Behavior Of Shock Waves Research Articles

Optical generation and control of spatial Riemann waves.

We extend the concept of Riemann waves (RWs) to the spatial domain and demonstrate for the first time, to the best of our knowledge, Riemann beams with a propagation scenario allowing controllable shock formation in a nonlinear optical system. Similar to their standard counterparts, "shifted" RWs are characterized by a local propagation speed proportional to their local amplitude. Their steepening dynamics can be judiciously controlled by means of an additional phase term. In particular, RWs are generated by properly tailoring the initial phase of an optical beam propagating through a thermal solution of an m-cresol/nylon mixture that exhibits a giant self-defocusing nonlinearity. The experimental results show a controllable steepening and shock wave behavior, in good agreement with the prediction from the simple inviscid Burgers equation.

Numerical modelling of shock-bubble interactions using a pressure-based algorithm without Riemann solvers

The interaction of a shock wave with a bubble features in many engineering and emerging technological applications, and has been used widely to test new numerical methods for compressible interfacial flows. Recently, density-based algorithms with pressure-correction methods as well as fully-coupled pressure-based algorithms have been established as promising alternatives to classical density-based algorithms based on Riemann solvers. The current paper investigates the predictive accuracy of fully-coupled pressure-based algorithms without Riemann solvers in modelling the interaction of shock waves with one-dimensional and two-dimensional bubbles in gas-gas and liquid-gas flows. For a gas bubble suspended in another gas, the mesh resolution and the applied advection schemes are found to only have a minor influence on the bubble shape and position, as well as the behaviour of the dominant shock waves and rarefaction fans. For a gas bubble suspended in a liquid, however, the mesh resolution has a critical influence on the shape, the position and the post-shock evolution of the bubble, as well as the pressure and temperature distribution.

Shock Wave Kinematics in a Relaxing Gas with Dust Particles

Abstract In this article, we considered the evolutionary behaviour of one-dimensional shock waves propagating through a relaxing gas with dust particles in a duct with spatially varying cross section. We adopted the procedure based on the kinematics of a one-dimensional motion to derive an infinite hierarchy of transport equations, which describe the evolutionary behaviour of shock of arbitrary strength propagating through the medium. The first three truncation approximations are considered, and the results are compared with existing results in the absence of relaxation and dust particles. The effects of dust particles and relaxation are studied using numerical computations. The results are depicted for different values of dust and relaxation parameters.

Insights into local shockwave behavior and thermodynamics in granular materials from tomography-initialized mesoscale simulations

Interpreting and tailoring the dynamic mechanical response of granular systems relies upon understanding how the initial arrangement of grains influences the compaction kinetics and thermodynamics. In this article, the influence of initial granular arrangement on the dynamic compaction response of a bimodal powder system (soda-lime distributed throughout a porous, fused silica matrix) was investigated through continuum-level and mesoscale simulations incorporating real, as-tested microstructures measured with X-ray tomography. By accounting for heterogeneities in the real powder composition, continuum-level simulations were brought into significantly better agreement with previously reported experimental data. Mesoscale simulations reproduced much of the previously unexplained experimental data scatter, gave further evidence of low-impedance mixture components dominating shock velocity dispersion, and crucially predicted the unexpectedly high velocities observed experimentally during the early stages of compaction. Moreover, only when the real microstructure was accounted for did simulations predict that small fractions of the fused silica matrix material would be driven into the β-quartz region of phase space. These results suggest that using real microstructures in mesoscale simulations is a critical step in understanding the full range of shock states achieved during dynamic granular compaction and interpreting solid phase distributions found in real planetary bodies.

Instability of relativistic shock waves: Numerical study on the basis of model equation of state

The behavior of unstable relativistic shock waves is studied with the use of specially developed model equation of state (EOS). The EOS admits the Taub-Hugoniot adiabats with segments on which the criteria of the relativistic shock wave stability are violated. The instability segments are overlapped by the regions with ambiguous representation of the shock-wave discontinuity. The simulations are fulfilled for L < − 1 and L > (1 + 2M + v0v1)/(1 − v0v1) instability conditions, where L is relativistic analog of Dyakov parameter, M is post-shock Mach number, v0 and v1 are pre- and post-shock velocities in the shock attached reference frame. Under the condition of ambiguous representation of the shock-wave discontinuity in the former case the splitting of the unstable shock with formation of a composite compression wave with Lorentz factor dependent structure is observed. It is shown that the latter condition leads to two-dimensional non-stationary solutions characterized by presence of strong transverse waves.

Explicit radial basis function collocation method for computing shallow water flows

A simple Explicit Radial Basis Function (RBF) is used to solve the shallow water equations (SWEs) for flows over irregular, frictional topography involving wetting and drying. At first we construct the MQ-RBF interpolation corresponding to space derivative operators. Next, we obtain numerical schemes to solve the SWEs, by using the gradient of the interpolant to approximate the spatial derivative of the differential equation and a third-order explicit Runge-Kutta scheme to approximate the temporal derivative of the differential equation. Then, we verify our scheme against several idealized one-dimensional numerical experiments including dam-break and open channel flows over non-uniform beds (involving shock wave behavior), and moving wet-dry fronts over irregular bed topography. Promising results are obtained.

A comparison of shockwave dynamics in stochastic and periodic porous polymer architectures

Dynamic loading of materials is fundamental in understanding the mechanical response of cellular solids and elucidates time dependent properties that pertain to energy absorption under extreme conditions. Of particular interest is how the discrete behavior of the individual cell in a stochastic foam affects the dynamic shockwave behavior. The deformation mechanism in a stochastic open-cell foam is bending-dominated versus stretch-dominated in periodic lattice structures, resulting in a decrease in the plastic yield stress. Here, we investigate shockwave dynamics in stochastic open-cell foams through phase contrast imaging and finite element modeling. We observe that the distribution of pore sizes and the proximity of each produces a random topology with varying cell wall thicknesses that cause points of high strain creating irregularity in the shock wave at higher impact speeds. The shockwave dynamics of the stochastic foam are compared to periodic additive manufactured (AM) foams with similar density and it can be observed that modulation via microstructural control in elastomer foams has a dramatic effect on shockwave dynamics.

Sequential observation of rebound shock wave generated by collapse of vapor bubble in BOS system

The paper reports on a pressure measurement of underwater shock waves generated by collapse of a vapor bubble using the background-oriented schlieren (BOS) technique. In the BOS system, the vapor bubble is induced by an underwater electric discharge. To estimate background-element displacement induced by the underwater shock wave, a spatiotemporal derivative (STD) algorithm is applied in image processing. Furthermore, the accuracy of the STD algorithm is evaluated using the images obtained with our BOS system relative to the cross-correlation method. Subsequently, the pressure distributions are obtained by solving the Poisson equation and applying a filtered-back projection algorithm. An experiment to visualize the behaviors of the underwater shock waves is also carried out using the shadowgraph method. As a result, the pressure waveforms estimated by the BOS technique keep consistent with that in experimental profiles. The pressure attenuations behind the underwater shock wave are also in good agreements with the experimental measurements. It is expected that the BOS technique will probably overcome the problems associated with the conventional method of pressure measurement related to the collapse of microbubbles, and becomes a promising means of quantitatively measuring high-speed phenomena.

Effect of consolidation pressure on the impact behavior of UHMWPE composites

Abstract For the first time, the influence of the manufacturing process on the dynamic performance of ultra-high molecular weight polyethylene (UHMWPE, Dyneema® HB26) composites is investigated. The material is significantly influenced by the hot-pressing parameters temperature and pressure. The ballistic resistance and shock wave behavior was characterized for the UHMWPE composite consolidated with three different pressures. In the case of UHMWPE composites, higher consolidation pressures result in a better ballistic performance. The shock wave behavior converges to high-density polyethylene (HDPE). Based on these observations, an analytical approach is proposed describing the equation of state as a function of consolidation pressure.

The relief of energy convergence of shock waves by using the concave combustion chamber under severe knock

In internal combustion engines, severe knock is a destructive phenomenon that would converge the energy released by fuel burning to damage the piston so that the engine can’t work anymore, which should be avoided. The destruction mechanism have been revealed in previous researches in which the focusing of shock waves is considered as a main reason to cause the energy convergence and the destruction. However, the method to alleviate such shock wave focusing hasn’t been put forward yet. Based on the destruction mechanism proposed before, in this research, a concave combustion chamber has been designed to alleviate the energy convergence of shock waves under severe knock so that the destruction of the piston under severe knock can be avoided. To validate the alleviation effect of the concave chamber, detonation bomb experiments have been conducted separately for the typical cone chamber and the redesigned concave chamber. Four pressure sensors installed in different positions of either chamber were used to monitor the shock wave behaviors and compare the energy convergence intensity for both of these two chambers. The experimental results prove that the concave chamber can efficiently alleviate the energy convergence in the center region. Furthermore, a series of numerical simulations have been conducted to reveal the alleviation mechanism of the concave chamber. Two kinds of alleviation mechanism have been obtained which are separately: the shock wave diffraction and the shock wave breaking up. These mechanism can efficiently alleviate the energy convergence of shock waves. The research results can be used as a theoretical basis for the chamber design to avoid the destruction under severe knock.

Numerical study of the Kadomtsev–Petviashvili equation and dispersive shock waves

A detailed numerical study of the long time behaviour of dispersive shock waves in solutions to the Kadomtsev–Petviashvili (KP) I equation is presented. It is shown that modulated lump solutions emerge from the dispersive shock waves. For the description of dispersive shock waves, Whitham modulation equations for KP are obtained. It is shown that the modulation equations near the soliton line are hyperbolic for the KPII equation while they are elliptic for the KPI equation leading to a focusing effect and the formation of lumps. Such a behaviour is similar to the appearance of breathers for the focusing nonlinear Schrödinger equation in the semiclassical limit.

Investigation on the flow characteristics of a VNT turbine under pulsating flow conditions

The turbines used in turbochargers naturally experience unsteadiness caused by inlet pulsating flow conditions and stator–rotor interaction. The unsteadiness has an influence on turbine performance. Meanwhile, under certain small-nozzle opening conditions, strong shock waves can be generated. The synergistic effect of turbine inlet pulsation and shock waves has a significant influence on the turbine performance, rotor blade loading as well as the excitation force exerted on the turbine rotor, which is responsible for turbine rotor high cycle fatigue. In order to understand the influence of pulsating flows on turbine performance and the shock wave characteristic at nozzle trailing edge as well as the incidence angle characteristic of the rotor blade, unsteady numerical simulations were performed to investigate the effect of pulsating flow conditions on the performance, flow characteristics in frequency domain and shock wave behavior in a variable nozzle turbine. The results indicate that the turbine inlet pressure pulsation has strong influence on the turbine performances. Meanwhile, the turbine inlet pulsation flow has a strong influence on the intensity of the shock wave and clearance leakage flow in the nozzle, which causes significant flow losses in the turbine. In addition, at the turbine rotor inlet, the unsteadiness caused by the turbine inlet pulsation varies significantly along the circumferential direction and spanwise. Up to two-thirds of the unsteadiness caused by the turbine inlet pulsation dissipates before entering the rotor due to the flow dissipation and mixing process along the nozzle streamwise. The excitation force exerted on the rotor blade leading edge caused by the turbine inlet pulsation is about the same level as that caused by the stator–rotor interaction.

The Progressive Wave Approach Analyzing the Evolution of Shock Waves in Dusty Gas

In the present paper the theory of progressive waves is used to analyze the finite amplitude disturbances, moderately small amplitude disturbances in a dusty gas for generalized geometry. The conditions, under which a complete history of the evolutionary behavior of shock waves including weak shock can be traced out, are determined. It is also assessed as to how the presence of dust particles in the gas affects the existence of shock or no shock. Further the effect of variation of mass fraction of the dust particles on the growth and decay behavior of shock in cylindrically symmetric and spherically symmetric flows are discussed.

격벽착화기 화약의 충격파와 민감도 분석

격벽착화기의 최적 설계를 위하여 여폭약에 의해 생성되는 충격파의 감쇄 특성과 수폭약의 민감도에 관하여 연구하였다. 충격파의 감쇄 특성은 레이저 광간섭계인 VISAR를 이용하여 측정한 격벽의 자유 표면 속도로부터 유도하였고 수폭약의 민감도는 SSGT (Small Scale Gap Test) 결과로부터 구하였다. 격벽착화기의 기폭시험을 통하여 SSGT로부터 구한 화약의 민감도가 격벽착화기와 같이 소량의 화약을 사용하는 시스템에는 충격파 지속 시간이 상이하여 적합하지 않다는 것을 밝혀내었다. We studied attenuation characteristics of shock waves induced by a donor charge and the sensitivity of an acceptor for optimal design of a TBI (Through-bulkhead initiator). The attenuation behavior of shock waves was studied by measuring free surface velocity using a VISAR (Velocity Interferometer System for Any Reflector), and the sensitivity of the acceptor explosives was analyzed via SSGT (Small Scale Gap Test). It was found that the acceptor sensitivity obtained by the SSGT may be inappropriate for the design of the small-scale explosive devices such as TBI due to the different shock duration time.

Characteristic behavior of shock pattern and primary vortex loop of a supersonic square jet

The initial flow fields of the supersonic underexpanded square jets with different nozzle pressure ratios were investigated numerically. The governing equations of large eddy simulation (LES) for compressible flow have been employed and solved numerically with the combination of high-order hybrid schemes. The numerical result provides the 3D shock wave structures embedded in the underexpanded square jet. Moreover, the effect of nozzle pressure ratio on the 3D characteristic behavior of near-nozzle shock wave and the jet boundary are discussed, it is found that the near-nozzle shock wave structure suppresses the jet boundary at the corner position expansion along the diagonal direction, and accelerates the jet boundary near the sidewall position to move in normal direction to the nozzle side, finally resulting in a remarkable cross-shaped jet cross section at the downstream. Besides, the 3D behavior of streamwise vortices during the self-induced deformation of primary vortex loop is identified using the iso-vorticity field, and their role in the axis-switching behavior of supersonic square vortex loop is analyzed in detail.

Experimental and computational investigation of confined laser-induced breakdown spectroscopy

This paper presents an experimental and computational study on laser-induced breakdown spectroscopy (LIBS) for both unconfined flat surface and confined cavity cases. An integrated LIBS system is employed to acquire the shockwave and plasma plume images. The computational model consists of the mass, momentum, and energy conservation equations, which are necessary to describe shockwave behaviors. The numerical predictions are validated against shadowgraphic images in terms of shockwave expansion and reflection. The three-dimensional (3D) shockwave morphology and velocity fields are displayed and discussed.

Ernst formulation of axisymmetric fields inf(R)gravity: Applications to neutron stars and gravitational waves

The Ernst formulation of the Einstein equations is generalised to accommodate $f(R)$ theories of gravity. It is shown that, as in general relativity, the axisymmetric $f(R)$ field equations for a vacuum spacetime that is either stationary or cylindrically symmetric reduce to a single, non-linear differential equation for a complex-valued scalar function. As a worked example, we apply the generalised Ernst equations to derive a $f(R)$ generalisation of the Zipoy-Voorhees metric, which may be used to describe the gravitational field outside of an ellipsoidal neutron star. We also apply the theory to investigate the phase speed of large-amplitude gravitational waves in $f(R)$ gravity in the context of soliton-like solutions that display shock-wave behaviour across the causal boundary.

The design and influence of port arrangement on an improved wave rotor refrigerator performance

The port width and the offset between them are important structure parameters of a wave rotor refrigerator (WRR). The arrangement of ports decides the wave diagram in the wave rotor, which has a huge influence on the WRR performance. Designing a wave rotor mainly focuses on predicting the behavior of shock and expansion waves in wave rotor channels. This paper first presents an analytical design procedure for the pressure exchanger refrigerator, also known as WRR, to afford a theoretical port arrangement of the WRR rapidly. Then, the analytical design results are used as initial numerical model for CFD calculation. Based on the numerical simulation results, the port arrangements can be optimized. Charts and explanations are presented for the optimum design. Furthermore, a series of experiments were conducted to investigate the WRR performance under the optimized port sizes and offset. The results suggest that the COP of the system greatly changes with the geometrical arrangements. The highest COP of the system may be reduced by 41.8% with improper port widths or positions. The analysis of the WRR refrigeration system performance has revealed that expansion efficiency can be adversely affected by the compression efficiency, which means the improved WRR system have a great resistance to the working condition of volatility.

Experimental study on gas-particle two-phase flows in a micro shock tube

Recently, micro shock tubes have been widely used in various fields such as aerospace, combustion and medical science. Needle-free drug delivery device is a typical example of the application of the micro shock tube used in the field of medical science. Compared to the macro shock tube, the flow viscosity and micro scale effects considerably influence the shock wave propagation in the micro shock tube, which makes shock wave behaviors significant difference from the theoretical prediction. Boundary layers which develop behind the moving shock wave attenuate the shock wave propagation as well. Additionally, the gas-particle flows are also shown the different characteristics compared to the single gas flow in the micro shock tube. Particles are induced by the shock wave inside the micro shock tube and accelerated in the supersonic nozzle. Supersonic flows and particle velocity make experimental studies difficult to be performed in the micro shock tube. Even though micro shock tubes have been studied for decades, shock flow characteristics and particle dynamics inside the micro shock tube are not well known to date. For the present study, pressure measurements and optical visualization have been carried out in a micro shock tube. Static pressure measurements were used for investigating the shock wave propagation in the driven section, and Pitot pressure measurements were used for obtaining flow characteristics at the exit of nozzles. Two high sensitive pressure transducers were used for recording pressure changes as the shock wave moved through pressure transducers and the shock Mach number was calculated. Particle tracking velocimetry was conducted to analyze particle-gas two-phase flows. Particle distribution and velocity were obtained in the present experiment study.

Experimental verification of shock sterilization for marine Vibrio sp. using microbubbles interacting with underwater shock waves

In this paper, shock sterilization using the motions of microbubbles induced by underwater shock waves is verified experimentally. A bio-experiment is carried out using marine Vibrio sp.. Underwater shock waves are produced by electric discharge in a semi-ellipsoidal discharge reflector. The shock waves are focused to increase the pressure that the generated microbubbles are exposed to. The microbubbles are generated independently. The microbubble generator can produce microbubbles of around 50 μm diameter by means of Kelvin–Helmholz instability and Venturi effect. Propagation behavior of shock waves and generation process of microbubbles are captured by high-speed camera. The experimental results show that the supply of microbubbles increases the potential of shock sterilization. In addition, it is found that shock waves without microbubbles also have the capacity of sterilization, and this means that cavitation bubbles generated behind converging shock waves contribute to inactivating marine bacteria.