球形纳米颗粒Brown凝并碰撞效率的新表达式

研究了邻苯二甲酸二辛酯纳米颗粒在Brown凝并过程中的碰撞效率．在考虑Stokes阻力、润滑力、van der Waals力和颗粒变形恢复力的情况下推导了一组碰撞方程,通过数值求解这组方程,得到了当颗粒半径从50 nm到500 nm变化时,颗粒碰撞效率和半径之间的关系,计算得到的结果和实验结果符合较好．计算结果表明,在颗粒半径为50 nm到500 nm的情况下,颗粒的碰撞效率随颗粒半径的增加而减小．基于计算结果,提出了颗粒碰撞效率的新表达式．     

平面射流中纳米粒子积聚的矩方法

应用大涡模拟方法求解平面湍射流场,矩方法求解纳米粒子的一般动力学方程．通过对每种情况3 000个时间步的平均,得到了Schmidt数和Damkohler数对纳米粒子动力学特性的影响．结果发现, 当气体参数不变时,Schmidt数的变化只对直径小于1 nm的颗粒数密度的分布产生影响．直径小的颗粒其颗粒数密度沿流动方向下降迅速,而具有大Schmidt数的颗粒,沿横向的分布较窄．较小的颗粒容易发生积聚和扩散,并且体积增长较快,因而颗粒多分散性较为明显．小的颗粒积聚时间尺度能增强颗粒的碰撞和积聚频率,导致颗粒尺寸迅速增大．Damkohler数越大,颗粒的多分散也越明显．     

平行双射流场纳米颗粒的形成与凝聚的研究

对平行双射流中H2SO4蒸气扩散进行了大涡模拟,给出了硫酸/水系统成核生成纳米颗粒及颗粒的凝聚过程中颗粒的分布特性,分析了燃料中硫的浓度、环境相对湿度以及射流Reynolds数对于颗粒浓度和粒径分布的影响．结果表明,硫酸/水系统会成核生成大量的纳米颗粒,在双管射流的中间和射流场周围,颗粒具有较高的浓度;颗粒的凝聚过程使颗粒的数量减少、直径变大;随着硫的浓度的增加,流场中的颗粒浓度有明显增加,而成核后形成的颗粒直径减小;环境湿度和Reynolds数的增大,有利于成核过程,因而导致形成更多的颗粒．     

双尺度二阶矩颗粒相湍流模型经验系数的影响

基于将颗粒脉动分成湍流引起的大尺度脉动和颗粒间碰撞产生的小尺度脉动的概念,建立了双尺度二阶矩两相湍流模型．用该模型对下行床内两相流动进行了数值模拟,颗粒体积浓度、平均速度的计算结果和实验数据吻合较好．分析了双尺度二阶矩两相湍流模型经验系数变化对预报结果的影响:在经验系数的一定变化范围内,预报结果并无明显的影响,但是变化范围增大,预报结果会产生较大变化．     

纳米流体在粘性耗散和Newton传热组合影响下的Sakiadis流动分析

就两类以水为基本流体的Newton纳米流体:内含金属颗粒铜(Cu),或者非金属颗粒二氧化钛(TiO2),研究粘性耗散和Newton传热对移动平板边界层流动的组合影响.利用相似变换,将偏微分的控制方程转换为常微分方程组,并用Runge-Kutta-Fehlberg法和打靶法,对其进行数值求解.由此得到结论,随着纳米颗粒体积分数和Newton传热的增加,移动平板表面的热交换率也增加,但是,随着Brinkmann数的增加,移动平板表面的热交换率反而减小.此外,纳米工作流体Cu-水的移动平板表面热交换率,高于纳米工作流体TiO2-水.     

三维矩形槽道中颗粒沉降的数值模拟

采用三维格子Boltzmann方法对矩形通道中的颗粒沉降进行了模拟研究．单颗粒沉降的模拟结果表明,颗粒最终的稳定沉降位置沿槽道中心线,不受颗粒初始位置和直径的影响．颗粒和壁面之间的两体相互效应可以用无因次沉降速度定量描述,无因次沉降速度的模拟结果和实验结果定量上吻合一致．模拟分析了双颗粒沉降的DKT（drafting, kissing and tumbling）过程,探讨了颗粒直径比以及壁面效应对DKT过程的影响．模拟发现当颗粒直径相同时,双颗粒的沉降过程为周期性的DKT过程,从而形成双螺旋形式的沉降轨迹,此螺旋沉降轨迹的频率和振幅受颗粒初始位置影响．从模拟结果中还得到颗粒群的最终稳定构型,并进行了构型对比分析．最后对包含49个颗粒的颗粒群沉降行为进行了模拟,说明多体相互作用在对称性的情况下可以简化．     

基于嵌套网格的环空流体内旋转杆柱与井筒碰撞特性研究北大核心CSCD

针对浸没在流体中杆管柱间相互接触问题,基于嵌套网格技术,该文建立了环空流体内旋转杆柱与井筒间碰撞的数值求解方法.将环空流体域分为相互嵌套的子区域:背景网格和组件网格,推导了各嵌套区域流场边界传递信息的插值计算公式,采用分域方法对环空流体域与杆柱固体域耦合进行求解.通过静止流体中球形颗粒与壁面正、斜碰撞实验对比,验证该文数值方法的正确性.研究了不同流体黏度、杆柱旋转速度条件下杆柱与井筒的碰撞特性,结果表明:1)杆柱与井筒碰撞的碰撞力、速度随黏度增大而降低,即杆柱与井筒碰撞的剧烈程度与流体黏度负相关;2)随着杆柱旋转速度增大,杆柱与井筒的碰撞力、速度也增大,即杆柱与井筒碰撞的剧烈程度与转速正相关.     

非线性耦合Roessler系统的相位同步化

讨论了具有1：1和1：2内共振非线性耦合系统的混沌相位同步．通过引入混沌运动的相位定义说明对于不同的内共振系统，在相对小的参数下两个子系统的平均频率差接近于0，即在弱相互作用下两个振子相位同步．随着耦合力的增加，平均频率差有波动，与1：2内共振情形相比，在主共振条件下两个子系统平均频率差的波动较小，即使在弱作用下也是如此．线性耦合力的增加增强了相位同步效应，而非线性耦合力的增加使得两个子系统由相位同步向不同步转化，且相位动力学与Liapunov的变化有关，这也可以通过扩散云图来证实．     

室内细颗粒物碰撞模型及碰撞结果讨论

为了研究室内细颗粒物凝并机理,基于统计平均及颗粒物随机运动的思想对室内细颗粒物碰壁数和细颗粒物之间发生对心碰撞的概率进行了总结计算,并对碰撞之后的结果进行了定量和定性的分析,得到了0.3μm的DOP颗粒的最终压缩变形与碰撞发生初始速度以及碰撞效率随粒径变化曲线.颗粒物碰撞后凝并的可能性会随着颗粒碰撞初速度的增加而降低,小粒径颗粒发生碰撞后凝并的可能性一般会大于大粒径颗粒,碰撞效率随粒径的增大而减小.     

剪切平行板间密集颗粒流的接触力分布及各向异性分析

研究了剪切平行板间密集颗粒流的接触力分布规律、接触力网络的各向异性、颗粒摩擦因数对宏观流变特性及细观力链分布的影响等．为了研究以上内容,应用计算机建立了离散元数值分析模型．数值分析结果表明,颗粒之间的接触力分布按幂函数规律变化;接触角分布服从指数函数规律,平均法向接触力随平均接触角任意上下振荡变化;波动速度大小为宏观流变顺畅与否的关键性评价指标,而在细观力链方面,当剪切平行板间颗粒流变不畅时会伴随着超强力链数目显著增加．     

A further discussion on basic equations for two-phase flow

The following points are argued: (i) there are two independent kinds of interaction on interfaces, i.e. the interaction between phases and the collision interaction, and the jump relations on interfaces can accordingly be resolved; (ii) the stress in a particle can also be divided into background stress and collision stress corresponding to the two kinds of interaction on interfaces respectively; (iii) the collision stress, in fact, has no jump on interface, so the averaged value of its derivative is equal to the derivative of its averaged value; (iv) the stress of solid phase in the basic equations for two-phase flow should include the collision stress, while the stress in the expression of the inter-phase force contains the background one only. Based on the arguments, the strict method for deriving the equations for two-phase flow developed by Drew, Ishii et al. is generalized to the dense two-phase flow, which involves the effect of collision stress.     

An estimate of the time of a direct-axis collision of a body of finite mass and a semiinfinite cylindrical shell with fluid

The problem of a direct-axis collision of a body affinite mass and a semi-infinite cylindrical shell with fluid is considered, and is solved using an analytic-numerical method, which is based on an application of the Laplace-Carson transform with its subsequent numerical inverse. An expression is found for the interaction force for the body and the hydro-elastic system, which allows us to determine the time of collision. Numerical results of calculations of the interaction force and the time of collision are given.Translated from Dinamicheskie Sistemy, No. 7, pp. 29–32, 1988.     

Critical solution for a Hill's type problem

We study the problem of two satellites attracted by a center of force. Assuming that the motion of the center of mass of the two satellites is a Keplerian circular orbit around the center of force, we regularize the collision between them using the Levi-Civita procedure. The existence of a constant of motion in the extended phase space allows us to study the stability of the solution, where the two satellites are tied together in their circular motion around the center of force. We call this solution the critical solution. A theorem of M. Kummer is applied to prove, in specific conditions, the existence of two one-parametric families of almost periodic orbits for the satellites motion that bifurcates from the critical solution.     

Maximin Approach to the Ship Collision Avoidance Problem via Multiple-Subarc Sequential Gradient-Restoration Algorithm

The ideal strategy for ship collision avoidance under emergency conditions is to maximize wrt the controls the timewise minimum distance between a host ship and an intruder ship. This is a maximin problem or Chebyshev problem of optimal control in which the performance index being maximinimized is the distance between the two ships. Based on the multiple-subarc sequential gradient-restoration algorithm, a new method for solving the maximin problem is developed.Key to the new method is the observation that, at the maximin point, the time derivative of the performance index must vanish. With the zero derivative condition being treated as an inner boundary condition, the maximin problem can be converted into a Bolza problem in which the performance index, evaluated at the inner boundary, is being maximized wrt the controls. In turn, the Bolza problem with an added inner boundary condition can be solved via the multiple-subarc sequential gradient-restoration algorithm (SGRA).The new method is applied to two cases of the collision avoidance problem: collision avoidance between two ships moving along the same rectilinear course and collision avoidance between two ships moving along orthogonal courses. For both cases, we are basically in the presence of a two-subarc problem, the first subarc corresponding to the avoidance phase of the maneuver and the second subarc corresponding to the recovery phase. For stiff systems, the robustness of the multiple-subarc SGRA can be enhanced via increase in the number of subarcs. For the ship collision avoidance problem, a modest increase in the number of subarcs from two to three (one subarc in the avoidance phase, two subarcs in the recovery phase) helps containing error propagation and achieving better convergence results.     

Robust a Simulation for Shallow Flows with Friction on Rough Topography

In this paper, we propose a robust finite volume scheme to numerically solve the shallow water equations on complex rough topography. The major difficulty of this problem is introduced by the stiff friction force term and the wet/dry interface tracking. An analytical integration method is presented for the friction force term to remove the stiffness. In the vicinity of wet/dry interface, the numerical stability can be attained by introducing an empirical parameter, the water depth tolerance, as extensively adopted in literatures. We propose a problem independent formulation for this parameter, which provides a stable scheme and preserves the overall truncation error of $\mathbb{O}$∆$x^3$. The method is applied to solve problems with complex rough topography, coupled with $h$-adaptive mesh techniques to demonstrate its robustness and efficiency.     

Regularizing transformations in problems on optimal multiimpulse collisions

A method of constructing the optimal impulse collision, with respect to the total characteristic velocity, of two mass points moving in a central force field along trajectories passing near an attracting center is given. Some numerical results are mentioned.Translated from Dinamicheskie Sistemy, No. 9, pp. 3–10, 1990.     

直立圆柱二阶波浪力解析解

大直径直立圆柱体上的二阶波浪力目前已有一些研究结果,但仍存在一些值得进一步探讨之处.这一方面在于二阶辐射条件还不甚清楚:另一方面在于已有的二阶力公式或是所含积分的收敛精度不易保证,或是表达式繁杂,不利于实际计算.本文在求解这一问题时,不是对二阶势提出辐射条件,而是对二阶势的周向富里叶分量提出辐射条件──Sommerfeld辐射条件.求解中,利用本文推导出的数学公式,简化了二阶自由面条件非齐次项的表达式,得到了形式简单,易于计算的二阶波浪力精确公式.二阶力计算结果与实验结果吻合良好.