应用数学和力学

2011 Vol. 32, No. 6

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Effect of Thermal Radiation on MHD Viscous Fluid Flow and Heat Transfer Over a Non-Linear Shrinking Porous Sheet

G. C. Shit, R. Haldar

2011, 32(6): 635-646. doi: 10.3879/j.issn.1000-0887.2011.06.001

Abstract(1811) PDF(728)

Abstract:
Of concern was an investigation of the effects of thermal radiation on magnetohydrodynamic (MHD)flow and heat transfer over a non-linear shrinking porous sheet.The surface velocity of the shrinking sheet and the transverse magnetic field were assumed to vary as a power function of the distance from the origin.The temperature dependent viscosity and the thermal conductivity were also assumed to vary as an inverse function and a linear function of the temperature respectively.A generalized similarity transformation was used to reduce the governing partial differential equations into its non-linear coupled ordinary differential equations and were solved numerically by using finite difference scheme.The numerical results concern with the velocity and temperature profiles as well as the skin-friction coefficient and the rate of heat transfer at the porous sheet for different values of the parameters of interest.

Peristaltic Flow of Walter’s B Fluid in an Endoscope

S. Nadeem, Noreen Sher Akbar, T. Hayat, Awatif A. Hendi

2011, 32(6): 647-657. doi: 10.3879/j.issn.1000-0887.2011.06.002

Abstract(1670) PDF(815)

Abstract:
The peristaltic flow of a Walter's B fluid in an endoscope was studied.The problem was model in cylindrical coordinates system.The main theme of the present analysis was to study the endoscopic effects on the peristaltic flow of Walter's B fluid,because to the best of authors'knowledge no investigation had been made up to yet in peristaltic literature to study the Walter's B fluid in an endoscope.The analytical solutions were carried out using regular perturbation method by taking delta as erturbation parameter.The approximate analytical solutions for pressure rise and friction forces were evaluated using numerical integration.The effects of emerging parameters of Walter's B fluid were presented graphically.

Wave Transmission Through Laminated Composite Double-Walled Cylindrical Shell Lined With Porous Materials

K. Daneshjou, H. Ramezani, R. Talebitooti

2011, 32(6): 658-673. doi: 10.3879/j.issn.1000-0887.2011.06.003

Abstract(1587) PDF(686)

Abstract:
A study on free harmonic wave propagation in a double-walled cylindrical shell whose walls sandwich a layer of porous material was presented within the framework of the classic theory for laminated composite shells.The most effective component of the wave propagation through porous core was estimated by the aid of a flat panel with the same geometrical properties.Through considering the effective wave component,the porous layer was modeled as a fluid with equivalent properties.Thus,the model was simplified as a double-walled cylindrical shell trapping the fluid media.Finally,the transmission loss(TL) of the structure was estimated in a broadband frequency and then,the results were compared.

Analysis of Non-Linear Stability and Post-Buckling for the Euler-Type Beam-Column Structure

ZHU Yuan-yuan, HU Yu-jia, CHENG Chang-jun

2011, 32(6): 674-682. doi: 10.3879/j.issn.1000-0887.2011.06.004

Abstract(1954) PDF(971)

Abstract:
Based on the assumption of finite deformation,the Hamilton variational principle was extended to a nonlinear elastic Euler-type beam-column structure located on a nonlinear elastic foundation,and the corresponding 3-dimension mathematical model for analyzing the non-linear mechanical behaviors of structures was established,in which the effects of rotation inertia,non-linearity of material and geometry were considered.As application,the non-linear stability and the post-buckling for a linear elastic beam with equal cross-section and located on an elastic foundation were analyzed,here,one end of beam was fully fixed,and the other was partially fixed and subjected to an axial force.A new numerical technique was proposed to calculate the trivial solution,bifurcation points and bifurcation solutions by the shooting method and Newton-Raphson interactive method.The first and the second bifurcation points and the corresponding bifurcation solutions were calculated successfully.The effects of foundation resistances and inertia moments on the bifurcation points were considered.

PIV Measurements of Tip Vortex Wake Structure of a Wind Turbine

XIAO Jing-ping, WU Jie, CHEN Li, SHI Zhe-yu

2011, 32(6): 683-692. doi: 10.3879/j.issn.1000-0887.2011.06.005

Abstract(1660) PDF(896)

Abstract:
Large-view flow field measurements using PIV(particle image velocimetry)technique with high resolution CCD cameras on a rotating 1/8 scale blade model of NREL UAE PhaseⅥwind turbine were conducted in the engineering-oriented Ø3.2 m wind tunnel at the Low Speed Aerodynamics Institute of China Aerodynamics Research and Development Center.The motivation behind the tests was to establish the database of the initiation and development of the tip vortex in order to investigate the flow structure and mechanism of the wind turbine.The results showed that the tip vortex firstly moved inward for a very short time and then moved outward with the wake expansion while its vorticity decreased with time after just trailed from the trailing edge of the blade tip and then increased continuously with rapid roll-up to form a strong tip vortex.The measurements also indicated that the downstream movement of the tip vortex was nearly linear in the very near wake under the test condition.

Improved NSGA-Ⅱ in Multi-Objective Optimization Studies of Wind Turbine Blades

WANG Long, WANG Tong-guang, LUO Yuan

2011, 32(6): 693-701. doi: 10.3879/j.issn.1000-0887.2011.06.006

Abstract(1709) PDF(1027)

Abstract:
The non-dominated sorting genetic algorithm was improved with controlled elitism and dynamic crowding distance,obtaining a novel multi-objective optimization design algorithm for wind turbine blades.As an example,a 5 MW wind turbine blade design,taking maximum power coefficient and minimum blade mass as the optimization objectives,was presented.It is illustrated from the optimal results that this algorithm has a good performance in handling multi-objective optimization of wind turbine and it gives a Pareto-optimal solutions set rather than the optimum solution from the conventional multi-objective optimization problems.The wind turbine blade optimization method presented provides a new idea and general algorithm for multi-objective optimization of wind turbine.

An Active Control Scheme for Improving Mass Resolution of Film Bulk Acoustic Resonators

HE Xue-feng, LIU Xing, YIN Xian-fang, WEN Zhi-yu, CHEN Ke-wan

2011, 32(6): 702-709. doi: 10.3879/j.issn.1000-0887.2011.06.007

Abstract(1515) PDF(790)

Abstract:
High mass resolution of sensors based on film bulk acoustic resonators(FBARs)was required for detection of small molecules with low concentration.An active control scheme was herein presented for improving the mass resolution of FBAR sensors by adding a feedback voltage,which was obtained by giving a constant gain and a constant phase shift to the current on the electrodes of the FBAR sensors,onto the driving voltage between two electrodes of the FBAR sensors.The acoustic energy produced by the feedback voltage partly compensates the acoustic energy loss from the material damping and the acoustic scattering,which as a consequence improves the quality factor and the mass resolution of FBAR sensors. The explicit expression relating the impedance to the frequency for an FBAR sensor with the active control was derived based on continuum theory by neglecting the influence of the electrodes.Numerical simulations show that the impedance of the FBAR sensor strongly depends on the gain and phase shift of the feedback voltage and the mass resolution of the FBAR sensor can be greatly improved when appropriate gain and phase shift of the feedback voltage are used.Above active control scheme is also an effective solution to improve the resolution of the quartz crystal microbalance(QCM).

Analysis on High-Temperature Oxidation and the Growth Stress of Iron-Based Alloy Using Phase Field Method

YANG Fan, LIU Bin, FANG Dai-ning

2011, 32(6): 710-717. doi: 10.3879/j.issn.1000-0887.2011.06.008

Abstract(1232) PDF(837)

Abstract:
High-temperature oxidation was an important property to evaluate the thermal protection materials.However,as oxidation was a complex process involving microstructure evolution,its quantitative analysis had always been a challenge issue.A phase field method based on thermodynamics theory was developed to simulate oxidation behavior and oxidation induced growth stress.It involves microstructure evolution,and solves the problem of quantitatively computational analysis for oxidation behavior and growth stress.Employing this method,the diffusion process,oxidation performance and stress evolution were predicted for Fe-Cr-Al-Y alloys.Numerical results agree with experiment data well.The linear relationship between maximum growth stress and the environment oxygen concentration is found.This phase field method provides a powerful tool to investigate high temperature oxidation in complex environment.

Experimental and Numerical Investigation on Sound Generation From Airfoil-Flow Interaction

JIANG Min, LI Xiao-dong, ZHOU Jia-jian

2011, 32(6): 718-729. doi: 10.3879/j.issn.1000-0887.2011.06.009

Abstract(1567) PDF(763)

Abstract:
The aerodynamic noise due to the interaction of the incoming turbulence with rotating blades was one of the most important components of wind turbine noise.The rod-airfoil configuration was utilized to investigate the interaction phenomenon both experimentally and numerically.The distribution of unsteady pressure on the airfoil surface was measured for different rod positions and airfoil attack angles.Investigated in the present were two NACA airfoils,NACA0012 and NACA0018,and two wind turbine airfoils,s809 and s825.In addition,for the cases with low angles of attack,the flow field around airfoil leading edge was investigated by particle image velocimetry(PIV).The experimental results indicate that the unsteady pressure disturbances on airfoil surface are relevant to the rod vortex shedding.Meanwhile, the interaction flow field of the rod and NACA0012 airfoil was simulated by unsteady Reynolds averaged Navier-Stokes method(URANS)and the pressure spectra obtained was compared with the experimental results.

Stability and Dispersion Analysis of Reproducing Kernel Collocation Method for Transient Dynamics

LUO Han-zhong, LIU Xue-wen, HUANG Xing-chun

2011, 32(6): 730-740. doi: 10.3879/j.issn.1000-0887.2011.06.010

Abstract(1703) PDF(1054)

Abstract:
Reproducing kernel collocation method based on strong formulation was introduced for transient dynamics.von Neumann stability and dispersion analysis of reproducing kernel collocation method with central difference temporal discretization was derived to evaluate the stability condition for second order wave problem.The stability analysis algorithm proposed firstly given an approach to predict critical time step for second order wave problem which can greatly save computational time in application.A numerical test was conducted to validate this algorithm.The comparison of numerical critical time step and predicted results shows good agreement.The guidance to choose a proper support size of reproducing kernel shape function is also given.The results by radial basis collocation method are also listed for comparison.

Essential Consistency of Pressure Poisson Equation Method and Projection Method on Staggered Grid

WANG Yi

2011, 32(6): 741-745. doi: 10.3879/j.issn.1000-0887.2011.06.011

Abstract(1793) PDF(1070)

Abstract:
A new pressure Poisson equation method was established on staggered grid by keeping the viscous terms in the source of pressure Poisson equation.The derivations show that newly established pressure equation has the identical form of the equation in projection method.The results show that selection between the two methods does not affect velocity and pressure values,and CPU times have slight differences.

Stokes Flow Before a Plane Boundary With Mixed Stick-Slip Boundary Conditions

N. Akhtar, G. A. H. Chowdhury, S. K. Sen

2011, 32(6): 746-753. doi: 10.3879/j.issn.1000-0887.2011.06.012

Abstract(1892) PDF(874)

Abstract:
A general theorem for Stokes flow about a plane boundary with mixed stick-slip boundary conditions was established.This was done by making use of a representation for the velocity and pressure fields in three-dimensional Stokes flow,in terms of a biharmonic function A and a harmonic function B. The earlier theorem on Stokes flow before a no-slip plane boundary was shown to be a special case of the present theorem.Furthermore,a corollary of the theorem was also derived which offers the solution to a problem of axisymmetric Stokes flow about a rigid plane with stick-slip boundary conditions,in terms of the Stokes stream function.The formulae for the drag and torque exerted by the fluid on the boundary were found.An illustrative example was given.

Almost Surely T-Stability and Convergence for Random Iterative Algorithms

ZHANG Shi-sheng, WANG Xiong-rui, LIU Min, ZHU Jin-hua

2011, 32(6): 754-760. doi: 10.3879/j.issn.1000-0887.2011.06.013

Abstract(1673) PDF(832)

Abstract:
The purpose was to study the almost surely T-stability and convergence of Ishikawa-type and Mann-type random iterative algorithms for some kind of φ-weakly contractive type random operators in a separable Banach space.Under suitable conditions the Bochner integrability of random fixed points for this kind of random operators and the almost surely T-stability and convergence for these two kinds of random iterative algorithms were proved.