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Register a new userShock formation and the ideal shape of ramp compression waves
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We derive expressions for shock formation based on the local curvature of the flow characteristics during dynamic compression. Given a specific ramp adiabat, calculated for instance from the equation of state for a substance, the ideal nonlinear shape for an applied ramp loading history can be determined. We discuss the region affected by lateral release, which can be presented in compact form for the ideal loading history. Example calculations are given for representative metals and plastic ablators. Continuum dynamics (hydrocode) simulations were in good agreement with the algebraic forms. Example applications are presented for several classes of laser-loading experiment, identifying conditions where shocks are desired but not formed, and where long duration ramps are desired.
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A general formulation was developed to represent material models for applications in dynamic loading. Numerical methods were devised to calculate response to shock and ramp compression, and ramp decompression, generalizing previous solutions for scal
ar equations of state. The numerical methods were found to be flexible and robust, and matched analytic results to a high accuracy. The basic ramp and shock solution methods were coupled to solve for composite deformation paths, such as shock-induced impacts, and shock interactions with a planar interface between different materials. These calculations capture much of the physics of typical material dynamics experiments, without requiring spatially-resolving simulations. Example calculations were made of loading histories in metals, illustrating the effects of plastic work on the temperatures induced in quasi-isentropic and shock-release experiments, and the effect of a phase transition.
Here, we provide a theoretical framework revealing that a steady compression ramp flow must have the minimal dissipation of kinetic energy, and can be demonstrated using the least action principle. For a given inflow Mach number $M_{0}$ and ramp angle $alpha$, the separation angle $theta_{s}$ manifesting flow system states can be determined based on this theory. Thus, both the shapes of shock wave configurations and pressure peak $p_{peak}$ behind reattachment shock waves are predictable. These theoretical predictions agree excellently with both experimental data and numerical simulations, covering a wide range of $M_{0}$ and $alpha$. In addition, for a large separation, the theory indicates that $theta_{s}$ only depends on $M_{0}$ and $alpha$, but is independent of the Reynolds number $Re$ and wall temperature $T_{w}$. These facts suggest that the proposed theoretical framework can be applied to other flow systems dominated by shock waves, which are ubiquitous in aerospace engineering.
Numerical simulations of magnetosonic wave formation driven by an expanding cylindrical piston are performed to get better physical insight into the initiation and evolution of large-scale coronal waves. Several very basic initial configurations are employed to analyze intrinsic characteristics of the MHD wave formation that do not depend on specific properties of the environment. It turns out that these simple initial configurations result in piston/wave morphologies and kinematics that reproduce common characteristics of coronal waves. In the initial stage the wave and the expanding source-region cannot be clearly resolved. During the acceleration stage of the source-region inflation, the wave is driven by the piston expansion, so its amplitude and phase-speed increase, whereas the wavefront profile steepens. At a given point, a discontinuity forms in the wavefront profile. The time/distance required for the shock formation is shorter for a more impulsive source-region expansion. After the piston stops, the wave amplitude and phase-speed start decreasing. During the expansion, most of the source region becomes strongly rarified, which reproduces the coronal dimming left behind the eruption. On the other hand, the density increases at the source-region boundary, and stays enhanced even after the expansion stops, which might explain stationary brightenings that are sometimes observed at the edges of the erupted coronal structure. In addition, in the rear of the wave a weak density depletion develops, trailing the wave, which is sometimes observed as weak transient coronal dimming. Finally, we find a well defined relationship between the impulsiveness of the source-region expansion and the wave amplitude and phase speed. The results for the cylindrical piston are also compared with the outcome for a planar wave, to find out how different geometries affect the evolution of the wave.
The high-pressure melting curve of tantalum (Ta) has been the center of a long-standing controversy. Sound velocities along the Hugoniot curve are expected to help in understanding this issue. To that end, we employed a direct-reverse impact technique and velocity interferometry to determine sound velocities of Ta under shock compression in the 10-110 GPa pressure range. The measured longitudinal sound velocities show an obvious kink at ~60 GPa as a function of shock pressure, while the bulk sound velocities show no discontinuity. Such observation could result from a structural transformation associated with a negligible volume change or an electronic topological transition.
We investigate whether tidal forcing can result in sound waves steepening into shocks at the surface of a star. To model the sound waves and shocks, we consider adiabatic non-spherical perturbations of a Newtonian perfect fluid star. Because tidal forcing of sounds waves is naturally treated with linear theory, but the formation of shocks is necessarily nonlinear, we consider the perturbations in two regimes. In most of the interior, where tidal forcing dominates, we treat the perturbations as linear, while in a thin layer near the surface we treat them in full nonlinearity but in the approximation of plane symmetry, fixed gravitational field and a barotropic equation of state. Using a hodograph transformation, this nonlinear regime is also described by a linear equation. We show that the two regimes can be matched to give rise to a single mode equation which is linear but models nonlinearity in the outer layers. This can then be used to obtain an estimate for the critical mode amplitude at which a shock forms near the surface. As an application, we consider the tidal waves raised by the companion in an irrotational binary system in circular orbit. We find that shocks form at the same orbital separation where Roche lobe overflow occurs, and so shock formation is unlikely to occur.
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