Convective heat transfer from two rotating circular cylinders in tandem arrangement by using lattice Boltzmann method

The numerical investigation of the two-dimensional laminar flow past two ro- tating circular cylinders in the tandem arrangement is conducted by the lattice Boltzmann method. The numerical strategy is used for dealing with curved and moving boundaries of the second-order accuracy for velocity and temperature fields. The effects of various rotational speed ratios and gap spacing are studied with the Reynolds number of 100 and the Prandtl number of 0.71. A varied range of rotational speed ratios are investigated for four different gap spacing, i.e., 3.0, 1.5, 0.7, and 0.2. The results show that, for the first cylinder, the lift and drag coefficients for large gap spacing are similar to those for a single cylinder; for the second cylinder, the lift coefficient descends with the increase in the angular velocity for all gap spacing, while the drag coefficient ascends except for the gap spacing of 3.0. The results of the averaged periodic Nusselt number on the surface of the cylinders show that, for small distances between the cylinders and low angular velocities, conduction is a dominant mechanism of heat transfer, but for large distances and high angular velocities, convection is the main mechanism of heat transfer.     

Investigation of incompressible flow within ½ circular cavity using lattice Boltzmann method

A wall‐driven incompressible viscous flow in a ½ circular cavity is simulated, based on the lattice Boltzmann method (LBM). The treatment of curved boundary with second‐order accuracy is used. The force evaluation is based on the momentum‐exchange method. The streamlines and vorticity contours and the velocity component along the central line of a semi‐circular cavity are obtained for different Reynolds numbers. The numerical results show that the LBM can capture the formation of primary, secondary and tertiary vortices exactly as the Reynolds number increases and has a great agreement with those of current literatures. Copyright © 2008 John Wiley & Sons, Ltd.     

Flux modelling in the finite-volume lattice Boltzmann approach

In this article, a novel approach for flux treatment is presented in conjunction with cell-centred Finite-Volume Lattice Boltzmann Method (FVLBM). The distribution functions are determined by using a pressure-based flux weighting factor on a D₂Q₉ lattice. A consistent open and solid boundary treatment is also addressed, which resulted in a wider domain of stability and faster convergence. For time discretisation, a fifth-order Runge–Kutta algorithm was applied. An in-house FORTRAN code has been written by the authors which uses the time-marching along with FVLBM. Two test cases, namely, flow over a backward-facing step and around a circular cylinder are carried out. The results are compared with the available solutions in which favourable agreement was observed.     

Application of the modified method of multiple scales to solving the problem of a thin clamped circular plate of a very large deflection

In this paper,asymptotic behaviour of the solution to the problem of a thin clamped circular plate under uniform normal pressure at very large deflection is restudied by means of the modified method of multiple scales given in[1?].The result presented herein is in good agreement with the one obtained by professor Chien Wei-zang who first proposed the method of composite expansions to solve this problem in[3].However,by contrast,the advantage of the modified method of multiple scales it seems to be relatively simpler than the method used in[3].It is also shown that the restriction of the method of paper[1-2]pointed out in paper[4]is not essential,and several computation errors in[3]are corrected as well.     

基于浸入边界-格子Boltzmann通量求解法的椭圆柱流动特性分析

基于浸入边界-格子Boltzmann通量求解法,开展了雷诺数Re=100不同几何参数下单椭圆柱及串列双椭圆柱绕流流场与受力特性对比研究。结果表明,随长短轴比值的增加,单椭圆柱绕流阻力系数先减小后缓慢上升,最大升力系数则随长短轴比值的增大而减小;尾迹流动状态从周期性脱落涡到稳定对称涡。间距是影响串列圆柱及椭圆柱流场流动状态的主要因素,间距较小时,串列圆柱绕流呈周期性脱落涡状态,而椭圆柱则为稳定流动;随着间距增加,上下游圆柱及椭圆柱尾迹均出现卡门涡街现象,且串列椭圆柱临界间距大于串列圆柱。串列椭圆柱阻力的变化规律与圆柱的基本相同,上游平均阻力大于下游阻力;上游椭圆柱阻力随着间距的变大先减小,下游随间距的变大而增加,当间距达到临界间距时上下游阻力跃升,随后出现小幅度波动再逐渐增加,并趋近于相同长短轴比值下单柱体绕流的阻力。     

Application of local DFD method to simulate unsteady flows around an oscillating circular cylinder

In this paper, the recently proposed local domain‐free discretization (DFD) method is applied to simulate incompressible flows around an oscillating circular cylinder. It is found that it is very easy for the local DFD method to handle such moving boundary flow problems. This is because it does not need to move the mesh, which is indeed needed in traditional methods. Numerical experiments show that the present numerical results agree very well with the available data in the literature, and that the local DFD method is an effective tool for the computation of moving boundary flow problems. Copyright © 2008 John Wiley & Sons, Ltd.     

Vibration problems of flexible circular plates with initial deflection

In this paper,the differential equations of flexible circular plates with initialdeflection are derived.The stability of motion is investigated in phase plane.Theperiodical solutions of nonlinear vibration for circular plates with initial deflection areobtained by use of Galerkin method and Lindstedt-Poincare perturbation method.Theeffect of initial deflection on the dynamic behavior of the flexible plates are alsodiscussed.     

General solution for large deflection problems of nonhomogeneous circular plates on elastic foundation

In this paper, a new method is presented based on [1]. It can be used to solve the arbitrary nonlinear system of differential equations with variable coefficients. By this method, the general solution for large deformation of nonhomogeneous circular plates resting on an elastic foundation is derived. The convergence of the solution is proved. Finally, it is only necessary to solve a set of nonlinear algebraic equations with three unknowns. The solution obtained by the present method has large convergence range and the computation is simpler and more rapid than other numerical methods.Numerical examples given at the end of this paper indicate that satisfactory results of stress resullants and displacements can be obtained by the present method. The correctness of the theory in this paper is, confirmed.     

ON THE METHOD OF ORTHOGONALITY CONDITIONS FOR SOLVING THE PROBLEM OF LARGE DEFLECTION OF CIRCULAR PLATE

In this paper,we reexamine the method of successive approximation presented byProf.Chien Wei-zang for solving the problem of large deflection of a circular plate,and findthat the method could be regarded as the method of strained parameters in the singularperturbation theory.In terms of the parameter representing the ratio of the centerdeflection to the thickness of the plate,we make the asymptotic expansions of thedeflection,membrane stress and the parameter of load as in Ref.[1],and then give theorthogonality conditions(i.e.the solvability conditions)for the resulting equations,bywhich the stiffness characteristics of the plate could be determined.It is pointed out thatwith the solutions for the small deflection problem of the circular plate and theorthogonality conditions,we can derive the third order approximate relations between theparameter of load and the center deflection and the first-term approximation of membranestresses at the center and edge of the plate without solving the differential equ     

An evaluation of a 3D free‐energy‐based lattice Boltzmann model for multiphase flows with large density ratio

In this paper, the 3D Navier–Stokes (N–S) equation and Cahn–Hilliard (C–H) equations were solved using a free‐energy‐based lattice Boltzmann (LB) model. In this model, a LB equation with a D3Q19 velocity model is used to recover continuity and N–S equations while another LB equation with D3Q7 velocity model for solving C–H equation (Int. J. Numer. Meth. Fluids, 2008; 56 :1653–1671) is applied to solve the 3D C–H equation. To avoid the excessive use of computational resources, a moving reference frame is adopted to allow long‐time simulation of a bubble rising. How to handle the inlet/outlet and moving‐wall boundary conditions are suggested. These boundary conditions are simple and easy for implementation. This model's performance on two‐phase flows was investigated and the mass conservation of this model was evaluated. The model is validated by its application to simulate the 3D air bubble rising in viscous liquid (density ratio is 1000). Good agreement was obtained between the present numerical results and experimental results when Re is small. However, for high‐Re cases, the mass conservation seems not so good as the low‐Re case. Copyright © 2009 John Wiley & Sons, Ltd.     

An analytical method for a mixed boundary value problem of circular plates under arbitrary lateral loads

In this paper by using the concept of mixed boundary functions,an analytical method is proposed for a mixed boundary value problem of circular plates.The trial functions are constructed by using the series of particular solutions of the biharmonic equations in the polar coordinate system.Three examples are presented to show the stability and high convergence rate of the method.     

Numerical simulation of fluid flow of two rotating side-by-side circular cylinders by Lattice Boltzmann method

A numerical investigation of the two-dimensional laminar flow around side-by-side rotating circular cylinders using Lattice Boltzmann method is conducted. The effects of variation of rotational speed ratio β and different gap spacings g* at Reynolds number of 100 are studied. A various range of rotational speed ratio 0 ≤ β ≤ 2 for four different gap spacings of 3, 1.5, 0.7 and 0.2 are investigated. Flow conditions and its characteristics, such as lift and drag coefficients and Strouhal number, is studied. The results indicated that as β increases, the flow changes its condition from periodic to steady after a critical rotational speed. Results also indicated that variation of the gap spacing and rotational speed has significant effect on wake pattern. Wake pattern in turn has significant effect on the Strouhal number. Finally, the result is compared with experimental and other numerical data.     

A comparative study of lattice Boltzmann methods using bounce‐back schemes and immersed boundary ones for flow acoustic problems

In order to find applicable treatments of moving boundary conditions based on the lattice Boltzmann method in flow acoustic problems, three bounce‐back (BB) methods and four kinds of immersed boundary (IB) methods are compared. We focused on fluid–solid boundary conditions for flow acoustic problems especially the simulations of sound waves from moving boundaries. BB methods include link bounce‐back, interpolation bounce‐back and unified interpolation bounce‐back methods. Five IB methods are explicit and implicit direct‐forcing (Explicit‐IB and Implicit‐IB), two kinds of partially saturated computational methods and ghost fluid method. In order to reduce the spurious pressure generated by the fresh grid node changing from solid domain to fluid domain for BB methods and sharp IB methods, we proposed two new kinds of treatments and compared them with two existing ones. Simulations of the benchmark problems prove that the local evolutionary iteration (LI) is the best one in treatments of the fresh nodes. In addition, for standing boundary problems, although BB methods have a little higher accuracy, all the methods have similar accuracy. However, for moving boundary problems, IB methods are more appropriate than BB methods, because IB methods' smooth interpolation of pressure eld produces less disturbing spurious pressure waves. With improved treatments of fresh nodes, BB methods are also acceptable for moving boundary acoustic problems. In comparative tests in respective type, unified interpolation bounce‐back with LI, Implicit‐IB, and ghost fluid with LI are the best choices. Copyright © 2013 John Wiley & Sons, Ltd.     

Simulation of three‐dimensional flows over moving objects by an improved immersed boundary–lattice Boltzmann method

An improved immersed boundary–lattice Boltzmann method (IB–LBM) developed recently [28] was applied in this work to simulate three‐dimensional (3D) flows over moving objects. By enforcing the non‐slip boundary condition, the method could avoid any flow penetration to the wall. In the developed IB–LBM solver, the flow field is obtained on the non‐uniform mesh by the efficient LBM that is based on the second‐order one‐dimensional interpolation. As a consequence, its coefficients could be computed simply. By simulating flows over a stationary sphere and torus [28] accurately and efficiently, the proposed IB–LBM showed its ability to handle 3D flow problems with curved boundaries. In this paper, we further applied this method to simulate 3D flows around moving boundaries. As a first example, the flow over a rotating sphere was simulated. The obtained results agreed very well with the previous data in the literature. Then, simulation of flow over a rotating torus was conducted. The capability of the improved IB–LBM for solving 3D flows over moving objects with complex geometries was demonstrated via the simulations of fish swimming and dragonfly flight. The numerical results displayed quantitative and qualitative agreement with the date in the literature. Copyright © 2011 John Wiley & Sons, Ltd.     

Numerical simulation of laminar jet-forced flow using lattice Boltzmann method

In the paper, a numerical study on symmetrical and asymmetrical laminar jet-forced flows is carried out by using a lattice Boltzmann method （LBM） with a special boundary treatment. The simulation results are in very good agreement with the available numerical prediction. It is shown that the LBM is a competitive method for the laminar jet-forced flow in terms of computational efficiency and stability.     

A new technique for solving non-axially symmetrical large deflection of elastic and thin circular plates

I.IntroductionBecauseofthenonlinearityoflargedeflectionproblemofthinplates,itisquitedifficulttoobtainitsaccuratesolution.Thereforeanapproximatesolutiontoitobtainedbyanappropriatemethodisdesired.Thetechniquesocalledperturbation,beingabletogiveresultswithadequateprecision,isofaprevailingandeffectiveonetobegenerallyaccepted.W.Z.Chientl]succesfullyobtainedanapproximatesolutiontothelargedeflectionproblemofthincircularplatefie-curalaxisymmetricallybyperturbationtechnique.X.Z.Wangl'Jgainedthedispl…     

Nonsymmetrical large deformation bending problem of circular thin plates

To begin with, in this paper, the displacement governing equations and the boundary conditions of nonsymmetrical large deflection problem of circular thin plates are derived. By using the transformation and the perturbation method, the nonlinear displacement equations are linearized, and the approximate boundary value problems are obtained. As an example, the nonlinear bending problem of circular thin plates subjected to comparatively complex loads is studied.     

求解矩形夹层板在集中载荷下的稳定问题

在考虑了横向切应力和横向正应力对夹层板稳定影响的情况下,给出了矩形夹层板结构屈曲失稳的控制方程、基本解以及边界条件。应用功的互等定理求解了在均布载荷作用下的矩形夹层板的屈曲失稳问题。     

Unsymmetrical large deformation problem of orthotropic plates

Based upon the theory of ardsotropic plates, the unsymmetrical large deformation equations of orthotropic circular plates were derived. By using Fourier series, the partial differential equations of this problem can be transformed into sets of nonlinear differential equations . And the procedure to solve the problem using the iterative method is given .     

Iterative method for large deflection nonlinear problem of laminated composite shallow shells and plates

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