应用数学和力学

Thermocapillary Migration and Interaction of Two Nondeformable Droplets

YIN Zhao-hua, CHANG Lei, HU Wen-rui, GAO Peng

2011, 32(7): 761-773. doi: 10.3879/j.issn.1000-0887.2011.07.001

Abstract(1510) PDF(821)

Abstract:
A numerical study on interactions of two spherical drops in therm ocapillary migration in microgravity was presented. Finite-difference methods were adopted and the interfaces of drops were captured by the fronttracking technique. It is found that the arrangement of drops directly in fluences their migrations and interaction, and that the motion of one drop is mainly determined by the disturbed temperature field because of the existence of another drop.

Lift Enhancement of the Airfoil and Tip Flow Control for Wind Turbine

BAI Ya-lei, MA Xing-yu, MING Xiao

2011, 32(7): 774-784. doi: 10.3879/j.issn.1000-0887.2011.07.002

Abstract(1802) PDF(1120)

Abstract:
Two techniques that miprove the aerodynamic performance of wind turbine airfoils were described. The airfoil S809, often used forwind turbine design, and the airfoil FX60-100, having higher lift-dragratio, were selected to verify the flow control techniques. The flow deflector, fixed at the leadingedge, was employed to control the boundary layer separation on the a irfoil at high angle of attack. The multiisland genetic algorithm was used to optimize the parameters of the flow deflector. The results indicate that the flow deflector can suppress the flow separation, delay stall and enhance the lift. In the second part of this paper, the characteristics o f the blade tipvortex, wake vortex and the surface pressured istributions of blades are analyzed. The vortex diffuser, set up at the blade tip, was employed to control the blade tipvortex. The results show that the vortex diffuser can increase the total pressure coefficient of the core of the vortex, decrease the strength of blade tipvortex, lower the noise and improve the efficiency of the blade.

Hydromagnetic Flow Through a Uniform Channel Bounded by Porous Media

K. Ramakrishnan, K. Shailendhra

2011, 32(7): 785-794. doi: 10.3879/j.issn.1000-0887.2011.07.003

Abstract(1891) PDF(786)

Abstract:
The combined effects of magnetic field, permeable walls, Darcy velocity and slipparameter on the steady flow of a fluid in a channel of uniform width were studied. The fluid flowing in the channel was assumed to be homogeneous, incom pressible and Newtonian. Analytical so lutions were constructed for the governing equations using Beavers-Joseph slip boundary conditions. Effects of the magnetic field, permeability, Darcy velocity and slipparameter on the axial velocity, slipvelocity and shear stress were discussed in detail. It is seen that the Hartmann number, Darcyvelocity, porous parameter and slipparameter play avital role in altering the flow and in turn the shear stress.

A Reduced Finite Difference Scheme and Error Estimates Based on POD Method for the Non-Stationary Stokes Equation

LUO Zhen-dong, OU Qiu-lan, XIE Zheng-hui

2011, 32(7): 795-806. doi: 10.3879/j.issn.1000-0887.2011.07.004

Abstract(1899) PDF(928)

Abstract:
The properorthogonal decom position (POD) was amodel reduction technique for the simulation of physical processes governed by partial differen tial equations, e. g. fluid flows. It was success fully used in the reduced-ordermodeling of complex systems. The applications of POD method were extended, i. e., apply POD method to a classical finited ifference (FD) scheme for the non-stationary Stokes equation with real practical applied background, estab lish a reduced FD scheme with lowerd imensions and sufficiently high accuracy, and provide the errorestmi ates between the reduced FD solutions and the classical FD solutions. Some numerical examples illustrate the fact that the results of numerical computation are consistent with theoretical conclusions. Moreover, it is shown that the reduced FD schemebased on POD method is feasible and efficient for solving 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

SI Xin-yi, SI Xin-hui, ZHENG Lian-cun, ZHANG Xin-xin

2011, 32(7): 807-820. doi: 10.3879/j.issn.1000-0887.2011.07.005

Abstract(1792) PDF(655)

Abstract:
The flow of amicropolar fluid through a porous channel with expanding or contracting walls of different permeability was investigated. Two cases were considered in which the opposing walls undergoeither uniformor nonuniform motion. In the first case, homotopy analysis method (HAM) was employed to obtain the expressions for velocity and micro-rotation fields. Graphs were sketched for some values of the param eters. The first conclusion can be made that expan sion ratio and different perm eability have miportant effects on the dynamic characteristics of the fluid. Following Xu. smodel, the second and more general case is that the wall expansion ratiovaries with time. Under this assumption, the govern ing equations were transformed in to non linear partial differential equations that also are solved analytically using HAM procedure. In the process, both algebraic and exponen tialmodels were considered to describe the evolution of a (t) from the initial a₀ to a final state a₁. As a result, it is found that the tmie-dependent solutions approach very rapidly to the steady state behavior. The second important conclusion can be made that the time-dependent variation of the wall expansion ratio plays a secondary role which maybe justifiably ignored.

Multiple-Front Waves for Extended Form of Modified Kadomtsev-Petviashvili Equation

Abdul-Majid Wazwaz

2011, 32(7): 821-825. doi: 10.3879/j.issn.1000-0887.2011.07.006

Abstract(1659) PDF(838)

Abstract:
An extended form of the modified Kadom tsev-Petviashvili (mKP) equation was investigated. The simp lified form of Hirotas bilinear method established by Herem an and Nuseir was employed for a reliable study. Multiple-front waves solutions were formally derived for this equation, and hence to the mKP equation. That also shows that the extension terms do not kill the in tegrability of the mKP equation.

Wave Propagation at an Interface of Heat Conducting Micropolar Solid and Fluid Media

Rajneesh Kumar, Mandeep Kaur, S. C. Rajvanshi

2011, 32(7): 826-847. doi: 10.3879/j.issn.1000-0887.2011.07.007

Abstract(1901) PDF(680)

Abstract:
Wave propagation at an in terface of micropolar generalized thermoelastic solid half space and heat conducting micropolar fluid half space was investigated. Reflection and tran smission phenomenon of plane waves mipinging obliquely at aplane in terface between amicropolar generalized therm oelastic solid half space and heat conducting micropolar fluid half space were investigated. The incident wave was assumed to be striking at the plane interface after propagating through the micropolar generalized thermoelastic solid. Amplitude ratios of the various reflected and transmitted waves were obtained in closed form and it was found that these were functions of angle of incidence, frequency and were affected by the elastic properties of the media. Micropolarity and thermal relaxation effects are shown on these amplitude ratios fo raspecific model. Results of some earlier workers have also been deduced from the present investigation.

Nonlinear Stability of Timber Column Strengthened With Fiber Reinforced Polymer

OUYANG Yu, YANG Xiao, BAO Ruo-han

2011, 32(7): 848-859. doi: 10.3879/j.issn.1000-0887.2011.07.008

Abstract(1670) PDF(983)

Abstract:
Taking effect of the bimodulus for tension and compression, of the fiber reinforced polymer sheet (FRP Sheet) in the rein forcement layer into consideration, a generalmathematicalm odel for the non linear bending of a slender timber beam strengthened with FRP sheet was established under the hypothesis of the large deflection deformation of the beam, and non linear governingequations with the second order effect of the beam bending were derived. Then, the non linear stability of a smiply-supporteds lender timber column strengthened with FRP sheet was investigated, and the expression of the critical load of the simply-supported FRP-strengthened tmiber beam was obtained. The existence of postbuckling solution of the tmiber column was proved theoretically, and the asymptotic analytical solution of the postbuckling state in the vicinity of the critical load was obtained with the perturbation method. Parameter study was conducted, and it was shown that FRP rein forcement layer had a great influence on the critical load of the tmiber column, and a little in fluence on the dmiension less postbuckling state.

Mechanical Performance and Negative Pressure Instability for Venous Walls

REN Jiu-sheng

2011, 32(7): 860-865. doi: 10.3879/j.issn.1000-0887.2011.07.009

Abstract(1862) PDF(916)

Abstract:
Mechanical properties, such as the deformation and stress distributions for venous walls under the combined loadings of transmural pressure and axial stretch were examined with in the framework of nonlinear elasticity with one kind of hyper-elastic strain energy function. The negative pressure ins tability problem of the venous wall was explained through energy comparison. The deformation equation of the venous wall under the combined loads was obtained with a thin-walled circularcy lindrical tubeat first. The deformation curves and the stress distributions for the venous wall were given under the normal transmural pressure, and the regulations were discussed. Then, the deformation curves of the venous wall under negative transmural pressure, or when the in ternal pressure was less than the external pressure, were given. Finally, the negative pressure in stability problem was discussed through energy comparison.

Free Vibration of Functionally Graded Sandwich Plates Using Four Variable Refined Plate Theory

Lazreg Hadji, Hassen Ait Atmane, Abdelouahed Tounsi, Ismail Mechab, Noureddine Ziane, El Abbas Adda Bedia

2011, 32(7): 866-882. doi: 10.3879/j.issn.1000-0887.2011.07.010

Abstract(1839) PDF(910)

Abstract:
The novelty of this paper was the use of four variable refined plate theory for freevibration analysis of functionally graded material sand wich rectangular plates. Unlike any other theories, the numbe rofunknown functions involved was only four, as a gainst five in case of other shearde formation theories. The theory presented was variationally consistent, had strong smiilarity with classical plate theory in many a spects, did not require shear correction factor, and gave rise to tran sverse shear stress variation such that the trans verse shear stresses vary parabolically a cross the thickness satisfying shear stress free surface conditions. Two commonty pes of FGM sand wich plates, namely, the sand wich with FGM face sheet and homogeneouscore and the sandwich with homogeneous faceshee tand FGM core, were considered. The equation of motion for FGM sandwich plates was obtained through Hamilton. sprinciple. The closed form solutions were obtained by using Navierte chnique, and then fundamental frequencies were found by solving the results of eigenvalue problems. The validity of the present theory was investigated by comparing some of the present results with those of the classical, the firstorder and the other higherorder theories. It can be concluded that the proposed theory is a ccurate and simple in solving the free vibration beha vior of FGM sandwich plates.

Ultraconvergence for Averaging Discontinuous Finite Elements and Its Applications in Hamiltonian System

LI Can-hua, CHEN Chuan-miao

2011, 32(7): 883-894. doi: 10.3879/j.issn.1000-0887.2011.07.011

Abstract(1583) PDF(792)

Abstract:
The k-degree averaging discontinuous finite element solution for the initial value problem of ordinary differential equations was discussed. When k waseven, it was proved that the averaging numerical flux (the average of left and right lmiits for discon tinuous finite element at nodes) had the optmial order ultraconvergence 2k + 2. For non linear Hamiltonian systems (e. g., S chrêdinger equation and Kepler system) with momentum conservation, it was found that the discon tinuous finite element methods preserve momentum at nodes. These properties were confirmed by numerical expermients.

2011 Vol. 32, No. 7