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2010年 第31卷 第5期    刊出日期：2010-05-20

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Articles

Effect of disturbances at inlet on hypersonic boundary layer transition on a blunt cone at small angle of attack

刘建新 罗纪生

2010, 31(5):  535-544.  doi:10.1007/s10483-010-0501-z

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To investigate the effect of different disturbances in the upstream, we present numerical simulation of transition for a hypersonic boundary layer on a 5-degree half-angle blunt cone in a freestream with Mach number 6 at 1-degree angle of attack. Evolution of small disturbances is simulated to compare with the linear stability theory (LST), indicating that LST can provide a good prediction on the growth rate of the disturbance. The effect of different disturbances on transition is investigated. Transition onset distributions along the azimuthal direction are obtained with two groups of disturbances of different frequencies. It shows that transition onset is relevant to frequencies and amplitudes of the disturbances at the inlet, and is decided by the amplitudes of most unstable waves at the inlet. According to the characteristics of environmental disturbances in most wind tunnels, we explain why transition occurs leeside-forward and windside-aft over a circular cone at an angle of attack. Moreover, the indentation phenomenon in the transition curve on the leeward is also revealed.

Systems of generalized quasi-variational inclusion (disclusion) problems in FC-spaces

丁协平

2010, 31(5):  545-556.  doi:10.1007/s10483-010-0502-x

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By applying an existence theorem of maximal elements of set-valued mappings in FC-spaces proposed by the author, some new existence theorems of solutions for systems of generalized quasi-variational inclusion (disclusion) problems are proved in FC-spaces without convexity structures. These results improve and generalize some results in recent publications from closed convex subsets of topological vector spaces to FC-spaces under weaker conditions.

Transient free convection flow of a viscoelastic fluid over vertical surface

H.M.DUWAIRI R.A.DAMSEH A.J.CHAMKHA M.S.ABDEL_JABER

2010, 31(5):  557-564.  doi:10.1007/s10483-010-0503-6

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In this paper, the viscoelsatic boundary layer flow and the heat transfer near a vertical isothermal impermeable surface and in a quiescent fluid are examined. The governing equations are formulated and solved numerically using MackCormak’s technique. The results show excellent agreement with previously published results by a comparision. Representative results for the velocity and temperature profiles, boundary layer thicknesses, Nusselt numbers, and local skin friction coefficients are shown graphically for different values of viscoelsatic parameters. In general, it is found that the velocities increase inside the hydrodynamic boundary layers and the temperatures decrease inside the thermal boundary layers for the viscoelsatic fluid as compared with the Newtonian fluid due to favorable tensile stresses. Consequently, the coefficients of friction and heat transfer enhance for higher viscoelsatic parameters.

Nonlinear convection in a non-Darcy porous medium

M.K.PARTHA

2010, 31(5):  565-574.  doi:10.1007/s10483-010-0504-6

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In this paper, the natural convection in a non-Darcy porous medium is studied using a temperature-concentration-dependent density relation. The effect of the two parameters responsible for the nonlinear convection is analyzed for different values of the inertial parameter, dispersion parameters, Rayleigh number, Lewis number, Soret number, and Dufour number. In the aiding buoyancy, the tangential velocity increases steeply with an increase in the nonlinear temperature parameter and the nonlinear concentration parameter when the inertial effect is zero. However, when the inertial effect is non-zero, the effect of the nonlinear temperature parameter and the nonlinear concentration parameter on the tangential velocity is marginal. The concentration distribution varies appreciably and spreads in different ranges for different values of the double dispersion parameters, the inertial effect parameter, and also for the parameters which control the nonlinear temperature and the nonlinear concentration. Heat and mass transfer varies extensively with an increase in the nonlinear temperature parameter and the nonlinear concentration parameter depending on Dacry and non-Darcy porous media. The variation in heat and mass transfer when all the effects, i.e., the inertial effect, double dispersion effects, and Soret and Dufour effects, are simultaneously zero and non-zero. The combined effects of the nonlinear temperature parameter, the nonlinear concentration parameter and buoyancy are analyzed. The effect of the nonlinear temperature parameter and the nonlinear concentration parameter and also the cross diffusion effects on heat and mass transfer are observed to be more in Darcy porous media compared with those in non- Darcy porous media. In the opposing buoyancy, the effect of the temperature parameter is to increase the heat and mass transfer rate, whereas that of the concentration parameter is to decrease.

Numerical discussions on complete empirical correlation in Langtry’s transition model

张晓东 高正红

2010, 31(5):  575-584.  doi:10.1007/s10483-010-0505-6

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Recently, introducing a transition predicting model into the Reynolds averaged Navier-Stokes (RANS) environment has been paid more and more attention. Langtry proposed a correlation-based transition model in 2006, which was built strictly on local variables. However, two core correlations in the model had not been published until 2009. In this paper, after considerable analyses and discussions of the mechanism of this transition model and a series of numerical validations in the skin friction coefficient of flat plate boundary layers, a new correlation based on free-stream turbulence intensity is developed, and the empirical correlation of the transition onset momentum thickness Reynold number aiming at the hypersonic transition is improved. Low-speed/transonic airfoils and a hypersonic double wedge flat are tested to prove the reliability and practicability of this correlation.

Thrust generation and wake structure of wiggling hydrofoil

何国毅 张曙光 张星

2010, 31(5):  585-592.  doi:10.1007/s10483-010-0506-9

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Marine animals and micro-machines often use wiggling motion to generate thrust. The wiggling motion can be modeled by a progressive wave where its wavelength describes the flexibility of wiggling animals. In the present study, an immersed boundary method is used to simulate the flows around the wiggling hydrofoil NACA 65-010 at low Reynolds numbers. One can find from the numerical simulations that the thrust generation is largely determined by the wavelength. The thrust coefficients decrease with the increasing wavelength while the propulsive efficiency reaches a maximum at a certain wavelength due to the viscous effects. The thrust generation is associated with two different flow patterns in the wake: the well-known reversed Karman vortex streets and the vortex dipoles. Both are jet-type flows where the thrust coefficients associated with the reversed Karman vortex streets are larger than the ones associated with the vortex diploes.

Mechanics of formation and rupture of human aneurysm

任九生 袁学刚

2010, 31(5):  593-604.  doi:10.1007/s10483-010-0507-9

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The mechanical response of the human arterial wall under the combined loading of inflation, axial extension, and torsion is examined within the framework of the large deformation hyper-elastic theory. The probability of the aneurysm formation is explained with the instability theory of structure, and the probability of its rupture is explained with the strength theory of material. Taking account of the residual stress and the smooth muscle activities, a two layer thick-walled circular cylindrical tube model with fiber-reinforced composite-based incompressible anisotropic hyper-elastic materials is employed to model the mechanical behavior of the arterial wall. The deformation curves and the stress distributions of the arterial wall are given under normal and abnormal conditions. The results of the deformation and the structure instability analysis show that the model can describe the uniform inflation deformation of the arterial wall under normal conditions, as well as formation and growth of an aneurysm under abnormal conditions such as the decreased stiffness of the elastic and collagen fibers. From the analysis of the stresses and the material strength, the rupture of an aneurysm may also be described by this model if the wall stress is larger than its strength.

Response of loose bonding on reflection and transmission of elastic waves at interface between elastic solid and micropolar porous cubic crystal

Rajneesh KUMAR Meenakshi PANCHAL

2010, 31(5):  605-616.  doi:10.1007/s10483-010-0508-x

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The problem of reflection and transmission of plane periodic waves incident on the interface between the loosely bonded elastic solid and micropolar porous cubic crystal half spaces is investigated. This is done by assuming that the interface behaves like a dislocation, which preserves the continuity of traction while allowing a finite amount of slip. Amplitude ratios of various reflected and transmitted waves have been depicted graphically. Some special cases of interest have been deduced from the present investigation.

Mechanical analysis of interaction between plant roots and rock and soil mass in slope vegetation

言志信 宋云 江平 王后裕

2010, 31(5):  617-622.  doi:10.1007/s10483-010-0509-9

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With the help of plant roots, slope vegetation makes the slope soil mass become a composite material of soil and roots, and thus enhances shear strength of the slope soil mass and stability of the slope. However, the related studies at present are still qualitative. In this paper, quantitative analysis of the interaction between roots and soil mass are made. By the analysis of the interaction between herbaceous plant roots including lateral roots of woody plants and rock and soil mass, a mechanical model of the interaction between frictional roots and soil is established, and its correctness is shown. A mechanical model of the interaction between anchorage root, namely, woody plant taproot, and soil is also established. The establishment of the models provides a useful means in quantitative analysis of the interaction between plant roots and soil, and has practical values.

Analysis of a quasistatic contact problem with adhesion and nonlocal friction for viscoelastic materials

Arezki TOUZALINE

2010, 31(5):  623-634.  doi:10.1007/s10483-010-0510-z

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A mathematical model is established to describe a contact problem between a deformable body and a foundation. The contact is bilateral and modelled with a nonlocal friction law, in which adhesion is taken into account. Evolution of the bonding field is described by a first-order differential equation. The materials behavior is modelled with a nonlinear viscoelastic constitutive law. A variational formulation of the mechanical problem is derived, and the existence and uniqueness of the weak solution can be proven if the coefficient of friction is sufficiently small. The proof is based on arguments of time-dependent variational inequalities, differential equations, and the Banach fixed-point theorem.

Quasi-Green’s function method for free vibration of simply-supported trapezoidal shallow spherical shell

李善倾 袁鸿

2010, 31(5):  635-642.  doi:10.1007/s10483-010-0511-7

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The idea of quasi-Green’s function method is clarified by considering a free vibration problem of the simply-supported trapezoidal shallow spherical shell. A quasi-Green’s function is established by using the fundamental solution and boundary equation of the problem. This function satisfies the homogeneous boundary condition of the problem. The mode shape differential equations of the free vibration problem of a simplysupported trapezoidal shallow spherical shell are reduced to two simultaneous Fredholm integral equations of the second kind by the Green formula. There are multiple choices for the normalized boundary equation. Based on a chosen normalized boundary equation, a new normalized boundary equation can be established such that the irregularity of the kernel of integral equations is overcome. Finally, natural frequency is obtained by the condition that there exists a nontrivial solution to the numerically discrete algebraic equations derived from the integral equations. Numerical results show high accuracy of the quasi-Green’s function method.

Parallel finite element algorithm based on full domain partition for stationary Stokes equations

尚月强 何银年

2010, 31(5):  643-650.  doi:10.1007/s10483-010-0512-x

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Based on the full domain partition, a parallel finite element algorithm for the stationary Stokes equations is proposed and analyzed. In this algorithm, each subproblem is defined in the entire domain. Majority of the degrees of freedom are associated with the relevant subdomain. Therefore, it can be solved in parallel with other subproblems using an existing sequential solver without extensive recoding. This allows the algorithm to be implemented easily with low communication costs. Numerical results are given showing the high efficiency of the parallel algorithm.

Local projection stabilized finite element method for Navier-Stokes equations

覃燕梅 冯民富 罗鲲 吴开腾

2010, 31(5):  651-664.  doi:10.1007/s10483-010-0513-z

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This paper extends the results of Matthies, Skrzypacz, and Tubiska for the Oseen problem to the Navier-Stokes problem. For the stationary incompressible Navier-Stokes equations, a local projection stabilized finite element scheme is proposed. The scheme overcomes convection domination and improves the restrictive inf-sup condition. It not only is a two-level approach but also is adaptive for pairs of spaces defined on the same mesh. Using the approximation and projection spaces defined on the same mesh, the scheme leads to much more compact stencils than other two-level approaches. On the same mesh, besides the class of local projection stabilization by enriching the approximation spaces, two new classes of local projection stabilization of the approximation spaces are derived, which do not need to be enriched by bubble functions. Based on a special interpolation, the stability and optimal prior error estimates are shown. Numerical results agree with some benchmark solutions and theoretical analysis very well.