Shock Wave Curve Research Articles

Hermite-Shannon-Cosine Interval Wavelet and Its Application in Adaptive Distribute Interpolation on Curves

<p indent="0mm">The dynamic curve is a common tool to describe the transformation law of various phenomena. To capture the characteristic points dynamically and approximate the dynamic curve accurately, a Shannon-Cosine wavelet function with interpolation, smoothness, tight support, and symmetry is constructed. Firstly, by means of the wavelike property and continuity of the Shannon wavelet function, a parameterized window function is designed based on the integral median theorem, in which the support and smoothness of Shannon-Cosine wavelet can be chosen to meet the requirement of the approximated curves. Secondly, based on the theory analysis and numerical experiments, the discontinuity near the boundary of the curve is identified as the major factors which result in the boundary effect appeared on the wavelet transform on the curve, and then the interval wavelet is constructed by using the two-point cubic Hermite interpolation function. Finally, the multi-scale Shannon-Cosine wavelet is used to perform multi-scale adaptive subdivision and approximation of the propagation of shock wave curve and the reflected Burger curve. It is able to capture the characteristic points of the curve adaptively, which can be used to reconstruct the curve. Burger curve is taken as the example to test the proposed method, the numerical experiments show that, compared with other methods, the method of Hermite Shannon-Cosine interval wavelet approximation curve has higher numerical accuracy and lower algorithm complexity.

Effects of confining layer and ablating layer on laser-induced shock wave characteristics during laser shock processing by PVDF gauge

The PVDF sensor is used to obtain the time variation curves of the shock wave pressure in the four states of the laser shock peening with or without confining layer and with or without ablating layer, the effects of confining layer and ablating layer on shock wave characteristics are analyzed. The results show that the confining layer limits the plasma expansion area, and the inverse bremsstrahlung absorption effect is enhanced, so that the peak pressure and pulse width of the shock wave are increased to 10 times and 2 times that under the condition of the without confining layer; The ablating layer significantly increases the peak pressure of the shock wave by improving the laser energy coupling efficiency. However, the influence of the ablating layer on the peak pressure tends to saturate with the increase of power density, the difference of the peak pressure is only 8.5% when the laser power density is 4.53GW/cm2. In addition, the ablating layer complicates the shock wave propagation process, and the shock wave curve presents a multi-peak structure.

Concentration and Cavitation in the Vanishing Pressure Limit of Solutions to a Simplified Isentropic Relativistic Euler Equations

We identify and analyze the phenomena of concentration and cavitation by studying the vanishing pressure limit of solutions to a simplified isentropic relativistic Euler equations. Firstly, both the explicit expressions and geometric properties of the rarefaction wave curve and shock wave curve based on any left state are given with the help of Lorentz invariance, and the Riemann problem for this system is considered. Then, we rigorously prove that, as pressure vanishes, any two-shock Riemann solution tends to a delta-shock solution of the pressureless relativistic Euler equations, and the intermediate density between the two shocks tends to a weighted $$\delta $$ -measure, which forms the delta shock wave. This describes the phenomenon of mass concentration. On the other hand, any two-rarefaction Riemann solution tends to a two-contact-discontinuity solution of the pressureless relativistic Euler equations and the nonvacuum intermediate state in between tends to a vacuum state, which reveals the phenomenon of cavitation. Both concentration and cavitation are fundamental and physical in fluid dynamics.

The Riemann solutions to the compressible ideal fluid flow

In this paper, we study the exact solutions of Riemann problem for the compressible ideal fluid flow, where the external force is a continuous function of time. The exact expressions for contact discontinuity curve, shock wave curve and rarefaction wave curve are provided. Six types of exact solutions of the Riemann problem are also obtained. In particular, a vacuum arises at t>0 although the initial data never involves the vacuum, and these solutions do not possess self-similarity in the (t,x)-plane.

Computational simulation of shock wave generated by the detonation of explosives for civil use

When conducting a research concerning the propagation of a shock wave generated by the detonation of civil use explosives, the first thing that comes to mind should be if the detonation process takes place in an obstacle-free field, or the area has obstacles such as rocks, metals structures, wood etc, obstacles that can and will influence the final results, the shock wave curve being obturated by it. On one hand, the paper presents the experimental results obtained after the detonation of a freely suspended load, placed at 0.5m above a concrete surface. On the other hand, it compares the values of explosion pressure as shock wave, measured on 4 sensors linearly disposed at the same elevation to the ground, at a distance of 2,3,4 respectively 6 meters from the explosive charge. These values are determined through computerized simulation, using ANSYS AUTODYN software, by virtually reproducing the real scenario. Following the two experiments (real and virtual), one can conclude that computerized simulation proves to be a very useful instrument in an a priori evaluation of hazardous situations/utility of peak values for shock wave, by allowing the user to develop prevention measures/optimization of the analysed processes and also in further investigations

Novel design methodology of integrated waverider with drip-like intake based on planform leading-edge definition method

Based on the planform leading-edge definition method, a novel methodology for designing an inlet-airframe integrated waverider vehicle, has been proposed and the resulting intake owns the superiority of the drip-like shape. In this study, the design of the vehicle contour relies on the axisymmetric basic flowfield and leading-edge planform curves, namely the former is presently generated by a shock wave curve, and the latter produces a drip-like intake, on account of the 3D cowl lip curve. Importantly, defining the leading edge on the horizontal projection plane facilitates to adjust the planform shape of the integrated waverider and the sweep angle of the wing. At last, the new design methodology is proved to be effective to design an integrated hypersonic waverider vehicle. This study provides more options for designing novel inlet-airframe integrated hypersonic vehicles.

Shock Wave Characteristics of Hydraulic Shock Wave Simulator with Variable Damping

For simulating the shock wave with high peak force in a short duration, a novel variable damping hydraulic shock wave simulator was developed, and it was used for simulating the cannon recoil motion. The working principle of this simulator was explained with the assistance of established mathematical model and the flow behavior in damping channel was analyzed. The shock wave characteristics curves were obtained by using the numerical computation method. The results showed that the shock wave characteristics were directly related to the sectional area of the damping channel and the damping fluid medium characteristic; the shock wave curve can be simulated by adjusting the variable damping parameters. The computational results agreed well with the theory analysis, which meant that the proposed mathematical model can be used for supplying theoretical references for the cannon recoil motion in artillery fire shock simulation test.

The Effect of Nano-Aluminumpowder on the Characteristic of RDX based Aluminized Explosives Underwater Close-Filed Explosion

In order to investigate the effect of nano-aluminum powder on the characteristic of RDX based aluminized explosives underwater closed-filed explosions, the scanning photographs along the radial of the charges were gained by a high speed scanning camera. The photographs of two different aluminized explosives underwater explosion have been analyzed, the shock wave curves and expand curves of detonation products were obtained, furthermore the change rules of shock waves propagation velocity, shock front pressure and expansion of detonation products of two aluminized explosives were investigated, and also the parameters of two aluminized explosives were contrasted. The results show that the aluminized explosive which with nano-aluminum whose initial shock waves pressure propagation velocity, shock front pressure are smaller than the aluminized explosive without nano-aluminum and has lower decrease rate attenuation of energy.

Methods for Characterizing and Comparing Populations of Shock Wave Curves

At Los Alamos National Laboratory, engineers conduct experiments to evaluate how well detonators and high explosives work. The experimental unit, often called an “onionskin,” is a hemisphere consisting of a detonator and a booster pellet surrounded by high explosive material. When the detonator explodes, a streak camera mounted above the pole of the hemisphere records when the shock wave arrives at the surface. The output from the camera is a two-dimensional image that is transformed into a curve that shows the arrival time as a function of polar angle. The statistical challenge is to characterize the population of arrival time curves and to compare the baseline population of onionskins to a new population. The engineering goal is to manufacture a new population of onionskins that generate arrival time curves with the same shape as the baseline. We present two statistical approaches that test for differences in mean curves and provide simultaneous confidence bands for the difference: (i) a B-Spline basis approach and (ii) a Bayesian hierarchical Gaussian process approach. In problems that involve complex modeling with modest sample sizes, it is important to apply multiple approaches with complementary strengths such as these to determine whether all approaches provide similar results. Solid performances of the two approaches are demonstrated on several simulations that were constructed to mimic the actual onionskin analysis. Finally, an analysis of onionskin data is presented. This article also has supplementary materials available online.

A generalized Goursat-Riemann problem for plane waves in isotropic elastic solids

A generalized Goursat-Riemann problem for plane waves propagating in an isotropic elastic half space with constant initial and non-constant boundary conditions is investigated. By the application of the temporal perturbation of the solutions near t = 0, we are able to evaluate the modifications of the wave patterns from the solution of the Goursat-Riemann problem. Four basic wave patterns were found to be of importance for which the initial and final stress states are on (i) a fast simple wave curve, (ii) a slow simple wave curve, (iii) a fast shock wave curve, and on (iv) a slow shock wave curve. The analysis shows that the geometry of the stress paths and the curvilinear wave fronts depend on the impact at the boundary and the partition in the stress space. In particular, the wave fronts are straight lines and the stress in the region between the wave fronts is constant if the impact at the boundary is pointed to the direction of the eigenvector for the slow simple wave or to some specific directions; otherwise the wave fronts are curvilinear.

Stability of Godunov’s method for a class of 2×2 systems of conservation laws

We prove stability and convergence of the Godunov scheme for a special class of genuinely nonlinear 2 × 2 2 \times 2 systems of conservation laws. The class of systems, which was identified and studied by Temple, is a subset of the class of systems for which the shock wave curves and rarefaction wave curves coincide. None of the equations of gas dynamics fall into this class, but equations of this type do arise, for example, in the study of multicomponent chromatography. To our knowledge this is the first time that a numerical method other than the random choice method of Glimm has been shown to be stable in the variation norm for a coupled system of nonlinear conservation laws. This implies that subsequences converge to weak solutions of the Cauchy problem, although convergence for 2 × 2 2 \times 2 systems has been proved by DiPerna using the more abstract methods of compensated compactness.

Systems of conservation laws with invariant submanifolds

Systems of conservation laws with coinciding shock and rarefaction curves arise in the study of oil reservoir simulation, multicomponent chromatography, as well as in the study of nonlinear motion in elastic strings. Here we characterize this phenomenon by deriving necessary and sufficient conditions on the geometry of a wave curve in order that the shock wave curve coincide with its associated rarefaction wave curve for a system of conservation laws. This coincidence is the one dimensional case of a submanifold of the state variables being invariant for the system of equations, and the necessary and sufficient conditions are derived for invariant submanifolds of arbitrary dimension. In the case of 2 × 2 2 \times 2 systems we derive explicit formulas for the class of flux functions that give rise to the coupled nonlinear conservation laws for which the shock and rarefaction wave curves coincide.

On a Quasi‐Conical Motion in Supersonic‐Hypersonic Flow, Considering the Entropy Effects

AbstractIn order to get analytical solutions for the supersonic‐hypersonic motion around a body of revolution, consisting of a cylinder and a truncated come, one proposes a perturbation method. Unlike the classical procedure where one considers small perturbations with respect to the general flow, parallel at upstream infinity, the basic state is a potential motion, close enough to the real one, that respresents an exact solution in several important limit cases. The method provides explicit formulae for the velocity field, as well as for the shock wave curve and for the entropy gradient.