DYNAMICS OF A SUBMERGED AND INCLINED CONCENTRIC PIPE SYSTEM WITH INTERNAL AND EXTERNAL FLOWS

In this paper, we formulate a mathematical model to study the dynamics of submerged and inclined concentric pipes with different lengths. The governing equations of motion for the inner pipe are derived under small deformation assumptions and with the consideration of gravitational forces, turbulent boundary layer thickness of external flow, fluid frictional forces, and inertia effects. We obtain discretized dynamical equations using spatial finite-difference schemes and calculate the resonant frequencies of a particular pipe system design. In addition, by varying the operating conditions, we identify a few critical parameters pertaining to the proper design of such pipe systems.     

分布式运动约束下悬臂输液管的参数共振研究

输液管道结构在航空、航天、机械、海洋、水利和核电等工程领域都有广泛应用,其稳定性、振动与安全评估备受关注.针对具有分布式运动约束悬臂输液管的非线性动力学模型,分别采用立方非线性弹簧和修正三线性弹簧来模拟运动约束的作用力,研究了管道在脉动内流激励下的参数共振行为.首先,从输液管系统的非线性控制方程出发,利用Galerkin方法进行离散化;然后,由Floquet理论得出线性系统在失稳前两个不同平均流速下脉动幅值和脉动频率变化时的共振参数区域;最后,考虑系统的几何非线性项和分布式非线性运动约束力的影响,求解了管道的非线性动力学响应,讨论了非线性项及运动约束力对管道参数共振行为的影响.研究结果表明,系统非线性共振响应的参数区域与线性系统的共振参数区域是一致的,分布式运动约束力对发生参数共振时管道的位移响应有显著影响;立方非线性弹簧和修正三线性弹簧模型所预测的分岔路径存有较大差异,但都可诱发管道在一定的参数激励下出现混沌运动.      

同心旋转圆柱间粘弹性流的非线性动力学模型

基于小间隙假设,将速度场和应力场有杉Ｆｏｕｒｉｅｒ展开式截断近似,推导了同心旋转圆柱间Ｏｌｄｒｏｙｄ－Ｂ型流体的六维动力系统,探讨了高分子添加对滑动轴承间油膜稳定性的影响。结果表明,少量的高分子添加剂具有推迟流体层流失稳的作用。     

NONLINEAR DYNAMICS AND SYNCHRONIZATION OF TWO COUPLED PIPES CONVEYING PULSATING FLUID

In this paper, the nonlinear dynamical behavior of two coupled pipes conveying pulsating fluid is studied. The connection between the two pipes is considered as a distributed linear spring. Based on this consideration, the equations of motion of the coupled two-pipe system are obtained. The two coupled nonlinear partial differential equations, discretized using the fourth- order Galerkin method, are solved by a fourth-order Runge-Kutta integration algorithm. Results show that the connection stiffness has a significant effect on the dynamical behavior of the coupled system. It is found that for some parameter values the motion types of the two pipes might be synchronous.     

Stability Analysis of Maxwell Viscoelastic Pipes Conveying Fluid with Both Ends Simply Supported

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接地惯容式减振器对悬臂输流管稳定性和动态响应的影响研究

输流管道广泛应用于机械、航空、核电和石油等重要工程领域.为防止管道结构因流致振动破坏造成的损失, 很有必要对其稳定性、动力学响应及其调控进行深入研究.本文提出一种由惯容器、弹簧和阻尼器并联组成的减振器模型, 研究了这种接地惯容减振器对悬臂输流管稳定性和非线性振动的影响. 首先, 基于哈密顿原理给出了带有接地惯容减振器非保守系统的非线性动力学模型; 然后, 利用高阶伽辽金方法对非线性方程进行离散化; 最后, 分别从线性和非线性角度分析了不同减振器参数下输流管道的被动控制效果, 着重讨论了惯容系数和减振器安装位置对悬臂管稳定性和动态响应的影响机制.线性理论模型的研究结果显示, 接地惯容减振器可显著影响悬臂管的失稳临界流速, 故通过调节减振器参数能有效提高输流管道的稳定性;惯容系数和弹簧刚度对系统稳定性的控制效果还与减振器的安装位置密切相关.非线性理论模型的分析结果显示, 惯容系数和减振器位置对输流管的非线性动态响应也有显著影响, 且这种影响还依赖于管道的流速取值; 在某些参数条件下, 减振器还可使输流管道由周期运动演化为复杂的混沌行为. 本文研究结果表明, 通过设计合理的惯容式减振器参数, 可提升悬臂输流管道的稳定性并有效抑制其颤振幅值.      

Synchronization of neutral complex dynamical networks with coupling time-varying delays

In this paper, the synchronization problem for a class of neutral complex dynamical networks with coupling time-varying delays is considered. A delay-dependent synchronization criterion is derived for the synchronization of neutral complex dynamical networks. By the use of a convex representation of the sector-restricted nonlinearity in system dynamics, the stability condition based on the discretized Lyapunov?CKrasovskii functional is obtained via LMI (linear matrix inequality) formulation. The effectiveness of our work is verified through a numerical example and simulation.     

结构力学的动态不稳定性

在本回顾性文章中,作者着重论述在结构的稳定性和超临界行为中需要采用动力学方法进行分析的问题．它们包括以下的动态不稳定性：（１）参数激励振动;（２）在冲击载荷下的结构响应;（３）空气－弹性和流体－弹性诱发的动态不稳定性;（４）在所谓随动力作用下的结构响应;（５）输气或输液管道的不稳定性;（６）转子由于转动摩擦或有关因素引起的不稳定性;（７）旋涡诱发的不稳定性;（８）构件的断裂作为一类动态不稳定性．本文的重点放在早期发展历史、开拓性的研究和基本概念,尤其是那些在过去产生过争论但至今在某些方面仍有启发性的题材．与此同时,还讨论一些新近结果和未来研究展望．     

In-plane dynamics of a fluid-conveying corrugated pipe supported at both ends

The dynamics and stability of fluid-conveying corrugated pipes are investigated. The flow velocity is assumed to harmonically vary along the pipe rather than with time. The dimensionless equation is discretized with the differential quadrature method(DQM). Subsequently, the effects of the mean flow velocity and two key parameters of the corrugated pipe, i.e., the amplitude of the corrugations and the total number of the corrugations, are studied. The results show that the corrugated pipe will lose stability by flutter even if it has been supported at both ends. When the total number of the corrugations is sufficient, this flutter instability occurs at a micro flow velocity. These phenomena are verified via the Runge-Kutta method. The critical flow velocity of divergence is analyzed in detail. Compared with uniform pipes, the critical velocity will be reduced due to the corrugations, thus accelerating the divergence instability. Specifically,the critical flow velocity decreases if the amplitude of the corrugations increases. However, the critical flow velocity cannot be monotonously reduced with the increase in the total number of the corrugations. An extreme point appears, which can be used to realize the parameter optimization of corrugated pipes in practical applications.     

Stability analysis of pipes conveying fluid with fractional viscoelastic model

Divergence and flutter instabilities of pipes conveying fluid with fractional viscoelastic model has been investigated in the present work. Attention is concentrated on the boundaries of the stability. Based on the Euler–Bernoulli beam theory for structural dynamics, viscoelastic fractional model for damping and, plug flow model for fluid flow, equation of motion has been derived. The effects of gravity, and distributed follower forces are also considered. By transferring the equation of motion to the Laplace domain and using the Galerkin method, the characteristic equations are obtained. By solving the eigenvalue problem, frequencies and dampings of the system have been obtained versus flow velocity. Some numerical test cases have been studied with viscoelastic fractional model and the effect of the fractional derivative order and the retardation time is investigated for various boundary conditions.

     

Extremely large-amplitude oscillation of soft pipes conveying fluid under gravity

In this work, the nonlinear behaviors of soft cantilevered pipes containing internal fluid flow are studied based on a geometrically exact model, with particular focus on the mechanism of large-amplitude oscillations of the pipe under gravity. Four key parameters, including the flow velocity, the mass ratio, the gravity parameter, and the inclination angle between the pipe length and the gravity direction, are considered to affect the static and dynamic behaviors of the soft pipe. The stability analyses show that, provided that the inclination angle is not equal to π, the soft pipe is stable at a low flow velocity and becomes unstable via flutter once the flow velocity is beyond a critical value. As the inclination angle is equal to π, the pipe experiences, in turn,buckling instability, regaining stability, and flutter instability with the increase in the flow velocity. Interestingly, the stability of the pipe can be either enhanced or weakened by varying the gravity parameter, mainly dependent on the value of the inclination angle.In the nonlinear dynamic analysis, it is demonstrated that the post-flutter amplitude of the soft pipe can be extremely large in the form of limit-cycle oscillations. Besides,the oscillating shapes for various inclination angles are provided to display interesting dynamical behaviors of the inclined soft pipe conveying fluid.     

FLUTTER INSTABILITY OF SUPPORTED PIPES CONVEYING FLUID SUBJECTED TO DISTRIBUTED FOLLOWER FORCES

In the past decades,it has been reported that divergence is the expected form of instability for fluid-conveying pipes with both ends supported.In this paper,the form of instability of supported pipes ...     

Nonlinear dynamics of extensible fluid-conveying pipes,supported at both ends

In this paper, the post-divergence behaviour of extensible fluid-conveying pipes supported at both ends is studied using the weakly nonlinear equations of motion of Semler, Li and Païdoussis. The two coupled nonlinear partial differential equations are discretized via Galerkin's method and the resulting set of ordinary differential equations is solved either by Houbolt's finite difference method or via AUTO. Typically, the pipe is stable at its original static equilibrium position up to the flow velocity where it loses stability by static divergence via a supercritical pitchfork bifurcation. The amplitude of the resultant buckling increases with increasing flow, but no secondary instability occurs beyond the pitchfork bifurcation. The effects of the system parameters on pipe behaviour as well as the possibility of a subcritical pitchfork bifurcation have also been studied.     

Spatial Instabilities of the Incompressible Attachment-Line Flow Using Sparse Matrix Jacobi–Davidson Techniques

We consider the linear stability of incompressible attachment-line flow within the spatial framework. No similarity or symmetry assumptions for the instability modes are introduced and the full two-dimensional representation of the modes is used. The perturbation equations are discretized on a two-dimensional staggered grid. A high order finite difference scheme has been developed which gives rise to a large, sparse, quadratic, eigenvalue problem for the instability modes. The benefits of the Jacobi–Davidson method for the solution of this eigenvalue system are demonstrated and the approach is validated in some detail. Spatial stability results are presented subsequently. In particular, instability predictions at very high Reynolds numbers are obtained which show almost equally strong instabilities for symmetric and antisymmetric modes in this regime.     

On the stability of plane parallel viscoelastic shear flows in the limit of infinite Weissenberg and Reynolds numbers

Elastic effects on the hydrodynamic instability of inviscid parallel shear flows are investigated through a linear stability analysis. We focus on the upper convected Maxwell model in the limit of infinite Weissenberg and Reynolds numbers. We study the effects of elasticity on the instability of a few classes of simple parallel flows, specifically plane Poiseuille and Couette flows, the hyperbolic-tangent shear layer and the Bickley jet.The equation for stability is derived and solved numerically using the spectral Chebyshev collocation method. This algorithm is computationally efficient and accurate in reproducing the eigenvalues. We consider flows bounded by walls as well as flows bounded by free surfaces. In the inviscid, nonelastic case all the flows we study are unstable for free surfaces. In the case of wall bounded flow, there are instabilities in the shear layer and Bickley jet flows. In all cases, the effect of elasticity is to reduce and ultimately suppress the inviscid instability.     

同心旋转圆柱间弱弹性流的非线性稳定性分析

基于同心旋转圆柱间Ｏｌｄｒｏｙｄ－Ｂ型流体的六维动力系统,探讨了小间隙大扰动条件下高分子添加剂对滑动轴承间油膜非线性稳定性的影响。结果表明,弱弹性流体的失稳结构与牛顿流体相似,随着转速的增加,流体以同宿轨道分岔失稳,与牛顿流体相比,少量的高分子添加剂具有推迟流体层流的稳的作用。     

Time dependent flow in equimolar micellar solutions: transient behaviour of the shear stress and first normal stress difference in shear induced structures coupled with flow instabilities

Recently we studied time dependent structural changes that are coupled with flow instabilities (Fischer 1998; Wheeler 1998; Fischer 2000). Within a stability analysis, a classification scheme for the feedback circuit of coupled shear-induced structure and flow instabilities was derived by Schmitt et al. (1995) and applied to our samples. Here, inhomogeneous flow layers of different concentration and viscosity are generated by shear-induced diffusion (spinodal demixing) and, as consequence, one no longer observes a homogeneous solution but a type of shear banding that is seen here for the first time. In this paper we present the behaviour of the first normal stress difference observed in the critical shear-rate regime where transient shear-induced structure is coupled with flow instability. Similar to the oscillations of the shear stresses (strain-controlled rheometer) one observes oscillations in the first normal stress difference. This behaviour indicates that elastic structures are built up and destroyed while the shear-induced structures occur and that the induced phase is more elastic than the initial one. Oscillations of shear stress and first normal stress difference are in phase and indicate that both phenomena are caused by the same mechanism. Received: 30 June 1999/Accepted: 14 December 1999     

Stability of a numerical algorithm for gas bubble modelling

A free-surface-tracking algorithm based on the SOLA-VOF method is analysed for numerical stability when modelling gas bubble evolution in a fluid. It is shown that an instability can arise from the fact that the bubble pressure varies with its volume. A time step stability criterion is introduced which is a function of the natural oscillation period but does not depend on the mesh size. This dependence suggests that the instability is likely to arise in the case of a general motion of a bubble, especially if break-up occurs. The effect is shown using linear Fourier analysis of the discretized equation for radial bubble oscillation and demonstrated numerically using a CFD code FLOW-3D. One- and three-dimensional situations are considered: a bubble in a fluid bounded by two concentric surfaces and a bubble floating in a fluid chamber with and without gravity. In cases where no analytical solution is available, a numerical method for the stability time step limit calculation is suggested based on finding the natural oscillation frequency. The nature of the instability suggests that it can be a feature of any numerical algorithm which models transient fluid flow with a free surface.     

Instability of sintering of porous bodies

Sintering models are discussed and used to analyze flow instabilities that may arise during preliminary compaction of powders. These instabilities can be at the origin of heterogeneities in the densification. The material is modeled as a viscoplastic thermal sensitive porous material. The modeling includes the limit case of a linear viscous material. The effects of sintering conditions (temperature and pressure in the case of pressure sintering) and the effects of material characteristics such as porosity, heat capacity, theoretical density, surface tension, particle size and creep parameters on stability of sintering are investigated. The heat release associated with the plastic flow is shown to sometimes have an important role. Stability criteria are derived and applied to the analysis of sintering and hot isostatic pressing, using various sintering models. These stability criteria can be used to optimize the densification process; one can control, for example, temperature so as to avoid any instability. Stability maps enabling an optimization of temperature–pressure regime in hot isostatic pressing are built for sample metal (nickel) powder.     

Visualizations of the flow inside an open cavity at medium range Reynolds numbers

The interaction between a laminar boundary layer and an open cavity is investigated experimentally for medium range Reynolds numbers. Flow visualizations are carried out for three different observation directions in order to understand the spatial development of dynamical structures. In particular, synchronized visualizations in two parallel planes picture the transverse development of the flow. The study is conducted by changing the cavity aspect ratio, the Reynolds number and therefore the flow patterns inside the cavity. The issue is to emphasize the 3-D development of the flow. In particular, we show that the dynamical structures are not due to secondary shear layer instabilities.