应用数学和力学

2010 Vol. 31, No. 5

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Effect of Disturbances at Inlet on Hypersonic Boundary Layer Transition on a Blunt Cone at Small Angle of Attack

LIU Jian-xin, LUO Ji-sheng

2010, 31(5): 505-515. doi: 10.3879/j.issn.1000-0887.2010.05.001

Abstract(1825) PDF(801)

Abstract:
Toinvestigate the effect of different disturbances in the up stream, we present numerical smiulation of transition for a hypersonic boundary layer on a 5-degree half-angle bluntcone in a freestream with Math number 6 at 1-degree angle of attack. Evolution of small disturbances is simulated to compare with linear stability theory(LST), indicating that LST can provide a good prediction on the growth rate of the disturbance. The effect of difference disturbances on transition was inves tigated. Transition on set distributions along the azmiuthal direction are obtained with two groups of disturbances of different frequencies. It shows that transition on set is relevant to the frequencies and amplitudes of the disturbances at the in let, and is decided by the amplitudes of themost unstable wave at the in let. According to the characters of the environmental disturbances in most wind tunnels, we explain why transition occurs leeside-forward and windside-aftovera circular coneatanangle of attack are explained. Moreover, the indentation phenom enon in transition curve on the leeward is also unpuzzled.

Systems of Generalized Quasi-Variational Inclusion (Disclusion) Problems in FC-Spaces

DING Xie-ping

2010, 31(5): 516-525. doi: 10.3879/j.issn.1000-0887.2010.05.002

Abstract(1348) PDF(754)

Abstract:
By applying an existence theorem of maximal elements of setvalued mappings in FC-spaces due to the author, some new existence theorems of solutions for systems of genera-lized quasivariational in clusion(disclusion) problems were proved in FC-spaces without convexity structure. These results miprove and generalize some results in recent literature from closed convex subsets of topological vector spaces to FC-spaces under weaker conditions.

Transient Free Convection Flow of a Visco-Elastic Fluid Over a Vertical Surface

H. M. Duwairi, Rebhi. A. Damseh, A. J. Chamkha, Mu'tasim S. Abdel-Jaber

2010, 31(5): 526-532. doi: 10.3879/j.issn.1000-0887.2010.05.003

Abstract(1801) PDF(645)

Abstract:
The viscoelsatic boundary layer flow and heat transfer near a verticaliso therm al impermeable surface and in a quiescent fluid were examined. The governing equations were formulated and solved numerically using the MackCormak's technique. A comparison with previously published results on special cases of the problem shows excellent agreement. Represen tative results for the velocity and temperature profiles, boundary layer thicknesses, Nusselt numbers and localsk in friction coefficients are shown graphically for different values of viscoelsatic parameter. Ingeneral, it is found that the velocities in creaseinside the hydrodynamic boundary layers and the temperatures decrease in side the thermal boundary layers for the viscoe lsatic fluid as compared to the Newtonian fluid due to favorable tensile stresses. Consequently the coefficient of friction and heat transfer are enhanced for higher viscoe lsatic parameter.

Non-Linear Convection in a Non-Darcy Porous Medium

M. K. Partha

2010, 31(5): 533-543. doi: 10.3879/j.issn.1000-0887.2010.05.004

Abstract(1621) PDF(752)

Abstract:
Natural convection in a non-Darcy porous medium was studied using the temperature-concentration-dependent density relation. The effect of two parameters a₁ and a₂ responsible for non-linear convection was analyzed for different values of inertial parameter, dispersion parameters, Rayleigh number, Lew is number, So retnumber and Dufour number. In the aiding buoyancy, tangential velocity f' increases steeply with an in crease in the parameters of non-linear temperature and concentration (a₂ & a₁), when the inertial effect is zero. But, when it is non-zero, the effect of a₂ or a₁ on f' is marginal. The concen tration distribution varies appreciably and spreads in different ranges for different values of double dispersion parameters, inertial effect parameter and also for parameters which control non-linear temperature and concentration. Heat and masstrans fervary extensively with an increase in a₁ and a₂ depending on Dacry and non-Darcy porous medium. Variation in heat and masstrans fer when all the effects (inertial effect, double dispersion effects and Soret and Dufour effects) are smiultan eously zero and non-zero and com bined effect of param eters of non-linear temperature and concentration and Buoyancy are analyzed. The effect of a₁ and a₂ and also the cross diffusion effects on heat and masstran sferare observed to be more in Darcy porous medium com pared to non-Darcy porous medium. In the opposing buoyancy, it is observed that the effect of a₁ is to in crease the heat and masstran sferrate, whereas that of a₂ is to decrease.

Numerical Discuss to Complete Empirical Correlation in Langtry’s Transition Model

ZHANG Xiao-dong, GAO Zheng-hong

2010, 31(5): 544-552. doi: 10.3879/j.issn.1000-0887.2010.05.005

Abstract(2204) PDF(1017)

Abstract:
Recently, introducing a transition predicting model in to RANS environment was paidore and more attention to. Langtry proposed a correlation-based transition model in 2006,which was built strictly on local variables. However, two core correlations had not been pubished by the originator of the model until 2009. The mechanism of this transition model was anlyzed and discussed, after a series of numerical validations in skin friction coefficien to fflatlate boundary layers, a new correlation based on freestream turbulence in ten sity was developed, and the empirical correlation of transition onset momentum thickness Reynold number aiming at the hyperson ic transition was miproved. Finally, low-speed/transonic airfoil and a hypersonic double wedge flatare tested to prove the reliability and practicab ility of this correlation.

Thrust Generation and Wake Structure of a Wiggling Hydrofoil

HE Guo-yi, ZHANG Shu-guang, ZHANG Xing

2010, 31(5): 553-560. doi: 10.3879/j.issn.1000-0887.2010.05.006

Abstract(1398) PDF(854)

Abstract:
A wiggling motion is often used by marine anmials and micro-machines to generate thrust. The wiggling motion can be modeled by aprogressive wave where its wavelength describes the flexibility of wiggling anmials. In the present study, animmersed boundary method was used to smiulate the flows around the wiggling hydrofoil NACA-65-010 at low Reynolds numbers. It is found from the numerical s im ulations that the thrust generation is largely determined by the wave length: The thrust coefficients decrease with increasing the wavelength while the propulsive efficiency reaches maxmium at acertain wave length. The latter is due to the viscous effects. The thrust generation is associated with two different flow patterns in the wake: the well-known reversed Krmn vortex streets and the vortex dipoles. Both of them are jettype flows where the thrust coefficients associated with the reversed Krmn vortex streets are larger than the ones associated with vortex diploes.

Mechanics of the Formation and Rupture of Human Aneurysms

REN Jiu-sheng, YUAN Xue-gang

2010, 31(5): 561-572. doi: 10.3879/j.issn.1000-0887.2010.05.007

Abstract(1725) PDF(938)

Abstract:
Mechanical response of human arterial wall under the combined loading of in flation, axial extension and torsion was examined with in the framework of the large deformation hyperelastic theory. The probability for the formation of aneurysm was explained with the instability theory of structure and the probability for its rupture was explained with the strength theory of material. Taking account of the residual stress and the smooth muscleactivity, a two layer thick-walled circular cylindrical tube model with fiber-rein forced composite-based incompressible anisotropic hyper-elastic materials was employed to model the mechanical behavior of the arterial wall. The deformation curves and the stress distributions of the arterial wall are given both under normal conditions and abnormal conditions. With the results of the deformation and the structureins tability analysis, that not only the uniform in flation deformation of the arterial wall under normal conditions, but also the formation and growth of ananeurysm underabnormal conditions such as the stiffness of the elastic and collagen fibers is decreased to a certain degree may be described by this model. With the results of the stresses and the material strength analysis, that the rupture of aneurysm if the wall stress is larger than its strength may be described by this model, too.

Effect 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): 573-584. doi: 10.3879/j.issn.1000-0887.2010.05.008

Abstract(1711) PDF(713)

Abstract:
The problem of reflection and transmission of plane periodic waves incident on the interface between loosely-bonded elastic solid and micropolar porouscubic crystal half spaces was investigated by assum ing that the in terface behaves like adislocation which preserves the continuity of traction while allowing a finite amount of slip. Amplitude ratios of various reflected and transmitted waves were depicted graphically. Some special cases of in terest also were deduced from the present investigation.

Mechanical Analysis of Interaction Between Plant Roots and Soil Mass in Slope Vegetation

YAN Zhi-xin, SONG Yun, JIANG Ping, WANG Hou-yu

2010, 31(5): 585-590. doi: 10.3879/j.issn.1000-0887.2010.05.009

Abstract(1276) PDF(975)

Abstract:
With the help of plant roots, slope vegetation renders the slope soilmass a composite material of soil and roots, thereby conspicuously enhances the shears trength of slope soil mass and the stability of slope. Therefore, slope vegetation is always anoptmial choice forengineers. Nevertheless, present correlative studies still rema in at the stage of qualitative analysis. Some explorations in quantitatively analyzing the in teraction between roots and soil mass were achieved. Through analyzing the in teraction between herbaceous plant roots (in cluding lateral roots of woody plants) and rock and soil mass, amechanical model of the in teraction between frictional roots and soil was estab lished, and its correctness was verified. Mean while, amechanical model of the interaction between anchorage root, namely, woody plant taproot, and soilw as also established. The models provide asignificant theoretical guidance for quantitatively analyzing the in teraction between plant roots and soil and are of certain application value.

Quasistatic Bilateral Contact Problem With Adhesion and Nonlocal Friction for Viscoelastic Materials

Arezki Touzaline

2010, 31(5): 591-601. doi: 10.3879/j.issn.1000-0887.2010.05.010

Abstract(1908) PDF(795)

Abstract:
A mathematical model which describes a contact problem between a de form able body and a foundation was considered. The contact was bilateral and was modelled with non local friction law in which adhesion was taken in to account. The evolution of the bonding field was described by a firstorder differential equation and the material. s behavior was modelled with an on linear viscoe lastic constitutive law. A variational formulation of the mechanical problem was derived and the existence and uniqueness result of the weak so lution were proved if the coefficien to ffriction was sufficiently small. The proof is based on arguments of time-dependent variationa line qualities, differential equations and Banach fixed-point theorem.

Quasi-Green’s Function Method for Free Vibration of Simply-Supported Trapezoidal Shallow Spherical Shell

LI Shan-qing, YUAN Hong

2010, 31(5): 602-608. doi: 10.3879/j.issn.1000-0887.2010.05.011

Abstract(1726) PDF(696)

Abstract:
The idea of quasi Green's function method was clarified in detail by considering a free vibration problem of smiply-supported trapezoidal shallow spherical shell. A quasi-Green's function was established by using the fundamental solution and boundary equation of the problem. This function satis fies the homogeneous boundary condition of the problem. The mode shape differential equation of the free vibration problem of simply-supported trapezoidal shallow spherical shell is reduced to two smiultaneous Fredholm in tegral equations of the second kind by 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 in tegral equations is overcome. Finally, natural frequency is obtained by the condition that there exists a non trivial solution in the numerically discrete algebraic equations derived from the in tegral equations. Numerical results show highaccuracy of the quasi-Green's function method.

A Parallel Finite Element Algorithm Based on Full Domain Partition for the Stationary Stokes Equations

SHANG Yue-qiang, HE Yin-nian

2010, 31(5): 609-617. doi: 10.3879/j.issn.1000-0887.2010.05.012

Abstract(1725) PDF(831)

Abstract:
Based on full domain partition, a parallel finite element algorithm for the stationary Stokes equations was proposed and analyzed. In this algorithm, each subproblem was defined in the entiredomain with the vast majority of the degrees of freedom associated with the particular subdomain that it was responsible for, and hence could be solved in parallel with other subproblems using an existing sequential solver withou textensive recoding, a llowing the algorithm to beimplemented easily with low communication costs. Some numerical results are given which demonstrate the high efficiency of the paralle lalgorithm.

Local Projection Stabilized Finite Element Method for the Navier-Stokes Equations

QIN Yan-mei, FENG Min-fu, LUO Kun, WU Kai-teng

2010, 31(5): 618-630. doi: 10.3879/j.issn.1000-0887.2010.05.013

Abstract(1766) PDF(771)

Abstract:
The results of Matthies, Skrzypacz and Tubiska for the Oseen problem to the Navier-Stokes problem were extended. For the stationary incompressible Navier-Stokes equations, a local projection stabilized finite element scheme was proposed. The schem eovercomes convection dominated and ameliorates the restrictiveinf-supcondition. Local projection schemes were derived not only as a two-level approach but also for pairs of spaces which were defined on the samemesh. This class of stabilized schemes uses approxmiation and projection spaces defined on the same mesh and leads to much more compact stencils than in the two-level approach. On the same mesh, bes ides the class of local projection stabilization by enrichment of the approximation spaces, two new classes of local projection stabilization of the approximation spaces which dont. need to be enriched by bubble functions are derived. Based on a special in terpolation, the stability and an optimal priorierror estimates were shown. Finally, the numerical tests and the numerical computations show that the numerical results agree with some ben chmark solutions, which further poved the correctness of the theoretical analysis.

Statistic on the Papers and Authership of "Applied Mathematics and Mechanics" From 2001 to 2008

HUANG Shao-hong

2010, 31(5): 631-637. doi: 10.3879/j.issn.1000-0887.2010.05.014

Abstract(1573) PDF(241)

Abstract:
Based on the bibliometrics theory, a careful survey and an alysis of the papers and their authors in the Applied Mathematics and Mechanics. (2001~2005)were made. The author attempted to reflect some miportant features concerning this journal as well as its authorship. It is shown that this journal has high quality and some attentive problems are proposed as well.