改进特征线法在水下爆炸正反演问题中的应用

介绍了改进特征线法及其在水下爆炸正反演问题中的应用。将改进特征线法用于TNT炸药球水下爆炸的模拟,并与实验数据和AUTODYN程序的结果比较,结果表明,改进特征线法求解水下爆炸问题具有较好的准确性,且能够捕捉到流场中弱冲击的传播。而后应用改进的特征线法将正问题中的冲击波参数作为初值条件,利用逆序差分格式,对水气界面做反演求解;将反演的水气界面与正问题中的界面作比较,结果显示两者在近场吻合良好。     

水下爆炸非均熵二维定常流的三族特征线解法

针对二维定常可压缩超声速非等熵柱状流,提出一种特征线差分解法,通过在沿马赫线的相容方程中添加沿流线的熵变项以描述非等熵效应,得到等熵流和非等熵流均适用的三族特征线方程组。根据水下爆炸近场特点,建立无限长柱状装药的定常模型,将三族特征线方程组用有限差分法离散求解,通过构造合适的网格保证计算格式可以数值上收敛,由此编制程序并计算几种柱状炸药的水下爆炸近场冲击波。对比有限元模拟结果和实验结果发现,特征线差分法可以比较准确地捕捉冲击波形状并计算冲击波后流场,从而验证了所提出的三族特征线差分法的准确性。     

温压炸药坑道内爆炸冲击波的数值模拟研究

基于二次反应理论,采用AUTODYN程序对温压炸药(RDX/AP/AL/粘合剂=20/43/25/12,质量比)坑道内爆炸冲击波进行了数值模拟研究。将温压炸药与传统炸药TNT的计算结果进行了比较,结果表明:①在爆炸近区,温压炸药比TNT的爆炸冲击波超压峰值低。但在爆炸远区,温压炸药的爆炸冲击波超压峰值则逐渐超过了TNT,最高达到了TNT的1.48倍;温压炸药爆炸冲击波的冲量峰值始终高于TNT,约为TNT的1.33～1.43倍。②最小二乘拟合得到了温压炸药坑道内爆炸冲击波超压峰值随距离衰减的计算公式,具有一定参考价值。     

柱状含铝炸药水下爆炸近场的特征线法研究

基于之前提出的一种含熵变项的特征线法，通过控制非等熵流中的能量释放来刻画铝粉燃烧的影响，结合简单Chapman-Jouguet模型和JWL-Miller状态方程，计算了柱形含铝炸药水下爆炸的近场参数。对比模拟结果与实验数据，发现这种特征线法可以较好地预测近场冲击波的传播迹线、爆轰产物的膨胀轨迹以及内部压缩波的反射过程。结果表明，这种特征线法可用于含铝炸药水下爆炸的近场计算，进一步可用于评估含铝炸药性能或计算水下能量输出。     

炸药水中爆炸冲击因子的新型计算方法

针对水中爆炸冲击因子在近场范围内的一些不足,利用水中爆炸冲击波的最大峰值压力与正相冲量的乘积推导了冲击因子的表达式。通过水中爆炸实验,得到了几种典型炸药的冲击波参数及其相似方程。利用该公式计算了水中爆炸冲击因子及其装药指数,并与基于平面波的水下爆炸冲击因子进行了对比。结果表明:冲击因子中的装药指数n＝0.5不仅适合所有以TNT为基本组分的炸药,也适合于RDX、HMX基的炸药。在修正冲击波形状的基础上,由峰值压力与冲量的乘积推导的冲击因子计算公式,从冲击波的毁伤作用的角度表述了水中爆炸冲击因子的物理意义,在计算近场冲击因子时具有更高的准确性。     

水下爆炸冲击波的近场特性

通过求解球形一维流体动力学方程,模拟了水下爆炸冲击波的产生和传播过程。在数值模拟中,对TNT炸药采用标准的JWL状态方程,对水采用Two-phase状态方程。应用Level Set方法确定爆炸产物和水的交界面的位置。对裸药球在无限水域爆炸进行了数值计算,考察了网格大小对结果收敛性的影响,分析了水下爆炸冲击波压力和比冲量的近场特性。最后通过数值拟合得到了冲击波压力峰值、比冲量和时间衰减常数的近似回归公式。     

含铝纤维复合炸药的能量输出和力学强度

通过空中爆炸实验,研究了铝纤维对爆炸能量输出的影响,结果表明:wAl=0.20的TNT/Al,冲击 波压力峰值为TNT 的1.19倍,TNT 当量为TNT 的1.29倍;wAl=0.20的RDX/Al,冲击波压力峰值为 RDX的1.20倍,爆热为TNT的1.64倍,是RDX的1.31倍。通过抗压实验,研究了铝纤维对炸药力学强度 的影响,结果表明,铝纤维能增强TNT炸药的力学强度,破坏应力为6.8MPa,应变为0.043。铝纤维对炸药 能量和力学强度的双重增强特性,可以为现代高性能炸药设计提供参考。     

水下爆炸冲击波壁压理论及数值计算方法改进研究

水下爆炸冲击波是舰船抗冲击评估中重要的载荷成分,也是水中结构物毁伤程度快速预报的关键和依据。通过小当量实验发现,由于传统 Taylor 平板理论公式忽略了冲击波波速的非线性变化 ,导致其在预报近距离水下爆炸冲击波壁压脉宽时出现偏差。为此,给出了比例爆距R/W1/3为0.11～5.30 m/kg1/3 (R为爆距,W为炸药质量)下的冲击波速度拟合公式,对传统Taylor理论公式进行修正。修正后,在R/W1/3=0.11 m/kg1/3下,壁压脉宽及冲量偏差大幅减小;在R/W1/3≥0.21 m/kg1/3下,两者偏差均小于12%。此外,在处理水下近场和中远场爆炸问题时,发现数值耗散会导致壁压峰值被明显削弱,于是提出了一种可行的数值策略消除计算中数值耗散导致的削弱效应,结果与修正的Taylor平板理论公式吻合良好,峰值偏差均小于9%。改进后的冲击波壁压理论公式及数值计算方法可为舰船抗爆抗冲击领域提供理论和技术支撑。     

铝纤维对黑索今水下爆炸性能的影响

将铝纤维添加到RDX中得到新型非理想炸药,并与RDX进行水下爆炸对比实验,得到2种炸药在不同位置的压力时程曲线,经过分析计算得到两者水下爆炸的冲击波压力峰值、冲量、冲击波能、气泡脉动周期以及气泡能。结果表明:距离药柱相同位置处,铝纤维炸药的压力峰值低于RDX,铝纤维炸药的冲击波冲量高于RDX,其差值受离药柱的距离影响不大。与RDX相比,铝纤维炸药的比冲击波能降低了2%~5.2%,比气泡能提高了9.4%~23.36%,总能量平均提高了3.5%。铝纤维炸药比气泡能与总能量的比值为55%~60%,高于RDX的50%~53%,其总能量与爆热比值为74%~84%,低于RDX的89%~95%。     

近自由面水下爆炸冲击载荷特性三维数值模拟

基于三维SPH 方法,对传统链表搜索算法进行了变光滑长度改进,并提出了具有较好稳定性的多 相物质交界面的处理方法,模拟了三维无限域水下爆炸问题,验证了改进的三维SPH 方法模拟水下爆炸问题 的可行性和有效性。在此基础上,建立了水下爆炸三维数值模型,模拟了近自由面水下爆炸过程,研究了冲击 波传播特征、自由面下压力场和能量场特性以及水柱的产生过程。结果表明:自由面可将冲击波压力峰值和 压力冲量最大衰减到1/3和1/7;爆深的增加会导致压力比和冲量比的等值柱面曲率变小,产生的水柱也逐 渐由破碎的喷柱向高而窄的水冢过渡。     

New conditions of stability and convergence of Stokes and Newton iterations for Navier-Stokes equations

This paper considers Stokes and Newton iterations to solve stationary Navier- Stokes equations based on the finite element discretization. We obtain new sufficient conditions of stability and convergence for the two iterations. Specifically, when 0 < σ = (N‖f‖-1)/v² ≤ 1/($\sqrt{2}$+1), the Stokes iteration is stable and convergent, where N is defined in the paper. When 0 < σ ≤ 5/11, the Newton iteration is stable and convergent. This work gives a more accurate admissible range of data for stability and convergence of the two schemes, which improves the previous results. A numerical test is given to verify the theory.     

Resolvent Estimates and Maximal Regularity in Weighted L q -spaces of the Stokes Operator in an Infinite Cylinder

Let be an infinite cylinder of , n ≥ 3, with a bounded cross-section of C ^1,1-class. We study resolvent estimates and maximal regularity of the Stokes operator in for 1 < q, r < ∞ and for arbitrary Muckenhoupt weights ω ∈ A _r with respect to x′ ∈ Σ. The proofs use an operator-valued Fourier multiplier theorem and techniques of unconditional Schauder decompositions based on the -boundedness of the family of solution operators for a system in Σ parametrized by the phase variable of the one-dimensional partial Fourier transform. Supported by the Gottlieb Daimler- und Karl Benz-Stiftung, grant no. S025/02-10/03.     

Upscaling in Subsurface Transport Using Cluster Statistics of Percolation

Transport/flow problems in soils have been treated in random resistor network representations (RRNs). Two lines of argument can be used to justify such a representation. Solute transport at the pore-space level may probably be treated using a system of linear, first-order differential equations describing inter-pore probability fluxes. This equation is equivalent to a random impedance network representation. Alternatively, Darcys law with spatially variable hydraulic conductivity is equivalent to an RRN. Darcys law for the hydraulic conductivity is applicable at sufficiently low pressure head in saturated soils, but only for steady-state flow in unsaturated soils. The result given here will have two contributions, one of which is universal to any linear conductance problem, i.e., requires only the applicability of Darcys (or Ohms) law. The second contribution depends on the actual distribution of linear conductances appropriate. Although nonlinear effects in RRNs (including changes in resistance values resulting from current, analogous to changes in matric potential resulting from flow) have been treated within the framework of percolation theory, the theoretical development lags the corresponding development of the linear theory, which is, in principle, on a solid foundation. In practice, calculations of the nonlinear conductivity in relatively (compared with soils) well characterized solid-state systems such as amorphous or impure semiconductors, do not agree with each other or with experiment. In semiconductors, however, experiments do at least appear consistent with each other.In the limit of infinite system size the transport properties of a sufficiently inhomogeneous medium are best calculated through application of critical rate analysis with the system resistivity related to the critical (percolating) resistance value, R_c. Here well-known cluster statistics of percolation theory are used to derive the variability, W (R,x) in the smallest maximal resistance, R of a path spanning a volume x³ as well as to find the dependence of the mean value of the conductivity, (x). The functional form of the cluster statistics is a product of a power of cluster size, and a scaling function, either exponential or Gaussian, but which, in either case, cuts off cluster sizes at a finite value for any maximal resistance other than R_c. Either form leads to a maximum in W (R,x) at R=R_c. When the exponential form of the cluster statistics is used, and when individual resistors are exponential functions of random variables (as in stochastic treatments of the unsaturated zone by the McLaughlin group [see Graham and MacLaughlin (1991), or the series of papers by Yeh et al. (1985, 1995), etc.], or as is known for hopping conduction in condensed matter physics), then W (R,x) has a power law decay in R/R_c (or R_c/R, the power being an increasing function of x. If the statistics of the individual resistors are given by power law functions of random variables (as in Poiseiulles Law), then an exponential decay in R for W (R,x) is obtained with decay constant an increasing function of x. Use, instead, of the Gaussian cluster statistics alters the case of power law decay in R to an approximate power, with the value of the power a function of both R and x.     

Analytic elasticity solution of bi-modulus beams under combined loads

A unified stress function for bi-modulus beams is proposed based on its mechanic sense on the boundary of beams. Elasticity solutions of stress and displacement for bi-modulus beams under combined loads are derived. The example analysis shows that the maximum tensile stress using the same elastic modulus theory is underestimated if the tensile elastic modulus is larger than the compressive elastic modulus. Otherwise, the maximum compressive stress is underestimated. The maximum tensile stress using the material mechanics solution is underestimated when the tensile elastic modulus is larger than the compressive elastic modulus to a certain extent. The error of stress using the material mechanics theory decreases as the span-to-height ratio of beams increases, which is apparent when L/h ≤5. The error also varies with the distributed load patterns.     

An Example of Finite-time Singularities in the 3d Euler Equations

Let be the exterior of the closed unit ball. Consider the self-similar Euler system

金属薄板在圆锥头弹体正冲击下的破裂模式

临界破裂速度下（圆板产生破裂的最小速度）,对四种不同材料的薄金属圆板在不同圆锥半角的圆锥头子弹正冲击下的破裂模式进行了试验。研究发现随着圆锥半角的增加,板的破裂模式分别有刺透型、花瓣型和剪切型。通过试验分析,建立了在不同圆锥头子弹以临界破裂速度正冲击下,金属薄板的破裂模式和子弹圆锥半角及金属薄板材料性能的关系。分析中考虑了子弹和板壁接触区域内的局部变形,给出一临界圆锥半角c=arcsin exp(-0.5f)(f是金属薄板材料的真实破裂应变）。由此得到:临界破裂速度正冲击下,圆锥半角30时,薄板破裂由子弹直接刺透板壁引起;＞c且30时,薄板破裂模式是剪切型;当 30＜＜c时,薄板破裂模式是花瓣型。     

The Stationary Oseen Equations in $${\mathbb{R}}^{3}$$ . An Approach in Weighted Sobolev Spaces

In this paper we solve the stationary Oseen equations in . The behavior of the solutions at infinity is described by setting the problem in weighted Sobolev spaces including anisotropic weights. The study is based on a L^p theory for 1 < p < ∞.     

The Pressure Singularity for Compressible Stokes Flows in a Concave Polygon

A compressible Stokes system is studied in a polygon with one concave vertex. A corner singularity expansion is obtained up to second order. The expansion contains the usual corner singularity functions for the velocity plus an “associated” velocity singular function, and a pressure singular function. In particular the singularity of pressure is not local but occurs along the streamline emanating from the incoming concave vertex. It is observed that certain first derivatives of the pressure become infinite along the streamline of the ambient flow emanating from the concave vertex. Higher order regularity is shown for the remainder. This work was supported by the Com2MaC-SRC/ERC program of MOST/KOSEF (grant R11-1999-054), and by the U.S. National Science Foundation.     

Evaluation analysis of prediction methods for two-phase flow pressure drop in mini-channels

Two-thousand and ninety-two data of two-phase flow pressure drop were collected from 18 published papers of which the working fluids include R123, R134a, R22, R236ea, R245fa, R404a, R407C, R410a, R507, CO₂, water and air. The hydraulic diameter ranges from 0.506 to 12 mm; Re_l from 10 to 37,000, and Re_g from 3 to 4 × 10⁵. Eleven correlations and models for calculating the two-phase frictional pressure drop were evaluated based upon these data. The results show that the accuracy of the Lockhart–Martinelli method, Mishima and Hibiki correlation, Zhang and Mishima correlation and Lee and Mudawar correlation in the laminar region is very close to each other, while the Muller-Steinhagen and Heck correlation is the best among the evaluated correlations in the turbulent region. A modified Chisholm correlation was proposed, which is better than all of the evaluated correlations in the turbulent region and its mean relative error is about 29%. For refrigerants only, the new correlation and Muller-Steinhagen and Heck correlation are very close to each other and give better agreement than the other evaluated correlations.     

Drag of a sphere in an unsteady flow of viscous fluid at small reynolds numbers

An unsteady flow of viscous incompressible fluid past a sphere is investigated. The values of the inertial and unsteady terms in the Navier-Stokes equations are characterized by translational (R) and vibrational (R_k) Reynolds numbers, which are assumed small. The solution is constructed in the form of an expansion with respect to max(R, R _k ^1/2 ) by the method of matched asymptotic expansions. A correction to the Stokes force, correct to o[max(R, R _k ^1/2 )], is calculated. It is shown that the result depends strongly on the ratio R/R _k ^1/2 and goes over into the well-known equations for the cases R 0, R_k 0.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 11–16, January–February, 1988.