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The physics governing the response of materials to shock loading has many applications in various fields, ranging from Earth and planetary science to engineering and ballistics. Elucidating the behavior of materials experiencing the passage of shock waves motivates active research worldwide, including experimental developments with in situ and time-resolved measurements, modern computational approaches, and multi-scale simulations.
The structural components that comprise nuclear reactors and their supporting structures are subjected to harsh operating environments that can challenge their integrity, especially after exposure for extended durations or under accident condition. As one of the most significant components of a Reactor, the Reactor Pressure Vessel (RPV) is exposed to an aggressive environment during the operation time (e.g. more than 40 years). Ageing degradation mechanisms (e.g. thermo-fatigue) could grow initial defects up to a critical size, increasing the susceptibility to failure in the RPV. The conventional methods are mostly based on simple crack and structure geometries. Very limited studies consider the real conditions of the RPV subjected to a thermal shock due to a Loss of Coolant Accident (LOCA). During a LOCA event, the most severe conditions take place when the emergency core cooling (ECC) water is injected inside the cold legs filled initially with hotter water and/or steam. The rapid cooling of the down-comer and the internal RPV surface followed probably by re-pressurization of the RPV causes large temperature gradients and variation of pressure which induces thermal-mechanical stresses. In order to develop the model for integrity assessment of a reactor pressure vessel (RPV) subjected to pressurized thermal shock (PTS), a multi-physics simulation, which includes the thermo-hydraulic, thermo-mechanical and fracture mechanics analyses is necessary.
A linear analytical solution is derived for the gravitational shock wave produced by a particle of mass M that decays into a pair of null particles. The resulting space-time is shown to be unperturbed and isotropic, except for a discontinuous perturbation on a spherical null shell. Formulae are derived for the perturbation as a function of polar angle, as measured by an observer at the origin observing clocks on a sphere at distance R. The effect of the shock is interpreted physically as an instantaneous displacement in time and velocity when the shock passes the clocks. The time displacement is shown to be anisotropic, dominated by a quadrupole harmonic aligned with the particle-decay axis, with a magnitude δτ ~ GM/c 3 , independent of R. The velocity displacement is isotropic. The solution is used to derive the gravitational effect of a quantum state with a superposition of a large number of randomly oriented, statistically isotropic particle decays. This approach is shown to provide a well-controlled approximation to estimate the magnitude of gravitational fluctuations in systems composed of null point particles up to the Planck energy in a causal diamond of duration τ = 2R/c, as well as quantum-gravitational fluctuations of black holes and cosmological horizons. Coherent large-angle quantum distortions of macroscopic geometry from fluctuations up to the Planck scale are shown to grow linearly with the duration, with a variance $\langle$δτ 2 $\rangle$ ~ τtP much larger than that produced in models without causal quantum coherence.
The research efforts funded by the Uranus Data Analysis Program (UDAP) grant to the Bartol Research Institute (BRI) involved the study of magnetic field waves associated with the Uranian bow shock. Upstream wave studies are motivated as a study of the physics of collisionless shocks. Collisionless shocks in plasmas are capable of 'reflecting' a fraction of the incoming thermal particle distribution and directing the resulting energetic particle motion back into the upstream region. Once within the upstream region, the backward streaming energetic particles convey information of the approaching shock to the supersonic flow. This particle population is responsible for the generation of upstream magnetic and electrostatic fluctuations known as 'upstream waves', for slowing the incoming wind prior to the formation of the shock ramp, and for heating of the upstream plasma. The waves produced at Uranus not only differed in several regards from the observations at other planetary bow shocks, but also gave new information regarding the nature of the reflected particle populations which were largely unmeasurable by the particle instruments. Four distinct magnetic field wave types were observed upstream of the Uranian bow shock: low-frequency Alfven or fast magnetosonic waves excited by energetic protons originating at or behind the bow shock; whistler wave bursts driven by gyrating ion distributions within the shock ramp; and two whistler wave types simultaneously observed upstream of the flanks of the shock and argued to arise from resonance with energetic electrons. In addition, observations of energetic particle distributions by the LECP experiment, thermal particle populations observed by the PLS experiment, and electron plasma oscillations recorded by the PWS experiment proved instrumental to this study and are included to some degree in the papers and presentations supported by this grant.
Two-dimensional axisymmetric, reacting viscous flow over blunt projectiles is computed to study shock-induced combustion at Mach 5.11 and Mach 6.46 in hydrogen-air mixture. A finite-difference, shock-fitting method is used to solve the complete set of Navier-Stokes and species conservation equations. In this approach, the bow shock represents a boundary of the computational domain and is treated as a discontinuity across which Rankine-Hugoniot conditions are applied. All interior details of the flow such as compression waves, reaction front, and the wall boundary layer are captured automatically in the solution. Since shock-fitting approach reduces the amount of artificial dissipation, all the intricate details of the flow are captured much more clearly than has been possible with the shock-capturing approach. This has allowed an improved understanding of the physics of shock-induced combustion over blunt projectiles and the numerical results can now be explained more readily with one-dimensional wave-interaction model than before.
Two-dimensional axisymmetric, reacting viscous flow over blunt projectiles is computed to study shock induced combustion at Mach 5.11 and Mach 6.46 in hydrogen-air mixture. A finite-difference, shock-fitting method is used to solve the complete set of Navier Stokes and species conservation equations. In this approach, the bow shock represents a boundary of the computational domain and is treated as a discontinuity across which Rankine-Hugoniot conditions are applied. All interior details of the flow such as compression waves, reaction front, and the wall boundary layer are captured automatically in the solution. Since shock-fitting approach reduces the amount of artificial dissipation, all the intricate details of the flow are captured much more clearly than has been possible with the shock-capturing approach. This has allowed an improved understanding of the physics of shock-induced combustion over blunt projectiles and the numerical results can now be explained more readily with one dimensional wave-interaction model than before.
We report on observations of the abundances of elements from Helium to Nickel in over 50 different solar energetic particle events using the Solar Isotope Spectrometer (SIS) on-board the Advanced Composition Explorer (ACE) spacecraft. It had originally been expected that the energy spectra of different elements would show spectral roll-overs at energies related to the Q/M ratio of each element. Due to the partial stripping of Fe and essentially complete stripping of O, it was expected that the Fe/O ratio would be observed to decrease with increasing energy. While many events show this pattern, others have Fe/O which is constant with energy, while for yet others Fe/O actually increases with energy. Events having constant Fe/O could simply have their spectral breaks outside of the observed energy range. However, events which show increasing Fe/O cannot be explained within the framework of spectral breaks. Possible explanations include injection of remnant heavy ions from earlier impulsive events, hybrid Events consisting of a combination of flare-accelerated and shock-accelerated particles from a single solar event, and some new physical process in shock acceleration. We will report on efforts to distinguish these possible explanations.
Ultraviolet spectra of supernova remnants obtained with the IUE satellite provide unique information concerning the shock conditions and elemental abundances in the optically bright filaments. High temperature species such as N V provide diagnostics for shock velocities above 100 k/s, and strong lines of carbon and silicon in the IUE spectral range make it possible to study the destruction of refractory grains in shocked interstellar gas. Observations of a nonradiative shock at the edge of the Cygnus Loop provide constraints on the physics of the shock front itself. Most of the very young remnants whose optical spectra show anomalous elemental abundances are too highly reddened for IUE observations, but extensive observations of the Crab Nebula and a spectrum of the supernova remnant in NGC 4449 yield carbon to oxygen ratios from which the mass of the progenitor may be estimated.
The key process in shock wave formation is related to energy dissipation, and the nature of the operative dissipation mechanism determines the basic character of the resulting shock. In the case of collisionless plasmas, the primary problem consists in the identification of the processes which can provide the necessary dissipation in relatively short spatial scale lengths. The present investigation is concerned with the various collisionless dissipation mechanisms which can operate in weak shocks, taking into account the effects of different mechanisms on shock structure. Particular attention is given to a restricted class of quasi-perpendicular low beta low Mach number shocks. Such shocks are traditionally called 'laminar shocks'. Resistive shocks are considered along with subcritical shocks observed with the aid of the ISEE spacecraft.
Precise, highly reproducible control of the laser energy is required for high confidence laser–matter interaction research such as in dynamic compression science and high energy density physics. The energy must be adjustable without affecting the pulse shape (time varying intensity) or beam smoothness. We have developed a convenient two-stage energy tuning method for a nominal 100 J, 351 nm (UV) laser. The energy is adjusted in 10 J (10%) increments by operating the laser at full energy and inserting a beam splitter in the laser output. As the splitter is located after the final frequency tripling optics, the UV pulse shape is unchanged. The energy is varied by substituting a splitter of different reflectivity. For finer 3 J (3%) increments, the infrared pulse is attenuated inside the laser before the final amplifier. This requires modest tuning to preserve the pulse shape. The demonstrated variation in shot-to-shot reproducibility is less than +/–2.5 J (5% of the full energy), irrespective of the laser output energy. These approaches can be adapted to most ~100 J class lasers. We describe these techniques and show two examples where they have elucidated the underlying physics in laser shock compression experiments. One used only the beam splitters to establish the pressure for melting in iron. The other combined both techniques to finely increment the peak stress (~2 GPa steps) in germanium to precisely determine the onset and completion of melting—including the melting kinetics. Furthermore, these unambiguous results would not be possible without the developments described here.
The ability to make simultaneous, multipoint measurements of field and plasma properties has substantially increased knowledge of the structure and physics of collisionless shocks in space. In addition to allowing the determination of the large-scale macroscopic structure of such shocks as well as reliable estimates of shock normal direction, multipoint measurements have made it possible to measure shock thicknesses and speeds under a variety of upstream conditions. This ability has enabled a number of quantitative analyses of shock structure, including the confirmation of the dispersive whistler-mode character at low Mach numbers, the assessment of the relative importance of magnetic and electrostatic forces within the shock, and a detailed examination of possible dissipation mechanisms.
Gamma-ray bursts (GRBs) are the most energetic explosions in the Universe, and their afterglow emission provides an opportunity to probe the physics of relativistic shock waves in an extreme environment. Several key pieces for completing the picture of GRB afterglow physics are still missing, including jet properties, the emission mechanism, and particle acceleration. Here, we present a study of the afterglow emission of GRB 221009A, the most energetic GRB ever observed. Using optical, X-ray, and gamma-ray data up to approximately 2 days after the trigger, we trace the evolution of the multiwavelength spectrum and the physical parameters behind the emission process. The broadband spectrum is consistent with the synchrotron emission emitted by relativistic electrons with its index of p = 2.29 ± 0.02. We identify a break energy at keV and an exponential cutoff at GeV in the observed multiwavelength spectrum. The break energy increases in time from $16.0^{+7.1}_{-4.9}$ keV at 0.65 days to $46.8^{+25.0}_{-15.5}$ keV at 1.68 days, favoring a stellar-wind-like profile of the circumburst medium with k = 2.4 ± 0.1 as in ρ(r) ∝ r -k . The high-energy attenuation at around 0.4 to 4 GeV is attributed to the maximum of the particle acceleration in the relativistic shock wave. This study confirms that the synchrotron process can explain the multiwavelength afterglow emission and its evolution.
The structure of a strong plane shock wave in a monatomic rarefied perfect gas is one of the simplest problems able to be posed in kinetic theory, and one of the hardest to solve. Its simplicity lies in the absence of solid boundaries, geometrical complications, or internal molecular energy. Its difficulty arises from the great departure of the gas from equilibrium within the shock, which invalidates many of the techniques used successfully elsewhere in kinetic theory. In addition to this theoretical challenge, the modern development of ballistics and hypersonic flight has helped to stimulate extensive theoretical and experimental interest in the shock problem. The experimenters in turn have encountered great difficulties on account of the very small physical dimensions of shocks. In fact, until very recently indeed, any close comparisons of theoretical and experimental shock structure results have been rather unprofitable due to the inadequacies of both theory and experiment. During the last few years this situation has been appreciably improved by development of the Monte Carlo method. This allows idealized 'experiments' to be performed on large computers instead of in wind tunnels, using a known intermolecular force law. The most developed of these methods has been shown to be equivalent theoretically to the Boltzmann equation and to give results which agree extremely closely with measurements of high accuracy. Thus Monte Carlo results not only form the soundest basis for our present theoretical knowledge of shock wave structure, but, for purposes of developing other theories, can also be considered a very valuable experimental resource. However, such results remain very expensive to obtain. In this thesis we develop more economical kinetic theory methods for the approximate prediction of shock structure, and compare our results with those of the Monte Carlo method.
An adaptive H-/p-refinement strategy using a novel sensor is devised and tested in a block-spectral compressible Euler code equipped with adaptive-mesh refinement (AMR) and high-order flux-reconstruction numerics. At each Gauss quadrature point (or solution point) within each spectral block (or mesh element) the discrete velocity jump ΔU = ∂U/∂y 1 Δy 1 + ∂V/∂y 2 Δy 2 + ∂W/∂y 3 Δy 3 is calculated and normalized by the local speed of sound, a. Here, the grid spacing, Δx i , is calculated in each direction as the distance between auxiliary Gauss-Lobatto points, staggered relative to the solution points. The polynomial order is increased from p = 0 to p = p max in regions of weak compression, (ΔU/a) crit < ΔU/a < 0 and kept at p = p max in regions of flow expansion ΔU/a ≥ 0, while staying at the H = 0 base mesh level. Regions experiencing strong compressions, i.e. ΔU/a < (ΔU/a) crit , are H-refined up to H = H max where H max is applied at the location of maximum compression, ΔU/a = min(ΔU/a) in the domain, while keeping p = 0 to guarantee robustness and monotonicity of the solution in the H refined region. The critical value of (ΔU/a) crit = -0.06 is found to effectively separate smooth and non-smooth solution regions, supported by a 1D detonation initiation test case in ideal gas and a shock-to-detonation transition in high explosives. Using this value, the Sod shock tube, Shu-Osher problem, double Mach reflection and a 2D detonation in a high-explosive are simulated with the proposed adaptive H-/p-refinement. In the Sod shock tube case, p-refinement resolves the (weak) contact discontinuity while H-refinement enhances the grid resolution in the shock exploiting the monotonicity of the p = 0 reconstruction. For the Shu-Osher problem, p-refinement captures the small-scale oscillations trailing the shock that would be otherwise attenuated, while H-refinement triggered by the ΔU-sensor appropriately tracks the shock. In the double Mach reflection problem, H-refinement confines the numerical diffusion around the reflected shock while p-refinement recaptures many physical features trailing the shock. Finally, in the 2D high-explosive detonation case, H-refinement follows the leading shock and resolves the curvature of the detonation wave, while p-refinement adds resolution to the trailing reaction zone. Finally, the proposed methodology is tested in a detonation-wave propagation test case in high-explosives with numerical predictions comparing favorably against experiments.
A complex two-dimensional, unsteady, viscous hypersonic shock wave interaction is numerically simulated by a high-resolution, second-order fully implicit shock-capturing scheme. The physical model consists of a nonstationary oblique shock impinging on the bow shock of a blunt body. Studies indicated that the unsteady flow patterns are slightly different from their steady counterparts. However, for the sample cases investigated the peak surface pressures for the unsteady flows seem to occur at very different impingement locations than for the steady flow cases.
A complex two-dimensional, unsteady, viscous hypersonic shock wave interaction is numerically simulated by a high-resolution, second-order fully implicit shock-capturing scheme. The physical model consists of a nonstationary oblique shock impinging on the bow shock of a blunt body. Studies indicate that the unsteady flow patterns are slightly different from their steady counterparts. However, for the sample cases investigated the peak surface pressures for the unsteady flows seem to occur at very different impingement locations than for the steady flow cases.
Precise temperature determination is a significant challenge in extreme environments of dynamic compression studies. How can radiance measurements taken in high-pressure shock experiments constrain temperature in a meaningful and physically consistent way? Experiments maintaining sample compression against a transparent window can be tailored to present a uniform measurement area with uncertain spectral emissivity. We compare several methods to analyze radiance collected at multiple wavelengths, applying statistical methods and physical principles to improve temperature inference. With proper radiance collection and analysis, dynamic temperature uncertainties become comparable to thermomechanical ambiguities of the emitting surface.
A survey of selected crossings far downstream from the subsolar shock is presented in which the overall plasma wave (PW) behavior of a selected set of nearly perpendicular crossings and another set of limited Mach number but broad geometry are delinated. The result is a generalizable PW signature, or signatures, of low Mach number shocks and some likely implications of those signatures for the weak shock's plasma physical processes on the flank. The data are found to be consistent with the presence of ion beam interactions producing noise ahead of the shock in the ion acoustic frequency range. The presence or absence, and the amplitudes, of PW activity are explainable by the presence or absence of a population of upstream ions controlled by the component of the interplanetary magnetic field normal to the solar wind flow.