlinear steepening is balanced by gyroviscosity of the reflected ions as the shock ramp scale is given by the convected gyroradius in the overshoot. At higher Mach numbers the shock becomes unsteady the ramp scale can become as small as several electron inertial length during a part of the reformation cycle. At still higher Mach number microinstabilities in the foot may have growth times much shorter than the inverse ion gyrofrequency so that they can lead to ion heating, and a steady resistive shock will result.

Numerical simulations of core-collapse supernovae imposing steady shock approximation

We carried out one-dinensional long-term numerical simulations of core-collapse supernovae imposing steady shock approximation. As a result of a computation, we found core does not explode and shock wave stalls within several hundreds milliseconds from bounce. However, we execute long-term numerical simulation until 3.5 seconds from bounce with short CPU time using Personal Computer.