Table of Content

18 August 2008, Volume 29 Issue 8

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Articles

Floquet instability of a large density ratio liquid-gas coaxial jet with periodic fluctuation

LI Zhen;HU Guo-hui;ZHOU Zhe-wei

2008, 29(8):  975-984 .  doi:10.1007/s10483-008-0801-y

Abstract ( 1547 )   PDF (256KB) ( 667 )  

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By numerical simulation of basic flow, this paper extends Floquet stability analysis of interfacial flow with periodic fluctuation into large density ratio range. Stability of a liquid aluminum jet in a coaxial nitrogen stream with velocity fluctuation is investigated by Chebyshev collocation method and the Floquet theory. Parametric resonance of the jet and the influences of different physical parameters on the instability are discussed. The results show qualitative agreement with the available experimental data.


Inflow boundary condition for DNS of turbulent boundary layers on supersonic blunt cones

DONG Ming;ZHOU heng

2008, 29(8):  985-998 .  doi:10.1007/s10483-008-0802-3

Abstract ( 1673 )   PDF (469KB) ( 795 )  

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For direct numerical simulation (DNS) of turbulent boundary layers, generation of an appropriate inflow condition needs to be considered. This paper proposes a method, with which the inflow condition for spatial-mode DNS of turbulent boundary layers on supersonic blunt cones with different Mach numbers, Reynolds numbers and wall temperature conditions can be generated. This is based only on a given instant flow field obtained by a temporal-mode DNS of a turbulent boundary layer on a flat plate. Effectiveness of the method is shown in three typical examples by comparing the results with those obtained by other methods.

Elasticity solutions for functionally graded plates in cylindrical bending

YANG Bo;DING Hao-jiang;CHEN Wei-qiu

2008, 29(8):  999-1004 .  doi:10.1007/s10483-008-0803-9

Abstract ( 1544 )   PDF (149KB) ( 944 )  

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The plate theory of functionally graded materials suggested by Mian and Spencer is extended to analyze the cylindrical bending problem of a functionally graded rectangular plate subject to uniform load. The expansion formula for displacements is adopted. While keeping the assumption that the material parameters can vary along the thickness direction in an arbitrary fashion, this paper considers orthotropic materials rather than isotropic materials. In addition, the traction-free condition on the top surface is replaced with the condition of uniform load applied on the top surface. The plate theory for the particular case of cylindrical bending is presented by considering an infinite extent in the y-direction. Effects of boundary conditions and material inhomogeneity on the static response of functionally graded plates are investigated through a numerical example.

Fracture analysis for torsion problems of a composite cylinder with curvilinear cracks

PAN Tian-wei;WANG Yin-bang

2008, 29(8):  1005-1012 .  doi:10.1007/s10483-008-0804-1

Abstract ( 1525 )   PDF (174KB) ( 694 )  

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The Saint-Venant torsion problems of a composite cylinder with curvilinear cracks were investigated. By considering the bimaterial interface as a boundary of the outer bar or inner one, the problem was reduced to the solution of boundary integral equations on the crack, external boundary and interface. Using the new boundary element method, some typical torsion problems of a composite cylinder involving a straight or kinked crack were calculated. The obtained results were compared with data in the literature to show validity and applicability of the present method.

Steering laws analysis of SGCMGs based on singular value decomposition theory

ZHANG Jing-rui

2008, 29(8):  1013-1021 .  doi:10.1007/s10483-008-0805-2

Abstract ( 1443 )   PDF (1057KB) ( 952 )  

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The steering laws of single gimbal control moment gyros (SGCMGs) are analyzed and compared in this paper for a spacecraft attitude control system based on singular value decomposition (SVD) theory. The mechanism of steering laws escaping singularity, especially how the steering laws affect singularity of gimbal configuration and the output torque error, is studied using SVD theory. Performance of various steering laws are analyzed and compared quantitatively by simulation. The obtained results can be used as a reference for designers.

Changes in the natural frequency of a ferromagnetic rod in a magnetic field due to magnetoelastic interaction

WANG Xing-zhe

2008, 29(8):  1023-1032 .  doi:10.1007/s10483-008-0806-x

Abstract ( 1662 )   PDF (140KB) ( 764 )  

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Based on the magnetoelastic generalized variational principle and Hamilton's principle, a dynamic theoretical model characterizing the magnetoelastic interaction of a soft ferromagnetic medium in an applied magnetic field is developed in this paper. From the variational manipulation of magnetic scale potential and elastic displacement, all the fundamental equations for the magnetic field and mechanical deformation, as well as the magnetic body force and magnetic traction for describing magnetoelastic interaction are derived. The theoretical model is applied to a ferromagnetic rod vibrating in an applied magnetic field using a perturbation technique and the Galerkin method. The results show that the magnetic field will change the natural frequencies of the ferromagnetic rod by causing a decrease with the bending motion along the applied magnetic field where the magnetoelastic buckling will take place, and by causing an increase when the bending motion of the rod is perpendicular to the field. The prediction by the mode presented in this paper qualitatively agrees with the natural frequency changes of the ferromagnetic rod observed in the experiment.

Enhancement of natural convection heat transfer from a fin by triangular perforation of bases parallel and toward its tip

Abdullah H. AlEssa

2008, 29(8):  1033-1044 .  doi:10.1007/s10483-008-0807-x

Abstract ( 1773 )   PDF (469KB) ( 2093 )  

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This study examines the heat transfer enhancement from a horizontal rectangular fin embedded with triangular perforations (their bases parallel and toward the fin tip) under natural convection. The fin's heat dissipation rate is compared to that of an equivalent solid one. The parameters considered are geometrical dimensions and thermal properties of the fin and the perforations. The gain in the heat transfer enhancement and the fin weight reduction due to the perforations are considered. The study shows that the heat dissipation from the perforated fin for a certain range of triangular perforation dimensions and spaces between perforations result in improvement in the heat transfer over the equivalent solid fin. The heat transfer enhancement of the perforated fin increases as the fin thermal conductivity and its thickness are increased.

Stress field near interface crack tip of double dissimilar orthotropic composite materials

LI Jun-lin;ZHANG Shao-qin;YANG Wei-yang

2008, 29(8):  1045-1051 .  doi:10.1007/s10483-008-0808-7

Abstract ( 1467 )   PDF (137KB) ( 734 )  

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In this paper, double dissimilar orthotropic composite materials interfacial crack is studied by constructing new stress functions and employing the method of composite material complex. When the characteristic equations' discriminates Δ1>0 and Δ2>0, the theoretical formula of the stress field and the displacement field near the mode I interface crack tip are derived, indicating that there is no oscillation and inter-embedding between the interfaces of the crack.

Magneto-elastic combination resonances analysis of current-conducting thin plate

HU Yu-da;LI Jing;

2008, 29(8):  1053-1066 .  doi:10.1007/s10483-008-0809-y

Abstract ( 1819 )   PDF (3491KB) ( 672 )  

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Based on the Maxwell equations, the nonlinear magneto-elastic vibration equations of a thin plate and the electrodynamic equations and expressions of electromagnetic forces are derived. In addition, the magneto-elastic combination resonances and stabilities of the thin beam-plate subjected to mechanical loadings in a constant transverse magnetic filed are studied. Using the Galerkin method, the corresponding nonlinear vibration differential equations are derived. The amplitude frequency response equation of the system in steady motion is obtained with the multiple scales method. The excitation condition of combination resonances is analyzed. Based on the Lyapunov stability theory, stabilities of steady solutions are analyzed, and critical conditions of stability are also obtained. By numerical calculation, curves of resonance-amplitudes changes with detuning parameters, excitation amplitudes and magnetic intensity in the first and the second order modality are obtained. Time history response plots, phase charts, the Poincare mapping charts and spectrum plots of vibrations are obtained. The effect of electro-magnetic and mechanical parameters for the stabilities of solutions and the bifurcation are further analyzed. Some complex dynamic performances such as period-doubling motion and quasi-period motion are discussed.

Stabilization meshless method for convection-dominated problems

ZHANG Xiao-hua;OUYANG Jie;WANG Jian-yu

2008, 29(8):  1067-1075 .  doi:10.1007/s10483-008-0810-y

Abstract ( 1563 )   PDF (1946KB) ( 893 )  

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It is well-known that the standard Galerkin is not ideally suited to deal with the spatial discretization of convection-dominated problems. In this paper, several techniques are proposed to overcome the instability issues in convection-dominated problems in the simulation with a meshless method. These stable techniques included nodal refinement, enlargement of the nodal influence domain, full upwind meshless technique and adaptive upwind meshless technique. Numerical results for sample problems show that these techniques are effective in solving convection-dominated problems, and the adaptive upwind meshless technique is the most effective method of all.

Two dimensional analytical solution for a partially vegetated compound channel flow

HUAI Wen-xin;XU Zhi-gang;YANG Zhong-hua;ZENG Yu-hong

2008, 29(8):  1077-1084 .  doi:10.1007/s10483-008-0811-y

Abstract ( 1448 )   PDF (197KB) ( 704 )  

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The theory of an eddy viscosity model is applied to the study of the flow in a compound channel which is partially vegetated. The governing equation is constituted by analyzing the longitudinal forces acting on the unit volume where the effect of the vegetation on the flow is considered as a drag force item. The compound channel is divided into 3 sub-regions in the transverse direction, and the coefficients in every region's differential equations were solved simultaneously. Thus, the analytical solution of the transverse distribution of the depth-averaged velocity for uniform flow in a partially vegetated compound channel was obtained. The results can be used to predict the transverse distribution of bed shear stress, which has an important effect on the transportation of sediment. By comparing the analytical results with the measured data, the analytical solution in this paper is shown to be sufficiently accurate to predict most hydraulic features for engineering design purposes.

Nonlinear coupled dynamics of liquid-filled spherical container in microgravity

YUE Bao-zeng

2008, 29(8):  1085-1092 .  doi:10.1007/s10483-008-0812-y

Abstract ( 1341 )   PDF (162KB) ( 709 )  

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Nonlinear coupled dynamics of a liquid-filled spherical container in microgravity are investigated. The governing equations of the low-gravity liquid sloshing in a convex axisymmetrical container subjected to lateral excitation is obtained by the variational principle and solved with a modal analysis method. The variational formulas are transformed into a frequency equation in the form of a standard eigenvalue problem by the Galerkin method, in which admissible functions for the velocity potential and the liquid free surface displacement are determined analytically in terms of the Gaussian hypergeometric series. The coupled dynamic equations of the liquid-filled container are derived using the Lagrange's method and are numerically solved. The time histories of the modal solutions are obtained in numerical simulations.

Influence of magnetic field and Hall currents on blood flow through a stenotic artery

Kh. S. Mekheimer;M. A. El Kot

2008, 29(8):  1093-1104 .  doi:10.1007/s10483-008-0813-x

Abstract ( 1576 )   PDF (447KB) ( 649 )  

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A micropolar model for blood simulating magnetohydrodynamic flow through a horizontally nonsymmetric but vertically symmetric artery with a mild stenosis is presented. To estimate the effect of the stenosis shape, a suitable geometry has been considered such that the horizontal shape of the stenosis can easily be changed just by varying a parameter referred to as the shape parameter. Flow parameters, such as velocity, the resistance to flow (the resistance impedance), the wall shear stress distribution in the stenotic region, and its magnitude at the maximum height of the stenosis (stenosis throat), have been computed for different shape parameters, the Hartmann number and the Hall parameter. This shows that the resistance to flow decreases with the increasing values of the parameter determining the stenosis shape and the Hall parameter, while it increases with the increasing Hartmann number. The wall shear stress and the shearing stress on the wall at the maximum height of the stenosis possess an inverse characteristic to the resistance to flow with respect to any given value of the Hartmann number and the Hall parameter. Finally, the effect of the Hartmann number and the Hall parameter on the horizontal velocity is examined.

Singular perturbation for the weakly nonlinear reaction diffusion equation with boundary perturbation

MO Jia-qi;

2008, 29(8):  1105-1110 .  doi:10.1007/s10483-008-0814-x

Abstract ( 1671 )   PDF (95KB) ( 848 )  

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In this paper, a class of nonlinear singularly perturbed initial boundary value problems for reaction diffusion equations with boundary perturbation are considered under suitable conditions. Firstly, by dint of the regular perturbation method, the outer solution of the original problem is obtained. Secondly, by using the stretched variable and the expansion theory of power series the initial layer of the solution is constructed. And then, by using the theory of differential inequalities, the asymptotic behavior of the solution for the initial boundary value problems is studied. Finally, using some relational inequalities the existence and uniqueness of solution for the original problem and the uniformly valid asymptotic estimation are discussed.