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2012年 第33卷 第6期    刊出日期：2012-06-10

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论文

Applications of parabolized stability equation for predicting transition position in boundary layers

李佳;罗纪生

2012, 33(6):  679-686.  doi:10.1007/s10483-012-1579-7

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The phenomenon of laminar-turbulent transition exists universally in nature and various engineering practice. The prediction of transition position is one of crucial theories and practical problems in fluid mechanics due to the different characteristics of laminar flow and turbulent flow. Two types of disturbances are imposed at the entrance, i.e., identical amplitude and wavepacket disturbances, along the spanwise direction in the incompressible boundary layers. The disturbances of identical amplitude are consisted of one two-dimensional (2D) wave and two three-dimensional (3D) waves. The parabolized stability equation (PSE) is used to research the evolution of disturbances and to predict the transition position. The results are compared with those obtained by the numerical simulation. The results show that the PSE method can investigate the evolution of disturbances and predict the transition position. At the same time, the calculation speed is much faster than that of the numerical simulation.

Iterative and adjusting method for computing stream function and velocity potential in limited domains and convergence analysis

黎爱兵;张立凤;臧增亮;张云

2012, 33(6):  687-700.  doi:10.1007/s10483-012-1580-9

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The stream function and the velocity potential can be easily computed by solving the Poisson equations in a unique way for the global domain. Because of the various assumptions for handling the boundary conditions, the solution is not unique when a limited domain is concerned. Therefore, it is very important to reduce or eliminate the effects caused by the uncertain boundary condition. In this paper, an iterative and adjusting method based on the Endlich iteration method is presented to compute the stream function and the velocity potential in limited domains. This method does not need an explicitly specifying boundary condition when used to obtain the effective solution, and it is proved to be successful in decomposing and reconstructing the horizontal wind field with very small errors. The convergence of the method depends on the relative value for the distances of grids in two different directions and the value of the adjusting factor. It is shown that applying the method in Arakawa grids and irregular domains can obtain the accurate vorticity and divergence and accurately decompose and reconstruct the original wind field. Hence, the iterative and adjusting method is accurate and reliable.

Numerical simulation of trajectory and deformation of bubble in tip vortex

倪宝玉;张阿漫;姚熊亮;汪斌

2012, 33(6):  701-716.  doi:10.1007/s10483-012-1581-9

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According to the behaviors of a bubble in the ship wake flow, the numerical simulation is divided into two stages, quasi-spherical motion and non-spherical motion, based on whether the bubble is captured by the vortex or not. The one-way coupled particle tracking method (PTM) and the boundary element method (BEM) are adopted to simulate these two stages, respectively. Meanwhile, the initial condition of the second stage is taken as the output of the first one, and the entire simulation is connected and completed. Based on the numerical results and the published experimental data, the cavitation inception is studied, and the wake bubble is tracked. Besides, the split of the bubble captured by the vortex and the following sub-bubbles are simulated, including motion, deformation, and collapse. The results provide some insights into the control on wake bubbles and optimization of the wake flow.

Flow on oscillating rectangular duct for Maxwell fluid

M. NAZAR;F. SHAHID;M. SAEED AKRAM;Q. SULTAN

2012, 33(6):  717-730.  doi:10.1007/s10483-012-1582-6

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This paper presents an analysis for the unsteady flow of an incompressible Maxwell fluid in an oscillating rectangular cross section. By using the Fourier and Laplace transforms as mathematical tools, the solutions are presented as a sum of the steady-state and transient solutions. For large time, when the transients disappear, the solution is represented by the steady-state solution. The solutions for the Newtonian fluids appear as limiting cases of the solutions obtained here. In the absence of the frequency of oscillations, we obtain the problem for the flow of the Maxwell fluid in a duct of a rectangular cross-section moving parallel to its length. Finally, the required time to reach the steady-state for sine oscillations of the rectangular duct is obtained by graphical illustrations for different parameters. Moreover, the graphs are sketched for the velocity.

Computational study of combined effects of conduction-radiation and hydromagnetics on natural convection flow past magnetized permeable plate

M. ASHRAF;S. ASGHAR;M. A. HOSSAIN

2012, 33(6):  731-748.  doi:10.1007/s10483-012-1583-7

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The computational study of the combined effects of radiation and hydro- magnetics on the natural convection flow of a viscous, incompressible, and electrically conducting fluid past a magnetized permeable vertical plate is presented. The governing non-similar equations are numerically solved by using a finite difference method for all values of the suction parameter ζ and the asymptotic solution for small and large values of ζ. The effects of varying the Prandtl number P_r, the magnetic Prandtl number Pr_m, the magnetic force parameter S, the radiation parameter R_d, and the surface temperature θ_w on the coefficients of the skin friction, the rate of heat transfer, and the current density are shown graphically and in tables. An attempt is made to examine the effects of the above mentioned physical parameters on the velocity profile, the temperature distribution, and the transverse component of the magnetic field.

MHD axisymmetric flow of third grade fluid between porous disks with heat transfer

T. HAYAT;A. SHAFIQ;M. NAWAZ;A. ALSAEDI

2012, 33(6):  749-764.  doi:10.1007/s10483-012-1584-9

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The magnetohydrodynamic (MHD) flow of the third grade fluid between two permeable disks with heat transfer is investigated. The governing partial differential equa-tions are converted into the ordinary differential equations by suitable transformations. The transformed equations are solved by the homotopy analysis method (HAM). The expressions for square residual errors are defined, and the optimal values of convergence-control parameters are selected. The dimensionless velocity and temperature fields are examined for various dimensionless parameters. The skin friction coefficient and the Nus-selt number are tabulated to analyze the effects of dimensionless parameters.

Thermophoresis and Brownian motion effects on boundary layer flow of nanofluid in presence of thermal stratification due to solar energy

N. ANBUCHEZHIAN;K. SRINIVASAN;K. CHANDRASEKARAN;R. KANDASAMY

2012, 33(6):  765-780.  doi:10.1007/s10483-012-1585-8

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The problem of laminar fluid flow, which results from the stretching of a vertical surface with variable stream conditions in a nanofluid due to solar energy, is in- vestigated numerically. The model used for the nanofluid incorporates the effects of the Brownian motion and thermophoresis in the presence of thermal stratification. The sym- metry groups admitted by the corresponding boundary value problem are obtained by using a special form of Lie group transformations, namely, the scaling group of transfor- mations. An exact solution is obtained for the translation symmetrys, and the numerical solutions are obtained for the scaling symmetry. This solution depends on the Lewis number, the Brownian motion parameter, the thermal stratification parameter, and the thermophoretic parameter. The conclusion is drawn that the flow field, the temperature, and the nanoparticle volume fraction profiles are significantly influenced by these param- eters. Nanofluids have been shown to increase the thermal conductivity and convective heat transfer performance of base liquids. Nanoparticles in the base fluids also offer the potential in improving the radiative properties of the liquids, leading to an increase in the efficiency of direct absorption solar collectors.

Engineering measures for preventing upheaval buckling of buried submarine pipelines

刘润;王武刚;闫澍旺;吴新利

2012, 33(6):  781-796.  doi:10.1007/s10483-012-1586-6

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In-service hydrocarbons must be transported at high temperature and high pressure to ease the flow and to prevent the solidification of the wax fraction. The high temperature and high pressure will induce the additional stress in the pipeline, which results in the upheaval buckling of the pipeline. If such expansion is resisted, e.g., by the frictional effects of the foundation soil over a kilometer or of a pipeline, the compressive axial stress will be set up in the pipe-wall. When the stress exceeds the constraint of the foundation soil on the pipeline, suddenly-deforming will occur to release the internal stress, similar to the sudden deformation of the strut due to stability problems. The upheaval buckling may jeopardize the structural integrity of the pipeline. Therefore, effective engineering measures against this phenomenon play an important role in the submarine pipeline design. In terms of the pipeline installation and protection measures commonly used in Bohai Gulf, three engineering measures are investigated in great details. An analytical method is introduced and developed to consider the protection effect of the anti-upheaval buckling of the pipeline. The analysis results show that the amplitude of the initial imperfection has a great effect on the pipeline thermal upheaval buckling. Both trenching and burial and discrete dumping are effective techniques in preventing the pipeline from buckling. The initial imperfection and operation conditions of the pipelines determine the covered depth and the number of layers of the protection measures.

Reflection and refraction of attenuated waves at boundary of elastic solid and porous solid saturated with two immiscible viscous fluids

M. KUMAR;R. SAINI

2012, 33(6):  797-816.  doi:10.1007/s10483-012-1587-6

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The propagation of elastic waves is studied in a porous solid saturated with two immiscible viscous fluids. The propagation of three longitudinal waves is represented through three scalar potential functions. The lone transverse wave is presented by a vector potential function. The displacements of particles in different phases of the aggregate are defined in terms of these potential functions. It is shown that there exist three longitudinal waves and one transverse wave. The phenomena of reflection and refraction due to longitudinal and transverse waves at a plane interface between an elastic solid half-space and a porous solid half-space saturated with two immiscible viscous fluids are investigated. For the presence of viscosity in pore-fluids, the waves refracted to the porous medium attenuate in the direction normal to the interface. The ratios of the amplitudes of the reflected and refracted waves to that of the incident wave are calculated as a non- singular system of linear algebraic equations. These amplitude ratios are used to further calculate the shares of different scattered waves in the energy of the incident wave. The modulus of the amplitude and the energy ratios with the angle of incidence are computed for a particular numerical model. The conservation of the energy across the interface is verified. The effects of variations in non-wet saturation of pores and frequencies on the energy partition are depicted graphically and discussed.

Asymptotic analysis on weakly forced vibration of axially moving viscoelastic beam constituted by standard linear solid model

王波

2012, 33(6):  817-828.  doi:10.1007/s10483-012-1588-8

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The weakly forced vibration of an axially moving viscoelastic beam is investigated. The viscoelastic material of the beam is constituted by the standard linear solid model with the material time derivative involved. The nonlinear equations governing the transverse vibration are derived from the dynamical, constitutive, and geometrical relations. The method of multiple scales is used to determine the steady-state response. The modulation equation is derived from the solvability condition of eliminating secular terms. Closed-form expressions of the amplitude and existence condition of nontrivial steady-state response are derived from the modulation equation. The stability of nontrivial steady-state response is examined via the Routh-Hurwitz criterion.