一种模拟动边界绕流的锐利界面浸入边界法

为避免复杂贴体网格的更新和畸形对动边界流场计算效率、精度的影响,以充分掌握结构场的受力特性,采用一种改进的锐利界面（sharp-interface）浸入边界法模拟具有动边界绕流的流动问题。该方法将计算域中的固体视为流体,固体边界离散为若干个拉格朗日网格点,通过在界面单元处插值重构流动参数（速度）,将其直接作为流动求解器的边界条件,由此来反映固体边界的影响。即通过构造“虚拟点—受力点—垂足点”的计算结构,借助双线性插值得到虚拟点的速度,再通过强制满足固体边界的无滑移条件计算出受力点的速度,以此为边界条件,最终求解基于浸入边界法的耦合系统方程,实现复杂动边界的流动数值模拟。采用C++编写该浸入边界法的数值程序,以单圆柱绕流为验证算例,通过与文献和实验结果的对比,验证了该方法的准确性和可靠性。在此基础上,对主动运动椭圆柱绕流问题进行了精细计算,探讨了不同轴长比(A_R)、不同攻角($ \theta $)下的椭圆柱对尾涡结构分布特征和水力不稳定现象的影响。捕捉到了反对称S型、“P+S” Ⅰ型、“P+S” Ⅱ型尾涡脱落模态,漩涡强度、涡脱频率和升阻比随A_R和$ \theta $的变化规律,以及确定了升阻比临界攻角(25°)。

     

一种新的高功率微波折叠式谐振腔径向速调管振荡器

 提出一种高功率微波折叠式谐振腔径向速调管振荡器，用电子与电磁场相互作用的一维单电子模型分析了这种折叠式谐振腔径向速调管振荡器的特点。其特点为：径向尺寸小，起振电流低。用二维半PIC程序对折叠式谐振腔径向速调管振荡器进行数值模拟研究。结果表明，当二极管电压为380kV，电流为18kA时，输出微波功率峰值为1GW，主要微波频率为1.52GHz，输出微波为多频率成分微波。通过折叠式谐振腔的电子束得到很强的调制。     

Charge renormalization of cylinders and spheres: Ion size effects

The effect of the counterion size on the degree of counterion condensation onto a cylindrical macroion and a spherical one in the absence of salt is studied theoretically within a modified Poisson–Boltzmann approach. We find that excluded volume interactions reduce the degree of condensation. Using a simple variational free energy we show that this reduction can be attributed to an effective increase in the macroion size due to the contribution of the condensed counterions. We also find that for a charged cylinder, the reduction in charge renormalization vanishes at infinite dilution because of the extended nature of the condensed layer. In contrast, excluded volume interactions can reduce the degree of charge renormalization of a sphere even at high dilutions. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 3598–3615, 2004     

两个垂直圆柱在水波中的水动力相互作用

基于线性势流理论研究了两个垂直圆柱在水波中的水动力相互作用．两个圆柱中的一个固定在底部，另一个铰接在底部且可以在入射波方向以小振幅振动．本文研究了绕射波和辐射波，运用加法定理得到了每个圆柱表面速度势的简单的解析表达式，用级数形式显式表示了圆柱上的波浪激励力和力矩及振动圆柱的附加质量和辐射阻尼系数．级数的系数由代数方程组的解决定．给出了一些数值例子以说明诸如间距、圆柱的相对大小、入射角等各种参数对一阶力、定常二阶力、附加质量和辐射阻尼系数以及振动圆柱的响应等的影响．     

DC-electrokinetic motion of colloidal cylinder(s) in the vicinity of a conducting wall

The boundary effects on DC-electrokinetic behavior of colloidal cylinder(s) in the vicinity of a conducting wall is investigated through a computational model. The contribution of the hydrodynamic drag, gravity, electrokinetic (i.e., electrophoretic and dielectrophoretic), and colloidal forces (i.e., forces due to the electrical double layer and van der Waals interactions) are incorporated in the model. The contribution of electrokinetic and colloidal forces are included by introducing the resulting forces as an external force acting on the particle(s). The colloidal forces are implemented with the prescribed expressions from the literature, and the electrokinetic force is obtained by integrating the corresponding Maxwell stress tensor over the particles' surfaces. The electrokinetic slip-velocity together with the thin electrical double layer assumption is applied on the surfaces. The position and velocity of the particles and the resulting electric and flow fields are obtained and the physical insight for the behavior of the colloidal cylinders are discussed in conjunction with the experimental observations in the literature.     

Extremal problems on triangle areas in two and three dimensions

The study of extremal problems on triangle areas was initiated in a series of papers by Erd?s and Purdy in the early 1970s. In this paper we present new results on such problems, concerning the number of triangles of the same area that are spanned by finite point sets in the plane and in 3-space, and the number of distinct areas determined by the triangles.In the plane, our main result is an O(n44/19)=O(n^2.3158) upper bound on the number of unit-area triangles spanned by n points, which is the first breakthrough improving the classical bound of O(n7/3) from 1992. We also make progress in a number of important special cases. We show that: (i) For points in convex position, there exist n-element point sets that span Ω(nlogn) triangles of unit area. (ii) The number of triangles of minimum (nonzero) area determined by n points is at most ; there exist n-element point sets (for arbitrarily large n) that span (6/π²−o(1))n² minimum-area triangles. (iii) The number of acute triangles of minimum area determined by n points is O(n); this is asymptotically tight. (iv) For n points in convex position, the number of triangles of minimum area is O(n); this is asymptotically tight. (v) If no three points are allowed to be collinear, there are n-element point sets that span Ω(nlogn) minimum-area triangles (in contrast to (ii), where collinearities are allowed and a quadratic lower bound holds).In 3-space we prove an O(n17/7β(n))=O(n^2.4286) upper bound on the number of unit-area triangles spanned by n points, where β(n) is an extremely slowly growing function related to the inverse Ackermann function. The best previous bound, O(n8/3), is an old result of Erd?s and Purdy from 1971. We further show, for point sets in 3-space: (i) The number of minimum nonzero area triangles is at most n²+O(n), and this is worst-case optimal, up to a constant factor. (ii) There are n-element point sets that span Ω(n4/3) triangles of maximum area, all incident to a common point. In any n-element point set, the maximum number of maximum-area triangles incident to a common point is O(n4/3+ε), for any ε>0. (iii) Every set of n points, not all on a line, determines at least Ω(n2/3/β(n)) triangles of distinct areas, which share a common side.     

Wake structures and vortex-induced vibrations of a long flexible cylinder—Part 2: Drag coefficients and vortex modes

Drag coefficients and vortex structures in the wake of a vertical long flexible cylinder vibrating at low mode numbers are presented in this paper. A model with an external diameter of 16 mm and a total length of 1.5 m giving an aspect ratio of about 94 was used to perform more than 100 runs in which Reynolds numbers ranged between 1200 and 12 000. Only the lower 40% of its length was exposed to the water current in the flume and applied top tensions varied from 15 to 110 N giving fundamental natural frequencies in the range from 3 to 7.1 Hz. Reduced velocities based on the fundamental natural frequency up to 16 were reached. The mass ratio was 1.8 and the combined mass-damping parameter about 0.05. The largest drag coefficients were found related to the largest x–y synchronised motions. Digital particle image velocimetry was used to investigate the vortex structures in the wake of the cylinder model. Two modes of vortex shedding were observed, depending on the response branch and the position along the length of the model at which the interrogations were performed.     

平面剪切来流作用下串列布置三圆柱流致运动特性研究

基于四步半隐式特征线分裂算子有限元方法,对Re=100时,剪切来流作用下串列三圆柱体双自由度流致振动问题进行了数值计算. 首先,与现有文献结果进行对比验证该方法的正确性. 然后,着重分析剪切率、固有频率比和折减速度三个关键参数对串列三圆柱体结构流致动力响应及流场特性的影响. 数值计算结果表明:剪切率、固有频率比与折减速度对结构振幅和运动轨迹的影响较大. 随剪切率的增大,上游圆柱最大振幅的变化与单圆柱工况类似. 中下游圆柱最大振幅会增大且会出现双向共振现象,同时,发生共振响应区域会扩大. 随固有频率比的增大,上游圆柱顺流向锁定区间范围会减小,而中下游圆柱双向锁定区间会扩大. 另一方面,均匀来流作用下,结构运动轨迹以"8"字形和不规则形状为主. 随剪切率的增大,锁定区间内运动轨迹会由"8"字形转变为"雨滴"形. 在大剪切率与高固有频率比工况下,中游圆柱体结构运动轨迹会出现"双雨滴"形状. 最后,通过对流场特性的分析,揭示了剪切来流作用下串列三圆柱结构流致运动响应的内在机理.      

Hydrodynamic interaction between two vertical cylinders in water waves

I.IntroductionWiththeconstructionoflargeoffshorestructures-wavediffractionandradiationproblemscausedbyseveralbodiesbecomeincreasinglyimportant.LargeoffShoreplatforms,wave-powerextractiondevices,Iargestoragefacilitiesandoffshorefloatingairportsl']havebeenp…     

The cone phase of liquid crystals: Triangular lattice of double-tilt cylinders

We predict the existence of a new defect-lattice phase near the nematic-smectic-C(NC) transition. This tilt-analogue of the blue phase is a lattice of double-tilt cylinders which are disclination lines in the smectic layer normal as well as the c-field. We discuss the structure and stability of the cone phase. We suggest that many ‘nematics’ exhibiting short range layering and tilt order may in fact be in the molten cone phase, which is a line liquid.