Symplectic analysis for wave propagation in one-dimensional nonlinear periodic structures

The wave propagation problem in the nonlinear periodic mass-spring structure chain is analyzed using the symplectic mathematical method. The energy method is used to construct the dynamic equation, and the nonlinear dynamic equation is linearized using the small parameter perturbation method. Eigen-solutions of the symplectic matrix are used to analyze the wave propagation problem in nonlinear periodic lattices. Nonlinearity in the mass-spring chain, arising from the nonlinear spring stiffness effect, has profound effects on the overall transmission of the chain. The wave propagation characteristics are altered due to nonlinearity, and related to the incident wave intensity, which is a genuine nonlinear effect not present in the corresponding linear model. Numerical results show how the increase of nonlinearity or incident wave amplitude leads to closing of transmitting gaps. Comparison with the normal recursive approach shows effectiveness and superiority of the symplectic method for the wave propagation problem in nonlinear periodic structures.     

AN ANALYTICAL SOLUTION OF SECOND－ORDER WAVE FORCE ON A VERTICAL CIRCULAR CYLINDER

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Experimental investigation of the flow around a radially vibrating circular cylinder

This work aims to develop a process for controlling a cylinder wake, especially the von Karman vortex street, in such way so as to drastically reduce the drag coefficient. A new technique for influencing the cylinder wake is proposed in the present experimental study. The flow around a circular cylinder is perturbed by temporarily changing the cylinder diameter. Experiments have been performed for Reynolds numbers in the range Re=9,500 to Re=31,500. Three values of the controlling frequencies are considered: fs₁=0.41, fs₂=0.54 and fs₃=0.73, in addition to the stationary case corresponding to a non-deformable cylinder, fs₀=0. The visualisation flow shows that the pulsing motion of the cylinder walls greatly influences both the near and far wake dynamics. A decrease of the drag is expected.

Experimental investigation of a confined flow downstream of a circular cylinder centred between two parallel walls

In this work, we present an experimental study of the wall confinement effect on the wake formation behind a circular cylinder of diameter d_c=10 mm and of length L_c=30d_c. The experiments were performed in a water tunnel with the dimensions (length=300d_c, height=3d_c, span L_c=30d_c). The confinement rate was r=1/3 and the Reynolds number was in the range of 30–277. The experiments were done using 2-D PIV measurements. The first instability was delayed by the confinement and the von Kármán vortices characteristics are different from the unconfined case. Proper orthogonal decomposition (POD) of the flow was used for a filtering purpose and to extract the energetic contribution of the different modes. A low-order representation of the flow, constructed from the first pair of modes in the well-defined region of the flow, shows that von Kármán vortices are equivalent to vanishing progressive waves. Measurements done above the cylinder show the presence of 3-D span instabilities showing great similarities with “Mode A” and “Mode B” found in the unconfined case.     

Steady flow around,and drag on a circular cylinder moving at low speeds in a viscous liquid between two parallel planes 1

The present paper deals with the two-dimensional viscous flow around a circular cylinder moving at low speeds along the central plane parallel to two parallel side planes. It is semi-analytically solved by applying the collocation method for the stream function. The present results for velocity, pressure and viscous stress agree well with other numerical results. The pressure drag and the friction drag on a cylinder are obtained from the pressure distribution and the viscous stress distribution at the surface of a circular cylinder, respectively. It is shown that the pressure drag is larger than the friction drag and the ratio of the former to the latter decreases with increase of the distance between the two parallel side planes. An empirical formula for the drag which fits the present results is obtained by modifying Faxen's analytical formula. The new formula covers a wider range of the distance between the two side planes than Faxen's one.     

Milu-CG method and the numerical study on the flow around a rotating circular cylinder

I.IntroductionTilenowaroundarotatitlgcircularcylinderisacomplexunsteadyone.ItincludesmanycomplicatedtlowphenomenaSuchastheunsteadyboundarylayerseparation,thegenerationandsheddingofvorticesandtheinteractionwitllwakesetc..Therotationofacircularcylillderarounditsaxiswilldecreaseandsuppresstheflowseparationandvortexsheddingononesideofthecylinder,whileincreasinganddevelopingonanothel,side.Atransverseliftforcewillactonthecylinder,andthisphenomenoniscalledtheMagnuseffect.Themost.importantparameterf…     

Numerical solution for the flow of viscoelastic fluids around an inclined circular cylinder.

Finite difference solutions have been obtained by the perturbation method to investigate the influence of shear thinning and elasticity on the flow around an inclined circular cylinder of finite length in a uniform flow. In this numerical analysis a generalized upper-convected Maxwell model, in which the viscosity changes according to the Cross model, has been used.The local flow over the cylinder is only slightly deflected. However, in the wake flow behind the cylinder the particle path is remarkably influenced by the axial flow and rapidly flows up parallel to the cylinder's axis. Then it gradually rejoins direction of the incoming flow. It is found that viscoelastic fluids are prone to flow axially in the vicinity of the cylinder. The numerical predictions generally agree with the flow visualization results.The numerical solutions also demonstrate that elasticity has a strong effect on the velocity profile especially around both ends of the cylinder; elasticity increases the asymmetric profiles of both circumferential velocity and axial velocity with respect to equal to 90° and decreases a difference in the circumferential velocity between the windward end and the leeward end.For non-Newtonian fluids, the length of the wake flow is influenced by not only the Reynolds number but also the cylinder diameter and it is larger for the cylinder with the smaller diameter at the same Reynolds number.Partly presented at the 9th Australasian Fluid Mechanics Conference, University of Auckland, New Zealand, 8–12 December, 1986     

A numerical study of the vortex motion in oscillating flow around a circular cylinder at low and middlieKc numbers

A new hybrid model, which is based on domain decomposition and proposed by the authors, is used for calculating the flow around a circular cylinder at low and middle Keulegan-Carpenter numbers (Kc=2−18) respectively. The vortex motion patterns in asymmetric regime, single pair (or transverse) regime and double pair (or diagonal) regime are successfully simulated. The calculated drag and inertial force coefficients are in better agreement with experimental data than other recent computational results. The project supported by the National Natural Science Foundations of China and the LNM, Institute of Mechanics, Academia Sinica     

Unsteady characteristics of the cavity flow around a rough circular cylinder

Effects of surface roughness on the unsteady cavitating flow around a two-dimensional circular cylinder were experimentally investigated at Reynolds numbers from 1.36 × 10⁵ to 1.78 × 10⁵. Two patterns of surface roughness were investigated, a double-cut pattern and a single-cut pattern. The cavity elongates with an increase of the surface roughness, especially in supercavitating flow. However, for some roughness parameters tested, the cavity length exhibits an extreme decrease. In a particular case of the double-cut pattern, there exists the minimum cavity behind the cylinder.     

非线性转子-轴承系统的周期解及近似解析表达式

通过对普通打靶方法进行改造提出一种确定非线性系统周期轨道及周期的新型打靶算法。首先通过改变系统的时间尺度,将非线性系统周期轨道的周期显式地出现在非线性系统的系统方程中,然后对传统打靶法进行改造,将周期也作为一个参数一起参与打靶法的迭代过程,迭代过程包含对周期轨道和周期的求解,迭代过程中的增量通过优化方法选择,从而能迅速确定出系统的周期轨道及其周期。应用所求的结果结合谐波平衡方法求得了非线性系统的周期轨道的近似解析表达式,理论上通过增加谐波的阶数任何精度的周期解都可以得到。最后将该方法应用于非线性转子轴承系统,求出了在某些参数下转子的周期解及其近似解析表达式,通过与四阶Runge-Kutta数值积分结果比较,验证了方法的有效性,计算结果对于转子系统运动的定量控制有重要理论指导意义。     

Suppression of vortex shedding for flow around a circular cylinder using optimal control

Adjoint formulation is employed for the optimal control of flow around a rotating cylinder, governed by the unsteady Navier–Stokes equations. The main objective consists of suppressing Karman vortex shedding in the wake of the cylinder by controlling the angular velocity of the rotating body, which can be constant in time or time‐dependent. Since the numerical control problem is ill‐posed, regularization is employed. An empirical logarithmic law relating the regularization coefficient to the Reynolds number was derived for 60?Re?140. Optimal values of the angular velocity of the cylinder are obtained for Reynolds numbers ranging from Re=60 to Re=1000. The results obtained by the computational optimal control method agree with previously obtained experimental and numerical observations. A significant reduction of the amplitude of the variation of the drag coefficient is obtained for the optimized values of the rotation rate. Copyright © 2002 John Wiley & Sons, Ltd.     

An approximate analytical solution of the cylindrical detonation wave generated by the linear explosion

The solution of the cylindrical detonation wave generated by the linear explosion was obtained by numerical method in ref.[1].In this paper,when the ratio of specific heatγ》1 by using the enlargement coordinate method,the first-order analytical solutions are obtained.The perturbation parameter isε=1/γ~2 .The correction of these solutions is checked at the end of this paper.     

On the topological bifurcation of flows around a rotating circular cylinder

Flow fields around a rotating circular cylinder in a uniform stream are computed using a low dimensional Galerkin method. Reslts show that the formation of a Fopple vortex pair behind a stationary circular cylinder is caused by the structural instability in the vicinity of the saddle located at the rear of the cylinder. For rotating cylinder a bifurcation diagram with the consideration of two parameters, Reynolds numberRe and rotation parameter α, is built by a kinematic analysis of the steady flow fields. The project supported by the National Natural Science Foundation of China     

A new method for the periodic solution of strongly nonlinear systems

A new method for the periodic solution of strongly nonlinear system is given. By using this method, the existance and stability of the periodic solution can be decided, and the approximate expression of the periodic solution can also be found. The project supported by the National Natural Science Foundation of China     

The motion of rodlike particles in the pressure-driven flow between two flat plates

The motion of freely suspended rodlike particles has been observed in the pressure-driven flow between the two flat plates of a Hele Shaw flow cell at low Reynolds numbers. Data are reported for rodlike particles with aspect ratios of 12.0 suspended in a Newtonian fluid for gap thickness to particle length ratios of 3, 6, and 20; and for rodlike particles with aspect ratios between 5 and 8 in a non-Newtonian fluid (79.25 wt.% water, 20.2 wt.% glycerine, and 0.55 wt.% polyacrylamide). For the Newtonian fluid, the time-dependent orientation of the particles near and far from walls was shown to be in quantitative agreement with Jeffery's theory for ellipsoids suspended in a simple shear flow if an effective aspect ratio is calculated from the experimental period of rotation. Particles aligned with the flow direction and less than a particle half-length from a wall interacted irreversibly with the wall. For the non-Newtonian fluid, the timedependent orientation far from a wall was shown to be in qualitative agreement with Leal's theory for a second-order fluid; however, particles that were aligned with the flow direction and were near walls did not rotate.     

NUMERICAL STUDY ON THE FLOW AROUND A CIRCULAR CYLINDER WITH SURFACE SUCTION OR BLOWING USING VORTICITY-VELOCITY METHOD

A vorticity-velocity method was used to study the incompressible viscous fluid flow around a circular cylinder with surface suction or blowing. The resulted high order implicit difference equations were effeciently solved by the modified incomplete LU decomposition conjugate gradient scheme (MILU-CG). The effects of surface suction or blowing ' s position and strength on the vortex structures in the cylinder wake, as well as on the drag and lift forces at Reynoldes number Re = 100 were investigated numerically. The results show that the suction on the shoulder of the cylinder or the blowing on the rear of the cylinder can effeciently suppress the asymmetry of the vortex wake in the transverse direction and greatly reduce the lift force; the suction on the shoulder of the cylinder, when its strength is properly chosen , can reduce the drag force significantly , too.     

四角点支承四边自由矩形薄板屈曲问题的新解析解

角点支承矩形薄板的屈曲问题是板壳力学的一类重要课题，控制方程和边界条件的复杂性导致寻求该类问题的解析解十分困难。虽然各类近似/数值方法可用于解决此类难题，但作为基准的精确解析解在公开文献中鲜有报道。本文基于近年来提出的辛叠加方法，解析求解了四角点支承四边自由矩形薄板的屈曲问题。首先将问题拆分为两个子问题，接着利用分离变量与辛本征展开推导出子问题的解析解，最后通过叠加获得原问题的解。由于求解过程从基本控制方程出发，逐步严格推导，无需假定解的形式，因此本文解法是一种理性的解析方法。数值算例给出了不同长宽比和不同面内载荷比情况下，四角点支承四边自由矩形薄板的屈曲载荷和典型屈曲模态，并经有限元方法验证，确认了解析解的正确性。