Effect of yaw on the starting point of curvature for reflected diffracted shock wave (subsonic and sonic cases)

Lighthill (Proc. R. Soc. A 198, 454–470, 1949) considered the diffraction of a normal shock wave passing over a small bend. The bend being small Lighthill was able to linearize the flow equations and solved the problem through several mathematical techniques. Following Lighthill (Proc. R. Soc. A 198, 454–470, 1949), Srivastava and Chopra (J. Fluid Mech. 40, 821–831, 1970) extended the work to the diffraction of oblique shock waves. Srivastava (AIAAJ 33, 2230–2231, 1995) considered the problem of starting point of curvature and extended the work to yawed wedges (Srivastava in Proceedings of the 14th International Mach reflection symposium Sun Marina Hotel, Yonezawa, Japan, 1–5 October 2000, pp. 225–249, 2002). Srivastava (Shock waves 13, 323–326, 2003) considered the problem for starting point of curvature when the relative outflow behind reflected shock before diffraction has been subsonic and sonic. The present work is an extension of the work published in Srivastava (Shock waves 13, 323–326, 2003) when the wedge has been yawed through an angle. The results have been obtained for two angles χ = 60° and χ = 40° (χ is the angle of yaw).      

激波管双爆轰驱动段性能的数值模拟研究

采用频散可控的耗散格式(DCD)，求解Euler方程和一种改进的二阶段化学反应模型， 对氢氧反向-正向双爆轰驱动段激波管进行了数值模拟. 计算结果表明：当辅驱动段与主驱动 段初始压力比小于临界值时，Taylor波仍会出现，但波扇夹角较单一前向爆轰驱动段小，入 射激波马赫数衰减率变小；当初始压力比等于临界值时，主驱动段中的Taylor波完全被消除， 入射激波马赫数不再衰减. 当初始压力比大于临界值时，在主驱动段中能产生过驱动爆轰波， 不仅Taylor波被完全消除，而且驱动能力较单一前向爆轰驱动段强.     

The shock–vortex interaction patterns affected by vortex flow regime and vortex models

We have used a third-order essentially non-oscillatory method to obtain numerical shadowgraphs for investigation of shock–vortex interaction patterns. To search different interaction patterns, we have tested two vortex models (the composite vortex model and the Taylor vortex model) and as many as 47 parametric data sets. By shock–vortex interaction, the impinging shock is deformed to a S-shape with leading and lagging parts of the shock. The vortex flow is locally accelerated by the leading shock and locally decelerated by the lagging shock, having a severely elongated vortex core with two vertices. When the leading shock escapes the vortex, implosion effect creates a high pressure in the vertex area where the flow had been most expanded. This compressed region spreads in time with two frontal waves, an induced expansion wave and an induced compression wave. They are subsonic waves when the shock–vortex interaction is weak but become supersonic waves for strong interactions. Under a intermediate interaction, however, an induced shock wave is first developed where flow speed is supersonic but is dissipated where the incoming flow is subsonic. We have identified three different interaction patterns that depend on the vortex flow regime characterized by the shock–vortex interaction.      

Failure mechanisms of concrete slab–soil double-layer structure subjected to underground explosion

The failure mechanism of a concrete slab–soil double-layer structure subjected to an underground explosion was investigated by experimental and numerical methods in this paper. Two underground explosion depths of 150 and 350 mm were tested. The typical failure modes such as the conoid spall of concrete, the bulge of the concrete slab and the cavity in the soil were obtained experimentally. Numerical simulations of the experiments were performed using a hydrodynamic code to analyze the effects of both the stress wave and the expansion of the blast products. Based on the experimental and numerical results, the effects of explosive depth, blast wave front and expansion of the blast products on the failure modes and failure mechanisms were discussed. The underground explosion process at different explosion depths was also analyzed. The results show that attenuation of the stress wave in the soil is significant. The blast wave front and the expansion of the blast products play different roles at different explosion depths. At the explosion depth of 150 mm, the failure mode is mainly caused by a point load induced by the blast wave front, whereas at the depth of 350 mm a sphere-shaped load resulting from the expansion of the blast products is a key factor for failure.     

Effect of rigid boundary on propagation of torsional surface waves in porous elastic layer

The paper presents the effect of a rigid boundary on the propagation of torsional surface waves in a porous elastic layer over a porous elastic half-space using the mechanics of the medium derived by Cowin and Nunziato (Cowin, S. C. and Nunziato, J. W. Linear elastic materials with voids. Journal of Elasticity, 13(2), 125–147 (1983)). The velocity equation is derived, and the results are discussed. It is observed that there may be two torsional surface wave fronts in the medium whereas three wave fronts of torsional surface waves in the absence of the rigid boundary plane given by Dey et al. (Dey, S., Gupta, S., Gupta, A. K., Kar, S. K., and De, P. K. Propagation of torsional surface waves in an elastic layer with void pores over an elastic half-space with void pores. Tamkang Journal of Science and Engineering, 6(4), 241–249 (2003)). The results also reveal that in the porous layer, the Love wave is also available along with the torsional surface waves. It is remarkable that the phase speed of the Love wave in a porous layer with a rigid surface is different from that in a porous layer with a free surface. The torsional waves are observed to be dispersive in nature, and the velocity decreases as the oscillation frequency increases.     

斜爆轰的多波结构及其稳定性研究进展

斜爆轰是气相爆轰物理的一个重要研究方向,在航空航天新型动力领域有重要的潜在应用价值.作为激波诱导的高速燃烧, 斜爆轰波可以简化为包含能量添加的间断面.然而, 斜爆轰流动中往往涉及激波、湍流等多种的流体力学现象,它们和燃烧放热耦合在一起, 导致流动和燃烧机理非常复杂. 一方面,斜爆轰波具有的多尺度和非线性的特征, 理论研究难以深入; 另一方面,爆轰波流场高温、高压、高速的特点, 又给实验研究带来了很大的困难.过去20年, 主要借助数值方法,研究者对斜爆轰波开展了系统的模拟和分析,在诸多方面取得了明显的进展.本文首先介绍了理想情况下的起爆区波系结构和波面稳定性研究进展;其次着眼于推进系统的问题,关注了非均匀来流效应以及斜爆轰波与稀疏波的作用;最后对未来的研究工作提出一些建议.      

Extended Polar Decompositions for Plane Strain

In a finite deformation at a particle of a continuous body, a triad of infinitesimal material line elements is said to be “unsheared” when the angles between the three pairs of line elements of the triad suffer no change. In a previous paper, it has been shown that there is an infinity of unsheared oblique triads. With each oblique unsheared triad may be associated an “extended polar decomposition” F = QG = HQ of the deformation gradient F, in which Q is a rotation tensor, and G, H are not symmetric. Both G and H have the same real eigenvalues which are the stretches of the elements of the triad. In this paper, a detailed analysis of extended polar decompositions is presented in the case when the finite deformation is that of plane strain. Then, we may deal with a 2 × 2 deformation gradient F′ = Q′G′ = H′Q′ instead of the full 3 × 3 tensor F. In this case, the extended polar decompositions are associated with “unsheared pairs,” i.e., pairs of infinitesimal material line elements in the plane of strain which suffer no change in angle in the deformation. If one arm of an unsheared pair is chosen in the plane of strain, then, in general, its companion in the plane is determined. It follows that all possible extended polar decompositions may then be described in terms of a single parameter, the angle that the chosen arm makes with a coordinate axis in the plane. Explicit expressions for G′ and H′ are obtained, and various special cases are discussed. In particular, we note that the expressions for G′ and H′ remain valid even when the chosen arm is along a “limiting direction,” that is the direction of a line element which has no companion element in the plane forming an unsheared pair with it. The results are illustrated by considering the cases of simple shear and of pure shear.Dedicated to Professor Piero Villaggio as a symbol of our friendship and esteem.     

Analysis of Elastic Band Structures for Oblique Incidence

We propose a canonical basis that is used in the expansion of eigensolutions for a problem of oblique incidence of elastic waves on a doubly periodic array of cylindrical channels. We apply a multipole method to study the spectral properties of waves in such a structure. Dispersion diagrams constructed on the basis of an analytical solution show the presence of a full phononic band gap when the angle of oblique incidence exceeds certain critical value. Explicit asymptotic formulae are presented for the effective refractive index associated with shear waves in oblique incidence.     

Counterexamples to the Sonic Criterion

We consider self-similar (pseudo-steady) shock reflection at an oblique wall. There are three parameters: wall corner angle, Mach number, angle of incident shock. Ever since Ernst Mach discovered the irregular reflection named after him, researchers have sought to predict precisely for which parameters the reflection is regular. Three conflicting proposals—the detachment, sonic and von Neumann criteria—have been studied extensively without a clear result. We demonstrate that the sonic criterion is not correct. We consider polytropic potential flow and prove that there is an open nonempty set of parameters that admit a global regular reflection with a reflected shock that is transonic. We also provide a clear physical reason: the flow type (sub- or supersonic) is not decisive; instead the reflected shock type (weak or strong) determines whether structural perturbations decay towards the reflection point.     

Numerical Simulation of Riblet Controlled Spatial Transition in a Zero-Pressure-Gradient Boundary Layer

To analyze the fundamental physical mechanism which determines the damping effect of a riblet surface on three-dimensional transition several numerical simulations of spatial transition in a flat plate zero-pressure-gradient boundary layer above a riblet wall are performed in this study. Two types of forced transition scenarios are investigated. The first type of transition is defined by K-type transition induced by a dominant two-dimensional Tollmien–Schlichting (TS) wave and a weak spanwise disturbance. The second type of transition is purely excited by two oblique waves. By a qualitative analysis of the occurring maximum wall-normal and spanwise velocity components and the Fourier modes of the disturbances the two-dimensional TS waves are found to be amplified by riblets, whereas three-dimensional structures, i.e., Λ-, hairpin, and streamwisely aligned vortices, are damped. At oblique transition the breakdown to turbulence is delayed by the riblets compared to transition on a clean surface. The investigation of the near wall flow structure reveals secondary flows induced by the riblets and reduced wall normal ejections as well as a reduced downwash.     

Strain Separation on a Nonplanar Object Using a Luminescent Photoelastic Coating

This paper presents the theoretical modeling and corresponding experimental results of the oblique incidence response of a luminescent photoelastic coating (LPC) applied to a cylinder under load. LPC is a measurement technique to acquire full-field maximum shear strain and its principal strain direction. The technique uses an absorption dye and a luminescent dye within a photoelastic coating, and the coating is applied on the surface of the specimen using conventional aerosol techniques. On 3D objects, the response of the emission field is dependent on the excitation orientation due to the surface inclination of the structural component and the out-of-plane strain component within the coating. Full-field strain separated results have been previously demonstrated on a 2D specimen. The extension of the strain separation technique to a 3D specimen—a cylinder in bending—is the focus of this investigation. Two different responses were obtained from normal and oblique excitation. As a result, the principal strain was separated over ±56° of circumference of the cylinder with RMS error relative to the theoretical result of 87 μɛ for maximum principal strain and 78 μɛ for minimum.     

Waveriders of complicated shape

The shape of a waverider formed by streamsurfaces behind oblique shocks and rarefaction waves is complicated by equipping the lifting body with a wing and fins. The joining of the wing to the body and the possibility of reducing the wave drag are considered. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 158–165, July–August, 1998.     

Analysis of plane and cylindrical nonlinear hyperelastic waves in materials with internal structure

A comparative analysis of two types of hyperelastic waves—plane waves (with plane front) and cylindrical waves (with curved front)—is offered. The propagation of the waves is studied theoretically for quadratically nonlinear hyperelastic media and numerically for a class of unidirectional fibrous composite materials. Hyperelasticity is described using the classical Murnaghan potential and a structural model of the first order—the model of effective constants. The internal structure of materials is described by this model and is at the micro-or nanolevels in numerical analysis. Particular attention is given to the evolution of the wave profile. It is studied in three stages: (i) derivation of nonlinear wave equations, (ii) construction of solutions in the form of plane and cylindrical waves, and (iii) numerical analysis of the evolution of these waves in composites with microlevel (Thornel) or nanolevel (Z-CNT) fibers. The main similarities and differences between plane longitudinal and cylindrical waves are shown. The most unexpected result is the striking difference between the evolution patterns numerically observed for plane and cylindrical wave profiles __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 10, pp. 21–46, October 2006.     

Explosive dispersal of solid particles

Abstract. The rapid dispersal of inert solid particles due to the detonation of a heterogeneous explosive, consisting of a packed bed of steel beads saturated with a liquid explosive, has been investigated experimentally and numerically. Detonation of the spherical charge generates a blast wave followed by a complex supersonic gas-solid flow in which, in some cases, the beads catch up to and penetrate the leading shock front. The interplay between the particle dynamics and the blast wave propagation was investigated experimentally as a function of the particle size (100–925 m) and charge diameter (8.9–21.2 cm) with flash X-ray radiography and blast wave instrumentation. The flow topology during the dispersal process ranges from a dense granular flow to a dilute gas-solid flow. Difficulties in the modeling of the high-speed gas-solid flow are discussed, and a heuristic model for the equation of state for the solid flow is developed. This model is incorporated into the Eulerian two-phase fluid model of Baer and Nunziato (1986) and simulations are carried out. The results of this investigation indicate that the crossing of the particles through the shock front strongly depends on the charge geometry, the charge size and the material density of the particles. Moreover, there exists a particle size limit below which the particles cannot penetrate the shock for the range of charge sizes considered. Above this limit, the distance required for the particles to overtake the shock is not very sensitive to the particle size but remains sensitive to the particle material density. Overall, excellent agreement was observed between the experimental and computational results. Received 16 August 1999 / Accepted 26 June 2000     

Effect of laser supported detonation wave confinement on termination conditions

A laser supported detonation (LSD) wave was driven using line-focusing laser optics, in which an induced blast wave expanded laterally from the LSD region to surrounding air in two-dimensional space. The LSD wave was confined in quasi-1D space using a wedge nozzle to restrict the lateral expansion of a blast wave. The LSD termination threshold and the blast wave energy were deduced from shadowgraphs showing the blast wave expansion. The respective threshold laser intensities for cases with and without confinement were estimated as 17 and 34 GW/m², indicating that the lateral expansion strongly influenced on the LSD termination condition.      

箱型结构内部爆炸破坏研究进展

结构内部爆炸破坏机理和规律是常规武器毁伤效能预测与评估、建筑物和舰船抗爆防护设计的重要支撑。基于结构内爆炸载荷、内部爆炸作用下结构塑性响应、内部爆炸作用下箱壁结构破坏模式、内部爆炸作用下多箱型结构破坏模式和分布四个方面详细论述了箱型结构内部爆炸破坏的研究现状及存在的问题,并对内部爆炸后续研究给出了建议。建议研究并建立更加复杂的结构内部爆炸载荷和破坏效应描述模型、内部爆炸作用下箱壁的动力响应机理、多箱型结构与内部爆炸波产生的耦合效应、内部爆炸作用下结构的破坏模式和破坏范围的快速准确预测方法等。     

Reflection and Transmission of Elastic Waves from the Interface of a Fluid-saturated Porous Solid and a Double Porosity Solid

The reflection and transmission characteristics of an incident plane P1 wave from the interface of a fluid-saturated single porous solid and a fluid-saturated double porosity solid are investigated. The fluid-saturated porous solid is modeled with the classic Biot’s theory and the double porosity medium is described by an extended Biot’s theory. In a double-porosity model with dual-permeability there exist three compressional waves and a shear wave. The effects of the incident angle and frequency on amplitude ratios of the reflected and transmitted waves to the incident wave are discussed. Two boundary conditions are discussed in detail: (a) Open-pore boundary and (b) Sealed-pore boundary. Numerical results reveal that the characteristics of the reflection and transmission coefficients to the incident angle and the frequency are quite different for the two cases of boundary conditions. Properties of the bulk waves existing in the fluid-saturated porous solid and the double porosity medium are also studied.     

爆炸荷载作用下饱和半空间中衬砌隧道弹性动力响应IBIEM模拟

基于Biot两相介质理论,采用一种高精度间接边界积分方程法（IBIEM）研究了饱和半空间中浅埋衬砌隧道在内部爆炸荷载作用下的瞬态弹性动力反应。通过典型算例,给出了爆炸荷载作用下隧道附近地表位移、衬砌动应力、围岩径向位移和衬砌表面孔隙水压的时程响应,并对比分析了饱和半空间和全空间中隧道动力响应的区别。研究表明：覆土层厚度对浅埋隧道-围岩整体动力响应特征具有明显影响;衬砌表面透水状态对爆炸荷载的时程响应的影响不显著;随半空间饱和介质孔隙率增加,围岩受隧道内部爆炸影响程度降低,衬砌承担的爆炸作用增大;当和直达波、衬砌内部反射波的峰值叠加作用时,半空间表面反射波对衬砌隧道拱顶附近响应影响显著,使得衬砌动应力幅值、径向位移相比深埋情况大幅度增加。     

Sound generation by interacting vortices in a subsonic turbulent jet

The results of an experimental investigation of sound generation by the interacting toroidal and oblique vortices formed in a subsonic turbulent jet under the action of saw-tooth finite-amplitude sound waves with simultaneous longitudinal internal and transverse external excitation are presented (the sound pressure level on the jet edge is 165–175 dB). The direct schlieren method with an exposure time −3·10⁻⁷ s was employed. This made it possible to visualize not only the jet and the vortices formed in it but also the sound waves. It was confirmed experimentally that the vortex interaction may be accompanied by sound generation of fairly high intensity. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 54–60, January–February, 2000.     

Cylindrical shock waves generated by a spark discharge and their interaction with the shock waves from a pulsed induction discharge

An experimental investigation of a spark discharge in argon is described. The existence of a shock wave and a following thermal wave is demonstrated. The experimental law of propagation of the thermal wave front is obtained. The effect of the discharge parameters on the dynamics of both waves is studied. The interaction between the cylindrical shock waves generated by a pulsed induction discharge and the shock waves formed in a spark discharge is considered. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 166–170, January–February, 1994.