Structure Of Strong Shock Waves Research Articles

Recent progresses on numerical investigations of microscopic structure of strong shock waves in fluid

Shock wave appears widely in various complex systems and plays an important role in the fundamental research and engineering applications. Much effort has been devoted to getting insight into the microscopic structure and dynamic features on the shock front and obtaining the shock hugoniot of materials. The scope of this review would be limited to strong shock waves in fluid, considering that materials behave as fluid under strong impact loading. The development of methods used to study shock waves has been reviewed and the applicable conditions and features of these method has been summarized. The microscopic structures, non-equilibrium effects and dynamic processes on the shock front have been discussed, which have reference value for the modeling of shock wave in complex system.

Molecular dynamics simulations of microscopic structure of ultra strong shock waves in dense helium

Hydrodynamic properties and structure of strong shock waves in classical dense helium are simulated using non-equilibrium molecular dynamics methods. The shock speed in the simulation reaches 100 km/s and the Mach number is over 250, which are close to the parameters of shock waves in the implosion process of inertial confinement fusion. The simulations show that the high-Mach-number shock waves in dense media have notable differences from weak shock waves or those in dilute gases. These results will provide useful information on the implosion process, especially the structure of strong shock wave front, which remains an open question in hydrodynamic simulations.

A role for electron viscosity in plasma shock heating

The contribution of electron viscosity to shock heating of high-Z plasmas is investigated. A classical shock profile calculation is employed to show that the electron viscosity substantially affects the structure of strong shock waves in a fully ionized plasma by reducing the overheating of the ions in the viscous subshock. This effect is present for an average ion charge Z above 10. Computer simulations of Z-pinch implosions are then employed to demonstrate that this effect of electron viscosity can also be accounted for in Lagrangian hydrodynamic simulations that use artificial viscosity. This is accomplished by dividing the corresponding viscous heat release between the ion and electron components of the plasma according to the ratio of their physical viscosities. When this is done in the time-varying, ionizing plasma environment of Z-pinch implosions that are theoretically designed to generate K-shell emission in titanium and krypton, it is found that electron viscous heating can be substantial, leading to sizable reductions in ion temperatures and 10%–20% increases in K-shell emission under certain implosion conditions.

Plane steady shock waves in Isreal-Stewart fluids

The plane steady shock wave solutions of the Israel-Stewart theory of relativistic dissipative fluids are studied. The Israel-Stewart theory is shown to fail to adequately describe the structure of strong shock waves. Physically acceptable solutions do not exist above a maximum upstream Mach number in any thermally nonconducting, viscous fluid described by the Israel-Stewart theory because the solutions become multiple-valued when the characteristic velocity is exceeded. It is also proven that physically acceptable solutions do not exist for thermally conducting, viscous fluids above either a maximum upstream Mach number, or else below a minimum downstream Mach number (or both). These limiting Mach numbers again correspond to the characteristic velocities of the fluid. Only extremely weak plane steady continuous shock solutions exist in the Israel-Stewart theory for the ultrarelativistic Boltzmann gas, or for the degenerate free Fermi gas.

The structure of strong hydromagnetic shock waves in a thermally-radiating gas

The structure of strong shock waves in a thermally-radiating and electrically-conducting fluid is studied by method of asymptotic matching principle. It is assumed that upstream of the shock the gas is cold and does not radiate thermally while the Mach number (M) is very high so that after being shocked the gas now thermally radiates. The viscosity of the gas (μ) depends on temperature (T) in the simple manner μαTω where ω is a constant exponent. The problem is worthy of note in high-temperature phenomena in hypersonic flow.

The structure of detonation waves in supernovae

The theory of gaseous detonation is applied to thermonuclear detonation waves in supernovae. First, the two-temperature structure of strong shock waves in a dense degenerate plasma is considered. The ion-electron energy transfer rate is calculated for a plasma with arbitrary degeneracy of electrons. It is shown that the non-equilibrium heating of ions is unimportant for detonation. The steady planar one-dimensional structure of detonation waves both in C + O mixtures and in pure helium 4He is computed for densities from 106 to 3 × 109 g cm−3. The thickness of the detonation waves is obtained as a function of the initial density of the matter. The self-sustained detonation of helium is a Chapman–Jouguet detonation at all the densities considered. The self-sustained detonation of C + O mixtures is a Chapman–Jouguet detonation only at densities less than ∼ 107 g cm−3. At higher densities it is a pathological detonation with some velocity |$D^\ast \gt D_\text{CJ}$|⁠. Products of detonation are Fe-peak nuclei if the NSE state occurs in a detonated matter. The products are the intermediate mass nuclei Si, S, Ca, etc. in the case of incomplete detonation of C + O mixtures. The products are the partially unburned helium and Fe-peak nuclei with extremely small fractions of intermediate mass nuclei in the case of incomplete detonation of 4He. The thickness of detonation waves in C + O mixtures differs appreciably from that in helium.

The structure of supernova shock waves

The structure of strong shock waves is calculated over the range of shock energies (1 to 100 MeV nucleon/sup -1/) and initial number densities (10/sup 15/--10/sup 22/ cm/sup -3/) believed likely to occur in the red-giant-like envelopes of stars undergoing Type II supernova explosions. The general equations governing the structure of such shocks are developed on the basis of a plasma composed of ions, electrons, positrons, and photons, making use of diffusion theory to evaluate the dissipative and transfer terms. The present treatment differs from previous calculations in that the effects of radiation transport on the energy and momentum balance in the shock are taken into account, as well as the relativistic contributions to radiative emission rates due to nondipole electron-ion bremsstrahlung, electron-electron bremsstrahlung, and radiative Compton scattering. An implicit treatment of inverse Compton scattering is also developed in terms of the creation and diffusion of effective photons.Severalmodels of strong shock structure are formulated and solved on the basis of these equations and physical processes. (AIP)

Structure of strong shock waves in xenon. I: Electron temperature measurements

Time-resolved electron temperature measurements were taken behind incident normal shock waves in an arc-driven shock tube using xenon as the test gas at an initial driven tube pressure of 0.1 Torr. At shock wave velocities from 6 to 10 km/sec, the two-line intensity ratio technique involving the spectral lines of XeII was used to determine the electron temperature. The data indicate an electron temperature peak almost immediately behind the shock front which is well above the predicted equilibrium temperature. This peak temperature decays rapidly (∼ 1 μsec) to a plateau temperature well below the predicted equilibrium temperature. The importance of both radiative energy loss and ionizing collisions on the electron temperature decay is considered in the interpretation of the data.

Structure of strong shock waves in xenon. II: Further experiments and theoretical interpretation

Electron temperature measurements in the ionized xenon gas downstream of a shock front are obtained using brightness observations of the XeII 5292-Å line. The results show good agreement with previous measurements obtained using a two line intensity ratio technique. A theoretical model of the shock structure is developed which considers nonequilibrium collisional and continuum radiative transitions. The theoretical calculations agree qualitatively with the experimental observations and indicate the paramount importance of radiative heating of the electron gas within that portion of the shock structure which is otherwise dominated by elastic and inelastic electron-heavy particle collisions. The theoretical calculations also provide a detailed time history of the populations of the first four excited levels of XeII and indicate that the higher excited levels may justifiably be assumed in equilibrium with each other in a Boltzmann sense at the local electron temperature. Considered are shock velocities between 6.0 and 10.0 km/sec at an upstream pressure of 0.1 Torr.

The structure of strong shock waves using the Fokker-Planck model

The structure of strong shock waves in monatomic gases is studied using the Fokker-Planck model to represent the particle collisions and the Mott-Smith distribution to describe the distribution function within the shock front. The differential equation governing the variation of the density within the shock is derived by using the variational principle. The thickness of the shock front is evaluated numerically for various monatomic gases for Mach numbers varying from 2 to 20, and besides, the variation of the shock thickness with viscosity is also studied for different gases. Several parameters of physical interest within the shock, such as density, temperature and mean velocity of flow are evaluated numerically and detailed curves showing their variation within the shock are presented for different Mach numbers. It is found that the temperature rises very steeply, reaches a maximum within a distance less than half the thickness of the shock and then diminishes slowly to attain its asymptotic downstream values. The variation of the mean velocity is slow for weak shocks, but for higher Mach numbers, the mean velocity diminishes steeply and reaches the downstream values within half the thickness of the shock.

Aspects of the Structure of Strong Shock Waves

The direct simulation Monte Carlo method has been used to study the structure of strong shock waves in a gas of point center of repulsion molecules. The values obtained for the maximum density slope thicknesses agree with the predictions of the Mott-Smith method. The results for the effect of molecular model on the rate of change of this thickness with shock Mach number are in agreement with the common prediction of the Mott-Smith and Navier-Stokes theories. The velocity distribution function within the wave is illustrated by computer display photographs with the molecules represented as dots in the plane of longitudinal and lateral velocity. This also gives qualitative support to the bimodal model. However, it is found that the density profile has a significant degree of asymmetry, contrary to the bimodal prediction. Results are also presented for the profiles of the higher moments of the distribution function.

Structure of Strong Shock Waves

A model is proposed for the structure of strong shock waves which explicitly accounts for the existence of a near molecular beam, hypersonic flow upstream, and of a subsonic, hot continuum flow downstream. This is accomplished by considering the conversion of the beam into the continuum through collisions. Appropriate continuum equations are derived including the input of mass, momentum, and energy from the beam particles. The particles in the molecular beam are assumed to be converted into members of the continuum in a single collision; and the collision transport phenomena associated with the continuum are assumed to be governed by the Chapman-Enskog expressions. Comparisons with other models for shock structure and with experimental results are given. In view of its simplicity the present model should be applicable to other hypersonic, rarefied flow problems.