Table of Content

27 February 2014, Volume 35 Issue 2

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Articles

Accurate solutions for viscoelastic boundary layer flow and heat transfer over stretching sheet

A. MASTROBERARDINO

2014, 35(2):  133-142.  doi:10.1007/s10483-014-1778-7

Abstract ( 800 )   HTML   PDF (308KB) ( 490 )  

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In this article, we present accurate analytical solutions for boundary layer flow and heat transfer of an incompressible and electrically conducting viscoelastic fluid over a linearly stretching surface subject to a transverse uniform magnetic field using the homotopy analysis method (HAM) for two general types of non-isothermal boundary conditions. In addition, we demonstrate that the previously reported analytical solutions for the temperature field given in terms of Kummer’s function do not converge at the boundary. We provide a graphical and numerical demonstration of the convergence of the HAM solutions and tabulate the effects of various parameters on the skin friction coefficient and wall heat transfer.

Prediction of hypersonic boundary layer transition on sharp wedge flow considering variable specific heat

MAO Xu;CAO Wei

2014, 35(2):  143-154.  doi:10.1007/s10483-014-1779-7

Abstract ( 672 )   HTML   PDF (693KB) ( 416 )  

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When the air temperature reaches 600K or higher, vibration is excited. The specific heat is not a constant but a function of temperature. Under this condition, the transition position of hypersonic sharp wedge boundary layer is predicted by using the improved eN method considering variable specific heat. The transition positions with different Mach numbers of oncoming flow, half wedge angles, and wall conditions are computed. The results show that for the same oncoming flow condition and wall condition, the transition positions of hypersonic sharp wedge boundary layer move much nearer to the leading edge than those of the flat plate. The greater the oncoming flow Mach number, the closer the transition position to the leading edge.

Mixed convection stagnation-point flow on vertical stretching sheet with external magnetic field

F. M. ALI; R. NAZAR; N. M. ARIFIN; I.POP

2014, 35(2):  155-166.  doi:10.1007/s10483-014-1780-8

Abstract ( 904 )   HTML   PDF (549KB) ( 340 )  

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The problem of steady laminar magnetohydrodynamic (MHD) mixed convection stagnation-point flow of an incompressible viscous fluid over a vertical stretching sheet is studied. The effect of an externally magnetic field is taken into account. The transformed boundary layer equations are solved numerically by using an implicit finite-difference scheme. Numerical results are obtained for various values of the mixed convection parameter, Hartmann number, and Prandtl number. The effects of an externally magnetic field on the skin friction coefficient, local Nusselt number, velocity, and temperature profiles for both A > 1 and A < 1, where A is the velocity ratio parameter, are presented graphically and discussed in detail. Both assisting and opposing flows are considered, and it is found that dual solutions exist for the opposing flow.

Solitary wave solutions to higher-order traffic flow model with large diffusion

JIAN Xiao-Xia;ZHANG Peng; S. C. WONG; QIAO Dian-Liang;CUI Qi-Zhu

2014, 35(2):  167-176.  doi:10.1007/s10483-014-1781-x

Abstract ( 681 )   HTML   PDF (287KB) ( 349 )  

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This paper uses the Taylor expansion to seek an approximate Kortewegde Vries equation (KdV) solution to a higher-order traffic flow model with sufficiently large diffusion. It demonstrates the validity of the approximate KdV solution considering all the related parameters to ensure the physical boundedness and the stability of the solution. Moreover, when the viscosity coefficient depends on the density and velocity of the flow, the wave speed of the KdV solution is naturally related to either the first or the second characteristic field. The finite element method is extended to solve the model and
examine the stability and accuracy of the approximate KdV solution.

Acoustic radiation induced by bubble motion in compressible fluid

YE Xi;PANG Fu-Zhen;ZHANG A-Man

2014, 35(2):  177-190.  doi:10.1007/s10483-014-1782-6

Abstract ( 861 )   HTML   PDF (1074KB) ( 493 )  

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Based on the theory of compressible fluid, a three-dimension boundary element method is utilized to research the motion of bubble. The far-field noise radiation during the growth and contraction is calculated by the Kirchhoff formula and the Ffowcs Williams-Hawkings (FW-H) formula with a fixed radiation surface being arranged at the near-field of bubble as a new acoustic source. The results show that the amplitude of the sound pressure induced by non-spherical bubble is lower than that of spherical bubble in the contraction phase. The retardance effect is more obvious when the observer is farther away from the bubble. In the anaphase of contraction, the observer with the maximum amplitude of sound pressure moves up with the obvious jet. Larger buoyance parameters will generate lower sound pressure amplitudes in the anaphase, while larger intensive parameters will cause higher sound pressure amplitudes in the whole procedure of bubble motion.

Robust design of natural laminar flow supercritical airfoil by multi-objective evolution method

ZHAO Ke;GAO Zheng-Hong;HUANG Jiang-Tao

2014, 35(2):  191-202.  doi:10.1007/s10483-014-1783-6

Abstract ( 844 )   HTML   PDF (592KB) ( 825 )  

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A transonic, high Reynolds number natural laminar flow airfoil is designed and studied. The γ-θ transition model is combined with the shear stress transport (SST) k-w turbulence model to predict the transition region for a laminar-turbulent boundary layer. The non-uniform free-form deformation (NFFD) method based on the non-uniform rational B-spline (NURBS) basis function is introduced to the airfoil parameterization. The non-dominated sorting genetic algorithm-II (NSGA-II) is used as the search algorithm, and the surrogate model based on the Kriging models is introduced to improve the efficiency of the optimization system. The optimization system is set up based on the above technologies, and the robust design about the uncertainty of the Mach number is carried out for NASA0412 airfoil. The optimized airfoil is analyzed and compared with the original airfoil. The results show that natural laminar flow can be achieved on a supercritical airfoil to improve the aerodynamic characteristic of airfoils.

Perturbation solutions for asymmetric laminar flow in porous channel with expanding and contracting walls

ZHANG Yan;LIN Ping;SI Xin-Hui

2014, 35(2):  203-220.  doi:10.1007/s10483-014-1784-8

Abstract ( 636 )   HTML   PDF (541KB) ( 394 )  

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The cases of large Reynolds number and small expansion ratio for the asymmetric laminar flow through a two-dimensional porous expanding channel are considered. The Navier-Stokes equations are reduced to a nonlinear fourth-order ordinary differential equation by introducing a time and space similar transformation. A singular perturbation method is used for the large suction Reynolds case to obtain an asymptotic solution by matching outer and inner solutions. For the case of small expansion ratios, we are able to obtain asymptotic solutions by double parameter expansion in either a small Reynolds number or a small asymmetric parameter. The asymptotic solutions indicate that the Reynolds number and expansion ratio play an important role in the flow behavior. Numerical methods are also designed to confirm the correctness of the present asymptotic solutions.

Underlay mechanism in lift-drag phase diagrams for shear flow over cylinder

ZHANG Hui;FAN Bao-Chun;CHEN Zhi-Hua;LI Yan-Ling

2014, 35(2):  221-228.  doi:10.1007/s10483-014-1785-8

Abstract ( 641 )   HTML   PDF (339KB) ( 290 )  

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The characteristics of a uniform-shear flow over a circular cylinder are investigated numerically by using the alternative-direction implicit (ADI) algorithm and a fast Fourier transform (FFT) one in the exponential-polar coordinates for Re=150 and 0K 0.46. The diagram of lift-drag phase, implying the detail information about the fluctuations of drag and lift as well as the flow patterns in the wake and fluctuating pressure on the cylinder surface, is used to describe the effects of the shear rate on the flow. Results show that the upper (or lower) closed curve of a phase diagram corresponds to the first (or second) half shedding cycle. The lift-drag phase diagram will move down-left with the increase of shear rate K such that the lift is exerted from the upper side to the lower side, and the drag on the first half shedding cycle is smaller than that on the second half.

Nonlinear characteristics of circular-cylinder piezoelectric power harvester near resonance based on flow-induced flexural vibration mode

WANG Hai-Ren;XIE Jie-Min;XIE Xuan;HU Yuan-Tai;WANG Ji

2014, 35(2):  229-236.  doi:10.1007/s10483-014-1786-6

Abstract ( 663 )   HTML   PDF (241KB) ( 405 )  

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The nonlinear behaviors of a circular-cylinder piezoelectric power harvester (CCPPH) near resonance are analyzed based on the flow-induced flexural vibration mode. The geometrically-nonlinear effect of the cylinder is studied with considering the in-plane extension incidental to the large deflection. The boundary electric charges generated from two deformation modes, flexure and in-plane extension, were distinguished with each other because the charge corresponding to the latter mode produces no contribution to the output current. Numerical results on output powers show that there are multivaluedness and jump behaviors.

New nonconforming finite element method for solving transient Naiver-Stokes equations

XIE Chun-Mei;FENG Min-Fu

2014, 35(2):  237-258.  doi:10.1007/s10483-014-1787-6

Abstract ( 731 )   HTML   PDF (302KB) ( 343 )  

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For transient Naiver-Stokes problems, a stabilized nonconforming finite element method is presented, focusing on two pairs inf-sup unstable finite element spaces, i.e., PNC1 /PNC1 triangular and PNQ1 /PNQ1 quadrilateral finite element spaces. The semiand full-discrete schemes of the stabilized method are studied based on the pressure projection and a variational multi-scale method. It has some attractive features: avoiding higher-order derivatives and edge-based data structures, adding a discrete velocity term only on the fine scale, being effective for high Reynolds number fluid flows, and avoiding increased computation cost. For the full-discrete scheme, it has second-order estimations of time and is unconditionally stable. The presented numerical results agree well with the theoretical results.

Proximity point algorithm for low-rank matrix recovery from sparse noise corrupted data

ZHU Wei;SHU Shi;CHENG Li-Zhi

2014, 35(2):  259-268.  doi:10.1007/s10483-014-1788-6

Abstract ( 593 )   HTML   PDF (190KB) ( 284 )  

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The method of recovering a low-rank matrix with an unknown fraction whose entries are arbitrarily corrupted is known as the robust principal component analysis (RPCA). This RPCA problem, under some conditions, can be exactly solved via convex optimization by minimizing a combination of the nuclear norm and the l1 norm. In this paper, an algorithm based on the Douglas-Rachford splitting method is proposed for solving the RPCA problem. First, the convex optimization problem is solved by canceling the constraint of the variables, and then the proximity operators of the objective function are computed alternately. The new algorithm can exactly recover the low-rank and sparse components simultaneously, and it is proved to be convergent. Numerical simulations demonstrate the practical utility of the proposed algorithm.