Shock waves in dense granular flows down a chute

Large scale, three dimensional computer simulations of monosized, viscoelastic, spherical glass particles flowing in an inclined duct were performed using a phenomenological model based on the modified Kelvin–Maxwell model. The particle flow rate in the model duct was regulated using a stationary wedge located in the middle of the duct. At low flow rates of glass particles, a continuous flow was observed similar to that excited by steadily and rapidly adding glass particles to the top of a heap. However, at high flow rates, a totally different situation arises where a flow with a different nature was established in the duct. The situation was found to be analogous to the case of a supersonic gas flow in a duct, where a curved-bow shock was observed to have formed on the upper edges of the duct adjacent to the wedge. In addition, in supersonic granular flows the viscous and conductance effects spread the shock changes over a finite shock layer.     

Computing the aeroelastic disk vibrations in a hard disk drive

The turbulent flow of air caused by the spinning of a single disk inside a typical hard disk drive casing is calculated using large eddy simulation (LES). The pressure acting on the disk is recorded as a function of time and is used to compute the vibrations of the spinning disk using a self-developed hybrid-spectral finite-difference code. This unidirectional fluid–structure interaction problem is computed for two commonly occurring cases: a disk actuated on one side only (Case 1) and a disk actuated on both sides (Case 2). The pressure loading on the disk is characterized in terms of its mean, root-mean-square (r.m.s.) and its spectral content. The mean pressure acting on the disk is asymmetrical in the case where the disk is actuated on one side only, leading to a mean deformation of the disk to one side. The r.m.s. vibrations of Case 2 are higher than those for Case 1 and their spectral distributions are almost identical. Large pressure fluctuations of the flow are found in the wake of the actuator arm and near the region where the shroud expands to accomodate the actuator. The spectral content of the excitation force due to the pressure is mainly in the low kHz frequency range, while higher frequencies are seen at the disk edge. This typically results in the excitation of the first 3–4 modes of the disk; however, (asymmetric) Case 1 displays the excitation of higher modes compared with (symmetric) Case 2.     

Shock waves in reactive hydrodynamics

Using the weakly non-linear geometrical acoustics theory, we obtain the small amplitude high frequency asymptotic solution to the basic equations in Eulerian coordinates governing one dimensional unsteady planar, spherically and cylindrically symmetric flow in a reactive hydrodynamic medium. We derive the transport equations for the amplitudes of resonantly interacting waves. The evolutionary behavior of non-resonant wave modes culminating into shock waves is also studied.      

Shock waves at microscales

We present a model for the effects of scale, via molecular diffusion phenomena, on the generation and propagation of shock waves. A simple parametrization of the shear stresses and heat flux at the wall leads to the determination of new jump conditions, which show that, for a given wave Mach number at small scales, the resulting particle velocities are lower but the pressures are higher. Also, the model predicts that the flow at small scale is isothermal and that the minimum wave velocity can be subsonic. Experiments with a miniature shock tube using low pressures to simulate the effects of small scale have shown qualitative agreement with the proposed model. In fact, the effects of scale appear even more important than what has been incorporated in the model.PACS: 47.40.-xReceived: 14 November 2002, Accepted: 2 April 2003, Published online: 18 June 2003     

Atomistic phenomena in dense fluid shock waves

The shock structure problem is one of the classical problems of fluid mechanics and at least for non-reacting dilute gases it has been considered essentially solved. Here we present a few recent findings, to show that this is not the case. There are still new physical effects to be discovered provided that the numerical technique is general enough to not rule them out a priori. While the results have been obtained for dense fluids, some of the effects might also be observable for shocks in dilute gases.     

Shock waves in a particulate suspension

A continuum theory for the distribution of incompressible particles in an incompressible fluid is employed to study the behaviour of plane shock waves in a particulate suspension. An expression is derived for the speed of displacement in terms of the jump in the volume fraction of one of the constituents across the shock. A differential equation is derived to govern the evolutionary behaviour of the shock wave propagating into a region which is in a uniform equilibrium state before the arrival of the shock wave. The implications of this equation are examined in detail.     

Shock waves in incompressible elastic solids

Summary The thermodynamic theory of shock waves in incompressible elastic solids is reviewed, and the Hugoniot relation and the propagation condition for the shock speed are derived. Expanding the equations, for weak shock waves, in powers of the shock strength some well-known results of gasdynamics are generalized to the dynamics of shock waves in incompressible elastic media.

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Zusammenfassung Die thermodynamische Theorie der Stoßwellen in inkompressiblen elastischen Körpern wird zusammenfassend dargestellt, die Hugoniot-Relation und die Ausbreitungsbedingung für die Stoßgeschwindigkeit werden abgeleitet. Durch Reihenentwicklung nach Potenzen der Stoßstärke werden für schwache Stoßwellen einige bekannte Ergebnisse der Gasdynamik für die Dynamik der Stoßwellen in inkompressiblen elastischen Medien verallgemeinert.

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With 2 figures     

Inhomogeneous plane waves in viscous fluids

The propagation of elliptically polarised inhomogeneous plane waves in a linearly viscous fluid is considered. The angular frequency and the slowness vector are both assumed to be complex. Use is made throughout of Gibbs bivectors (complex vectors). It is seen that there are two types of solutions—the zero pressure solution, for which the increment in pressure due to the propagation of the wave is zero, and a universal solution which is independent of the viscosity.Since the waves are attenuated in time, the usual mean energy flux vector is not a suitable way of measuring energy flux. A new energy flux vector, appropriate to these waves is defined, and results relating it with energy dissipation and energy density are obtained. These results are related to a result derived directly from the balance of energy equation.     

硬盘驱动器冲击激励的头盘碰撞分析

根据Winchester型硬盘驱动器在冲击载荷作用下头盘碰撞的动力学方程,利用数值模拟方法分析了在正弦半波激励条件下头盘系统的动力学响应过程。当头盘系统发生碰撞时,冲击激励峰值加速度与作用时间的倒数之间具有近似线性关系。随激励强度和作用时间的变化,硬盘驱动器具有性能退化、盘面局部损坏和头盘系统结构破坏三种失效形式。磁头浮动块与磁盘盘面发生多次碰撞,碰撞位置可能在浮动块尾端,也可能在浮动块的前端。硬盘驱动器冲击失效的理论分析结果得到了爆炸冲击环境条件下试验现象的验证。     

坑道内化爆冲击波的传播规律

装药在坑道内部爆炸时将产生沿坑道传播的空气冲击波,由于受到坑道洞壁的限制,空气冲击波在坑道内的传播规律异于在自由大气中的传播。利用三维数值模拟计算程序,对长坑道中的化爆流场进行了数值计算,归纳出空气冲击波沿坑道方向的传播规律。计算结果与试验结果符合较好。     

Shock waves in saturated thermoelastic porous media

The objective of this paper is to develop and present the macroscopic motion equations for the fluid and the solid matrix, in the case of a saturated porous medium, in the form of coupled, nonlinear wave equations for the fluid and solid velocities. The nonlinearity in the equations enables the generation of shock waves. The complete set of equations required for determining phase velocities in the case of a thermoelastic solid matrix, includes also the energy balance equation for the porous medium as a whole, as well as mass balance equations for the two phase. In the special case of a rigid solid matrix, the wave after an abrupt change in pressure propagates only through the fluid.     

Shock and expansion waves in transonic flow

Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, No. 1, pp. 62–65, January–February, 1992.     

Inhomogeneous plane waves in compressible viscous fluids

The propagation of inhomogeneous plane waves in a compressible viscous fluid is considered. The frequency and the slowness vector are both allowed to be complex. There are seen to be two types of solutions: (a) two transverse waves, which involve no density or pressure fluctuations, (b) a longitudinal wave, which involves no fluctuations in vorticity. For each type, a propagation condition is obtained giving the (complex) squared length of the slowness vector as a function of frequency. Each depends also on the viscosities. It is seen how to recover the incompressible case as the limit in which the inviscid acoustic wave speed tends to infinity. Each wave is shown to be linearly stable for real frequencies. These waves are attenuated in space and time but nevertheless it is possible to define constant weighted mean values (over a cycle of the propagating part of the wave) of the energy density, energy flux and dissipation. The energy-dissipation equation and the propagation conditions are used to derive relationships between these constant weighted means, some of which are generalizations to compressible fluids of previously known results for incompressible fluids. Explicit expressions in terms of frequency are given for the weighted means.     

Shock waves in liquids containing gas bubbles

Results of theoretical and experimental studies on shock wave propagation in boiling and nonboiling liquids with gas bubbles are reviewed. The structure of shock waves, their reflection and attenuation in two-phase gas-liquid media are considered.     

Shock waves in aviation security and safety

Accident investigations such as of Pan Am 103 and TWA 800 reveal the key role of shock-wave propagation in destroying the aircraft when an on-board explosion occurs. This paper surveys shock wave propagation inside an aircraft fuselage, caused either by a terrorist device or by accident, and provides some new experimental results. While aircraft-hardening research has been under way for more than a decade, no such experiments to date have used the crucial tool of high-speed optical imaging to visualize shock motion. Here, Penn State's Full-Scale Schlieren flow visualization facility yields the first shock-motion images in aviation security scenarios: 1) Explosions beneath full-size aircraft seats occupied by mannequins, 2) Explosions inside partially-filled luggage containers, and 3) Luggage-container explosions resulting in hull-holing. Both single-frame images and drum-camera movies are obtained. The implications of these results are discussed, though the overall topic must still be considered in its infancy. Received 22 July 2001 / Accepted 19 July 2002 Published online 4 November 2002 Correspondence to: G.S. Settles (e-mail: gss2@psu.edu) An abridged version of this paper was presented at the 23rd International Symposium on Shock Waves at Fort Worth, Texas, from July 22 to 27, 2001.