应用数学和力学

1998 Vol. 19, No. 8

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On the Mechanism of Turbulent Coherent Structure (Ⅲ)——A Statistical and Dynamical Model of Coherent Structure and Its Heat Transfer Mechanism

Lu Zhiming, Liu Yulu

1998, 19(8): 659-665.

Abstract(2656) PDF(983)

Abstract:
Following Tsai&Ma^[1] and Tsai & Liu^[2],a statistical and dynamical near-wall turbulent coherent structural model with separate consideration of two different portions:locally generated and up-stream transported large eddies has been established.With this model,heat transfer in a fully developed open channel in the absence of pressure gradient is numerically simulated.Database of fluctuations of velocity and temperature has also been set.Numerical analysis shows the existence of high-low temperature streak caused by near-wall coherent structure and its swing in the lateral direction. Numerical results are in accordance with the computations and experimental results of other researchers.

Backlund Transformation and Exact Solutions for Whitham-Broer-Kaup Equations in Shallow Water

Fan Engui, Zhang Hongqing

1998, 19(8): 667-670.

Abstract(2705) PDF(830)

Abstract:
By using a new method and Mathematica,the Backlund transformations for Whitham-Broer-Kaup equations(WBK)are derived.The connections between WBK equation,heat equation and Burgers equation are found,which are used to obtain three families of solutions for WBK equations, one of which is the family of solitary wave solutions.

Numerical Research on the Coherent Structure in the Viscoelastic Second-Order Mixing Layers

Yu Zhaosheng, Lin Jianzhong

1998, 19(8): 671-677.

Abstract(2473) PDF(469)

Abstract:
Numerical simulations have been performed in time-developing plane mixing layers of the viscoelastic second-order fluids with pseudo-spectral method.Roll-up,pairing and merging of large eddies were examined at high Reynolds numbers and low Deborah numbers.The effect of viscoelastics on the evolution of the large coherent structure was shown by making a comparison between thesecond-order and Newtonian fluids at the same Reynolds numbers.

An Implicit Solution of Bi-Penalty Approximation with Orthogonality Projection for the Numerical Simulation of Bingham Fluid Flow

Sha Desong, Guo Xinglin, Gu Yuanxian

1998, 19(8): 678-688.

Abstract(2259) PDF(492)

Abstract:
An implicit algorithm of Bi-penalty approximation with orthogonality projection for the numerical simulation of Bingham fluid flow problems is proposed in this paper.A Newton fluid flow with two kinds of artificial viscosit y subjected to the inequality constraint is introduced to approximate the Bingham fluid flow.This approach can effectively simulate the Bingham fluid flow with floating rigid cores or fixing rigid cores.

Study on the Generalized Prandtl-Reuss Constitutive Equation and the Corotational Rates of Stress Tensor

Shen Lijun, Pan Lizhou, He Fubao

1998, 19(8): 689-696.

Abstract(3122) PDF(856)

Abstract:
In this paper,the generalized Prandtl-Reuss(P-R)constitutive equations of elastic-plastic material in the presence of finite deformations through a new approach are studied.I t analyzes the generalized P-R equation based on t he material corotational rate and clarifies the puzzling problem of the simple shear stress oscillation mentioned in some literature.The paper proposes a modified relative rotational rate with which to constitute the objective rates of stress in the generalized P-R equation and concludes that the decomposition of total deformation rate into elastic and plastic parts is not necessary in developing the generalized P-R equations.Finally,the stresses of simple shear deformation are worked out.

Applications of Wavelet Galerkin FEM to Bending of Beam and Plate Structures

Zhou Youhe, Wang Jizeng, Zheng Xiaojing

1998, 19(8): 697-706.

Abstract(2598) PDF(682)

Abstract:
In this paper,an approach is proposed for taking calculations of high order differentials of scalng functions in wavelet theory in order to apply the wavelet Galerkin FEM to numerical analysis of hose boundary-value problems with order higher than 2.After that,it is realized that the wavelet alerkin FEM is used to solve mechanical problems such as bending of beams and plates.The numercal results show that this method has good precision.

Application of Convection-Diffusion Equation to the Analyses of Contamination between Batches in Multi-Products Pipeline Transport

Deng Songsheng, Pu Jianing

1998, 19(8): 707-714.

Abstract(2342) PDF(674)

Abstract:
Contamination between batches in multi-products pipeline transport is st udied.The influences of convection and diffusion on the contamination are sudied in detail.Diffusion equations,which are mainly controlled by convection,are developed under turbulent pipe flow.The diffusion equation is separated into a pure convection equation and a pure diffusion equat ion which are solved by characteristics method and finite difference method respectively to obtain numerical solutions.The results of numerical computation explain the forming and developing of contamination very well.

Convergent Families of Approximate Inertial Manifolds for Nonautonomous Evolution Equations

Wang Zongxing, Fan Xianling, Zhu Zhengyou

1998, 19(8): 715-724.

Abstract(1867) PDF(530)

Abstract:
In this paper,the long time behavior of nonautonomous infinite dimensional dynamical systems is studied.A family of convergent approximate inertial manifolds for a class of evolution equations has been constructed when the spectral gap condition is satisfied.

Conservation of Mass for a Particle Moving with High Velocity

Yang Wenxiong

1998, 19(8): 725-729.

Abstract(2412) PDF(649)

Abstract:
By using the revision of the momentum for a particle moving with high velocity and by investigating the famous Bucherer's experiment of an electron deflecting with high velocity in the electromagnetic fields in 1908,the paper determines that mass of the electron with high velocity is still to observe the law of coservation of mass.

MILU-CG Method and the Numerical Study on the Flow around a Rotating Circular Cylinder

Ling Guoping, Ling Guocan

1998, 19(8): 731-739.

Abstract(2745) PDF(526)

Abstract:
A hybrid finite difference method and vortex method(HDV),which is based on domain decomposition and proposed by the authors(1992),is improved by using a modified incomplete LU decomposition conjugate gradient method(MIL U-CG),and a high order implicit difference algorithm.The flow around a rotating circular cylinder at Reynolds number Re=1000,200 and the angular to rectilinear speed ratio A I(0.5,3.25)is studied numerically.The long-time full developed features about the variations of the vortex patterns in the wake,and drag,lift forces on the cylinder are given.The calculated streamline contours agreed well with the experimental visualized flow pictures. The existence of critical states and the vortex pat terns at the states are given for the first time.The maximum lift to drag force ratio can be obtained nearby the critical states.

An Analytical Solution of Rectangular Laminated Plates by Higher-Order Theory

Fan Yeli, Lin Fangyong

1998, 19(8): 741-752.

Abstract(2781) PDF(635)

Abstract:
On the basis of the Reddy.s higher-order theory of composites,this paper introduces a displacement function 5 into it and transforms its three differential equations for symmetric cross-ply composites into only one eight-order differential equation generated by the displacement-function.When a proper 5 is chosen,both solutions are obtained,namely,the Navier-type solution of simply supported rectangular laminated plates and the Levy-type solution with the boundary condition where two opposite edges are simply supported and remains are arbitrary.The numerical examples show that the present results concide well with the existing results in the references,thus validating that the present solving method is reliable.The higher-order theory of Reddy is simpler in calculation but has higher precision than the first-order shear deformation theory because the former has fewer unknows than the latter and requires no shear coefficients.