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2011年 第32卷 第7期    刊出日期：2011-07-03

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Articles

Thermocapillary migration and interaction of two nondeformable drops

尹兆华 常磊 胡文瑞 高鹏

2011, 32(7):  811-824.  doi:10.1007/s10483-011-1461-x

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A numerical study on the interaction of two spherical drops in the thermocapillary migration is presented in the microgravity environment. Finite-difference methods are adopted. The interfaces of the drops are captured by the front-tracking technique. It is found that the arrangement of the drops directly influences their migration and interaction, and the motion of one drop is mainly determined by the disturbed temperature field because of the existence of the other drop.

Lift enhancement of airfoil and tip flow control for wind turbine

白亚磊 马兴宇 明晓

2011, 32(7):  825-836.  doi:10.1007/s10483-011-1462-8

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Two techniques that improve the aerodynamic performance of wind turbine airfoils are described. The airfoil S809, designed specially for wind turbine blades, and the airfoil FX60-100, having a higher lift-drag ratio, are selected to verify the flow control techniques. The flow deflector, fixed at the leading edge, is employed to control the boundary layer separation on the airfoil at a high angle of attack. The multi-island genetic algorithm is used to optimize the parameters of the flow deflector. The results indicate that the flow deflector can suppress the flow separation, delay the stall, and enhance the lift. The characteristics of the blade tip vortex, the wake vortex, and the surface pressure distributions of the blades are analyzed. The vortex diffuser, set up at the blade tip, is employed to control the blade tip vortex. The results show that the vortex diffuser can increase the total pressure coefficient of the core of the vortex, decrease the strength of the blade tip vortex, lower the noise, and improve the efficiency of the blade.

Hydromagnetic flow through uniform channel bounded by porous media

K. RAMAKRISHNAN;K. SHAILENDHRA

2011, 32(7):  837-846.  doi:10.1007/s10483-011-1463-7

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The combined effects of the magnetic field, permeable walls, Darcy velocity, and slip parameter on the steady flow of a fluid in a channel of uniform width are studied. The fluid flowing in the channel is assumed to be homogeneous, incompressible, and Newtonian. Analytical solutions are constructed for the governing equations using Beavers-Joseph slip boundary conditions. Effects of the magnetic field, permeability, Darcy velocity, and slip parameter on the axial velocity, slip velocity, and shear stress are discussed in detail. It is shown that the Hartmann number, Darcy velocity, porous parameter, and slip parameter play a vital role in altering the flow and in turn the shear stress.

Reduced finite difference scheme and error estimates based on POD method for non-stationary Stokes equation

罗振东 欧秋兰 谢正辉

2011, 32(7):  847-858.  doi:10.1007/s10483-011-1464-9

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The proper orthogonal decomposition (POD) is a model reduction technique for the simulation of physical processes governed by partial differential equations (e.g., fluid flows). It has been successfully used in the reduced-order modeling of complex systems. In this paper, the applications of the POD method are extended, i.e., the POD method is applied to a classical finite difference (FD) scheme for the non-stationary Stokes equation with a real practical applied background. A reduced FD scheme is established with lower dimensions and sufficiently high accuracy, and the error estimates are provided between the reduced and the classical FD solutions. Some numerical examples illustrate that the numerical results are consistent with theoretical conclusions. Moreover, it is shown that the reduced FD scheme based on the POD method is feasible and efficient in solving the FD scheme for the non-stationary Stokes equation.

Homotopy analysis solution for micropolar fluid flow through porous channel with expanding or contracting walls of different permeabilities

司新毅 司新辉 郑连存 张欣欣

2011, 32(7):  859-874.  doi:10.1007/s10483-011-1465-6

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The flow of a micropolar fluid through a porous channel with expanding or contracting walls of different permeabilities is investigated. Two cases are considered, in which opposing walls undergo either uniform or non-uniform motion. In the first case, the homotopy analysis method (HAM) is used to obtain the expressions for the velocity and micro-rotation fields. Graphs are sketched for some parameters. The results show that the expansion ratio and the different permeabilities have important effects on the dynamic characteristics of the fluid. Following Xu’s model, in the second case which
is more general, the wall expansion ratio varies with time. Under this assumption, the governing equations are transformed into nonlinear partial differential equations that can also be solved analytically by the HAM. In the process, both algebraic and exponential models are considered to  describe the evolution of α(t) from the initial state α0 to the final state α1. As a result, the time-dependent solutions are found to approach the steady state very rapidly. The results show that the time-dependent variation of the wall expansion ratio can be ignored because of its limited effects.

Multi-front waves for extended form of modified Kadomtsev-Petviashvili equation

A. M. WAZWAZ

2011, 32(7):  875-880.  doi:10.1007/s10483-011-1466-6

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An extended form of the modified Kadomtsev-Petviashvili (mKP) equation is investigated. The simplified form of the Hirota bilinear method established by Hereman and Nuseir is employed. Multi-front wave solutions are formally derived to the extended mKP equation and the mKP equation. The results show that the extension terms do not kill the integrability of the mKP equation.

Wave propagation at interface of heat conducting micropolar solid and fluid media

R. KUMAR;M.KAUR;S. C. RAJVANSHI

2011, 32(7):  881-902.  doi:10.1007/s10483-011-1467-6

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The present investigation is concerned with the wave propagation at an interface of a micropolar generalized thermoelastic solid half space and a heat conducting micropolar fluid half space. Reflection and transmission phenomena of plane waves are investigated, which impinge obliquely at the plane interface between a micropolar generalized thermoelastic solid half space and a heat conducting micropolar fluid half space. The incident wave is assumed to be striking at the interface after propagating through the micropolar generalized thermoelastic solid. The amplitude ratios of various reflected and transmitted waves are obtained in a closed form. It is found that they are a function of the angle of incidence and frequency and are affected by the elastic properties of the media. Micropolarity and thermal relaxation effects are shown on the amplitude ratios for a specific model. The results of some earlier literatures are also deduced from the present investigation.

Nonlinear stability of timber column strengthened with fiber reinforced polymer

欧阳煜 杨骁 包若涵

2011, 32(7):  903-916.  doi:10.1007/s10483-011-1468-7

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By taking into account the effect of the bi-modulus for tension and compression of the fiber reinforced polymer (FRP) sheet in the reinforcement layer, a general mathematical model for the nonlinear bending of a slender timber beam strengthened with the FRP sheet is established under the  hypothesis of the large deflection deformation of the beam. Nonlinear governing equations of the second order effect of the beam bending are derived. The nonlinear stability of a simply-supported slender timber column strengthened with the FRP sheet is then investigated. An expression of the critical load of the simply-supported FRP-strengthened timber beam is obtained. The existence of postbuckling solution of the timber column is proved theoretically, and an asymptotic analytical solution of the postbuckling state in the vicinity of the critical load is obtained using the perturbation method. Parameters are studied showing that the FRP reinforcement layer has great influence on the critical load of the timber column, and has little influence on the dimensionless postbuckling state.

Mechanical performance and negative pressure instability for venous walls

任九生

2011, 32(7):  917-924.  doi:10.1007/s10483-011-1469-8

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Mechanical properties, such as the deformation and stress distributions for venous walls under the combined load of transmural pressure and axial stretch, are examined within the framework of nonlinear elasticity with one kind of hyper-elastic strain energy functions. The negative pressure instability problem of the venous wall is explained through energy comparison. First, the deformation equation of the venous wall under the combined loads is obtained with a thin-walled circular cylindrical tube. The deformation curves and the stress distributions for the venous wall are given under the normal transmural pressure, and the regulations are discussed. Then, the deformation curves of the venous wall under the negative transmural pressure or the internal pressure less than the external pressure are given. Finally, the negative pressure instability problem is discussed through energy comparison.

论文

Free vibration of functionally graded sandwich plates using four-variable refined plate theory

L. HADJI;H. A. ATMANE;A. TOUNSI;I. MECHAB;E.A.ADDABEDIA

2011, 32(7):  925-942.  doi:10.1007/s10483-011-1470-9

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This paper uses the four-variable refined plate theory (RPT) for the free vibration analysis of functionally graded material (FGM) sandwich rectangular plates. Unlike other theories, there are only four unknown functions involved, as compared to five in other shear deformation theories. The theory presented is variationally consistent and strongly similar to the classical plate theory in many aspects. It does not require the shear correction factor, and gives rise to the transverse shear stress variation so that the transverse shear stresses vary parabolically across the thickness to satisfy free
surface conditions for the shear stress. Two common types of FGM sandwich plates are considered, namely, the sandwich with the FGM facesheet and the homogeneous core and the sandwich with the homogeneous facesheet and the FGM core. The equation of motion for the FGM sandwich plates is obtained based on Hamilton’s principle. The closed form solutions are obtained by using the Navier technique. The fundamental frequencies are found by solving the eigenvalue problems. The validity of the theory is shown by comparing the present results with those of the classical, the first-order, and the other higher-order theories. The proposed theory is accurate and simple in solving the free vibration behavior of the FGM sandwich plates.

Articles

Ultraconvergence for averaging discontinuous finite elements and its applications in Hamiltonian system

李灿华 陈传淼

2011, 32(7):  943-956.  doi:10.1007/s10483-011-1471-8

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This paper discusses the k-degree averaging discontinuous finite element solution for the initial value problem of ordinary differential equations. When k is even, the averaging numerical flux (the average of left and right limits for the discontinuous finite element at nodes) has the optimal-order ultraconvergence 2k + 2. For nonlinear Hamiltonian systems (e.g., Schr¨odinger equation and Kepler system) with momentum conservation, the discontinuous finite element methods preserve momentum at nodes. These properties are confirmed by numerical experiments.