应用数学和力学

2012 Vol. 33, No. 1

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Dynamic Analysis of a Two-Degree-of-Freedom Airfoil With Freeplay and Cubic Nonlinearities in Supersonic Flow

GUO Hu-lun, CHEN Yu-shu

2012, 33(1): 1-13. doi: 10.3879/j.issn.1000-0887.2012.01.001

Abstract(2165) PDF(1142)

Abstract:
The nonlinear aeroelastic response of a two-dimensional airfoil with freeplay and cubic nonlinearities in supersonic flow were investigated. The second-order piston theory was employed to analyze a double wedge airfoil. Then, the fold bifurcation and the amplitude jump phenomenon were detected using averaging method and multi-variable Floquet theory. The analytical results were further verified by numerical simulations. Lastly, the influence of the freeplay parameters on the aeroelastic response was analyzed in detail.

Unsteady Peristaltic Transport of Maxwell Fluid Through a Finite Length Tube: Application to Oesophageal Swallowing

S.K.Pandey, Dharmendra Tripathi

2012, 33(1): 14-23. doi: 10.3879/j.issn.1000-0887.2012.01.002

Abstract(1421) PDF(903)

Abstract:
Unsteady peristaltic transport of Maxwell fluid in a finite tube was investigated. The walls of the tube were subjected to contraction waves that do not cross the stationary boundaries. The analysis was carried out by using long wavelength approximation in non-dimensional form. The expressions for axial and radial velocities were derived and pressures across a wavelength and also across the tube-length were also estimated. The reflux phenomenon was discussed that culminates into determination of the reflux limit. Mathematical formulations were physically interpreted for the flow of masticated food materials such as bread, white eggs etc. in the oesophagus. It is revealed that Maxwell fluids are favorable to flow in the oesophagus in comparison with Newtonian fluids. This endorses the experimental finding of Tomoko Takahashi et al.It is further revealed that relaxation time affects neither shear stress nor reflux limit. It is found that the peaks of pressure are identical in the integral case while the peaks are different in the non-integral case.

Analytical Investigation of Jeffery-Hamel Flow With High Magnetic Field and Nano Particle by Adomian Decomposition Method

M.Sheikholeslami, D.D.Ganji, H.R.Ashorynejad, Houman B.Rokni

2012, 33(1): 24-34. doi: 10.3879/j.issn.1000-0887.2012.01.003

Abstract(2023) PDF(924)

Abstract:
The effect of magnetic field and nano particle on the Jeffery-Hamel flow were studied by a powerful analytical method that was called Adomian decomposition method (ADM). The traditional Navier-Stokes equation of fluid mechanics and Maxwell’s electromagnetism governing equations were reduced to nonlinear ordinary differential equations to model this problem. The obtained results by this method are well agreed with the numerical (Runge-Kutta method) results and tabulated in a table. The plots confirm that the used method is in high accuracy for different α,Ha and Re numbers. First the flow field inside the divergent channel was studied for various values of Hartmann number and angle of channel and at last the effect of nanoparticle volume fraction in absence of magnetic field was investigated.

Experimental and Numerical Investigation of the Inclined Air/SF-6 Interface Instability Under Shock Wave

WANG Tao, LIU Jin-hong, BAI Jing-song, JIANG Yang, LI Ping, LIU Kun

2012, 33(1): 35-47. doi: 10.3879/j.issn.1000-0887.2012.01.004

Abstract(2104) PDF(942)

Abstract:
Shock tube experiments of inclined Air/SF-6 interface instability under shock wave with mach numbers 1.23 and 1.41 were conducted, and were numerically simulated by the parallel algorithm and code MVFT (multi-viscous-fluid and turbulence) of large-eddy simulation (LES). The developing process of interface accelerated by shock wave was reproduced by simulations, the complex waves structure, e.g. the propagation, refraction and reflection of shock wave were revealed clearly in flows. The simulated evolving images of interface are consistent with experimental ones. The simulated width of turbulent mixing zone (TMZ), the displacements of bubble and spike also agree well with the experimental data. And the reliability and effectiveness of MVFT to simulate this problem of interface instability are validated. The more energy is injected into the TMZ when the shock wave has a larger mach number, the perturbed interface is developing faster.

MHD Flow and Heat Transfer of a Micropolar Fluid Between Two Porous Disks

Muhammad Ashraf, A.R.Wehgal

2012, 33(1): 48-60. doi: 10.3879/j.issn.1000-0887.2012.01.005

Abstract(1532) PDF(805)

Abstract:
A numerical study of axisymmetric steady laminar incompressible flow of an electrically conducting micropolar fluid between two infinite parallel porous disks with constant uniform injection through the surface of the disks was carried out when the fluid was subjected to an external transverse magnetic field. The governing nonlinear equations of motion were transformed in dimensionless form through von Karman’s similarity transformation. An algorithm based on finite difference scheme was used to solve the reduced coupled ordinary differential equations with associated boundary conditions. Effects of Reynolds number, magnetic parameter, micropolar parameter and Prandtl number on the flow velocity and temperature distribution were discussed. Results compare well with the previously published work for special case. Investigations predict that the heat transfer rate at the surfaces of the disks increased with an increase in the values of Reynolds number, magnetic parameter and Prandtl number. The shear stresses decreased by increasing the injection while these stresses increased with increased applied magnetic field. The shear stress factor was lower for micropolar fluids than for Newtonian fluids, which may be beneficial in flow and thermal control of polymeric processing.

High-Order Numerical Methods of the Fractional Order Stokes’ First Problem for a Heated Generalized Second Grade Fluid

YE Chao, LUO Xian-nan, WEN Li-ping

2012, 33(1): 61-75. doi: 10.3879/j.issn.1000-0887.2012.01.006

Abstract(2011) PDF(852)

Abstract:
High-order implicit finite difference methods for solving the Stokes’ first problem for a heated generalized second grade fluid with fractional derivative were studied. The stability, solvability and convergence of the numerical scheme were discussed via fourier analysis and matrix analysis method. An improved implicit scheme was also obtained. Finally, two numerical examples were presented to demonstrate the effectiveness of the mentioned schemes.

Mixed FE-DQM for Free and Forced Vibration, and Buckling Analysis of Rectangular Plates

S.A.Eftekhari, A.A.Jafari

2012, 33(1): 76-93. doi: 10.3879/j.issn.1000-0887.2012.01.007

Abstract(2236) PDF(954)

Abstract:
A very first combined application of finite element method (FEM) and differential quadrature (DQ) method to vibration and buckling problems of rectangular plates was presented. The mixed scheme combines the geometry flexibility of the FEM and high accuracy and efficiency of the DQ method. The accuracy of the proposed method was demonstrated by comparing the calculated results with those available in the literature. It is shown that highly accurate results can be obtained using a small number of finite elements and DQM sample points. The proposed method is suitable for the problems considered due to its simplicity and potential for further development.

Fractional Four-Step Finite Element Method for Analysis of Thermally Coupled Fluid-Solid Interaction Problems

A.Malatip, N.Wansophark, P.Dechaumphai

2012, 33(1): 94-112. doi: 10.3879/j.issn.1000-0887.2012.01.008

Abstract(1701) PDF(825)

Abstract:
An integrated fluid-thermal-structural analysis approach, where the heat conduction in a solid was coupled with the heat convection in viscous flow of the fluid resulting in the thermal stress in the solid, was presented.The fractional four-step finite element method and streamline upwind Petrov-Galerkin method were used for the analysis of viscous thermal flow in the fluid whereas the analyses of heat transfer and thermal stress in solid were performed using the Galerkin method.The second-order semi-implicit Crank-Nicolson scheme was applied for time integration and the resulting nonlinear equations were linearized to improve the computational efficiency.The integrated analysis method employ the three-node triangular element with equal-order interpolation functions for all variables of the fluid velocity components, pressure, temperature and the solid displacements in order to simplify the overall finite element formulation.The main advantage of the presented method was to consistently couple heat transfer along the fluid-solid interface.Results from several tested problems illustrated the effectiveness of the presented finite element method that can provide insight into the integrated fluid-thermal-structural interaction phenomena.

Stress Concentration Factor Expression for a Tension Strip With an Eccentric Elliptical Hole

2012, 33(1): 113-124. doi: 10.3879/j.issn.1000-0887.2012.01.009

Abstract(2329) PDF(1598)

Abstract:
First, an explicit stress concentration factor expression for a tension finite-width strip with a central elliptical hole was formulated by using a semi-analytical and semi-empirical method. Comparing the results from this expression with those from Durelli’s photo-elastic experiment, Isida’s formula and finite element analysis, its accuracy was proved to be adequate and its application scope was wider. Then another explicit stress concentration factor expression for a tension strip with an eccentric elliptical hole was also obtained by using the similar method. Comparing results from the expression with the ones from Isida’s formula and finite element analysis, it is shown that this formula is with a wider application scope and more accurate. And when the eccentricity of elliptical hole was in a certain range, the error is less than 8%. Based on the relation between stress concentration central and stress intensity factor, a stress intensity factor expression for tension strips with a center or an eccentric crack was derived with the obtained stress concentration factor expressions. Compared with existing formulae and finite element analysis, this stress intensity factor expression is also with sufficient accuracy.

Uniform Blow-Up Rate for a Compressible Reactive Gas Model

XU Run-zhang, JIANG Xiao-li, LIU Jie

2012, 33(1): 125-134. doi: 10.3879/j.issn.1000-0887.2012.01.010

Abstract(1793) PDF(1027)

Abstract:
The Dirichlet initial-boundary value problem of a compressible reactive gas model equation with nonlocal nonlinear source term was studied. For certain conditions, it is proved that the blow-up rate is uniform in all compact subsets of the domain and the blow-up rate is irrelative to the exponent of the diffusion term, but relative to the exponent of the nonlocal nonlinear source.