Elastic response of water-filled fiber composite tubes under shock wave loading

We experimentally and numerically investigate the response of fluid-filled filament-wound composite tubes subjected to axial shock wave loading in water. Our study focuses on the fluid–structure interaction occurring when the shock wave in the fluid propagates parallel to the axis of the tube, creating pressure waves in the fluid coupled to flexural waves in the shell. The in-house-developed computational scheme couples an Eulerian fluid solver with a Lagrangian shell solver, which includes a new and simple material model to capture the response of fiber composites in finite kinematics. In the experiments and simulations we examine tubes with fiber winding angles equal to 45° and 60°, and we measure the precursor and primary wave speeds, hoop and longitudinal strains, and pressure. The experimental and computational results are in agreement, showing the validity of the computational scheme in complex fluid–structure interaction problems involving fiber composite materials subjected to shock waves. The analyses of the measured quantities show the strong coupling of axial and hoop deformations and the significant effect of fiber winding angle on the composite tube response, which differs substantially from that of a metal tube in the same configuration.     

多障碍物通道中激波诱导气相爆轰的数值研究

应用数值模拟方法,研究了直通道中激波经过多块矩形障碍物时诱导 H2/O2混合气体起爆的物理机制. 研究表明：在前导激波强度不足以诱导波后气 体直接起爆的条件下,经过激波压缩的可燃气体也可能在远离激波的障碍物之间的凹槽部位 起爆;障碍物表面产生的压缩波、膨胀波和气流滑移面对可燃气体的起爆、爆轰波的形成和 传播过程有重要的影响;添加不同稀释比的氮气可以影响爆轰波后流场的温度分布;增加障 碍物的间距可以改变可燃气起爆位置.     

External shock loading on a submerged fluid-filled cylindrical shell

The interaction between a submerged fluid-filled elastic circular cylindrical shell and an external shock wave is considered. The study focuses on the internal acoustic field. A linear formulation of the problem is considered. A semi-analytical solution is obtained and used to simulate the interaction. A variety of phenomena are observed in the internal fluid, including the reflection and focusing of the internal acoustic wave as well as the radiation into the fluid of elastic waves propagating in the shell. Throughout the paper, the results of numerical simulations are compared with available experimental data, and a good agreement is observed. The solution developed appears to be suitable for use as a benchmark. Engineering relevance of the phenomena observed is discussed.     

Lattice Boltzmann simulations of viscoplastic fluid flows through complex flow channels

We present the results of lattice Boltzmann (LB) simulations for the planar-flow of viscoplastic fluids through complex flow channels. In this study, the Bingham and Casson model fluids are covered as viscoplastic fluid. The Papanastasiou (modified Bingham) model and the modified Casson model are employed in our LB simulations. The Bingham number is an essential physical parameter when considering viscoplastic fluid flows and the modified Bingham number is proposed for modified viscoplastic models. When the value of the modified Bingham number agrees with that of the “normal” Bingham number, viscoplastic fluid flows formulated by modified viscoplastic models strictly reproduce the flow behavior of the ideal viscoplastic fluids. LB simulations are extensively performed for viscoplastic fluid flows through complex flow channels with rectangular and circular obstacles. It is shown that the LB method (LBM) allows us to successfully compute the flow behavior of viscoplastic fluids in various complicated-flow channels with rectangular and circular obstacles. For even low Re and high Bn numbers corresponding to plastic-property dominant condition, it is clearly manifested that the viscosity for both the viscoplastic fluids is largely decreased around solid obstacles. Also, it is shown that the viscosity profile is quite different between both the viscoplastic fluids due to the inherent nature of the models. The viscosity of the Bingham fluid sharply drops down close to the plastic viscosity, whereas the viscosity of the Casson fluid does not rapidly fall. From this study, it is demonstrated that the LBM can be also an effective methodology for computing viscoplastic fluid flows through complex channels including circular obstacles.     

A sharp interface Cartesian grid method for viscous simulation of shocked particle-laden flows

A Cartesian grid-based sharp interface method is presented for viscous simulations of shocked particle-laden flows. The moving solid–fluid interfaces are represented using level sets. A moving least-squares reconstruction is developed to apply the no-slip boundary condition at solid–fluid interfaces and to supply viscous stresses to the fluid. The algorithms developed in this paper are benchmarked against similarity solutions for the boundary layer over a fixed flat plate and against numerical solutions for moving interface problems such as shock-induced lift-off of a cylinder in a channel. The framework is extended to 3D and applied to calculate low Reynolds number steady supersonic flow over a sphere. Viscous simulation of the interaction of a particle cloud with an incident planar shock is demonstrated; the average drag on the particles and the vorticity field in the cloud are compared to the inviscid case to elucidate the effects of viscosity on momentum transfer between the particle and fluid phases. The methods developed will be useful for obtaining accurate momentum and heat transfer closure models for macro-scale shocked particulate flow applications such as blast waves and dust explosions.     

On one-dimensional shock waves in composite materials modelled as interpenetrating solid continua

A one dimensional version of a theory of composite materials modelled as interpenetrating solid continua is used to study the propagation of shock waves in composites with two identifiable constituents. It is found that two distinct types of shock waves may propagate except when one of the constituents is a chopped fiber. The speeds at which the shock waves propagate are determined as are the differential equations which govern the evolutionary behaviour of the amplitudes of the waves. The implications of these results are studied in detail in a number of particular situations. Finally, the special results which hold when the amplitudes of the shock waves are infinitesimal are also presented.     

环形激波绕射, 反射和聚焦的数值模拟研究

应用频散可控耗散格式对环形激波在圆柱形激波管内绕射、反射和聚焦的问题进行了数值模拟研究，研究结果表明环形激波形成强烈聚焦的关键因素是环形激波在圆柱形管道中向对称轴运动时，绕射激波就不断加速而不作通常情况下的衰减；不同马赫数的环形激波绕射也产生不同马赫数及形状的准柱形激波，导致聚焦效果和位置的差异；另外，环形激波聚焦于一个点而圆柱形激波聚焦于一条线，两者有本质不同。     

Mechanism of deflagration-to-detonation transitions above repeated obstacles

Experiments are carried out to investigate the mechanism of the deflagration-to-detonation transition (DDT). Because, this mechanism has relevance to safety issues in industries, where combustible premixed gases are in general use. A stoichiometric gas of oxygen and hydrogen (oxy-hydrogen) is ignited in a tube, repeated obstacles are installed, and the DDT behaviours are visualized using a high-speed video camera. The pitch and height of the repeated obstacles and the initial pressure of the oxy-hydrogen premixed gas are varied in an attempt to obtain the optimum conditions that cause DDT a short distance from the ignition source. The experiments identified DDT as being essentially caused by one of the following mechanisms: (1) A deflagration wave is accelerated in terms of a vortex, which is generated behind the obstacle, and the flame acceleration induces a secondary shock wave. Eventually, the shock–flame interaction ahead of the obstacle causes DDT via a very strong local explosion. (2) Each shock wave generated by relatively weak local explosions between the obstacles is not sufficient to cause DDT directly, but DDT results from an accumulation of shock waves. The detonation induction distance is also examined, taking into account the physical and chemical parameters of the obstacles and the oxy-hydrogen premixed gas.     

Evaluation of adaptive mesh refinement and coarsening for the computation of compressible flows on unstructured meshes

The compressible gas flows of interest to aerospace applications often involve situations where shock and expansion waves are present. Decreasing the characteristic dimension of the computational cells in the vicinity of shock waves improves the quality of the computed flows. This reduction in size may be accomplished by the use of mesh adaption procedures. In this paper an analysis is presented of an adaptive mesh scheme developed for an unstructured mesh finite volume upwind computer code. This scheme is tailored to refine or coarsen the computational mesh where gradients of the flow properties are respectively high or low. The refinement and coarsening procedures are applied to the classical gas dynamic problems of the stabilization of shock waves by solid bodies. In particular, situations where oblique shock waves interact with an expansion fan and where bow shocks arise around solid bodies are considered. The effectiveness of the scheme in reducing the computational time, while increasing the solution accuracy, is assessed. It is shown that the refinement procedure alone leads to a number of computational cells which is 20% larger than when alternate passes of refinement and coarsening are used. Accordingly, a reduction of computational time of the same order of magnitude is obtained. Copyright © 2005 John Wiley & Sons, Ltd.     

Experimental investigations of the interaction of shock waves in soils containing obstacles

A model of water-saturated soil as an ideal liquid has already been proposed [1], Experimental investigations of shock waves [2] have shown that for small stresses in water-saturated soil features of a solid plastic body begin to manifest themselves. As regards its properties the soil approximates to the model proposed in [3].The results of tests on the interaction of a plane shock wave in the soil with a moving obstacle are given below. As a development of papers [2,4, 5] an approximate solution is given for the problem of the interaction of waves with an obstacle. At high pressures the ground is regarded as nonlinearly elastic, and at low pressures as a plastic medium. A similar approach may be applied to water-saturated and nonsaturated soils when the wave is a shock wave. Experimental values of the parameters of motion of the obstacle are compared with the results of calculation.The authors are grateful to S. D. Mizyakin for participating in the tests.     

Amplification of shock waves in a bubble-filled liquid with gas concentration gradient

The properties are studied of the propagation of unsteady shock waves in a gas-liquid system of bubble structure in the case when the volume concentration of the gas changes in the direction of motion of the shock wave. It is established that when there is a sufficiently rapid drop in the gas content, an effect of amplification of the shock wave is observed which is due to the deceleration of the medium behind the shock wave. A study is made of the laws of the evolution of long- and short-wave pulsed perturbations in such systems. The authors consider processes of reflection of waves from obstacles and their passage from a gas into a bubble liquid, from a two-phase mixture into a pure liquid. The contribution is determined of nonequilibrium effects to the process of amplification of a wave.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 49–54, January–February, 1988.The authors wish to express gratitude to R. I. Nigmatulin for his interest in the study and for useful discussions.     

Solution of Riemann problem for dusty gas flow

A direct approach is used to solve the Riemann problem for a quasilinear hyperbolic system of equations governing the one dimensional unsteady planar flow of an isentropic, inviscid compressible fluid in the presence of dust particles. The elementary wave solutions of the Riemann problem, that is, shock waves, rarefaction waves and contact discontinuities are derived and their properties are discussed for a dusty gas. The generalised Riemann invariants are used to find the solution between rarefaction wave and the contact discontinuity and also inside rarefaction fan. Unlike the ordinary gasdynamic case, the solution inside the rarefaction waves in dusty gas cannot be obtained directly and explicitly; indeed, it requires an extra iteration procedure. Although the case of dusty gas is more complex than the ordinary gas dynamics case, all the parallel results for compressive waves remain identical. We also compare/contrast the nature of the solution in an ordinary gasdynamics and the dusty gas flow case.     

Shock wave attenuation by grids and orifice plates

The interaction of weak shock waves with porous barriers of different geometries and porosities is examined. Installing a barrier inside the shock tube test section will cause the development of the following wave pattern upon a head-on collision between the incident shock wave and the barrier: a reflected shock from the barrier and a transmitted shock propagating towards the shock tube end wall. Once the transmitted shock wave reaches the end wall it is reflected back towards the barrier. This is the beginning of multiple reflections between the barrier and the end wall. This full cycle of shock reflections/interactions resulting from the incident shock wave collision with the barrier can be studied in a single shock tube test. A one-dimensional (1D), inviscid flow model was proposed for simulating the flow resulting from the initial collision of the incident shock wave with the barrier. Fairly good agreement is found between experimental findings and simulations based on a 1D flow model. Based on obtained numerical and experimental findings an optimal design procedure for shock wave attenuator is suggested. The suggested attenuator may ensure the safety of the shelter’s ventilation systems.     

On the role of turbulence in detonation induced by Mach stem reflection

A series of experiments conducted by Chan has shown that while some shock waves may not be strong enough to induce detonation when they collide with an obstacle the resulting Mach stem will induce detonation if it collides with a subsequent obstruction. A series of numerical simulations, however, failed to demonstrate the expected results if either the Euler or laminar Navier-Stokes equations are solved. On the other hand, calculations using the Favre averaged Navier-Stokes equations with a k--F turbulence model are able to reproduce the experimental results, indicating that turbulent effects may play an important role in the ignition process. A detailed examination of the results shows that turbulence causes the formation of activated kernels in a similar process to that observed in deflagration-detonation transition. The simulations in this paper have been undertaken using a modern high resolution hydrocode and a reduced kinetics mechanism for hydrogen combustion. The paper describes the reduced mechanism, the solution methods employed in the hydrocode and discusses the results of the simulations and their implications. Received 28 October 1997 / Accepted 30 April 1998     

Numerical investigations of the porosity effect on the shock focusing process

The effect of cylindrical obstacles and the porosity in between them along the path of a converging cylindrical shock is studied through numerical simulations. An initially cylindrical converging shock wave is perturbed by cylindrical obstacles placed radially in its path. High pressures and temperatures are achieved as the shock wave is focused. Results show that the shape of the shock wave close to the point of convergence as well as the porosity and type of shock wave reflection the converging shock undergoes influence the peak values. Various configurations of the obstacle size and number are considered. The Guderley constant for each case is compared with previous reported experimental values.     

群速度控制格式及二维Riemann解

强激波和强接触间断的数值模拟一直是计算流体力学里一个富有挑战性的课题,它们是很多实际流动的基础。三阶迎风紧致格式是一种具有较高分辨率的高精度方法,但是在计算激波时仍有数值振荡产生。本文根据数值解的群速度特性,在三阶迎风紧致格式的基础上提出了一种群速度控制格式,使得能够正确模拟含有强激波和强接触间断的复杂流动。在此基础上构造了求解包含大压力比和密度比的二维界面问题的数值方法。计算结果表明,方法对激波和接触间断的分辨效果是令人满意的。     

The initialization of nonlinear waves using an adjustment scheme

A procedure for initializing nonlinear free-surface simulations is developed and validated. Numerical simulations of nonlinear progressive waves are prone to developing spurious high-frequency standing waves unless the flow field is given sufficient time to adjust. An adjustment procedure is developed that allows nonlinear free-surface simulations to be initialized with linear solutions. The adjustment scheme allows the natural development of nonlinear self-wave (locked modes) and wave–wave (free modes) interactions. The implementation of the adjustment procedure is illustrated using a high-order spectral method. Comparisons are made to fully-nonlinear Stokes waves and Schrodinger theory.     

Unloading effects in the dynamic response of granular soil

Experimental studies are described in which two different types of air shock are used to induce stress waves in an elastically confined, cylindrical specimen of sand, the objective being to permit direct observation of the effects of unloading on the dynamic response of granular material. In one case, “pure” unloading waves are generated by suddenly subjecting the end of a prestressed specimen to pressures below atmospheric. In the second type of test, the specimens are impacted at one end by an air shock which has the form of a sharp front followed immediately by a rapid exponential decay of pressure. The decay of the shock pressure generates unloading waves which cause attenuation of the wave as it propagates in the granular material. As a result of the tests, it is suggested that seismic-wave velocity may be correlated to the modulus of unloading cycles in a quasi-static test and that, when strainrate effects are included, a relatively simple model may be used to predict the dynamic response of granular materials.     

Nonlinear wave propagation in binary mixtures of Euler fluids

In the present paper, we study the propagation of acceleration and shock waves in a binary mixture of ideal Euler fluids, assuming that the difference between the atomic masses of the constituents is negligible. We evaluate the characteristic speeds, proving that they can be separated into two groups: one is related to the case of a single Euler fluid, provided that an average ratio of specific heats is introduced; the other is new and related to the propagation speed due to diffusion. We evaluate the critical time for sound acceleration waves and compare its value to that of a single fluid. We then study shock waves, showing that three types of shock waves appear: sonic and contact shocks, which have counterparts in the single fluid case, and the diffusive shock, which is peculiar to the mixture. We discuss the admissibility of the shock waves using the Lax-Liu conditions and the entropy growth criterion. It is proved that the sonic and the characteristic shock obey the same properties as in the single fluid case, while for the diffusive shock there exists a locally exceptional case that is determined by a particular value of the concentration of the constituents, for which the genuine nonlinearity is lost and no shocks are admissible. For other values of the unperturbed concentration, the diffusive shock is stable in a bounded interval of admissibility.Received: 15 December 2002, Accepted: 28 June 2003 Correspondence to: T. RuggeriS. Simi: On leave from the Department of Mechanics, Faculty of Technical Sciences, University of Novi Sad, Serbia     

Modelling of dust lifting using the Lagrangian approach

The subject of this paper is dust lifting behind shock waves, a process that is important for the formation of explosive dust clouds in air. While Eulerian–Eulerian has been the standard numerical technique for such simulations, the Eulerian–Lagrangian technique has been used in this paper, making it possible to take into account more physical phenomena, such as particle–particle and particle–wall collisions. The results of the simulations are shown mainly graphically, as snapshots of particle positions at given times after the passing of the shock wave. The results show that the collisions, and the coefficient of restitution assumed for them, is important in determining the mobility and lifting of dust behind shock waves. The results also show that the idea of a horizontally travelling shock wave is an oversimplification: the strong pressure gradient at the surface results in a series of reflected waves generated at the surface and travelling into the gas phase.