Refraction Of Shock Wave Research Articles

Bio-inspired pulsed power switch under shock wave

The spark gap switch is a crucial component in the primary energy drive system for large pulse power devices. The switch electrodes are composed of high-density artificial graphite, possessing excellent erosion resistance. However, insufficient mechanical strength in the graphite electrodes makes them especially susceptible to mechanical damage under the enormous impact force caused by the increasing arc current, which seriously affects the reliability and service life of the switch. The distribution of the shock wave overpressure on the graphite electrode surface is deduced and calculated, and the refraction and reflection process of the shock wave from the air to the graphite interface is analyzed based on the Huygens–Fresnel principle. Furthermore, the doubling of refracted shock wave intensity into the graphite electrode is a preliminary characterization. The propagation process of stress wave after the shock wave enters the electrode is investigated by establishing two conventional graphite electrode structure models, namely T-shape and reverse T-shape, which reveal that severe stress concentration occurs in both structures. Drawing inspiration from the physiological structure of the woodpecker’s head, renowned for its exceptional impact resistance, the macroscopic geometry of the graphite electrode and the assembly structure of the switch have been bionically designed. The simulation results demonstrate that, in comparison to the conventional electrode structure, the bionic electrode structure eliminates stress concentration at the bolt end and electrode corner, while significantly reducing maximum equivalent stress and the degree of the stress concentration on the bottom surface of the electrode. These features contribute to the enhancement of the current capacity and reliability of the spark gap switch.

Magnetohydrodynamic shock refraction at an inclined density interface

Shock wave refraction at a sharp density interface is a classical problem in hydrodynamics. Presently, we investigate the strongly planar refraction of a magnetohydrodynamic (MHD) shock wave at an inclined density interface. A magnetic field is applied that is initially oriented either perpendicular or parallel to the motion of incident shock. We explore flow structure by varying the magnitude of the magnetic field governed by the non-dimensional parameter β∈(0.5,106) and the inclination angle of density interface α∈(0.30,1.52). The regular MHD shock refraction process results in a pair of outer fast shocks (reflected and transmitted) and a set of inner nonlinear magneto-sonic waves. By varying magnetic field (strength and direction) and inclination interface angle, the latter waves can be slow shocks, slow expansion fans, intermediate shocks, or slow-mode compound waves. For a chosen incident shock strength and density ratio, the MHD shock refraction transitions from regular (all nonlinear waves meeting at a single point) into irregular when the inclined density interface angle is less than a critical value. Irregular refraction patterns are not amenable to an analytical solution, and hence, we have obtained irregular refraction solutions by numerical simulations. Since the MHD shock refraction is self-similar, we further explore by converting the initial value problem into a boundary value problem (BVP) by a self-similar coordinate transformation. The self-similar solution to the BVP is numerically solved using an iterative method and implemented using the p4est adaptive mesh framework. The simulation shows that a Mach stem occurs in an irregular MHD shock refraction, and the flow structure can be an MHD equivalent to a single Mach reflection irregular refraction and convex-forwards irregular refraction that occur in hydrodynamic case. For Mach number M = 2, both analytical and numerical results show that perpendicular magnetics fields suppress the regular to irregular transition compared to the corresponding hydrodynamic case. As Mach number decreased, it is possible that strong perpendicular magnetics promote the regular to irregular transition, while moderate perpendicular magnetics suppress this transition compared to the corresponding hydrodynamic case.

Shock wave refraction patterns at a slow–fast gas–gas interface at superknock relevant conditions

Shock wave refraction theory and high-resolution numerical simulations were employed to predict the refraction pattern under superknock relevant conditions at slow–fast gas–gas interfaces which are characterized by a higher acoustic impedance in the incident phase than in the transmitted phase. First, our theoretical and computational methodologies were validated against results from the literature for planar shock–straight oblique interface interactions. Second, our framework was applied to planar shock-/cylindrical shock–cylindrical interface interactions. The theoretical regime diagram agrees well with the numerical predictions for the former configuration whereas significant discrepancies were observed for the latter. Numerical results show the formation of temperature and pressure peaks as the refraction structure transits from a free precursor refraction to a twin von Neumann refraction. This change in thermodynamic state can induce a significant reduction in ignition delay time, potentially leading to detonation onset.

A numerical method for self-similar solutions of ideal magnetohydrodynamics

We present a numerical method to obtain self-similar solutions of the ideal magnetohydrodynamics (MHD) equations. Under a self-similar transformation, the initial value problem (IVP) is converted into a boundary value problem (BVP) by eliminating time and transforming the system to self-similar coordinates (ξ≡x/t,η≡y/t). The ideal MHD system of equations is augmented by a generalized Lagrange multiplier (GLM) to maintain the solenoidal condition on the magnetic field. The self-similar solution to the BVP is solved using an iterative method, and implemented using the p4est adaptive mesh refinement (AMR) framework. Existing Riemann solvers (e.g., Roe, HLLD etc.) can be modified in a relatively straightforward manner and used in the present method. Numerical tests illustrate that the present self-similar solution to the BVP exhibits sharper discontinuities than the corresponding one solved by the IVP. We compare and contrast the IVP and BVP solutions in several one dimensional shock-tube test problems and two dimensional test cases include shock wave refraction at a contact discontinuity, reflection at a solid wall, and shock wave diffraction over a right angle corner.

Hydrodynamic instability at impact interfaces and planetary implications

Impact-induced mixing between bolide and target is fundamental to the geochemical evolution of a growing planet, yet aside from local mixing due to jetting – associated with large angles of incidence between impacting surfaces – mixing during planetary impacts is poorly understood. Here we describe a dynamic instability of the surface between impacting materials, showing that a region of mixing grows between two media having even minimal initial topography. This additional cause of impact-induced mixing is related to Richtmyer-Meshkov instability (RMI), and results from pressure perturbations amplified by shock-wave refraction through the corrugated interface between impactor and target. However, unlike RMI, this new impact-induced instability appears even if the bodies are made of the same material. Hydrocode simulations illustrate the growth of this mixing zone for planetary impacts, and predict results suitable for experimental validation in the laboratory. This form of impact mixing may be relevant to the formation of stony-iron and other meteorites.

Interaction of a Shock Wave with an Increased-Density Gas Bubble in the Neighborhood of the Wall

The problem of the interaction of a shock wave with an increased-density gas bubble in the neighborhood of the wall is investigated on the basis of numerical simulation of Euler’s equations in the two-dimensional plane formulation. The process of shock wave refraction and focusing, namely, reflection of transverse shocks from the plane of symmetry of flow and the wall, is described. It is found that qualitatively different flow regimes, in which the wave is focused in the plane of symmetry before or after the beginning of wave reflection from the wall, can be implemented depending on the constitutive parameters of the problem. It is shown that the presence of a heavy bubble in the neighborhood of the wall strengthens multiply the pulse shock-wave loading on the wall. The maximum pressure reached on the wall is found as a function of the impinging wave Mach number, the bubble gas density, and the initial distance between the bubble and the wall. In some cases such a dependence is essentially nonmonotonic with respect to the bubble gas density and the distance between bubble and wall.

The Effect of Gas Nonideality on the Interface Reflectivity When Interacting With a Shock Wave

The phenomenon of shock wave refraction on a gaseous interface with plasma was analyzed for nonideal gas effects. The developed model was applied to nondissociating diatomic nitrogen gas at 3000 K. Comparatively to ideal gas, the interface reflectivity was found noticeably decreased resulting in 12% more intense shock transmission. The transition point determining the character of reflected wave was also found shifted with its coordinate being strongly dependent on incident shock strength and sort of gas. It was found that a delay in gas pressure drop and a sharp reduction of vorticity generated in the postshock flow are possible. The influence of real-gas effects on the shock instability locus, interface distortion, and wave drag reduction is discussed.

ВЛИЯНИЕ РЕЛАКСАЦИОННЫХ ПРОЦЕССОВ НА ФОКУСИРОВКУ УДАРНОЙ ВОЛНЫ В ОБЛАКЕ ГАЗОВЗВЕСИ

In this paper, the interaction of a plane shock wave in air with a cylindrical region of a gas suspension and the effect of relaxation processes for various particle sizes on the refraction and focusing of the shock wave are studied. In the course of numerical modeling, the Euler approach is used to describe non-equilibrium motion of the gas and dispersed phases. A second order accuracy method in space and time is used. Verification of the method through test problems by comparing with exact solutions and calculations of other authors confirms a capability of detecting shock wave refraction effects and wave focusing with the appearance of peak profiles in a distribution of parameters. With an increase in particle sizes, the relaxation zones behind the shock wave and secondary waves, which propagate through a gas suspension cloud, have a significant impact on the shock wave refraction, focusing of transverse shock waves, and interface instability evolution. A focus point is shifted towards suspension cloud boundaries, while for sufficiently large particles, it moves beyond the boundaries (external focus mode). Thus, the reflection pressure of transverse waves and intensity of the instability at the interface reduce.

Progress in unsteady converging shock reflection and refraction

Unsteady shock reflection and refraction have become increasingly attractive in recent yearsdue to their significance in scientific and engineering areas. The unsteady phenomena of a planar shock wavereflecting over a curved wedge have been investigated. During this process, the shock intensity is unvaried whilethe incident angle keeps changing, which results in the transition between different wave patterns. When a curvedshock wave moves along a solid wall or an interface separating two different fluids, both the shock intensity andincident angle are changing, which probably have significant influences on wave patterns and their transitions.Nevertheless, it is a difficult problem to create a curved shock wave with regularities in laboratory. Based onshock dynamics theory, Zhai proposed a method to transform a planar shock wave into a cylindrically convergingone, and the investigations on reflection of a converging shock wave at a solid wall and on the refraction of aconverging shock wave at a fluid interface were carried out. In this work, the progress in unsteady cylindricallyconverging shock wave reflection and reflection phenomena in our laboratory has been discussed, focusing on theeffects of incident angle and flow unsteadiness on wave patterns transitions. Finally, we propose the following issuesfor future study.

Shock wave and flame front induced detonation in a rapid compression machine

The present study focuses on one mode of detonation initiation observed in a rapid compression machine (RCM). This mode is referred to as shock wave and flame front-induced detonation (SWFID). Experimental high-speed imaging and two-dimensional numerical simulations with skeletal chemistry are combined to unravel the dominant steps of detonation initiation under SWFID conditions. It is shown that the interaction between the shock wave generated by the end-gas auto-ignition and the spherical flame creates a region of high pressure and temperature which enables the acceleration of the flame front and the detonation onset. The experimental observation lacks adequate spatial and temporal resolution despite good reproducibility of the detonation onset. Based on the numerical results, phenomenological interpretation of the event within the framework of shock wave refraction indicates that the formation of a free-precursor shock wave at the transition between regular and irregular refraction may be responsible for detonation onset. The present results along with previous findings on shock wave reflection-induced detonation in the RCM indicate that super-knock occurs after the interaction of the shock wave generated by end-gas auto-ignition with the RCM walls, preignition flame, or another shock wave.

Flow and mixing in shock-accelerated elliptic helium gas cylinder process

In shock bubble interaction (SBI), the baroclinic vorticity generated by misalignment of pressure and density gradient will lead to flow instability which promotes the mixing between the bubbles and surrounding gas. A numerical study on the flow and mixing of shock-accelerated elliptic helium cylinder with the surrounding air is presented in this study. To well simulate the SBI, compressible multi-component two-dimensional Navier-Stokes equations are solved by combining with double-flux model and five-order weighted essentially non-oscillatory scheme. Both the wave system evolution and the interface deformation are clearly illustrated by using the present numerical method. Quantitatively, the length scales of distorted interface, compressibility of helium cylinder, circulation, and total mixing rates of helium are measured and compared to investigate the mixing mechanism and structure effect of the helium cylinder. It is found that the evolution of elliptic interface is closely related to its shape. In the case of elliptic gas cylinder shock-accelerated along major axis, the most remarkable feature is the air jet which grows constantly with time and penetrates the downstream interface boundary, forming two independent vortices. The penetration speed of the air jet is found to increase with ellipse eccentricity increasing. In addition, like the case of the circular helium cylinder, typical free-precursor irregular shock wave refraction occurs when incident shock wave passes through the interface. In the case of shock-accelerated elliptic gas cylinder along minor axis, a distinct flat structure appears due to the shock compression during the evolution of interface, and then vorticity concentrates at the two ends of the ellipses, which finally bends the interface severely. Simple regular shock wave refraction occurs in the large frontal area of the helium cylinder. These features also grow intensely with the eccentricity of the initial elliptic interface increasing. The distinct morphologies of these elliptic interfaces also lead to the different behaviors of the interface features including the length and height. The comprehensive analysis shows that for the elliptic helium cylinder, the structure effect not only affects the interface evolution in a length-scale manner but also plays a role in their mixing process. The mixing rate of helium cylinder shocked along the major axis is significantly superior to that along the minor axis.

Numerical investigation on unsteady refraction of planar shock wave at air/SF$_6$ gas interface

The unsteady refractions of a planar shock wave at a concave (convex) air/SF$_6$ interface are numerically studied. The finite difference method is utilized to solve the compressible multi-component Euler equations. Pressure oscillation near the interface due to the difference of the specific heat ratio is successfully overcome using Double-Flux algorithm. High temporal and spatial resolutions are achieved through combining the Double-Fluid algorithm with 5th WENO and 3rd Runge-Kutta.Different from pseudo-steady refraction, the continuous change of incident angle when a planar shock wave moves at a concave or convex interface will result in the transitions between different refraction wave patterns. It turns out that when the incident angle changes from 90$^\circ$ to 0$^\circ$ during the shock propagating along the concave interface, the refraction patterns of concave-forwards refraction (CFR), regular refraction with reflected shock (RRR) and transitioned regular refraction with reflected shock (TRRR) are observed in sequence. Compared with pseudo-steady refraction, the Mach type irregular refraction (MRR) is not observed while a new refraction pattern of TRRR occurs, which is possibly caused by hypothesis effect of the flow. With the incident angle increasing from 0$^\circ$ to 90$^\circ$ when the shock moves along the convex interface, only two refraction types of RRR and MRR are captured, and CFR, which occurs under pseudo-steady condition, does not occur. However, at the late stage, the Mach stem becomes curved and resembles the incident shock wave near the interface in CFR. Besides, the critical angle when RRR transits into MRR is delayed while the range of MRR is extended. From this work, it is shown that the flow unsteadiness has a significant influence on the refraction wave pattern.

Superposition of two incident shocks in R718 vapor flows

Although the positive values of the fundamental gas-dynamic derivative of R718 near vapor-liquid equilibrium line ensures no occurrence of the non-classical behavior like rarefaction shock waves, the occurrence of the homogenous condensations due to rarefaction waves must be taken into account when using the moving shocks and rarefaction waves in wave devices. In this article, the superposition behaviors such as shockwave refraction and reflection of two moving incident shocks for R718 vapor flows near this the vapor-liquid equilibrium zone, have been intensively studied. And the supercharging characteristic of two superposition moving incident shocks for R718 vapor flows achieves remarkable high boosting pressure ratios of about square of those of one primary equal-intensity shock. This inspiring result could be fully used for vapor recompression in multi-effect distillation technology (MED) for brine water treatment.

Numerical simulation of shock wave refraction on inclined contact discontinuity

Numerical simulation of shock wave refraction on inclined contact discontinuity

Interaction of a weak shock wave with a discontinuous heavy-gas cylinder

The interaction between a cylindrical inhomogeneity and a weak planar shock wave is investigated experimentally and numerically, and special attention is given to the wave patterns and vortex dynamics in this scenario. A soap-film technique is realized to generate a well-controlled discontinuous cylinder (SF6 surrounded by air) with no supports or wires in the shock-tube experiment. The symmetric evolving interfaces and few disturbance waves are observed in a high-speed schlieren photography. Numerical simulations are also carried out for a detailed analysis. The refracted shock wave inside the cylinder is perturbed by the diffracted shock waves and divided into three branches. When these shock branches collide, the shock focusing occurs. A nonlinear model is then proposed to elucidate effects of the wave patterns on the evolution of the cylinder. A distinct vortex pair is gradually developing during the shock-cylinder interaction. The numerical results show that a low pressure region appears at the vortex core. Subsequently, the ambient fluid is entrained into the vortices which are expanding at the same time. Based on the relation between the vortex motion and the circulation, several theoretical models of circulation in the literature are then checked by the experimental and numerical results. Most of these theoretical circulation models provide a reasonably good prediction of the vortex motion in the present configuration.

Dispersion, dissipation and refraction of shock waves in acoustically treated turbofan inlets

This paper describes a numerical investigation of the effects of the inlet duct liner on the acoustics of a high-bypass ratio turbofan rotor operating at supersonic tip relative flow conditions. The near field of the blade row is then composed of periodic shocks that evolve spatially both because of the varying mean flow and because of the presence of acoustic treatment. The evolution of this shock system is studied using a Computational Fluid Dynamics-based method incorporating a wall impedance boundary condition. The configuration examined is representative of a fan operating near the takeoff condition. The behavior of the acoustic power and the associated waveforms reveal that significant dispersion occurs to the extent that there are no shocks in the perturbation field leaving the entrance plane of the duct. The effect of wave refraction due to the high degree of shear in the mean flow near the entrance plane of the inlet is examined, and numerical experiments are conducted to show that the incorporation of liners in this region can be highly beneficial. The implications of these results for the design of aircraft engine acoustic liners are discussed.

The cumulative energy effect for improved ignition timing

A technique capable of improving timing in ignition applications is proposed. It is based on the use of shock waves propagating in a specific medium that allows achieving extremely high speeds and energies. The model uses the energy cumulation effect in the presence of the shock wave refraction on an interface with plasma. The problem was solved analytically and the effects were demonstrated for a cylindrically symmetrical geometry. Numerical results show very quick and uneven acceleration of different portions of the shock front. Its strong distortions lead to formation of a sharply focused jet near the axis of symmetry. The ability of the shock to achieve extremely high speeds and energies can be useful in design of efficient combustors for hypersonic systems, and possibly offers an alternative way of construction of a nuclear fusion reactor. Recommendations are given in terms of adjustment parameters and can be applied at any problem scale and for various combinations of the strengths of the effects involved in the problem.

Analysis on refraction of detonation wave at the explosive-metal interface

This paper analyzes theoretically and numerically the refraction phenomenon of detonation wave at the explosive-metal interface, motivated by the problem that there exist large discrepancies between the experimental results and the classical shock polar theory. After pointing out the major defects of the classical shock polar theory based on CJ model of detonation, an improved shock polar theory based on ZND model of detonation is presented to give the styles of the refraction of detonation wave and the pressure values at the interaction point between the refracted shock wave and the incident shock wave, to show the pressure values at free-surface of copper remarkably lower than the ones at the shock interaction point due to the attenuation effects from the chemical reaction expansion and the following Taylor rarefaction. A second-order cell-centered Lagrangian hydrodynamics method with high resolution based on the subcharacteristics theory is develped to solve the reactive flow equations of detonation in condensed explosive, and then to numerically simulate a representative refraction experiment about T2 explosive interacting with copper. The simulated pressure values at the interaction point agree well with the ones from the improved shock polar theory, and the simulated pressure values at free-surface of copper agree well with the experimental values, meanwhile, the refraction styles predicted by the improved shock polar theory are confirmed by the numerically simulated flowfield images. From the theoretical and numerical results, there exist three kinds of refraction styles of detonation waves at explosive-metal interface:i) the regular refraction with reflecting shock wave, ii) the irregular refraction with Mach reflection, and iii) the regular refraction without any reflecting wave; in particular, the regular refraction with no reflecting wave is a kind of refraction style unable to be predicted by the classical shock polar theory, meanwhile, the pressure values at the free-surface and the interaction point inside the shocked metal both monotonically decrease with the increase of the incident angle.

Analysis of a protective reinforced concrete slab subject to a vehicle-borne improvised explosive device

This paper describes the practical application of computational analysis to the design of a reinforced concrete structure subject to blast loading from a vehicle-borne improvised explosive device. The structure includes a protective slab designed to provide a barrier between the blast load and a densely occupied commercial floor. The blast load derivation was carried out using commercially available computational fluid dynamics (CFD) (hydrocode) software to predict shock wave propagation, reflection and refraction effects. Pressure–time histories were extracted and applied to the mesh of a decoupled finite-element (FE) model of the structural system. The structural analysis was carried out using a commercially available explicit dynamic solver, incorporating non-linear material representations of the primary structural components including the protective slab and supporting columns, beams and walls. The analysis methodology was based on a macro level of structural detail commensurate with the design objectives, with column and beams represented with line elements and walls and slabs represented with thin shell elements. The computational analysis successfully confirmed the adequacy of the proposed design for the specified threat level. The paper concludes that the performance of a reinforced concrete structural system can be cost-effectively assessed for blast loading, to a level appropriate for design purposes, using existing commercially available CFD and FE tools.

The Shock Wave Refraction in Supersonic Planar Mixing Layers

We analyze the shock wave refraction in a spatially developing shocked mixing layer by means of direct numerical simulation. Both regular and Mach reflections can occur depending on the relative strength of the induced shock wave over the vorticity of interacting vortex in the mixing layer. The stronger incident shock wave frequently refracts Mach reflection. The shock polar diagram is used to determine the shock wave refraction patterns. Moreover, the vortices are deformed and compressed by the shock wave, and their vorticities are increased. The interaction of shock wave and coherent structure can be helpful to enhance the mixing process.