二维双曲型守恒律的一种五阶松弛格式

松弛格式是Jin和Xin提出的无振荡有限差分方法,其主要思想是将守恒律转化为松弛方程组进行求解.本文用逐维五阶WENO重构和显隐式Runge-Kutta方法对松弛方程组的空间和时间进行离散,得到了一种求解二维双曲型守恒律五阶松弛格式.所得格式保持了松弛格式简单的优点,不用求解Riemann问题和计算通量函数的雅可比矩阵.通过二维Burgers方程和二维浅水方程的数值算例验证了格式的有效性.     

内爆炸爆轰产物运动过程二维数值模拟研究(一)——密闭空间

为了研究密闭空间内爆炸爆轰产物运动规律,采用五阶WENO有限差分格式,通过耦合求解爆轰产物质量分数输运方程与可压缩欧拉方程,自主编写了密闭空间内炸药爆炸过程二维数值计算程序。利用所开发的程序数值探讨了密闭空间内爆轰产物的传播过程及炸药形状、产物状态方程对爆轰产物运动的影响规律。研究表明:炸药形状的差异不仅改变了爆炸初期爆轰产物的膨胀形态,同时也改变了爆轰产物与周围空气的后期混合状态。状态方程对产物运动过程同样具有一定的影响,JWL状态方程中高压项可使得爆炸初期产物具有更大的膨胀能力。本文的研究可为进一步探讨考虑燃烧效应后爆轰产物扩张过程及毁伤评估提供一定的参考和指导。     

二维拟定常爆轰波反应区的初步研究

研究由现代爆轰渐近分析理论建立的关于二维拟定常爆轰波反应区的控制方程组，用数值积分方法求解该方程组，得到爆轰波反应区内压力、粒子速度、化学反应度随时间变化的规律。对乳化硝铵、PBX-9404和TATB炸药进行了计算，得到比较满意的结果。     

含铝炸药爆轰驱动的非线性特征线模型

针对含铝炸药爆轰的非理想特性,提出了含铝炸药爆轰产物膨胀的局部等熵假设,建立含铝炸药爆轰驱动的非线性特征线模型,为研究含铝炸药爆轰产物的非等熵流动和膨胀做功提供了一种新的理论分析方法。设计了5、50 μm含铝炸药和含LiF炸药驱动0.5、1 mm厚金属板实验,通过激光位移干涉仪测试金属板运动的速度历程,再通过实验结果计算得到铝粉在爆轰产物中的反应度变化规律,结合含铝炸药爆轰产物的非线性特征线模型,理论计算了含铝炸药驱动金属板的速度历程。对比理论与实验结果,理论方法能够很好地描述铝粉二次反应对炸药做功能力的贡献,同时验证了含铝炸药爆轰驱动的非线性特征线模型的正确性。     

基于四阶半离散中心迎风格式的虚拟流方法的应用

给出了求解多维无粘可压Euler方程组的四阶半离散中心迎风格式,该格式根据非线性波在网格单元边界上传播的局部速度来更准确地估计局部Riemann的宽度,避免了计算网格的交错,降低了格式的数值粘性。同时,考虑到Level Set函数能隐式地追踪到界面的位置,而虚拟流的构造能隐式地捕捉到界面的边界条件,因此再将新的四阶半离散中心迎风格式与Level Set方法以及虚拟流方法相结合,成功地处理了非反应激波和多介质流中爆轰间断的追踪问题。     

改进WENO格式及其在爆轰计算中的应用

对已有的一种改进型WENO-M格式进行了理论上的修正,得到了新的WENO权函数。与原WENO-M格式相比,新得到的WENO-M-P格式减少了约9%的CPU计算时间,同时也保证了在一阶极值点处不降低精度（经典的WENO格式在一阶极值点处精度下降）,仍然保持5阶精度。为了验证修正后的格式,采用二步反应模型数值模拟了几组一维和二维爆轰：在一维爆轰模拟中,对比了WENO-M格式和WENO-M-P格式在一定温度下的最低起爆压强以及一定压强下的最低起爆温度;在二维旋转爆轰的模拟中,对比了WENO-M格式和WENO-M-P格式的计算效果。结果表明：在同样的起爆温度下,WENO-M 格式和 WENO-M-P 格式的最低起爆压强均高于 WENO格式,但WENO-M-P格式比WENO-M格式的最低起爆压强低;三种格式在不同压强下的最低起爆温度相同;WENO-M-P格式具有和WENO-M格式一样的计算效果,优势是节省了计算时间。     

非均匀凝聚炸药冲击起爆的数值模拟

为探讨非均匀凝聚炸药的起爆机理,我们编制了一维计算机程序CHD-3。程序中固态炸药状态方程是根据Gr?neisen关系和Walsh技术得到的,爆轰产物采用JWL状态方程,并利用文献中的反应率方程进行计算。     

无粘可压缩流动的改进高精度方法

为更准确捕捉复杂流场的流动细节,通过对WENO格式的光滑因子进行改进,发展了一种新的五阶WENO格式。对三阶ENO格式进行加权可以得到五阶WENO格式,但是不同的加权处理,WENO格式在极值处保持加权基本无振荡的效果不同,本文构造了二阶精度的局部光滑因子,及不含一阶二阶导数的高阶全局光滑因子,从而实现WENO格式在极值处有五阶精度。基于改进五阶WENO格式,对一维对流方程、一维和二维可压缩无粘问题进行算例验证,并与传统WENO-JS格式和WENO-Z格式进行比较。计算结果表明,改进五阶WENO格式有较高的精度和收敛速度,有较低的数值耗散,能有效捕捉间断、激波和涡等复杂流动。     

内爆炸爆轰产物运动过程二维数值模拟研究(二)——泄压空间

为了研究泄压空间内爆炸爆轰产物运动及能量演化规律,采用五阶WENO有限差分格式,通过耦合求解两组分可压缩欧拉方程,自主编写了泄压空间内炸药爆炸过程二维数值计算程序。采用验证的程序数值探讨了泄压口大小、泄压口位置、炸药爆炸位置对爆轰产物运动及能量演化的影响规律。研究表明:上述因素不仅改变了爆轰产物的运动形态,同时改变了产物的泄出过程;泄压口的存在主要加快气体内能的泄出过程。本文研究可为舱室内爆炸毁伤评估提供一定的参考和依据。     

基于通用炸药状态方程分析飞板运动规律的特征线法

从小扰动波(马赫波)的物理概念出发,导出了不依赖流体状态方程表达形式的平面二维超声速定 常流的特征线方程;重新定义了以流体密度为单自变量的Prantl-Meyer函数,形成了求解平面二维超声速定 常流的封闭方程组。还利用这种通用物态方程的特征线差分解法,针对滑移爆轰驱动飞板运动问题构建了爆 轰产物流场内部和飞板边界特征线差分法格式。对TNT炸药和乳化炸药采用JWL状态方程和多方方程进 行了对比计算。结果表明,炸药爆轰对飞板的驱动能力与状态方程表示的炸药的做功能力是一致的。     

压装TNT的SDDT特性研究

本文报告厂将水箱技术同改型隔板试验结合起来研究凝聚炸药由冲击波经爆燃向爆轰转变(SDDT)的方法。实测了压装TNT(装药密度1.615g/cm~3)的SDDT曲线,并确定了其燃烧阈值和爆轰阈值(分别为2.1GPa和2.5-3.0GPa)。按照流体动力学特征线法计算了不同强度起爆冲击波作用下在炸药中形成的一系列冲击波、爆燃波和爆轰波的剖面,这些剖面反映了炸药SDDT的基本特征。所取得的信息对于炸药的实际应用和对冲击波起爆的深入研究均有价值。     

Relaxation of overdriven detonation waves with finite reaction rate

A numerical study is made of the interaction of a detonation wave having finite reaction velocity with a rarefaction wave of different intensity which approaches it from the rear, for the Zeldovich-Neumann-Doring (ZND) model with a single irreversible reaction A B. It is found that, for a fixed value of the parameter characterizing the initial supercompression (depending on the activation energy and the heating value of the mixture), the considered interaction leads either to a gradual relaxation of the detonation wave and its transition to the Chapman-Jouguet (CJ) regime, or to the development of undamped oscillations.Interest in the problems of detonation and supersonic combustion has increased in recent years. This is associated with the appearance and development of new experimental and theoretical techniques; it is also associated with the further development of air-breathing reaction engines, and other practical requirements. The present state of detonation theory is reflected in the survey [1].It has been established [2] that the detonation wave in gases nearly always has a complex nonuniform structure. Transverse disturbances are observed under a wide range of conditions and differ both in amplitude and wavelength. At the same time, behind the detonation leading front there is a region of uncompletely burned gas corresponding to the effective ignition induction period [3]. In spinning detonation the induction period is significantly longer than the heat release period and transverse detonation waves traveling in the induction zone of the head wave appear [3, 4]. Such a secondary detonation wave is free of transverse disturbances. The same is true of the detonation waves observed in the wake behind a body moving at high speed in a combustible medium [5] or in a gas which has been preheated by a shock wave [6].Although it is possible, under favorable conditions, to study in detail the system of discontinuities accompanying detonation, information on the extensive zones in which heat release takes place is scarce, the mechanism of detonation wave autonomy (in particular, the role of the rarefaction zone behind the wave) is not entirely clear, and the fact that, in spite of the complex structure, an autonomous detonation propagates with the CJ velocity calculated on the basis of one-dimensional theory has not yet been explained.In studying the nonlinear phenomena associated with the finite reaction rate it is quite acceptable to investigate only the simple one-dimensional detonation model, with which it is convenient to restrict ourselves to a single effective chemical reaction. This model is particularly reasonable since, in certain cases, the real detonation is virtually one-dimensional.The question of the stability of the one-dimensional detonation wave to disturbances of its structure has been examined by several authors [7–13]. The use of computers makes possible the direct computation of flows with heat release and the study of their properties. This method has been used in [11–13] to study the stability problem for a detonation wave with respect to finite disturbances.In the present paper we present a numerical study of the interaction of a detonation wave having finite chemical reaction rate with a rarefaction wave of different intensity approaching it from the rear for the ZND model with a single irreversible reaction A B. It is found that for a fixed value of the parameter characterizing the difference between detonation and the CJ waves, depending on the activation energy E and the mixture heating value Q_m, the interaction in question leads either to a gradual relaxation of the detonation wave and its transition to the CJ regime (this relaxation may be accompanied by decaying oscillations) or to the appearance of undamped oscillations (the unstable regime). The parameters E and Q_m affect the wave stability differently: with increase of Q_m, the wave is stabilized; with increase of E, it is destabilized. The boundary between the stable and unstable detonation wave propagation regimes is found. This boundary has a weak dependence on the rarefaction wave intensity. Estimates and calculated examples show that the amplitude of the unstable wave oscillations is finite and that the average detonation propagation velocity is close to the CJ velocity computed for the given heating value Qm.The author wishes to thank G. G. Chernyi for his guidance and L. A. Chudov for advice on computational questions.     

凝聚炸药非理想爆轰的数值模拟

本文对凝聚炸药非理想爆轰的数值模拟进行了系统介绍。对敏感、钝感炸药的理想与非理想爆轰的数值模拟方法、宏观反应速率方法及近年发展起来的ＤＳＤ（ＤｅｔｏｎａｔｉｏｎＳｈｏｃｋＤｙｎｔｉｍｉｃｓ）方法和波阵面追踪法,以及对这些方法的适应能力、存在的主要问题进行了分析与讨论。      

Resolution-optimised nonlinear scheme for secondary derivatives

A 5-point-stencil optimised nonlinear scheme with spectral-like resolution within the whole wave number range for secondary derivatives is devised. The proposed scheme can compensate for the dissipation deficiency of traditional linear schemes and suppress the spurious energy accumulation that occurs at high wave numbers, both of which are frequently encountered in large eddy simulation. The new scheme is composed of a linear fourth-order central scheme term and an artificial viscosity term. These two terms are connected by a nonlinear weight. The proposed nonlinear weight is designed based on Fourier analysis, rather than Taylor analysis, to guarantee a spectral-like resolution. Moreover, the accuracy is not affected by the optimisation, and the new scheme reaches fourth-order accuracy. The new scheme is tested numerically using the one-dimensional diffusion problem, one-dimensional steady viscous Burger’s shock, two-dimensional vortex decaying, three-dimensional isotropic decaying turbulence and fully developed turbulent channel flow. All the tests confirm that the new scheme has spectral-like resolution and can improve the accuracy of the energy spectrum, dissipation rate and high-order statistics of turbulent flows.     

孔隙度对PBX炸药冲击起爆影响的实验研究

为了研究孔隙度(装药密度)对PBX炸药冲击起爆爆轰成长的影响，采用炸药冲击起爆锰铜压阻一维拉格朗日实验测试系统，测量了不同孔隙度的PBXC03炸药(HMX的质量分数为87%，TATB的质量分数为7%，黏结剂的质量分数为6%)冲击起爆过程不同拉格朗日位置的压力-时间历史。结果显示:在本文装药范围和加载条件下，孔隙度对PBX炸药冲击起爆爆轰过程的影响不单调，中等密度的炸药冲击起爆和爆轰成长最快，这是热点点火过程与燃烧反应过程共同作用的结果。     

Numerical study of blast characteristics from detonation of homogeneous explosives

A new robust numerical methodology is used to investigate the propagation of blast waves from homogeneous explosives. The gas-phase governing equations are solved using a hybrid solver that combines a higher-order shock capturing scheme with a low-dissipation central scheme. Explosives of interest include Nitromethane, Trinitrotoluene, and High-Melting Explosive. The shock overpressure and total impulse are estimated at different radial locations and compared for the different explosives. An empirical scaling correlation is presented for the shock overpressure, incident positive phase pressure impulse, and total impulse. The role of hydrodynamic instabilities to the blast effects of explosives is also investigated in three dimensions, and significant mixing between the detonation products and air is observed. This mixing results in afterburn, which is found to augment the impulse characteristics of explosives. Furthermore, the impulse characteristics are also observed to be three-dimensional in the region of the mixing layer. This paper highlights that while some blast features can be successfully predicted from simple one-dimensional studies, the growth of hydrodynamic instabilities and the impulsive loading of homogeneous explosives require robust three-dimensional investigation.     

Head-on Collision of a Detonation with a Planar Shock Wave

The phenomenon that occurs when a Chapman–Jouguet (CJ) detonation collides with a shock wave is discussed. Assuming a one-dimensional steady wave configuration analogous to a planar shock–shock frontal interaction, analytical solutions of the Rankine–Hugoniot relationships for the transmitted detonation and the transmitted shock are obtained by matching the pressure and particle velocity at the contact surface. The analytical results indicate that there exist three possible regions of solutions, i.e. the transmitted detonation can have either strong, weak or CJ solution, depending on the incident detonation and shock strengths. On the other hand, if we impose the transmitted detonation to have a CJ solution followed by a rarefaction fan, the boundary conditions are also satisfied at the contact surface. The existence of these multiple solutions is verified by an experimental investigation. It is found that the experimental results agree well with those predicted by the second wave interaction model and that the transmitted detonation is a CJ detonation. Unsteady numerical simulations of the reactive Euler equations with both simple one-step Arrhenius kinetic and chain-branching kinetic models are also carried out to look at the transient phenomena and at the influence of a finite reaction thickness of a detonation wave on the problem of head-on collision with a shock. From all the computational results, a relaxation process consisting of a quasi-steady period and an overshoot for the transmitted detonation subsequent to the head-on collisions can be observed, followed by the asymptotic decay to a CJ detonation as predicted theoretically. For unstable pulsating detonations, it is found that, due to the increase in the thermodynamic state of the reactive mixture caused by the shock, the transmitted pulsating detonation can become more stable with smaller amplitude and period oscillation. These observations are in good agreement with experimental evidence obtained from smoked foils where there is a significant decrease in the detonation cell size after a region of relaxation when the detonation collides head-on with a shock wave.     

On the effect of grain size on shock sensitivity of heterogeneous high explosives

Analysis of available data on dependence of the critical detonation diameter of various heterogeneous condensed explosives on mean size of grains and voids demonstrated that in many cases surprising correlations between and the initial specific surface area of heterogeneous explosives exist, namely, or . The run distance to detonation in wedge test with sustained strong shock of constant amplitude also linearly correlates with , i.e. . At the same time, the shock sensitivity reversal effect is often observed when grain size of HE is reduced. Apart from that Moulard (1989) found that detonation critical diameter of plastic bonded explosive with mono- and bimodal RDX grain size distribution depends nonmonotonously on mean grain size. Complicated dependence of shock sensitivity of heterogeneous explosives on their specific surface area can be explained based on comparison of the critical hot spot size at given characteristic pressure behind shock wave with the mean heterogeneity size . At high characteristic pressure (relative to the critical ignition pressure) is small compared with and all specific surface area of heterogeneous explosive is available for the hot spot growth process in accordance with the grain burn concept. However, when characteristic pressure of shock wave decreases, increases and can become comparable with . In this case only relatively large potential hot spots with size can result in self-supported hot spot growth process and shock sensitivity is controlled by the specific surface area which corresponds to only larger heterogeneities and can be significantly smaller than initial specific surface area. Received 18 July 1996 / Accepted 6 November 1996