Instability theory of shock wave in a shock tube

The instability theory of shock wave in a shock tube including the effects of tube wall and contact surface is studied. The experimental data of unstable shock wave coincide with one of instability criteria derived in the present paper.     

Decay of shock waves in a dusty-gas shock tube

A numerical study is performed for the unsteady nonequilibrium flow of a gas-particle mixture in a shock tube, where a semi-empirical formula for a single particle is assumed to calculate the drag and heat transfer rate of the particle cloud. To simulate actual flows of the mixture in which the size of the particles is distributed over a finite range, the motion of the particles is analyzed by dividing them into several groups according to their different diameters. It is shown that the particles of diameter larger than the average value cause a significant delay in the relaxation of the gas-particle flow. Good agreement is obtained between the numerical and the experimental results of the decrease in the shock propagation velocity, except for strong shock waves transmitted into dusty gas with a high loading ratio.     

Characteristics of unsteady type IV shock/shock interaction

Characteristics of the unsteady type IV shock/shock interaction of hypersonic blunt body flows are investigated by solving the Navier–Stokes equations with high-order numerical methods. The intrinsic relations of flow structures to shear, compression, and heating processes are studied and the physical mechanisms of the unsteady flow evolution are revealed. It is found that the instantaneous surface-heating peak is caused by the fluid in the “hot spot” generated by an oscillating and deforming jet bow shock (JBS) just ahead of the body surface. The features of local shock/boundary layer interaction and vortex/boundary layer interaction are clarified. Based on the analysis of flow evolution, it is identified that the upstream-propagating compression waves are associated with the interaction of the JBS and the shear layers formed by a supersonic impinging jet, and then the interaction of the freestream bow shocks and the compression waves results in entropy and vortical waves propagating to the body surface. Further, the feedback mechanism of the inherent unsteadiness of the flow field is revealed to be related to the impinging jet. A feedback model is proposed to reliably predict the dominant frequency of flow evolution. The results obtained in this study provide physical insight into the understanding of the mechanisms relevant to this complex flow.     

A computational study of shock speeds in high-performance shock tubes

This paper describes U2DE, a finite-volume code that numerically solves the Euler equations. The code was used to perform multi-dimensional simulations of the gradual opening of a primary diaphragm in a shock tube. From the simulations, the speed of the developing shock wave was recorded and compared with other estimates. The ability of U2DE to compute shock speed was confirmed by comparing numerical results with the analytic solution for an ideal shock tube. For high initial pressure ratios across the diaphragm, previous experiments have shown that the measured shock speed can exceed the shock speed predicted by one-dimensional models. The shock speeds computed with the present multi-dimensional simulation were higher than those estimated by previous one-dimensional models and, thus, were closer to the experimental measurements. This indicates that multi-dimensional flow effects were partly responsible for the relatively high shock speeds measured in the experiments. Received 15 November 1996 / Accepted 3 February 1997     

Diaphragmless shock wave generators for industrial applications of shock waves

The prime focus of this study is to design a 50 mm internal diameter diaphragmless shock tube that can be used in an industrial facility for repeated loading of shock waves. The instantaneous rise in pressure and temperature of a medium can be used in a variety of industrial applications. We designed, fabricated and tested three different shock wave generators of which one system employs a highly elastic rubber membrane and the other systems use a fast acting pneumatic valve instead of conventional metal diaphragms. The valve opening speed is obtained with the help of a high speed camera. For shock generation systems with a pneumatic cylinder, it ranges from 0.325 to 1.15 m/s while it is around 8.3 m/s for the rubber membrane. Experiments are conducted using the three diaphragmless systems and the results obtained are analyzed carefully to obtain a relation between the opening speed of the valve and the amount of gas that is actually utilized in the generation of the shock wave for each system. The rubber membrane is not suitable for industrial applications because it needs to be replaced regularly and cannot withstand high driver pressures. The maximum shock Mach number obtained using the new diaphragmless system that uses the pneumatic valve is 2.125 ± 0.2%. This system shows much promise for automation in an industrial environment.     

Three-dimensional shock intersection

The flow field in the neighborhood of the three-dimensional intersection of two shocks of different families is investigated when in the plane perpendicular to the line of intersection the flow velocity component is subsonic behind at least one of the departing shocks. In the plane case these flows are not realized. The boundary of the domain of the key parameters for which these flows are possible is determined. The characteristics of the flow field are determined when: (1) behind the departing shocks the flow is homogeneous, and (2) the velocity vectors behind the departing and arriving shocks are parallel to a single plane which contains the intersection line. The flow in Mach-type shock intersection in the neighborhood of the intersection lines (triple points in the plane) is a particular case of the problem considered. It is shown that Mach-type shock intersection is not possible when the intensity of the arriving shocks is less than for their steady-state Mach intersection in the calculation plane. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, pp. 137–143, November–December, 1998.     

Weak shock diffraction

The diffraction of a weak shock by a rigid wedge is analyzed theoretically via the theory of weakly nonlinear geometrical acoustics, which is the same as Whitham's nonlinearization technique. First linear weakly nonlinear geometrical acoustics is explained. Then the linear acoustics results for weak shock diffraction by a wedge are presented. Next these results are modified according to the principles of weakly nonlinear geometrical acoustics. The results show that the compressive diffracted wavefronts of linear acoustics are actually shocks, and their positions and strengths are found. The infinite gradients of the linear acoustics rarefaction waves are found to be finite but discontinuous gradients. Finally the results are specialized to a shock hitting a right-angled wedge, a shock coming off a right-angled wedge, and a shock hitting a thin semi-infinite screen.     

Curved shock theory

Curved shock theory (CST) is introduced, developed and applied to relate pressure gradients, streamline curvatures, vorticity and shock curvatures in flows with planar or axial symmetry. Explicit expressions are given, in an influence coefficient format, that relate post-shock pressure gradient, streamline curvature and vorticity to pre-shock gradients and shock curvature in steady flow. The effect of pre-shock flow divergence/convergence, on vorticity generation, is related to the transverse shock curvature. A novel derivation for the post-shock vorticity is presented that includes the effects of pre-shock flow non-uniformities. CST applicability to unsteady flows is discussed.     

The interaction between shock waves and foam in a shock tube

An experimental study and a numerical simulation were conducted to investigate the mechanical and thermodynamic processes involved in the interaction between shock waves and low density foam. The experiment was done in a stainless shock tube (80 mm in inner diameter, 10 mm in wall thickness and 5 360 mm in length). The velocities of the incident and reflected compression waves in the foam were measured by using piezo-ceramic pressure sensors. The end-wall peak pressure behind the reflected wave in the foam was measured by using a crystal piezoelectric sensor. It is suggested that the high end-wall pressure may be caused by a rapid contact between the foam and the end-wall surface. Both open-cell and closed-cell foams with different length and density were tested. Through comparing the numerical and experimental end-wall pressure, the permeability coefficients α and β are quantitatively determined.     

Nonideal effects behind reflected shock waves in a high-pressure shock tube

Abstract. Shock tubes often experience temperature and pressure nonuniformities behind the reflected shock wave that cannot be neglected in chemical kinetics experiments. Because of increased viscous effects, smaller tube diameters, and nonideal shock formation, the reflected-shock nonidealities tend to be greater in higher-pressure shock tubes. Since the increase in test temperature () is the most significant parameter for chemical kinetics, experiments were performed to characterize in the Stanford High Pressure Shock Tube using infrared emission from a known amount of CO in argon. From the measured change in vibrationally equilibrated CO emission with time, the corresponding ddt (or for a known time interval) of the mixture was inferred assuming an isentropic relationship between post-shock temperature and pressure changes. For a range of representative conditions in argon (24–530 atm, 1275–1900 K), the test temperature 2 cm from the endwall increased 3–8 K after 100 s and 15–40 K after 500 s, depending on the initial conditions. Separate pressure measurements using a shielded piezoelectric transducer confirmed the isentropic assumption. An analytical model of the reflected-shock gas dynamics was also developed, and the calculated 's agree well with those obtained from experiment. The analytical model was used to estimate the effects of temperature and pressure nonuniformities on typical chemical kinetics measurements. When the kinetics are fast (s), the temperature increase is typically negligible, although some correction is suggested for kinetics experiments lasting longer than 500 s. The temperature increase, however, has a negligible impact on the measured laser absorption profiles of OH (306 nm) and CH (216 nm), validating the use of a constant absorption coefficient. Infrared emission experiments are more sensitive to temperature and density changes, so nonuniformities should be taken into account when interpreting ir-emission data. Received 25 April 2000 / Accepted 8 September 2000     

浮动冲击平台横向冲击谱受外形结构的影响

基于ABAQUS软件中的声固耦合法,采用设备、平台一体化分析方法,展开对中型浮动冲击平台的研究,探讨平台外形结构形式对平台冲击环境的影响,并提出了提高平台横向冲击谱谱值的设计方案。首先对外形结构进行初步设计,分析其对平台冲击谱的影响,并找到决定影响程度的关键因素。然后针对结构进行优化,使其更大幅度的提高平台冲击谱谱值。计算表明:在平台外部下方加装挡板结构不会明显影响平台垂向冲击谱,但可以提高平台横向冲击谱;舷侧底端向下延伸加装竖直挡板由于受到冲击波绕射和阻力的影响,增加横向谱值的效果不是很明显;平台底部流线型挡板可以有效增加平台对爆炸载荷的接收效果,同时可以尽量减小阻力影响,从而明显提高平台横向冲击谱谱值。     

A multiphase shock tube for shock wave interactions with dense particle fields

Currently there is a substantial lack of data for interactions of shock waves with particle fields having volume fractions residing between the dilute and granular regimes. To close this gap, a novel multiphase shock tube has been constructed to drive a planar shock wave into a dense gas–solid field of particles. A nearly spatially isotropic field of particles is generated in the test section by a gravity-fed method that results in a spanwise curtain of spherical 100-micron particles having a volume fraction of about 20%. Interactions with incident shock Mach numbers of 1.66, 1.92, and 2.02 are reported. High-speed schlieren imaging simultaneous with high-frequency wall pressure measurements are used to reveal the complex wave structure associated with the interaction. Following incident shock impingement, transmitted and reflected shocks are observed, which lead to differences in particle drag across the streamwise dimension of the curtain. Shortly thereafter, the particle field begins to propagate downstream and spread. For all three Mach numbers tested, the energy and momentum fluxes in the induced flow far downstream are reduced about 30–40% by the presence of the particle field.     

Oblique shock/bow shock interference in rarefied flow past a cylinder

Direct statistical simulation is employed to study the flow of a rarefied diatomic gas past a cylinder in the presence of an incident oblique shock. The distinctive features of the formation of a high-pressure compressed-gas jet in the case of interference between the oblique shock and the bow shock are studied for different Reynolds numbers. The variation of the pressure and the heat transfer to the surface with the shock position relative to the center of the cylinder, the Reynolds number, and the surface temperature is analyzed. The results obtained are compared with the experimental data and the results of the numerical solutions of the Euler and boundary layer equations. Free-molecular-to-continuum flow transition is demonstrated with reference to the example of interference-free flow past a cylinder.Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, 2004, pp. 171–180. Original Russian Text Copyright © 2004 by Gusev and Erofeev.     

浮动冲击平台冲击环境对设备响应的影响

对浮动冲击平台提供给设备的冲击环境及舰载设备在不同冲击环境下的响应进行了数值模拟和理论分析。以美国中型浮动冲击平台为计算模型,将设备基座的冲击环境与德国规范BV 043-85进行了比较,为分析两个体系在设备抗冲击要求中谱加速度的差异,对不同舰载设备进行数值模拟计算,并通过虚拟约束边界模态方法,提出不同冲击环境下基础激励的多自由度系统响应的计算方法。数值分析及理论计算结果表明:冲击谱中谱加速度对舰载设备响应影响较小,而谱位移和谱速度对设备响应有较大影响,理论计算得到的多自由度系统响应与数值模拟结果较一致,同时在进行浮动冲击平台设计时可不考虑谱加速度对设备响应的影响。     

Enhancement of shock waves

The flow field developed behind a shock wave propagating inside a constant cross-section conduit is solved numerically for two different cases. First, when the density of the ambient gas into which the shock propagates has a logarithmic change with distance. In the second, and the more practical case, the ambient gas is composed of pairs of air–helium layers having a continually decreasing width. It is shown that in both cases meaningful pressure amplification can be reached behind the transmitted shock wave. It is especially so in the second case. By proper choice of the number of air–helium layers and their width reduction ratio, pressure amplification as high as 7.5 can be obtained.      

Model of a viscous nonequilibrium shock layer with a thin shock wave

It is shown that the concept of a viscous shock layer with boundary conditions specified in a thin shock wave is unsuitable for analyzing the flow of a chemically reacting gas, even in the case of high Reynolds numbers; it may produce a finite error when determining the parameters of the shock layer.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 175–178, September–October, 1973.