Shock Wave Transition Research Articles

Structurally Stable Riemann Solutions

We study the structure of solutions of Riemann problems for systems of two conservation laws. Such a solution comprises a sequence of elementary waves,viz., rarefaction and shock waves of various types; shock waves are required to have viscous profiles. We construct a Riemann solution by solving a system of equations characterizing its component waves. A Riemann solution is “structurally stable” if the number and types of its component waves are preserved when the initial data and the flux function are perturbed. Under the assumption that rarefaction waves and shock states lie in the stricly hyperbolic region, we characterize Riemann solutions for which the definition equations have maximal rank and we prove that such solutions are structurally stable. Structurally stable Riemann solutions cannot contain overcompressive shock waves, but they can contain transitional shock waves, including doubly sonic transitional shock waves, including doubly sonic transitional shock waves that have not been observed before.

Real-time determination of the amount of removed material during short pulses laser micromachining

Short pulses laser generated shock waves in the air during the photoablation of different ceramics have been monitored by laser beam deflection technique. Using a model, we have related the shock wave transit time over a fixed distance to the shock wave energy. We have found that the instantaneous ablation rate is a linear function of the shock wave energy in the considered range of fluence. This technique is proved to be suitable for monitoring in real-time the laser ablation process.

燃料‐空気多重成層渦中の燃焼により発生する強い圧力波と火炎構造

A 2-step reaction model is used to analyze the interaction between (i) a fuel-air multi-stratified vortical mixing layer and (ii) strong pressure waves caused by rapid combustion of the mixed region. During the 1st-stage induction period where no heat release occurs, a large-scale vortical structure evolves, generating a wide contact surface and extended mixing between fuel and air. During the ensuing 2nd-stage exothermic reaction, the locally premixed fuel-air rapidly burns and produces strong pressure waves, where three different Da numbers are parametrically tested to evaluate the amplitude of generated pressure waves and to find out the possibility to trigger a detonation wave. The results show that (1) the 2nd-stage exothermic reaction starts at the core of each vortex where “Reaction Rate (YCH4)(YO2)2exp(-Ze/T*)” is high, (2) then the generated strong pressure waves promote the reaction at the outermost stratified region of each vortex, and (3) spot-like flames formed in the premixed region propagate toward the surrounding unburned region, due to conventional defraglation mechanism. (4) On the other hand, delayed combustion starts in the braid region where mixing is highly inactive. (5) Finally, after the consumption of premixed reactants, a diffusion flame with a low mass consumption rate prevails. The highest Da number simulation naturally has generated the strongest pressure waves, indicating the possibility of shock wave occurrence and transition to detonation.

A front tracking method for transitional shock waves

A front tracking method for transitional shock waves

Measurements of laser-induced shock waves in aluminium

A simple optical method for measurements of high-irradiance (3×1013 W cm-2) laser-induced shock waves is described. The shock wave velocity (~13 km s-1) was measured with an error not exceeding 5%. The laser-induced one-to-two-dimensional (1D-to-2D) shock wave transition was studied.

On the critical amplitudes of acceleration wave to shock wave transition in white noise random media

The problem of transition of acceleration waves into shock waves is addressed in the context of weakly random media. A class of random media is modeled by a vector white noise random process representing two material coefficients appearing in the Bernoulli equation governing the evolution of acceleration waves. The problem of shock formation, which involves a stochastic competition of dissipation and elastic nonlinearity, is treated using a diffusion formulation for the Markov process of the inverse amplitude. The first four moments of the critical inverse amplitude are derived explicitly as functions of the means and crosscorrelations of the underlying vector random process. It is found that the Stratonovich as well as the Ito interpretation of the stochastic Bernoulli equation lead to an increase of the average critical amplitude of the random medium problem over the critical amplitude of the deterministic homogeneous medium problem. Probability distribution of the critical inverse amplitude is found to be, in general, of Pearson's Type IV.

Scattering behavior of transitional shock waves

We study the stability and asymptotic behavior of transitional shock waves as solutions of a parabolic system of conservation laws. In contrast tp classical shock waves, transitional shock waves are semitive to the precise form of the parabolic term, not only in their internal structure but also in terms of the end states that they connect. In our numerical investigation, these waves exbibit robust stability. Moreover, their response to perturbation differs from that of classical waves; in particular, the asymptotic state of a perturbed transitional wave depends on the location of the perturbation relative to the shock wave. We develop a linear scattering model that predicts behavior agreeing quantitatively with our numerical results.

Interaction of a plane shock wave with slitted wedges

An experimental and numerical study was made of shock wave transition over slitted wedges. Experiments were conducted in a shock tube by using double exposure holographic interferometry. Shock Mach numbers ranged from 1.07 to 3.03 in air. Slitted wedge models having perforation ratios of 0.34 and 0.4 were installed in the test section. The critical transition angle was obtained analytically by the shock polar analysis where effects of boundary conditions, wall suction, and surface roughness were empirically taken into account. As the results, it was found that for stronger shock waves and a perforation ratio of 0.4, the critical transition angle was decreased by about 10° in comparison to the detachment criterion. A flow visualization study clarified various wave interaction mechanisms associated with the wall suction. The critical transition angle was successfully explained by the shock polar analysis. The PLM numerical simulation was also conducted. The numerical result agreed very well with the experimental findings.

Transitional Waves for Conservation Laws

A new class of fundamental waves arises in conservation laws that are not strictly hyperbolic. These waves serve as transitions between wave groups associated with particular characteristic families. Transitional shock waves are discontinuous solutions that possess viscous profiles but do not conform to the Lax characteristic criterion; they are sensitive to the precise form of the physical viscosity. Transitional rarefaction waves are rarefaction fans across which the characteristic family changes from faster to slower.This paper identifies an extensive family of transitional shock waves for conservation laws with quadratic fluxes and arbitrary viscosity matrices; this family comprises all transitional shock waves for a certain class of such quadratic models. The paper also establishes, for general systems of two conservation laws, the generic nature of rarefaction curves near an elliptic region, thereby identifying transitional rarefaction waves. The use of transitional waves in solving Riemann problems...

Streak camera recording of shock wave transit times at large distances using laser illumination

A pulsed laser illumination system for streak camera recording of impact-induced shock wave transit times (∼1 μs) during impact experiments is described. Laser illumination of centimeter-sized subjects offers many advantages over diffuse illumination techniques for streak photography. Source-to-sample and sample-to-camera distances of ∼100 to 102 m can be employed. Light filtering, and simultaneous recording of both the impact event and the camera streak rate calibration, can be carried out easily. For use in such a system we describe a Pockels cell controller in which the reference 10-MHz oscillator signal is synchronously divided down to 38 Hz to provide a trigger signal for laser and streak camera testing.

Weak spherical shock-wave transitions of N-waves in air with vibrational excitation

In order to clarify the effects of vibrational excitation on shock-wave transitions of weak, spherical N-waves, which were generated by using sparks and exploding wires as sources, the compressible Navier-Stokes equations were solved numerically, with a vibrational-relaxation equation for oxygen. An explosion from a small pressurized sphere filled with air was used to simulate the N-waves generated from the actual sources. By employing the random-choice method (r. c. m.) with an operator-splitting technique, the effects of artificial viscosity appearing in finite-difference schemes were eliminated and accurate profiles of the shock transitions were obtained. However, a slight randomness in the variation of the shock thickness remains. It is shown that a computer simulation is possible by using a proper choice of initial parameters to obtain the variations of N-wave overpressure and half-duration with distance from the source. The calculated rise times are also shown to simulate both spark and exploding-wire data. It was found that, in addition to the vibrational-relaxation time of oxygen, both the duration (N-wave effect) and the attenuation rate (non-stationary effect) of a spherical N-wave are important factors controlling its rise time. These effects are discussed in more detail in relation to Lighthill’s analytical solutions and the r. c. m. solutions for non-stationary plane waves and spherical N-waves. It is also shown that the duration and the attenuation rate of a spherical N-wave are affected by viscosity, and vibrational non-equilibrium, so that they can deviate from the results of classical, linear acoustic theory for very weak spherical waves.

Shock Wave Transit Through the Transition Region and Related Radio Fluctuations

The perturbing effects of a shock wave transit through the transition region are evaluated, using a simplified method of solution of the system of partial differential equations describing the fluid motion behind the shock passage. Calculated temperatures and densities are given at successive times during the shock transit. Based on these shocked models, time dependent brightness temperatures are derived at several decimetric wavelengths and compared with the unperturbed values to evaluate the amplitude of the induced brightness fluctuations. Finally, the possibility of detecting such shock induced phenomena is discussed.