Natural convection heat transfer from a horizontal ice cylinder

Heat transfer characteristics passing through the maximum density point around a horizontal ice cylinder immersed in water was studied both theoretically and experimentally. For the sake of a precise comparison, the stagnation point Nusselt number was measured and results then compared with those of the numerical computations that were obtained by solving the full Navier-Stokes equations. A fairly good agreement was seen between the theory and the experiment.At about 6°C of water temperature where the stagnation Nusselt number takes its minimum value, the instability of the flow was observed. It was found that two different computer solutions exist, which shows unstable aspects corresponding to the experimental result.     

Heat transfer on a cylinder in accelerated slip flow

The axisymmetric laminar boundary layer flow along the entire length of a semi-infinite stationary cylinder under an accelerated free-stream is investigated. Considering flow at reduced dimensions, the boundary layer equations are developed with the conventional no-slip boundary condition for tangential velocity and temperature replaced by a linear slip-jump boundary condition. Asymptotic series solutions are obtained for the heat transfer coefficient in terms of the Nusselt number. These solutions correspond to prescribed values of the momentum and temperature slip coefficients and the index of acceleration. Heat transfer at both small and large axial distances is determined in the form of series solutions; whereas at intermediate distances, exact and interpolated numerical solutions are obtained. Using these results, the heat transfer along the entire cylinder wall is evaluated in terms of the parameters of acceleration and slip.     

进动圆筒内液体流动不稳定的非线性特征

在建立进动充液圆筒内液体偏差流动方程的基础上，结合液体惯性波和轴向二次流动线性解，通过对定常二次流动的线性稳定性分析，提出了函数空间表达的流动不稳定性非线性分岔分析方程. 对非惯性坐标系下液体流动的Navier-Stokes方程进行了数值求解，并对惯性波发生破裂(实验提供的3种主模态下得出的共振破裂现象)时的压力时间序列进行分析，得出了液体流动不稳定的基本非线性特征.     

Shallow flow simulation on dynamically adaptive cut cell quadtree grids

A computationally efficient, high‐resolution numerical model of shallow flow hydrodynamics is described, based on dynamically adaptive quadtree grids. The numerical model solves the two‐dimensional non‐linear shallow water equations by means of an explicit second‐order MUSCL‐Hancock Godunov‐type finite volume scheme. Interface fluxes are evaluated using an HLLC approximate Riemann solver. Cartesian cut cells are used to improve the fit to curved boundaries. A ghost‐cell immersed boundary method is used to update flow information in the smallest cut cells and overcome the time step restriction that would otherwise apply. The numerical model is validated through simulations of reflection of a surge wave at a wall, a low Froude number potential flow past a circular cylinder, and the shock‐like interaction between a bore and a circular cylinder. The computational efficiency is shown to be greatly improved compared with solutions on a uniform structured grid implemented with cut cells. Copyright © 2006 John Wiley & Sons, Ltd.     

An immersed boundary finite difference method for LES of flow around bluff shapes

A three‐dimensional numerical model using large eddy simulation (LES) technique and incorporating the immersed boundary (IMB) concept has been developed to compute flow around bluff shapes. A fractional step finite differences method with rectilinear non‐uniform collocated grid is employed to solve the governing equations. Bluff shapes are treated in the IMB method by introducing artificial force terms into the momentum equations. Second‐order accurate interpolation schemes for all sorts of grid points adjacent to the immersed boundary have been developed to determine the velocities and pressure at these points. To enforce continuity, the methods of imposition of pressure boundary condition and addition of mass source/sink terms are tested. It has been found that imposing suitable pressure boundary condition (zero normal gradient) can effectively reproduce the correct pressure distribution and enforce mass conservation around a bluff shape. The present model has been verified and applied to simulate flow around bluff shapes: (1) a square cylinder and (2) the Tsing Ma suspension bridge deck section model. Complex flow phenomena such as flow separation and vortex shedding are reproduced and the drag coefficient, lift coefficient, and pressure coefficient are calculated and analyzed. Good agreement between the numerical results and the experimental data are obtained. The model is proven to be an efficient tool for flow simulation around bluff bodies in time varying flows. Copyright © 2004 John Wiley & Sons, Ltd.     

层状地基中单桩扭转振动特性分析

采用积分变换和Muki的方法求解了层状地基中单桩的扭转振动问题.在分析过程中,首先对基本控制方程进行Hankel变换,建立了单层地基的初参数解答和刚度矩阵,得到层状地基的递推矩阵;然后利用递推矩阵、边界条件和桩-土变形协调条件建立了层状地基中单桩扭转振动问题的基本积分方程并进行数值求解.文末数值算例给出了退化的层状地基中刚性单桩的扭转变形,其结果与已有经典解答吻合良好.同时,并研究了两层地基中单桩的扭转动力响应,分析了桩-土参数对动力响应的影响,所得结论对工程实践和桩基扭转波检测有一定的指导意义.     

Method of fundamental solutions for multidimensional Stokes equations by the dual-potential formulation

A simple and accurate boundary-type meshless method of fundamental solutions (MFS) is applied to solve both 2D and 3D Stokes flows based on the dual-potential formulation of velocity potential and stream function vector. Using the dual-potential concept, the solutions of both 2D and 3D Stokes flows are obtained by combining the much simpler fundamental solutions of Laplace (potential) and bi-harmonic equations without using the complicated singular fundamental solutions such as Stokeslets and their derivatives as well as source doublet hypersingularity. The developed algorithm is used to test five numerical experiments for 2D flows: (1) circular cavity, (2) wave-shaped bottom cavity and (3) circular cavity with eccentric rotating cylinder; and for 3D flows: (4) a uniform flow passing a sphere and (5) a uniform flow passing a pair of spheres. Good results are obtained as comparing with solutions of analytical and numerical methods such as FEM, BEM and other meshfree schemes.     

A new immersed boundary method for compressible Navier–Stokes equations

This paper presents an immersed boundary method for compressible Navier–Stokes equations in irregular domains, based on a local radial basis function approximation. This approach allows one to define a reconstruction of the radial basis functions on each irregular interface cell to treat both the Dirichlet and Neumann boundary conditions accurately on the immersed interfaces. Several numerical examples, including problems with available analytical solutions and the well-documented flow past an airfoil, are presented to test the proposed method. The numerical results demonstrate that the proposed method provides accurate solutions for viscous compressible flows.     

Electroelastic field of a piezoelectric annular finite cylinder

This paper presents a theoretical study of a piezoelectric annular cylinder under axisymmteric electromechanical loading. The piezoelectric material is assumed to be transversely isotropic and the general solutions of the governing equations are obtained in terms of a Fourier–Bessel series containing Bessel functions of the first and second kind. The boundary-value problems for vertical pressure and an electric charge loading applied to the ends of an annular cylinder are solved by expanding the applied loading in terms of a Fourier–Bessel series. Selected numerical results for the electroelastic field of an annular cylinder are presented for different aspect ratios of a cylinder and material properties.     

Immersed Boundaries in Large Eddy Simulation of Compressible Flows

Methods to immerse walls in a structured mesh are examined in the context of fully compressible solutions of the Navier–Stokes equations. The ghost cell approach is tested along with compressible conservative immersed boundaries in canonical flow configurations; the reflexion of pressure waves on walls arbitrarily inclined on a cartesian mesh is studied, and mass conservation issues examined in both a channel flow inclined at various angles and flow past a cylinder. Then, results from Large Eddy Simulation of a flow past a rectangular cylinder and a transonic cavity flow are compared against experiments, using either a multi-block mesh conforming to the wall or immersed boundaries. Different strategies to account for unresolved transport by velocity fluctuations in LES are also compared. It is found that immersed boundaries allow for reproducing most of the coupling between flow instabilities and pressure-signal properties observed in the transonic cavity flow. To conclude, the complex geometry of a trapped vortex combustor, including a cavity, is simulated and results compared against experiments.     

Wave propagation in a transversely isotropic solid cylinder of arbitrary cross-sections immersed in fluid

The wave propagation in an infinite, transversely isotropic solid cylinder of arbitrary cross-section immersed in fluid is studied using the Fourier expansion collocation method, within the framework of the linearized, three-dimensional theory of elasticity. The equations of motion of solid and fluid are respectively formulated using the constitutive equations of a transversely isotropic cylinder and the constitutive equation of an inviscid fluid. Three displacement potential functions are introduced to uncouple the equations of motion along the radial, circumferential and axial directions. The frequency equations of longitudinal and flexural (symmetric and antisymmetric) modes are analyzed numerically for an elliptic and cardioidal cross-sectional transversely isotropic solid cylinder of arbitrary cross-section immersed in fluid. The computed non-dimensional wavenumbers are presented in the form of dispersion curves for the material zinc. The general theory can be used to study any kind of cylinder with proper geometric relations.     

Analysis of the thermal stress behaviour of functionally graded hollow circular cylinders

This paper presents an analysis of the thermomechanical behavior of hollow circular cylinders of functionally graded material (FGM). The solutions are obtained by a novel limiting process that employs the solutions of homogeneous hollow circular cylinders, with no recourse to the basic theory or the equations of non-homogeneous thermoelasticity. Several numerical cases are studied, and conclusions are drawn regarding the general properties of thermal stresses in the FGM cylinder. We conclude that thermal stresses necessarily occur in the FGM cylinder, except in the trivial case of zero temperature. While heat resistance may be improved by sagaciously designing the material composition, careful attention must be paid to the fact that thermal stresses in the FGM cylinder are governed by more factors than are its homogeneous counterparts. The results that are presented here will serve as benchmarks for future related work.     

Orbital flow past a cylinder: A numerical approach

Orbital flow past a cylinder is relevant to offshore structures. The numerical scheme presented here is based on a finite-difference solution of the Navier–Stokes equations. Alternating-directional-implicit (ADI) and successive-over-relaxation (SOR) techniques are used to solve the vorticity-transport and stream-function equations. Theoretical simulations to low Reynolds number flows (up to 1000) are discussed for cases involving uniform flow past stationary and rotating cylinders and orbital flow past a cylinder. The separation points for cylinders that are rotating or immersed in an orbital flow are deduced from velocity profiles through the boundary layer using a hybrid mesh scheme. During the initial development of orbital flow surface vorticity on the impulsively started cylinder dominates the flow. A vortex then detaches from behind the cylinder and establishes the flow pattern of the orbit. After some time a collection of vortices circles the orbit and distorts its shape a great deal. These vortices gradually spiral outward as others detach from the cylinder and join the orbital path.     

基于群桩振动方程组的群桩基础阻抗函数求解及比较

本文首先在位移场叠加的基础上,对经典的单桩振动方程进行了修正得到群桩振动方程组;然后根据群桩振动方程组的近似求解,导出了群桩阻抗函数求解的常用方法一群桩阻抗方程方法。本文中给出的群桩阻抗方程方法在具体的表达形式上与常见的阻抗方程计算方法略有差别;而后根据振动方程组系数矩阵在复空间为正规阵的性质,提出了该四阶耦合微分方程组解耦求解的详细步骤,在直接求解微分方程组的基础上给出了群桩基础阻抗计算的一种新方法。与阻抗方程方法相比较,新方法未采用柔度因子来考虑桩与桩之间的相互影响,而是通过耦合的运动方程组对桩与桩之间的相互作用作了新的表述,并且近似地考虑了屏蔽效应。本文最后给出了上述两种计算方法的数值算例。     

A Pressure Field in an Acoustic Medium Containing a Cylindrical Solid and a Sphere Oscillating in a Predetermined Manner

A problem on the interaction of a spherical body oscillating in a predetermined fashion and a rigid cylinder is formulated. The bodies do not intersect, are immersed into an ideal compressible liquid, and their centers are in one plane. The solution is based on the possibility of representing the partial solution of the Helmholtz equation, written in cylindrical coordinates, in terms of partial solutions in spherical coordinates, and vice versa. An infinite system of linear algebraic equations is obtained by satisfying the boundary conditions on the sphere and cylinder surfaces. The system is intended for determining the coefficients of the expansion of the velocity potential into a series in terms of spherical and trigonometric functions. The system obtained is solved by the reduction method. The appropriateness of this method is substantiated. The hydrodynamic characteristics of the liquid surrounding the spherical and cylindrical bodies are determined. A comparison is made with the problem on a sphere oscillating in an infinite incompressible liquid that contains also a cylinder and in a compressible liquid that contains nothing more. Two types of motion of the sphere — pulsation and oscillation — are considered     

SIMPLIFIED CALCULATION METHOD FOR DEALING WITH ADDED WATER MASS FOR IMMERSED CANTILEVER CYLINDER 1)

采用解析方法研究了部分浸入水中的圆形悬臂柱的附连水质量分布,给出了无量纲的质量分布系数,通过对质量分布系数的数值拟合分析,附连水质量效应可最终表达为结构的等效质量密度,在振动计算中只需将浸入水中的悬臂柱密度用等效密度替代即可。采用试验方法测量了部分浸入水中的悬臂柱湿频率,简化附连水质量方法计算的湿频率结果与试验测量值吻合很好,表明本文的附连水质量简化公式可很好地描述附连水的质量效应。     

时变元法及其应用

研究了一类特殊的变形体－增长体的粘弹性力学问题，建立了基于移动网格的时变元模型及其数值方法。作为算例，分别计算了高度随时间变化的柱体以及内径随时间变化的厚壁筒的应力应变历程。     

表面堆载作用下群桩负摩擦研究

利用Biot固结理论和积分方程方法研究了表面有堆载的群桩负摩擦问题。根据基本解得出了群桩在圆形均布载荷作用下在时间域内的第二类Fredholm积分方程组。运用Laplace变换对上述积分方程组进行简化，求解上述积分方程组并进行相应的数值逆变换就可得出群桩在表面圆形均布载荷作用下的变形、轴力、孔压和桩侧摩阻力随时间的变化情况。     

Fine structure of unsteady diffusion-induced flow over a fixed plate

The program for calculating the fields of characteristic physical quantities in a twodimensional diffusion-induced flow over an impermeable strip immersed in a continuously stratified fluid at rest is developed on the basis of the fundamental system of equations. The flow patterns are presented with a high spatial resolution, the complicated structure of compensation flows near the strip edges is studied, and the ranges of applicability of the previously obtained analytical (asymptotic) solutions are determined. The calculated results are in agreement with the data of high-resolution shadow visualization of streaky structures adjoining the edges of the fixed strip immersed in a stratified fluid.     

轴对称压电-压磁圆柱夹层结构的圣维南端部效应

研究了半无限长轴对称压电-压磁夹层结构的圆柱体圣维南端部效应的衰减问题。圆柱的端部承受自平衡磁电弹载荷;圆柱的内外表面为机械自由表面,但承受不同的电磁边界条件,即电学短路或电学开路及磁学短路或磁学开路边界条件。基于横贯各向同性压电或压磁材料在轴对称圆柱坐标系下的本构方程,推导了关于衰减率的特征方程并求得问题的数值解。结果表明,边界条件、内外径之比、材料厚度比对结构的衰减率都有显著的影响。