用变分法估计热爆炸临界状态参数

本文利用作者给出的关于爆炸临界状态的变分原理,并用变分的直接方法,得到了六种不同形状(平板、无限长圆柱,球,无限长方形杆,有限长圆柱,正方体)系统的临界P-K参数和临界温度的近似公式,与精确的数值计算结果比较表明,对点火临界参数,本文公式均能给出较好的估计值。     

圆柱壳纯弯曲时塑性失稳临界曲率半径模型

薄壁管材在等曲率矫直生产中,塑性失稳临界曲率半径作为重要的工艺参数,直接决定了设备结构和产品质量。而目前现场仍沿用经验图表结合人工经验和反复试矫对其进行估定,亟待建立针对性的临界曲率半径数学模型以指导生产。在力学建模和分析时,就是确定具有初始曲率的圆柱壳体在纯弯曲条件下塑性失稳的临界曲率半径,为此从旋转壳体一般几何方程出发,基于J2形变理论和能量理论,运用里茨法建立了圆柱壳体在纯弯曲条件下塑性失稳时的临界弯矩,以此确定了临界曲率半径模型,并给出了数值解法。应用ANSYS/LS-DYNA进行了有限元动态仿真试验,证明了模型是近似正确的,并通过仿真对比分析证明了轴向起皱先于截面畸变是圆柱壳体在纯弯曲条件下塑性失稳的主要模态。     

边界条件对受液压作用圆柱壳稳定性的影响

本文用渐近方法分析了在各种可能面向(u或T_1,v或S_1)及非面向(w或,或G_1)边界条件下受液压作用的圆柱壳的稳定性.将临界载荷与屈曲形态函数展成λ~(1/2)的幂级数.文中不仅给出了求各次近似临界载荷的步骤,而且对各种边界条件得到了临界载荷与屈曲形态第一次近似的表达式,其误差为λ~(1/2)量级.以四种典型情况为例,求得了临界载荷第二次近似的表达式,其误差为λ量级.从本文的结果可以看出,对于受液压作用的圆柱壳,面向边界条件对稳定性起着主要的作用,而非面向边界条件的影响是次要的(λ~(1/2)量级).     

论粘性激波层理论的理论基础及其进一步发展

本文将Davis的量级分析方法改用匹配渐近展开方法,作为一级近似推导出了高超音速化学反应粘性激波层方程。证明了粘性激波层方程是NS方程在匹配渐近意义上的一级近似方程。进一步讨论了这一方程的基本假设条件。本文首次推导出的二级近似方程,是对Davis粘性激波层方程的修正。这种修正可以提高数值解的精度,有助于对问题获得更全面的了解,对进一步发展与完善高超音速钝头体绕流问题的数值求解方法起一定的作用。     

亚临界雷诺数下圆柱绕流的大涡模拟

本文应用Smagorinsky涡粘性模式和二阶精度的有限体积法对圆柱绕流的流场进行大涡模拟．求解了非正交曲线坐标系下的N-S方程,对雷诺数为100和20000的工况进行了计算．计算结果与实验及动力涡粘性模式的结果进行了比较,表明计算对于层流及高亚临界雷诺数的湍流流动是合理的     

圆柱绕流的非线性动力学

本文利用非线性动力学的概念和方法来研究粘性不可压缩流体的二维圆柱绕流问题．计算了定常流失稳以及出现混沌的临界雷诺数，并估计了混沌解的一些统计特征．     

圆柱绕流Strouhal数的测定一个新的综合性流体教学实验

亚临界状态下的圆柱绕流,背后卡门涡街旋涡脱落的频率与来流速度、圆柱直径有关,具体关系式为流体力学中一个有关不定常流动的相似参数—Strouhal数等于一个常数.用热线风速仪(或压力传感器)进行测量,并经微机采样和FFT运算,从功率谱可分析旋涡脱落的频率.文中验证了在亚临界范围内Strouhal数为常数的事实.     

爆炸载荷特征参数对无限长圆柱壳弹性动态响应的影响

采用含有三角脉冲载荷和准静压载荷的爆炸载荷加载,利用单自由度模型对无限长圆柱壳体（即等效平面应变圆环）的弹性动态响应进行了力学分析,获得了径向位移响应解析解及准静压阶段弹性响应振幅的解析解。基于所得解析解,通过控制变量法分析了载荷压力及载荷分界点时刻（即三角脉冲载荷与准静压载荷作用的分界点时刻）对径向位移最大值、准静压阶段弹性响应振幅的影响规律,更加深入地研究了爆炸载荷对结构响应的影响。本文主要从准静压幅值与三角脉冲峰值的比值以及载荷分界点时刻两个主要特征参数入手,结合结构的呼吸振动频率来研究爆炸载荷对无限长圆柱壳弹性动态响应的影响。在研究中发现存在临界时刻:当载荷分界点时刻早于临界时刻时,径向位移最大值出现在准静压阶段;当载荷分界点时刻晚于临界时刻时,获得了便于直观判断径向位移达到最大值时所处载荷阶段的分区图。基于前述解析解的分析,还获得了不同影响因素导致的振幅变化的单调性分区图,便于判别载荷压力的变化所致的准静压阶段振幅的增减趋势。通过研究获得的爆炸压力载荷对结构响应的影响规律,可为爆炸容器设计以及结构防护基础研究提供参考。     

长圆柱形扁壳蠕变跳跃问题

本文討論了长圓柱形夹层扁壳在法向恒定均布压力作用下由于蠕变引起的跳跃問題。认为扁壳形状完全規則,在跳跃发生前的变形是对称的,并設壳体各部分处在同一溫度状况下。本文将确定跳跃临界状态的問題和計算到达此状态的临界时間的問題分别考虑。将前一問題归結成为寻求一个最小的本征值,因而在一些情况能精确地确定发生跳跃的临界状态。計算第二問題时,我們采用了蠕变的流动理論,同时略去了弯矩的高次項及弹性变形。文內对这种近似步骤还作了簡略的分析。     

中厚夹层圆柱扁壳的屈曲分析

基于一阶剪切变形中厚圆柱壳理论,考虑夹心层的面内刚度,根据中厚夹层圆柱扁壳的几何方程、本构关系、平衡方程,建立了中厚夹层圆柱扁壳小挠度屈曲的微分方程;应用广义傅里叶级数解法,得到了四边简支条件下中厚夹层圆柱扁壳屈曲的临界荷载表达式。该表达式可以退化为硬夹心夹层板的表达式,表明本文推导过程的正确性。本文还讨论了夹心层的弹性模量和泊松比以及中厚夹心圆柱扁壳的长宽比和厚度对扁壳屈曲荷载的影响。结果表明:临界荷载与夹心层的弹性模量和泊松比成正比,与扁壳的长宽比和厚度成反比。     

Relation between the quasi-cylindrical approximation and the critical classification for swirling flow

It is shown that under the assumption of the quasi-cylindrical approximation with viscous effect the critical flow corresponds to a singularity, as flows approach the critical state from both sides, the radial components of velocity go separately to positive and negative infinity, and that for inviscid flow solution of the quasi-cylindrical approximation can only be trivial solution, i.e. strictly cylindrical flow. It is also shown that in subcritical range the iterative procedure accounting for non-linear effect of equations diverges necessarily. Projects Supported by the Science Fund of the Chinese Academy of Sciences.     

Effect of Volume Energy Supply on the Stability of a Subsonic Vortex Flow

Calculations of the stability of an axisymmetric vortex flow of viscous heat-conducting gas with volume energy supply are presented. The unperturbed axisymmetric vortex flow was found numerically using a quasi-cylindrical approximation of the Navier-Stokes equations under the assumption of constant peripheral-velocity circulation in the ambient co-current flow. The volume energy supply in the viscous vortex core was modeled by an additional source term in the energy equation. The stability characteristics of the viscous vortex flow in a longitudinal vortex with respect to both axisymmetric and non-axisymmetric three-dimensional waves traveling along the vortex axis and corresponding to both positive and negative values of the azimuthal wave number were found using the time-dependent formulation of the linear stability theory for compressible three-dimensional plane-parallel flows.     

管线振荡绕流对砂床的冲蚀

采用轻质模型砂在带砂槽的Ｕ型振荡水槽中对振荡流中管线下方的砂床冲蚀进行了实验研究,给出了管线下方砂床的平衡冲蚀深度随Ｋｃ数的变化规律以及发生冲蚀的临界ｅ／Ｄ和Ｋｃ的相关,并指出管线的存在使砂床开始形成砂波相应的振荡流临界振幅值下降．     

椭圆颗粒在剪切流中旋转特性的数值研究

研究颗粒在流体剪切作用下的运动特性是理解和预测颗粒悬浮流流动行为的关键.当流体的惯性不能忽略时,颗粒的运动往往变得非常复杂.本文采用格子Boltzmann方法对中等雷诺数下椭圆颗粒在剪切流中的旋转运动进行了模拟.首先,研究了雷诺数(0Re 170)的影响,结果表明当雷诺数低于临界值时,颗粒以周期性的方式旋转,角速度最小时对应的长轴方向随着雷诺数的增大而逐渐远离水平方向,而且这一倾角与雷诺数呈分段线性关系;当雷诺数大于临界值时,椭圆形颗粒最终保持静止状态,且静止时的转角与雷诺数呈幂函数关系,雷诺数越大,转角越小,椭圆的长轴越远离水平位置.其次,研究了椭圆颗粒的长短轴之比α(1α10)的影响,结果表明颗粒旋转的周期与α呈幂函数关系,α越大,颗粒旋转周期越小.此外,当α超过临界值时,颗粒也在水平位置附近保持静止状态,此时的转角与α也呈幂函数关系,α越大,转角越小.研究还发现,当雷诺数较大时椭圆颗粒在旋转过程中会产生过冲现象.     

Critical flow in a chemically reacting two-phase multicomponent mixture

A model that describes the critical flow of chemically reacting, two-phase, multicomponent mixtures in channels of constant cross section is discussed. As a consequence of an assumed interphase thermal and mechanical equilibrium the applicability of the model is restricted to situations where one phase is intimately mixed with the other, such that choking is determined by the sound speed in the homogeneous mixture. It is shown that under certain conditions the highly non-linear temperature dependency of the reaction rate promotes the possibility of a multiplicity of steady state solutions to the problem.     

On the existence of indeterminate solutions to the equations of motion under non-associated flow

Under certain conditions, an indeterminate solution exists to the equations of motion for dynamic elastic–plastic deformation of materials using constitutive laws based on non-associated flow that suggests that an initially unbounded dynamic perturbation in the stress can develop from a quiescent state on the yield surface. The existence of this indeterminate solution has been alleged to discourage use of non-associated flow rules for both dynamic and quasi-static analysis theoretically. It is shown in this paper that the indeterminate solution that may solve the equations of motion is intrinsically dynamic, and it determinately goes to zero in the quasi-static limit regardless of other indeterminate parameters. Consequently, the existence of this unstable dynamic solution has no impact on stability and use of non-associated flow rules for analysis of the quasi-static problem. More importantly, for dynamic applications, it is also shown that the indeterminate solution solves the equations of motion only if critical restrictions are applied to the constitutive equations such that the effective modulus during loading is constant and the direction of the perturbation is unidirectional over a finite time interval. It is shown that common components of the constitutive laws used in metal forming and deformation analysis are inconsistent with these restrictions. So, these common models can be generalized to include non-associated flow for analysis of the dynamic problem without concern that the solution will become indeterminate.     

泥石流的启动分析

分析了由于振动或冲刷等动载荷引起散体堆积物的液化或流态化而导致的泥石流．据此,认为这是在小坡角（１０°以内）条件下泥石流形成的主要原因．     

等速上仰翼型分离流动结构的研究

本文通过在翼型上游和翼表面边界层内放置产生氢气泡的铂丝的方法,清楚地显示了上仰翼型分离剪切层的结构。揭示了在不同的翼型转动角速度范围内,存在三种分离流结构。研究了失速涡,剪切涡及起动涡随时间的演变,它们之间的相互作用和转动角速度等参数的影响,分离剪切层的流动显示结果,结合翼型上气动力与流场中涡量矩的关系的理论,定性地解释了上仰翼型产生非定常高升力的原因。     

Short wave stability of homogeneous shear flows with variable topography

For the stability problem of homogeneous shear flows in sea straits of arbitrary cross section, a sufficient condition for stability is derived under the condition of inviscid flow. It is shown that there is a critical wave number, and if the wave number of a normal mode is greater than this critical wave number, the mode is stable.