旋涡动力学方程非定常动边界条件

详细讨论了旋涡动力学方程非定常动边界条件。给出了任意非定常运动边界上速度旋度的确定方法。并采用了“局部线性化及再校正”技术、时间滞后求解方法，求解每一时间步边界上速度旋度值。这样可以很大程度上节省计算时间。并讨论了数值实验结果，指出动边界问题的非线性特征，对这样复杂的非线性问题不宜作过份简化。

可动边界条件下含有具备二阶导数的二元函数的泛函变分

可动边界条件下含有具备二阶导数的二元函数的泛函变分具有重要的工程应用价值.根据变分原理建立了其泛函表达式,并推导出了该泛函的Euler-Ostrogradskii方程以及相应的横截条件.根据得到的微分方程和横截条件,进一步求解了均布载荷下圆形薄板与基底发生接触时的挠度以及临界载荷.这些分析结果对于工程设计,以及MEMS、生物的毛细黏附等有一定的参考价值.

可动边界高阶系统最优控制的必要条件研究

最优问题实际上是一个求极值问题,而变分法就是用来求泛函极值的一种方法。因此根据二阶导数在可动边界条件下的泛函极值定理,对高阶导数在可动边界条件下的泛函极值问题作进一步推广,从而给出了可动边界的高阶系统最优控制的必要条件及其证明。

速度进口边界条件对鼓泡床流动影响研究

进口边界条件是影响鼓泡流化床流体动力行为的重要因素之一。本文基于欧拉-欧拉双流体气固两相流模型,对具有中心射流进口的鼓泡流化床进行了数值模拟研究。分别采用脉动和定常进口气体速度边界条件,对鼓泡流化床内气泡的形成、长大、分离,气泡的大小进行了分析和研究。模拟结果与Kuipers等的实验结果进行了比较,研究结果表明考虑进口速度的脉动能够更加合理地预测和分析床内流体动力行为。

肺腺泡内流动与可入肺颗粒物沉积特性的数值模拟

研究肺腺泡区的三维流动特性、颗粒物沉积对于理解肺部的物质输运过程及治疗呼吸系统疾病具有重要的意义。本文建立了肺腺泡区的三维对称几何模型,并通过引入动肺泡壁条件反映肺部节律收缩/扩张的动力学机制,在此基础上对非稳态呼吸时肺腺泡区的气流特性以及颗粒物沉积特性进行模拟。结果表明:随着位置逐渐下移至末端,肺泡内的流线形态从循环状向放射状变化,且流线形态在呼与吸的半周期内保持不变,颗粒物的沉积率也随肺泡的位置下移而增加。此外,通过与既有二维固定壁模型对比表明,三维模型以及动肺泡壁条件对肺部颗粒物沉积具有重要影响,不可忽略。本文对三维肺腺泡流场和颗粒物沉积的特性研究,将为肺部物质输运以及相关领域的深入研究提供可靠的理论依据。

热连轧轧辊瞬态温度场研究

考虑水冷、空冷、轧辊与轧件接触热传导等动边界条件,采用有限差分法,建立了热连轧轧辊瞬态温度场变步长分析计算模型。该模型能实现轧辊温度场的动态分析和精确计算,预测轧制时以及终轧后空冷的轧辊瞬态温度场。试验和仿真结果表明,所建立的分析计算模型考虑因素全面、合理,计算精度较高,计算值与实测值吻合良好,真实地反映了轧辊的温度变化情况。

刚柔耦合柔性机械手二阶理论精准建模及实验研究

基于动边界条件和三种变形理论,选取Euler-Bernoulli梁模型,采用假想模态法并结合拉格朗日方程建立了双关节柔性机械手的精准动力学模型。根据理论计算仿真结果分析了动边界条件和变形理论对双关节柔性机械手理论建模精准性的影响,并通过实验对比双关节柔性机械手在不同动边界下理论模型和实验条件下的模态频率,验证了转动自由梁模型与实际工况更为贴近。

液滴形貌方程的能量描述

基于可动边界条件下的能量变分法,本文给出了一种关于任意液滴形貌的新的分析方法,推导出了液滴形貌的控制方程(Laplace方程)以及相应的横截性条件(Young方程).当液滴的尺寸远小于毛细长度时,这些方程退化为球缺形液滴的控制方程.通过求解液滴的形貌方程,发现液滴的形貌具有很强的尺寸效应,即液滴的体积越小,其形状越接近于球缺;体积越大则其形状越来越远离于球缺.这些分析结果对于微型传感器、超疏水表面、微流体器件等工业应用具有一定的参考价值,同时也可以对于我们加深可动边界条件以及液滴表面浸润性质的进一步理解.

SOLVABILITY RESULTS OF A CONDITIONAL INPUT-OUTPUT EQUATION BASED ON A TYPE OF NONLINEAR LEONTIEF MODEL

A class of nonlinear and continuous type Leontief model and its corresponding conditional input-output equation are introduced, and two basic problems under the so called positive or negative boundary assumption are presented. By approaches of nonlinear analysis some solvability results of this equation and continuous perturbation properties of the relative solution sets are obtained, and some economic significance are illustrated by the remark.

A nanofluid MHD flow with heat and mass transfers over a sheet by nonlinear boundary conditions: Heat and mass transfers enhancement

In this paper,we have numerically examined the steady boundary layer of a viscous incompressible nanofluid and its heat and mass transfers above a horizontal flat sheet.The boundary conditions considered were a nonlinear magnetic field,a nonlinear velocity and convection.Such nonlinearity in hydrodynamic and heat transfer boundary conditions and also in the magnetic field has not been addressed with the great details in the literature.In this investigation,both the Brownian motion and thermophoretic diffusion have been considered.A similarity solution is achieved and the resulting ordinary differential equations (nonlinear) are worked numerically out.Upon validation,the following hydrodynamic and heat and mass transfers parameters were found:the reduced Sherwood and Nusselt numbers,the reduced skin friction coefficient,and the temperature and nanoparticle volume fraction profiles.All these parameters are found affected by the Lewis,Biot and Prandtl numbers,the stretching,thermophoretic diffusion,Brownian motion and magnetic parameters.The detailed trends observed in this paper are carefully analyzed to provide useful design suggestions.

Numerical Simulation of the Flow around Two-dimensional Partially Cavitating Hydrofoils

In the present study, a new approach is applied to the cavity prediction for two-dimensional （2D） hydrofoils by the potential based boundary element method （BEM）. The boundary element method is treated with the source and doublet distributions on the panel surface and cavity surface by usethe of the Dirichlet type boundary conditions. An iterative solution approach is used to determine the cavity shape on partially cavitating hydrofoils. In the case of a specified cavitation number and cavity length, the iterative solution method proceeds by addition or subtraction of a displacement thickness on the cavity surface of the hydrofoil. The appropriate cavity shape is obtained by the dynamic boundary condition of the cavity surface and the kinematic boundary condition of the whole foil surface including the cavity. For a given cavitation number the cavity length of the 2D hydrofoil is determined according to the minimum error criterion among different cavity lengths, which satisfies the dynamic boundary condition on the cavity surface. The NACA 16006, NACA 16012 and NACA 16015 hydrofoil sections are investigated for two angles of attack. The results are compared with other potential based boundary element codes, the PCPAN and a commercial CFD code （FLUENT）. Consequently, it has been shown that the results obtained from the two dimensional approach are consistent with those obtained from the others.

The Influence of Edge Restraining Stiffness on the Transverse Vibrations of Rectangular Plate Structures

This paper presents an analytical study on the influence of edge restraining stiffness on the transverse vibrations of rectangular plate structure. An improved Fourier series method was employed to analyze the transverse vibration of plate structure with general elastically restrained boundary conditions. A linear combination of a double Fourier series and eight auxiliary terms was sought as the admissible function of the flexural displacement of the plate, each term being a combination of a polynomial function and a single cosine series expansion. The auxiliary terms were introduced to ensure and improve the smoothness of the original displacement function and its derivatives at the boundaries. Several numerical examples were given to demonstrate the validity and accuracy of the current solution. The influences of translational and rotational stiffness on the natural frequencies and mode shapes of plate were analyzed by numerical results. The results show that the translational stiffness has bigger influence on the natural frequencies than the rotational stiffness. It is generally well known that little change of the rotational stiffness has little influence on the mode shapes of plate. However, the current work shows that a very little change of rotational stiffness value may lead to a large change of the mode shapes of a square plate structure.

Elliptic Function Waves of Spinor Bose-Einstein Condensates in an Optical Lattice

An improved nonlinear Schrodinger equation different from usual one of spinor Bose-Einstein condensates （BECs） in an optical lattice are obtained by taking into account a nonlinear term in the equation of motion for probability amplitude of spins carefully. The elliptic function wave solutions of the model are found under specific boundary condition, for example, the two ends of the atomic chain are fixed. In the case of limit the elliptic function wave solutions are reduced into spin-wave-like or solitons.

Fully Nonlinear Simulation for Fluid/Structure Impact：A Review

This paper presents a review of the work on fluid/structure impact based on inviscid and imcompressible liquid and irrotational flow. The focus is on the velocity potential theory together with boundary element method （BEM）. Fully nonlinear boundary conditions are imposed on the unknown free surface and the wetted surface of the moving body. The review includes （1） vertical and oblique water entry of a body at constant or a prescribed varying speed, as well as free fall motion, （2） liquid droplets or column impact as well as wave impact on a body, （3） similarity solution of an expanding body. It covers two dimensional （2D）, axisymmetric and three dimensional （3D） cases. Key techniques used in the numerical simulation are outlined, including mesh generation on the multivalued free surface, the stretched coordinate system for expanding domain, the auxiliary function method for decoupling the mutual dependence of the pressure and the body motion, and treatment for the jet or the thin liquid film developed during impact.

The Impacts of Initial Perturbations on the Computational Stability of Nonlinear Evolution Equations

The impacts of initial perturbations on the computational stability of nonlinear evolution equations for non-conservative difference schemes and non-periodic boundary conditions are studied through theoretical analysis and numerical experiments for the case of onedimensional equations.The sensitivity of the difference scheme to initial values is further analyzed.The results show that the computational stability primarily depends on the form of the initial values if the difference scheme and boundary conditions are determined.Thus,the computational stability is sensitive to the initial perturbations.

Lateral static and dynamic characteristics of thin-walled box girder

To analyze the static and dynamic behaviors of the thin-walled box girder in its lateral webs in consideration of shear lag effect and shear deformation, an approach based on the minimum potential principle is introduced in this paper. Both static and dynamic response equations as well as the corresponding natural boundary conditions of the box girder are deduced. Meanwhile, three generalized displacement functions： w （x） , U（x） and O（x） are employed and their differences in the calculus of variation are quantitatively investigated. The comparison of finite shell element results with analytical results of calculation examples validates the feasibility of the proposed approach.

Convective heat and mass transfer effects in three-dimensional flow of Maxwell fluid over a stretching surface with heat source

Heat and mass transfer effects in three-dimensional flow of Maxwell fluid over a stretching surface were addressed.Analysis was performed in the presence of internal heat generation/absorption. Concentration and thermal buoyancy effects were accounted. Convective boundary conditions for heat and mass transfer analysis were explored. Series solutions of the resulting problem were developed. Effects of mixed convection, internal heat generation/absorption parameter and Biot numbers on the dimensionless velocity, temperature and concentration distributions were illustrated graphically. Numerical values of local Nusselt and Sherwood numbers were obtained and analyzed for all the physical parameters. It is found that both thermal and concentration boundary layer thicknesses are decreasing functions of stretching ratio. Variations of mixed convection parameter and concentration buoyancy parameter on the velocity profiles and associated boundary layer thicknesses are enhanced. Velocity profiles and temperature increase in the case of internal heat generation while they reduce for heat absorption. Heat transfer Biot number increases the thermal boundary layer thickness and temperature. Also concentration and its associated boundary layer are enhanced with an increase in mass transfer Biot number. The local Nusselt and Sherwood numbers have quite similar behaviors for increasing values of mixed convection parameter, concentration buoyancy parameter and Deborah number.

Navier’s slip condition on time dependent Darcy-Forchheimer nanofluid using spectral relaxation method

In industrial applications involving metal and polymer sheets, the flow situation is strongly unsteady and the sheet temperature is a mixture of prescribed surface temperature and heat flux. Further, a proper choice of cooling liquid is also an important component of the analysis to achieve better outputs. In this paper, we numerically investigate Darcy-Forchheimer nanoliquid flows past an unsteady stretching surface by incorporating various effects, such as the Brownian and thermophoresis effects, Navier’s slip condition and convective thermal boundary conditions. To solve the governing equations, using suitable similarity transformations, the nonlinear ordinary differential equations are derived and the resulting coupled momentum and energy equations are numerically solved using the spectral relaxation method. Through the systematically numerical investigation, the important physical parameters of the present model are analyzed. We find that the presence of unsteadiness parameter has significant effects on velocity, temperature, concentration fields, the associated heat and mass transport rates. Also, an increase in inertia coefficient and porosity parameter causes an increase in the velocity at the boundary.

Density Matrix for Mesoscopic Distributed Parameter Circuits

Under the Born-von-Karmann periodic boundary condition, we propose a quantization scheme for non-dissipative distributed parameter circuits (i.e. a uniform periodic transmission line). We find the unitary operator for diagonalizing the Hamiltonian of the uniform periodic transmission line. The unitary operator is expressed in a coordinate representation that brings convenience to deriving the density matrix rho(q,q',beta). The quantum fluctuations of charge and current at a definite temperature have been studied. It is shown that quantum fluctuations of distributed parameter circuits, which also have distributed properties, are related to both the circuit parameters and the positions and the mode of signals and temperature T. The higher the temperature is, the stronger quantum noise the circuit exhibits.

A Decay Result to an Elliptic Equation with Dynamical Boundary Condition

The decay estimations of the solution to an elliptic equation with dynamical boundary condition is considered.We proved that,for suitable initial datum,the energy of the solution decays "in time" exponentially if p=0,whereas the decay is polynomial order if p>0.