Numerical simulation of long-duration blast wave evolution in confined facilities

The objective of this research effort was to investigate the quasi-steady flow field produced by explosives in confined facilities. In this effort we modeled tests in which a high explosive (HE) cylindrical charge was hung in the center of a room and detonated. The HEs used for the tests were C-4 and AFX 757. While C-4 is just slightly under-oxidized and is typically modeled as an ideal explosive, AFX 757 includes a significant percentage of aluminum particles, so long-time afterburning and energy release must be considered. The Lawrence Livermore National Laboratory (LLNL)-produced thermo-chemical equilibrium algorithm, “Cheetah”, was used to estimate the remaining burnable detonation products. From these remaining species, the afterburning energy was computed and added to the flow field. Computations of the detonation and afterburn of two HEs in the confined multi-room facility were performed. The results demonstrate excellent agreement with available experimental data in terms of blast wave time of arrival, peak shock amplitude, reverberation, and total impulse (and hence, total energy release, via either the detonation or afterburn processes.     

空中强爆炸冲击波地面反射规律数值模拟研究

为准确预测空中强爆炸产生的冲击波载荷分布,基于欧拉坐标系建立了能够模拟具有高密度比、高压力比的强激波问题的二维多介质流体数值方法。结合网格自适应技术,对1 kt TNT当量的空中强爆炸在不同爆炸高度下的冲击波地面反射过程进行了数值模拟,并考虑了真实气体状态方程和空气随高度不均匀分布的影响。计算得到了地面上距爆心投影点大尺度范围内的反射超压和冲量等冲击波载荷分布,并给出了冲击波载荷随爆高的变化规律。

     

A Free-Lagrange method for unsteady compressible flow: simulation of a confined cylindrical blast wave

A Free-Lagrange numerical procedure for the simulation of two-dimensional inviscid compressible flow is described in detail. The unsteady Euler equations are solved on an unstructured Lagrangian grid based on a density-weighted Voronoi mesh. The flow solver is of the Godunov type, utilising either the HLLE (2 wave) approximate Riemann solver or the more recent HLLC (3 wave) variant, each adapted to the Lagrangian frame. Within each mesh cell, conserved properties are treated as piece-wise linear, and a slope limiter of the MUSCL type is used to give non-oscillatory behaviour with nominal second order accuracy in space. The solver is first order accurate in time. Modifications to the slope limiter to minimise grid and coordinate dependent effects are described. The performances of the HLLE and HLLC solvers are compared for two test problems; a one-dimensional shock tube and a two-dimensional blast wave confined within a rigid cylinder. The blast wave is initiated by impulsive heating of a gas column whose centreline is parallel to, and one half of the cylinder radius from, the axis of the cylinder. For the shock tube problem, both solvers predict shock and expansion waves in good agreement with theory. For the HLLE solver, contact resolution is poor, especially in the blast wave problem. The HLLC solver achieves near-exact contact capture in both problems. Received May 25, 1995 / Accepted September 11, 1995     

舱内爆炸角隅汇聚反射冲击波超压特性研究

为研究密闭舱室内爆角隅汇聚反射冲击波超压特性,利用缩比模型进行了某典型舱室内爆试验,得到远离角隅、两面角隅和三面角隅处的冲击波载荷,结合数值模拟研究了3种特征位置处冲击波传播规律及载荷特征。研究结果表明:远离角隅处壁面反射冲击波超压曲线呈现单峰结构,反射冲击波以球面波传播;距两面角隅一定范围内冲击波超压曲线呈现双峰结构,两面角隅冲击波超压曲线呈现单峰结构,角隅汇聚反射冲击波以椭球状传播;距三面角隅一定范围内冲击波超压曲线呈现多峰结构,三面角隅冲击波超压曲线呈现单峰结构,角隅汇聚反射冲击波以球面波传播;在合理假设条件下,根据量纲分析及数值模拟结果,得到首次冲击时角隅汇聚反射冲击波载荷经验计算公式。     

Evolution of blast wave profiles in simulated air blasts: experiment and computational modeling

Shock tubes have been extensively used in the study of blast traumatic brain injury due to increased incidence of blast-induced neurotrauma in Iraq and Afghanistan conflicts. One of the important aspects in these studies is how to best replicate the field conditions in the laboratory which relies on reproducing blast wave profiles. Evolution of the blast wave profiles along the length of the compression-driven air shock tube is studied using experiments and numerical simulations with emphasis on the shape and magnitude of pressure time profiles. In order to measure dynamic pressures of the blast, a series of sensors are mounted on a cylindrical specimen normal to the flow direction. Our results indicate that the blast wave loading is significantly different for locations inside and outside of the shock tube. Pressure profiles inside the shock tube follow the Friedlander waveform fairly well. Upon approaching exit of the shock tube, an expansion wave released from the shock tube edges significantly degrades the pressure profiles. For tests outside the shock tube, peak pressure and total impulse reduce drastically as we move away from the exit and majority of loading is in the form of subsonic jet wind. In addition, the planarity of the blast wave degrades as blast wave evolves three dimensionally. Numerical results visually and quantitatively confirm the presence of vortices, jet wind and three-dimensional expansion of the planar blast wave near the exit. Pressure profiles at 90° orientation show flow separation. When cylinder is placed inside, this flow separation is not sustained, but when placed outside the shock tube this flow separation is sustained which causes tensile loading on the sides of the cylinder. Friedlander waves formed due to field explosives in the intermediate-to far-field ranges are replicated in a narrow test region located deep inside the shock tube.     

低温和低压环境下炸药爆炸冲击波的传播特性

针对高海拔或高空的低温、低压环境对炸药爆炸冲击波传播的影响,利用量纲分析理论和AUTODYN有限元软件,研究了低温、低压及海拔高度对炸药爆炸冲击波参量（峰值超压、比冲量和波阵面运动轨迹）的影响规律,建立了相应的计算公式,并通过数值模拟和实验数据进行了对比验证。结果表明,该计算公式可以有效预测低温和低压环境下炸药爆炸冲击波参量。环境压力降低,爆炸冲击波峰值超压和爆炸远场（比例距离Z>0.2 m/kg1/3）比冲量减小,冲击波传播速度增大。环境温度降低,冲击波比冲量增大,传播速度降低,峰值超压影响不大。海拔高度在0～9 000 m范围内,每升高1 000 m冲击波峰值超压和爆炸远场比冲量分别平均降低约3.9%和3.2%。海拔升高,爆炸近场冲击波传播速度升高,爆炸远场冲击波传播速度则降低。高海拔环境下低压对冲击波峰值超压和比冲量的影响大于低温,爆炸近场冲击波传播速度取决于低压的影响,爆炸远场冲击波传播速度取决于低温的影响。     

大断面隧道钻爆冲击波的衰减规律

隧道开挖爆破产生的空气冲击波的破坏效应,将会对人员、机具设备与周围环境造成危害。隧道钻孔爆破冲击波的影响因素比裸露药包爆炸更多、更复杂,研究其衰减规律对采取合适的防护措施意义重大。本文中开展了时速350 km双线铁路大断面隧道钻孔爆破空气冲击波的现场测试,分析了不同工况下冲击波传播规律及影响因素。结果表明：钻爆冲击波超压时程曲线存在多个不同幅值的超压波峰,波峰之间具有明显微差延时的短间隔性,传播至远场未形成稳定的单一平面波,与单一药包爆炸冲击波的传播规律存在差异;钻爆冲击波超压信号由多段与微差延时相对应的子信号叠加而成,子信号数量与毫秒延期雷管段数相同,呈现出典型的时域特征;相同爆破条件下,大断面隧道钻爆时的乳化炸药冲击波转化因数小于小断面巷道工况下的;相较于总药量及最大段药量,按掏槽药量计算的超压峰值与实测超压峰值之间的相关性最强,钻爆冲击波最大超压峰值宜按掏槽段炸药TNT当量确定;隧道内大型机械设备等障碍物改变了钻爆冲击波流场的传播规律,呈现较明显的叠加放大效应。

     

Specific features of incident and reflected blast waves

On the basis of numerical modeling specific features of shock wave reflections were analyzed. It was found, that after diaphragm rupture self-modeling pressure and velocity distributions nearby the shock front establish. But in some special cases the temperature behind the shock front can rise. This peculiarity should be taken into account when performing experiments with high reactive gaseous mixtures. The temperature on the shock front and the velocity gradient behind it are uniform in the case of strong blast wave reflections. This effect is observed in the zone with an elevated temperature profile behind the incident blast wave. The reflected triangular waves conserve a quasi-self-modeling character by pressure. Typical experiments were carried out to verify the theoretical predictions. The effects of reflected wave acceleration in the case of triangular waves and the self-similar character of the pressure profiles were observed.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1.0 and the AMS fonts, developed by the American Mathematical Society.     

Formation of pressure peak in a channel behind a reflected shock

Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 178–181, November–December, 1990.     

Simulation of blast wave propagation over a cylinder

A numerical study of the interaction of plane blast waves with a cylinder is presented. Computations are carried out for various blast-wave durations and comparisons are obtained with the corresponding results of planar shock-wave. Both inviscid and viscous results based on the solution of the Euler and Navier-Stokes equations are presented. The equations are solved by an adaptive-grid method and a second-order Godunov scheme. The shock wave diffraction over the cylinder is investigated by means of various contour plots, as well as, pressure and skin-friction histories. The study reveals that the blast-wave duration significantly influences the unsteady flow over the cylinder. The differences between the viscous and inviscid results are also discussed. Received 2 March 1996 / Accepted 28 February 1997     

Calculation of reflection of a blast wave by a plane

Some results are given of calculation of the reflection of a blast wave by a rigid flat surface. A model of the explosion with a simple energy dissipation mechanism is considered, radiation being taken into account in the approximation of radiative heat conduction. The pressure distribution on the surface and the flow pattern in the region of propagation of the incident and reflected shock waves are obtained.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 179–182, September–October, 1982.We thank L. A. Chudov for helpful discussions of the work.     

Reflection of a spherical blast wave from a planar surface

Numerous authors have carried out rather extensive studies in the last twenty to thirty years of the problem of the interaction of shock and blast waves with obstacles in their paths. Owing to the complexity of the problem, they assumed certain limiting cases for the shock wave interactions in which the parameters behind the shock wave were usually taken to be constants. The first wave diffraction studies involving variable parameters behind the front were presented in [1, 2], wherein a development of the theory of “short waves” (blast waves at a substantial distance from the center of an explosion) and their reflection from a planar surface was given. The theory of short waves assumes that the jump in pressure at the wave front and the region over which the parameters vary are small. The problem concerning reflection of a blast wave from a surface was also considered in [3, 4], wherein a solution in the region behind the reflected wave was obtained at initial times. The initial stage in the reflection of a blast wave from a planar, cylindrical, or spherical surface (the one-dimensional case) was studied in [5]. In this paper we investigate the interaction of a spherical blast wave, resulting from a point explosion, with a planar surface; we consider both regular and non-regular reflection stages. In solving this problem we use S. L. Godunov's finite-difference method. We obtain numerical solutions for various values of the shock strength at the instant of its encounter with the surface. We present the pressure fields in the flow regions, the pressure distribution over the surface at various instants of time, and the trajectories of the triple point. The parameter values at the front of the reflected wave are compared with results obtained from the theory of regular reflection of shock waves.     

Parameter formation behind the reflected wave in a shock tube with a nozzle

The reflection of a shock wave from the inlet of a nozzle of very simple geometry is analyzed on the basis of calculations carried out in the two-dimensional formulation. The nozzle throat is a sharp-edged slit in the end face of the tube leading to an expanding duct with straight generators. In this formulation the results of the investigation are quite general, since they depend on a minimum number of the determining parameters varied in the calculations.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 153–159, July–August, 1987.The authors wish to thank G. N. Nikolaev and I. M. Naboko for useful discussion of their results.     

Shock wave attenuation in partially confined channels

An approximate analytical solution is presented for the attenuation of planar shock waves in channels with perforated walls. The problem is considered as quasi-one-dimensional. Good agreement is found between the theoretical results and available experimental data regarding the rate of shock wave attenuation within the range of initial shock Mach numbers between 1.1 and 4 and perforation ratios between 4.5 × 10^–3 and 0.53. A correlation for the discharge coefficient of a single hole perforation is presented which gives quantitatively good agreement with particular experimental observations.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1.0 and the AMS fonts, developed by the American Mathematical Society.     

Criterion of formation of a shock wave reflected from a cloud of particles

The problem of the formation of a “collective” shock wave reflected from a cloud of particles, which was previously observed in experiment, is considered. A criterion of formation of a reflected shock wave is obtained based on the numerical and analytical solutions of the problem. Institute of Theoretical and Applied Mechanics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 3, pp. 44–51, May–June, 1998.     

The interaction of a shock wave with the boundary layer in a reflected shock tunnel

The influence of a nontotal reflection on the interaction of a reflected shock wave with the boundary layer in a reflected shock tunnel has been investigated. The calculating method of the velocity, the temperature and the Mach number profiles in the boundary layer in reflected shock fixed coordinates has been obtained. To account for equilibrium real gas effects of nitrogen, the numerical results show that the minimum Mach number in the boundary layer has been moved from the wall into the boundary layer with the increasing of the incident shock Mach number. The minimum Mach number, the shock angle in the bifurcated foot and the jet velocity along the wall to the end plate are reduced owing to the increasing of the area of nozzle throat. The numerical results are in good agreement with measurements.