Simulating radiative shocks in nozzle shock tubes

We use the recently developed Center for Radiative Shock Hydrodynamics (CRASH) code to numerically simulate laser-driven radiative shock experiments. These shocks are launched by an ablated beryllium disk and are driven down xenon-filled plastic tubes. The simulations are initialized by the two-dimensional version of the Lagrangian Hyades code which is used to evaluate the laser energy deposition during the first 1.1 ns. Later times are calculated with the CRASH code. CRASH solves for the multi-material hydrodynamics with separate electron and ion temperatures on an Eulerian block-adaptive-mesh and includes a multi-group flux-limited radiation diffusion and electron thermal heat conduction. The goal of the present paper is to demonstrate the capability to simulate radiative shocks of essentially three-dimensional experimental configurations, such as circular and elliptical nozzles. We show that the compound shock structure of the primary and wall shock is captured and verify that the shock properties are consistent with order-of-magnitude estimates. The synthetic radiographs produced can be used for comparison with future nozzle experiments at high-energy-density laser facilities.     

Simulations of laser experiments of radiative and non-radiative shocks

The Center for Radiative Shock Hydrodynamics (CRASH) at the University of Michigan was established to study the properties of radiative shocks using both numerical simulation and shock-tube experiments on the Omega Laser at the University of Rochester. The laser accelerates a thin Be disk, which acts like a piston, driving a shock with an initial propagation velocity of 200 km/s into a tube filled with Xe. Analytic estimates indicate that a shock propagating with a velocity greater than about 60 km/s through Xe under these conditions should be strongly radiative. This paper discusses numerical simulations of a proposed modification to this experiment that produces a non-radiative shock. Comparison of the radiative and non-radiative cases provides an excellent opportunity for assessing the effects of radiation on shock structure and flow morphology. For the non-radiative case, the initial shock speed is reduced to 20 km/s by increasing the thickness of the Be disk and by decreasing the energy of the laser. Two-dimensional simulations of targets with cylindrical shock tubes and three-dimensional simulations of more complex targets with elliptical shock tubes are described. In addition, the effect of the shock speed on the cross-sectional area of the tube is discussed.     

Rayleigh-Taylor instability simulations with CRASH

CRASH is a code package developed for the predictive study of radiative shocks. It is based on the BATSRUS MHD code used extensively for space-weather research. We desire to extend the applications of this code to the study of hydrodynamically unstable systems. We report here the results of Rayleigh-Taylor instability (RTI) simulations with CRASH, as a necessary step toward the study of such systems. Our goal, motivated by the previous comparison of simulations and experiment, is to be able to simulate the magnetic RTI with self-generated magnetic fields produced by the Biermann Battery effect. Here we show results for hydrodynamic RTI, comparing the effects of different solvers and numerical parameters. We find that the early-time behavior converges to the analytical result of the linear theory. We observe that the late-time morphology is sensitive to the numerical scheme and limiter beta. At low-resolution limit, the growth of RTI is highly dependent on the setup and resolution, which we attribute to the large numerical viscosity at low resolution.     

Bow shocks formed by plasma collisions in laser irradiated semi-cylindrical cavities

The formation of shocks in plasmas created by short pulse laser irradiation (λ = 800 nm, I ≈ 1 × 10¹² W cm^?2) of semi-cylindrical cavities of different materials was studied combining visible and soft X-ray laser interferometry with simulations. The plasma rapidly converges near the axis to form a dense bright plasma focus. Later in time a long lasting bow shock is observed to develop outside the cavity, that is shown to arise from the collision of plasmas originating from within the cavity and the surrounding flat walls of the target. The shock is sustained for tens of nanoseconds by the continuous arrival of plasma ablated from the target walls. The plasmas created from the heavier target materials evolve more slowly, resulting in increased shock lifetimes.     

Long time evolution of collisionless shocks in laser produced counterstreaming plasmas

Long time evolution of collisionless shocks in laser-produced plasmas is discussed. By irradiating a double plane target a high Mach number collisionless shock has been observed in laser produced counterstreaming plasmas [Kuramitsu et al., Phys. Rev. Lett., 106, 175002 (2011)]. While in early time we observe the shock in front of one plane, which is irradiated with the laser, we observe another shock in front of the other plane in much later time than the first shock formation. These two shocks coexist and collide or merge with each other as time passes. This means that the upstream plasmas for the first and second shocks have to be provided from the second and first shock sides, respectively, i.e., both the first and second shock have to be collisionless. There are two major candidates to account for the long time evolution of the collisionless shocks. One is that the secondary plasmas at the planes can be continuously created by the plasmas from the other planes. Another is that the actual shock thickness is much thiner than the detection limit, as indicated by numerical simulations.     

Snow melting with radiative heating

This paper is concerned with the melting of a packed snow heated by the radiative energy which is the blackbody radiation having source temperature of 3200 °K and short radiative energy. A transfer of the radiation in snow is significantly affected by both the porosity of snow and water saturation. The internal melting in snow is greatly characteristic for radiative heating which is to be produced by absorbing of a comparatively short wave radiation. In this study, an analysis is attempted to predict the variation of snow density, the moving rate of dry-wet interface of snow due to percolation of melt water, and the transient temperature distribution in dry snow zone located under wet snow zone.     

PIV through moving shocks with refracting curvature

Particle image velocimetry (PIV) is applied to moving millimeter shock waves whose density jump and small radii of curvature make refraction significant. The motion of the shock front is also much larger than the motion of the corresponding mass at the front. A Lagrangian model of particle displacement in response to a moving shock is developed to investigate the relationship between particle displacements and the actual mass velocity behind the shock. Errors in PIV measurements due to light refraction across a curved, moving shock are investigated in terms of both position and velocity errors using a refraction model developed from geometrical optics. The model is experimentally validated and applied to 1-D slices of data extracted from PIV vector fields, and the resulting measurement errors are quantified.     

On the dissipation associated with equilibrium shocks in finite elasticity

Equilibrium fields with discontinuous displacement gradients can occur in finite elasticity for certain materials. The presence of such equilibrium shocks affects the energy balance in the elastostatic field, and the present paper is concerned with a notion of dissipation associated with this energy balance. A dissipation inequality is proposed for three-dimensional equilibrium shocks for both compressible and incompressible materials. The consequences of this inequality are studied for weak shocks in plane strain for compressible materials and for shocks of arbitrary strength in anti-plane strain for a class of incompressible materials. A thermodynamic argument for the dissipation inequality is also given.The results communicated in this paper were obtained in the course of an investigation supported by Contract N00014-75-C-0196 between the California Institute of Technology and the Office of Naval Research.     

流体与结构相互作用问题的FE-SPH耦合模拟

应用有限元(FE)-光滑粒子流体动力学(SPH)耦合法模拟了具有自由表面的不可压流体与结构的相互作用问题.流体和结构分别采用SPH法和有限元法同时求解,两者在交界面处的相互作用通过接触算法进行处理.为了避免隐式计算压力,通过引入人工压缩率,将不可压流体近似为人工可压缩流体.采用FE-SPH耦合法对弹性板在随时间变化的水压作用下的变形以及倒塌水柱冲击弹性结构两个问题进行了模拟.模拟结果与实验结果以及其他已有数值结果符合良好,说明FE-SPH耦合法用于流体与结构相互作用问题的模拟是可行和有效的.     

Interaction between shocks and clumps with self-contained magnetic fields

Problems involving magnetized clouds and clumps, especially their interaction with shocks are common in astrophysical environments and have been a topic of research in the past decade. Many previous numerical studies have focused on the problem of clumps immersed in a globally uniform magnetic field subject to an oncoming shock. However, realistic clumps may have tangled magnetic field self-contained within them. This magnetic field will be compressed by the shock and its energy spectrum and spatial structure may affect the evolution of the clump during the shock encounter. Using our parallel MHD code AstroBEAR, we set up an initial state with magnetized clumps of different contained magnetic field configurations. We then drive strong shocks through these clumps (including the effects of radiative cooling) and compare our results to previous studies of global uniform field scenarios.     

Numerical modelling of shocks in solids with elastic-plastic conditions

Results are presented for a range of one- and two-dimensional shock-wave problems in elastic-plastic and hydrodynamic metals. These problems were solved numerically using the Flux-Corrected Transport (FCT) technique which achieves high resolution without non-physical oscillations, especially at shock fronts, and has not been used before in elastic-plastic solids. The two-dimensional problems were solved using both operator- and non-operator-split techniques to highlight the significant differences between these techniques when solving shock-wave problems in elastic-plastic solids. Comparisons of the elastic-plastic solutions with the hydrodynamic solutions are made and illustrate the importance of including elastic-plastic conditions when modelling the behaviour of solids. Also, the errors in these solutions that are due to the initial conditions are discussed in detail.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1.0 and the AMS fonts, developed by the American Mathematical Society.     

Optimum overtaking compression shocks with restrictions imposed on the total flow-deflection angle

The problem of optimization of gasdynamic variables behind a system of two steady oblique compression shocks with restrictions imposed on the flow-defection angle is considered. The intervals of input parameters, in which this system turns out to be more effective than one shock, are determined. On the basis of an analysis of the system optimal for the static pressure, the physical meaning of the transition from one type of the reflected discontinuity to another is explained for the problem of interaction of overtaking oblique compression shocks. Baltic State Technical University, St. Petersburg 198005. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 4, pp. 99–108, July–August, 1999.     

On the dissipation inequality in equilibrium shocks

This paper presents expressions for the dissipation inequality corresponding to an equilibrium shock. These expressions are independent of the orientation of the shock. A sufficient condition on the constitutive equations for positive dissipation is given in the case of anti-plane deformations.     

Simulating surface tension with smoothed particle hydrodynamics

A method for simulating two‐phase flows including surface tension is presented. The approach is based upon smoothed particle hydrodynamics (SPH). The fully Lagrangian nature of SPH maintains sharp fluid–fluid interfaces without employing high‐order advection schemes or explicit interface reconstruction. Several possible implementations of surface tension force are suggested and compared. The numerical stability of the method is investigated and optimal choices for numerical parameters are identified. Comparisons with a grid‐based volume of fluid method for two‐dimensional flows are excellent. The methods presented here apply to problems involving interfaces of arbitrary shape undergoing fragmentation and coalescence within a two‐phase system and readily extend to three‐dimensional problems. Boundary conditions at a solid surface, high viscosity and density ratios, and the simulation of free‐surface flows are not addressed. Copyright © 2000 John Wiley & Sons, Ltd.