A numerical study of three-dimensional liquid sloshing in tanks

A numerical model NEWTANK (Numerical Wave TANK) has been developed to study three-dimensional (3-D) non-linear liquid sloshing with broken free surfaces. The numerical model solves the spatially averaged Navier–Stokes equations, which are constructed on a non-inertial reference frame having arbitrary six degree-of-freedom (DOF) of motions, for two-phase flows. The large-eddy-simulation (LES) approach is adopted to model the turbulence effect by using the Smagorinsky sub-grid scale (SGS) closure model. The two-step projection method is employed in the numerical solutions, aided by the Bi-CGSTAB technique to solve the pressure Poisson equation for the filtered pressure field. The second-order accurate volume-of-fluid (VOF) method is used to track the distorted and broken free surface. Laboratory experiments are conducted for both 2-D and 3-D non-linear liquid sloshing in a rectangular tank. A linear analytical solution of 3-D liquid sloshing under the coupled surge and sway excitation is also developed in this study. The numerical model is first validated against the available analytical solution and experimental data for 2-D liquid sloshing of both inviscid and viscous fluids. The validation is further extended to 3-D liquid sloshing. The numerical results match with the analytical solution when the excitation amplitude is small. When the excitation amplitude is large where sloshing becomes highly non-linear, large discrepancies are developed between the numerical results and the analytical solutions, the former of which, however, agree well with the experimental data. Finally, as a demonstration, a violent liquid sloshing with broken free surfaces under six DOF excitations is simulated and discussed.     

介孔SiO2薄膜孔结构的慢正电子技术表征

通过蒸发诱导自组装技术制备了具有不同有序结构的介孔SiO₂薄膜,并采用同步辐射X射线反射率以及慢正电子束流技术对其进行表征.实验结果表明,随着旋涂速率的增加,介孔结构由三维立方向二维六角结构转变,同时平均孔隙率随转速增加而减小.利用各向同性无机孔收缩模型和Fourier变换红外光谱,探讨了薄膜结构和正电子湮没参数的内在联系. 关键词： 同步辐射 X射线反射率 Doppler展宽 正电子素飞行时间谱     

Numerical study of an ion-exchanged glass waveguide using both two-dimensional and three-dimensional models

A numerical study is carried out to compare the two-dimensional (2-D) case and three-dimensional (3-D) case for the modelling of an ion-exchanged glass waveguide. It is shown that different waveguide widths on the photomask correspond to different ion concentration distributions after an annealing process. A numerical example is presented of two waveguide sections with different widths indicates that due to the abrupt change of the waveguide width, a 3-D theoretical model is required for an accurate prediction of the parameters of ion-exchanged glass waveguides. The good agreement between the modelled and measured results proves that the developed 3-D numerical model can be beneficially utilized in the generalized design of optical devices based on ion-exchange waveguides.     

Fracture mechanics of propagating 3-D fatigue cracks with parametric dislocations

Abstract

Propagation of 3-D fatigue cracks is analyzed using a discrete dislocation representation of the crack opening displacement. Three dimensional cracks are represented with Volterra dislocation loops in equilibrium with the applied external load. The stress intensity factor (SIF) is calculated using the Peach–Koehler (PK) force acting on the crack tip dislocation loop. Loading mode decomposition of the SIF is achieved by selection of Burgers vector components to correspond to each fracture mode in the PK force calculations. The interaction between 3-D cracks and free surfaces is taken into account through application of the superposition principle. A boundary integral solution of an elasticity problem in a finite domain is superposed onto the elastic field solution of the discrete dislocation method in an infinite medium. The numerical accuracy of the SIF is ascertained by comparison with known analytical solution of a 3-D crack problem in pure mode I, and for mixed-mode loading. Finally, fatigue crack growth simulations are performed with the Paris law, showing that 3-D cracks do not propagate in a self-similar shape, but they re-configure as a result of their interaction with external boundaries. A specific numerical example of fatigue crack growth is presented to demonstrate the utility of the developed method for studies of 3-D crack growth during fatigue.     

高速离心压气机叶轮性能预测及流场分析

用时间推进法数值求解相对圆柱坐标系下的雷诺平均N-S方程,模拟高速离心叶轮内部的三维粘性流场.计算是在设计转速9个不同的流动工况下进行的.与实验结果比较了三个不同流量下的轮缘周向平均静压,对典型通道位置截面的子午速度分布与实验进行了定量比较,最后得到了转子在设计转速下的压比和等熵效率曲线.研究结果表明,本文发展的数值方法可较好的预测离心压气机叶轮的性能曲线.     

水平内微肋管局部凝结换热性能实验与数值求解

以Ｒ１１为工质，蒸汽凝结压力为１４７－２６５ｋＰａ，质量流率４ｔｙ１５３ｋｇ／ｍ２ｓ，本文对二维内微肋管和三维内微肋管水平管内凝结分层流区局部换热系数进行了系统的实验。与光管比较，二维内微肋管和三维内微肋管局部凝结换热系数分别提高了１４７－７８３％和２６１－９９７％。本文首次从理论分析入手建立了二维内微肋管水平管内凝结分层流区局部换热系数分析模型并进行了数值求解。计算结果与本文实验相当吻合。     

二维非定常Navier-Stokes方程精确的对偶变分原理族

本文采用基于待定函数的系统反推法首次成功地导出了二维非定常粘性流动Navier-Stokes方程的精确变分原理,并进而应用轮转变换导出其对偶变分原理,从而为粘流,特别是湍流的直接数值模拟(通过有限元法或变分差分解法等)或求近似解析解奠定了重要的和严密的理论基础.     

On the use of higher-order azimuthal schemes in 3-D PE modeling

In this paper, the issue of using higher-order finite difference schemes to handle the azimuthal derivative term in a three-dimensional parabolic equation based model is addressed.The three-dimensional penetrable wedge benchmark problem is chosen to illustrate the accuracy and efficiency of the proposed schemes. Both point source and modal initializations of the pressure field are considered. For each higher-order finite difference scheme used in azimuth, the convergence of the numerical solution with respect to the azimuth is investigated and the CPU times are given. Some comparisons with solutions obtained from another 3-D model [J. A. Fawcett, J. Acoust. Soc. Am. 93, 2627-2632 (1993)] are presented. The numerical simulations show that the use of a higher-order scheme in azimuth allows one to reduce the required number of points in the azimuthal direction while still obtaining accurate solutions. The higher-order schemes have approximately the same efficiency as a FFT-based approach (in fact, may outperform it slightly); however, the finite difference approach has the advantage that it may be more flexible than the FFT approach for various PE approximations.     

谐振管中混合工质的热声分离效应

本文在可压缩SIMPLE算法的基础上,基于先求解二维热声谐振腔内的速度场和温度场,然后利用求出的速度和温度值求解组分浓度场的思路,对混合工质的热声分离现象进行了数值研究。研究结果表明:在热声效应和热扩散效应共同作用下,声波能够将混合物中的两种气体分别泵向谐振腔的压力腹点和节点,使得混合气体在声波传播方向上逐渐分离。另外,通过考察5种不同管径下谐振管内径向浓度的变化规律,详细研究了浓度边界层在径向上的影响范围以及不同管径下的分离效率,并提出最佳管径应为16倍浓度渗透深度左右。     

考虑量子效应的短沟道MOSFET二维阈值电压模型

通过数值方法求解泊松方程和薛定谔方程的自洽解，提出了考虑量子效应时不同于经典理论的阈值条件，并得出了精确的一维阈值电压模型，模拟结果与实验十分符合.在此基础上，基于准二维泊松方程，通过考虑短沟道效应和量子效应，建立了较为精确的适合于小尺寸MOSFET的量子修正阈值电压模型,模型同样适用于(超)深亚微米高k栅介质MOSFET电特性的模拟和结构参数的设计. 关键词： 阈值电压 量子效应 短沟道效应 高k栅介质     

A numerical model for the 3-D non-linear vibrations of an N-string

We present a non-linear numerical model describing the 3-D vibrations of a planar network of N sections of string which are connected together at one common mobile extremity. We call such a network N-string. For small-amplitude vibrations perpendicular to the N-string equilibrium plane, the numerical results coincide with the already known analytical solutions of the linear model. This non-linear model makes it possible to describe small- or large-amplitude 3-D vibrations of any kind of N-string subjected to an initial plucking. The equations of motion are also presented in a dimensionless form and a vast dimensionless physical parameter space is identified. The numerical model can be extended to more complex networks of strings.     

Modeling of humps formation during deep-penetration laser welding

A 3-D transient modeling based on the numerical resolution of the fluid flow ant the heat transfer equations is developed for deep-penetration laser welding at high-welding speed regime, which results in the humping phenomenon. The physical mechanisms included in our model concern matter melting, vaporization inducing a recoil pressure, and resolidification. The implementation of developed procedures called User Defined Functions (UDFs) working interactively with the CFD Fluent code and a dynamic mesh method allowed us to treat the problem with specific and complex boundary conditions. The recoil pressure, fusion, resolidification, and the temperature dependence of the physical properties were thus taken into account. As a result, regular humps could be observed after resolidification on the weld seam.     

基于模糊理论的土体渗流固结参数识别

基于模糊数学理论,根据埋置在土体内部的超孔隙水压力观测数据,建立了土体固结参数模糊识别数值方法.根据观测点的超孔隙水压力观测数据的统计特性,得到观测数据的隶属度函数.基于待识别土体渗流固结参数的先验信息即约束条件,建立了模糊约束的隶属度函数,进而得到模糊化的目标函数.以信息论方法为基础,研究了观测信息的随机不确定性和荷载的随机不确定性对参数识别结果的影响.研究表明,基于信息论的模糊参数识别方法所得到的参数识别结果同样具有随机不确定性.     

An efficient method for the incompressible Navier–Stokes equations on irregular domains with no-slip boundary conditions,high order up to the boundary

Common efficient schemes for the incompressible Navier–Stokes equations, such as projection or fractional step methods, have limited temporal accuracy as a result of matrix splitting errors, or introduce errors near the domain boundaries (which destroy uniform convergence to the solution). In this paper we recast the incompressible (constant density) Navier–Stokes equations (with the velocity prescribed at the boundary) as an equivalent system, for the primary variables velocity and pressure. equation for the pressure. The key difference from the usual approaches occurs at the boundaries, where we use boundary conditions that unequivocally allow the pressure to be recovered from knowledge of the velocity at any fixed time. This avoids the common difficulty of an, apparently, over-determined Poisson problem. Since in this alternative formulation the pressure can be accurately and efficiently recovered from the velocity, the recast equations are ideal for numerical marching methods. The new system can be discretized using a variety of methods, including semi-implicit treatments of viscosity, and in principle to any desired order of accuracy. In this work we illustrate the approach with a 2-D second order finite difference scheme on a Cartesian grid, and devise an algorithm to solve the equations on domains with curved (non-conforming) boundaries, including a case with a non-trivial topology (a circular obstruction inside the domain). This algorithm achieves second order accuracy in the L^∞ norm, for both the velocity and the pressure. The scheme has a natural extension to 3-D.     

海洋声学中三维抛物方程非均匀网格模型

在海洋声学中,三维抛物方程模型可以有效考虑三维空间的声传播效应。然而,采用三维抛物方程模型分析三维空间内的声传播问题时,计算时间较长,并且需要消耗较大的计算机内存,因此给远距离声场的快速精确计算带来了很大困难。为此,将非均匀网格Galerkin离散化方法用于三维直角坐标系下的水声抛物方程模型中,深度算子和水平算子Galerkin离散方式由均匀网格变为非均匀网格。仿真结果表明,三维直角坐标系下非均匀网格离散的抛物方程模型,在保持计算精度、提高计算速度的同时,可以实现远距离声场的快速预报。另外,针对远距离局部海底地形与距离有关的三维声传播问题,给出了声场快速计算方法;在海底保持水平的区域,采用经典Kraken模型,重构抛物方程算法的初始场,随后依次递推求解地形与距离有关海底下的三维声场。采用改进模型,证明了远距离楔形波导声强增强效应。      

聚合物驱试井分析叠加原理适用性的探索

建立考虑聚合物剪切变稀特性的聚驱试井数学模型,基于矩形网格和井筒周围径向加密的复合网格。采用有限体积方法求得数值解,将数值解与叠加原理得到的注聚井停注压降进行对比。结果表明：叠加原理计算得到的注聚井关井井底压力值远低于数值解,说明叠加原理不能用于聚合物驱试井解释。在实测注聚井压降资料解释中,叠加原理得到的渗透率明显偏低,进一步证明了叠加原理不适合非线性聚驱试井模型,数值方法更加适用于聚驱试井解释。研究结论适用于类似的非线性试井问题。     

Electrochemical synthesis and lithium storage properties of three-dimensional porous Sn–Co alloy/CNT composite

Three-dimensional (3-D) porous copper with stable pore structure is prepared by electroless plating. 3-D porous Sn–Co alloy/carbon nanotube (CNT) composite is synthesized by electrodeposition using 3-D porous copper as the substrate. The scanning electron microscope results indicate that 3-D porous Sn–Co alloy/CNT composite contains a large amount of interconnected pores with the diameter size of ~3 μm. Upon cycling, the pore structure gradually disappears, but no serious exfoliation appears due to porous structure and reinforcement by CNT. The charge/discharge results demonstrate that the 3-D porous Sn–Co alloy/CNT composite electrode delivers high first reversible specific capacity of 490 mAh g^?1, and remains 441 mAh g^?1 after 60 cycles tested at different current densities. Even at the current density of 3,200 mA g^?1, the reversible specific capacity remains 319 mAh g^?1, which is 65 % of the first specific capacity cycled at the current density of 100 mA g^?1.     

大气压射频氧气放电特性的数值模拟研究

基于漂移扩散近似,对大气压下氧气射频放电产生的等离子体建立了一维流体模型,包括了电子、正离子和负离子的连续性方程、电子能量方程及泊松方程。采用有限差分法对所建立的模型进行了自洽的数值模拟,得到了相应的数值结果。通过对所得数值结果的分析,研究了大气压下氧气放电的基本特性。研究表明,大气压氧气放电中等离子体密度可达到10¹²cm^-3 ,电子温度约在1.23eV,放电中主要的负离子是O^-离子;随着电压峰值的增加,电子密度、电子温度都增加,但n_O-/n_e 的比率先增加到7.5%又后减小到5%,在电压峰值为700V 时达到最大。     

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Based on diffuse and drift assumption, a 1-D fluid model of atmospheric pressure oxygen RF discharge was developed. The model includes continuity equations for electrons, positive and negative ions, and energy equation, and Poisson equation for eclectic potential. The finite difference method was adopted to solve the model by numerical simulation. The simulation results show that the electron density and electron temperature were 10¹²cm^-3 and 1.23eV, respectively, and the main negative ion was O^- . As the peak of voltage increased, the electron density and electron temperature increased, however, the ratio of O^-/n_e had a maximum value at 700V.     

Numerical methods for solving one-dimensional cochlear models in the time domain

In this article, a robust numerical solution method for one-dimensional (1-D) cochlear models in the time domain is presented. The method has been designed particularly for models with a cochlear partition having nonlinear and active mechanical properties. The model equations are discretized with respect to the spatial variable by means of the principle of Galerkin to yield a system of ordinary differential equations in the time variable. To solve this system, several numerical integration methods concerning stability and computational performance are compared. The selected algorithm is based on a variable step size fourth-order Runge-Kutta scheme; it is shown to be both more stable and much more efficient than previously published numerical solution techniques.