Wind-excited vibrations of transmission lines: A comparison of different mathematical models

In this paper, the modelling of wind-excited vibrations of conductor cables in overhead transmission lines is discussed. Only oscillations in the frequency range from 10 Hz to 50 Hz due to vortex shedding are considered. Different mathematical models are proposed for the cables, for the aerodynamic forces and for the dampers. The models are compared and their relative merits are summarized. Finally, a relatively simple approach is proposed for the calculation of the bending strains in the cables of a transmission line with dampers. The problem is an example of how mathematical modelling at different levels combines mathematical tools with engineering insight into the physical problem.     

Numerical simulation of vortex induced vibrations and its control by suction and blowing

The vortex formation and shedding behind bluff structures is influenced by fluid flow parameters such as, Reynolds number, surface roughness, turbulence level, etc. and structural parameters such as, mass ratio, frequency ratio, damping ratio, etc. When a structure is flexibly mounted, the Kármán vortex street formed behind the structure gives rise to vortex induced oscillations. The control of these flow induced vibrations is of paramount practical importance for a wide range of designs. An analysis of flow patterns behind these structures would enable better understanding of wake properties and their control. In the present study, flow past a smooth circular cylinder is numerically simulated by coupling the mass, momentum conservation equations along with a dynamical evolution equation for the structure. An active flow control strategy based on zero net mass injection is designed and implemented to assess its efficacy. A three actuator system in the form of suction and blowing slots are positioned on the cylinder surface. A single blowing slot is located on the leeward side of the cylinder, while two suction slots are positioned at an angle α = 100°. This system is found to effectively annihilate the vortex induced oscillations, when the quantum of actuations is about three times the free stream velocity. The dynamic adaptability of the proposed control strategy and its ability to suppress vortex induced oscillations is verified. The exact quantum of actuation involved in wake control is achieved by integrating a control equation to decide the actuator response in the form of a closed loop feed back system. Simulations are extended to high Reynolds number flows by employing eddy viscosity based turbulence models. The three actuator system is found to effectively suppress vortex induced oscillations.     

Magnetic field effects on Newtonian and non-Newtonian ferrofluid flow past a circular cylinder

The changes in the flow properties under the action of electromagnetic body forces are investigated numerically for ferrofluid flow past a circular cylinder. Ferrofluid is modeled as both a Newtonian and a non-Newtonian Power-Law fluid. Magnetic forces are applied by placing magnets at different locations on the surface of the cylinder. The magnetostatic effects on the structure of the wake region, on drag reduction and on vortex formation length and frequency are shown and compared in terms of Reynolds number, interaction parameter, Power-Law index and magnet location. It is shown that the increase in the interaction parameter reduces drag for both Newtonian and non-Newtonian model. This decrease is observed to be higher for shear thinning and lower for shear thickening fluid compared to Newtonian case. It is also shown that vortex street formation in the wake region behind the cylinder may be delayed under high magnetic effects. The Strouhal number is higher for shear thinning case at both low and high Reynolds numbers, and lower for shear thickening case at high Reynolds numbers, compared to Newtonian fluid. The vortex formation frequency also decreases under the action of the magnetic field in all cases, however the vortex formation length increases. Placing the magnet towards the front region of the cylinder increases considerably the drag coefficient for both Newtonian and non-Newtonian model. This increase in drag coefficient is higher in the shear thinning fluid and lower in the shear thickening fluid compared to the Newtonian case.     

The Vibrational Behavior of Bladed Disks in Consideration of Friction Damping and Contact Elasticity

Rotating turbine blading is subjected to fluctuating gas forces during operation that cause blade vibrations. One of the main tasks in the design of turbomachinery blading is the reduction of the vibration amplitudes of the blades to avoid high resonance stresses that could damage the blading. The vibration amplitudes of the blades can be reduced significantly to a reasonable amount by means of friction damping devices such as underplatform dampers. In the case of blade vibrations, relative displacements between the friction damping devices and the neighboring blades occur and friction forces are generated that provide additional damping to the structure due to the dry friction energy dissipation. In real turbomachinery applications, spatial blade vibrations caused by a complex blade geometry and distributed excitation forces acting on the airfoil accur. Therefore, a three dimensional model including an appropriate spatial contact model to predict the generalized contact forces is necessary to describe the vibrational behavior of the blading with sufficient accuracy, see [1] and [2]. In this paper the contact model presented in [2] is extended to include also local deformations in the contacts between underplatform dampers and the contact surfaces of the adjacent blades. The additional elasticity in the contact influences the resonance frequency of the coupled bladed disk assembly. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Diffraction of water waves by a slotted cylindrical breakwater

Permeable and slotted breakwaters are becoming more popular, in order to reduce the drawback of rigid coastal structures: namely large reflections, forces and overtopping. The linearized theory of water waves is used to examine the diffraction of incident regular waves by a vertically slotted cylindrical breakwater that consists of a number of distinct rigid cylindrical panels. Under the assumption that the wavelength is much greater than the thickness, each segment is replaced by a thin structure and the permeability is modelled by suitable boundary conditions. The first condition is the matching pressure and normal velocity conditions between two internal and external fluid regions and the second condition is zero normal velocity on rigid panels. The mixed boundary–value problem is transformed to dual series relations and the least–square method is applied to get the forces on the structure. The results are presented to illustrate the effects of permeability. Numerical results compare well with McCamy and Fuchs predictions for the limiting case of an impermeable rigid cylinder. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The effects of vortex breakdown bubbles on the mixing environment inside a base driven bioreactor

The bubble-type vortex breakdown inside a cylinder with flow driven by rotation of the base, has applications in mixing. We investigate this phenomena and its effect on the environment inside an open cylinder, with potential application as a tissue-engineering bioreactor, with tissue-scaffolds of two different geometries immersed in the fluid. Addition of scaffolds induces a blockage effect, hindering the flow in the central vortex core returning to the rotating base. This promotes early onset of vortex breakdown and alters the final shape of vortex breakdown bubbles. Placement of the scaffolds centrally on the cylinder axis yields almost identical levels and distributions of shear stress between the upper and lower surfaces of scaffolds. A change from a disk shaped to an ellipsoidal scaffold, of the same size, reduces the intensity of the maximum shear stresses at the scaffold surface by up to 50%. There is a range of Reynolds numbers where increasing Reynolds number, and hence possibly increasing mixing efficiency, leads to a decrease in the maximum levels of fluid forces at the scaffold surfaces. This is an important conclusion for scaffold based tissue engineering where improved mixing is sought, but often sacrificed in favor of minimizing fluid forces.     

Damping of structural vibrations using an electromotive eddy current damper

Structural vibrations are normally the cause for high cycle fatigue failure (HCF) in technical structures. For example, the blades of rotating bladed turbine disks are subjected to fluctuating gas forces during operation that cause blade vibrations. Therefore, one of the main tasks in the design of turbomachinery blading is the reduction of the vibration amplitudes of the blades and it is well known that the vibration amplitudes can be reduced significantly to a reasonable amount by means of friction damping devices such as underplatform dampers, tip shrouds and damping wires. If the temperature of the working fluid is not excessively high, the use of an electromotive eddy current damper can be a possible alternative to this well known classical friction damping devices. If a conducting material is moving in a stationary magnetic field, eddy currents are generated inside the conductor. These eddy currents cause an energy dissipation effect and damping forces are generated. This damping effect can be used to reduce the resonance amplitudes and therefore to decrease the risk of a HCF failure. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical study on viscoelastic fluid flow past a rigid body

Viscoelastic non-Newtonian fluids can be achieved by adding a small amount of polymer additives to a Newtonian fluid. In this paper, numerical simulations are used to investigate the influence of such polymer additives on the behavior of flow past a circular cylinder. A numerical method is proposed that discretizes the non-linear viscoelastic system on a uniform Cartesian grid, with a penalization method to model the presence of the cylinder. The drag of the cylinder and the flow behavior under the effect of different Reynolds numbers ($\mathrm{Re}$), Weissenberg numbers (Wi) and polymer viscosity ratios (ε) are studied. Numerical results show that different flow characteristics are exhibited in different parameter zones. The polymer viscosity ratio plays an important role at low Weissenberg and Reynolds numbers, but as the Reynolds and Weissenberg numbers increase, the influence of ε weakens. The drag force of the cylinder is mostly affected by the Reynolds and Weissenberg numbers. At low Reynolds numbers, the drag of the cylinder and the flow fields are only affected by a large value of Wi when the elastic forces are strong. Non-trivial drag reduction occurs only when there is vortex shedding in the wake flow, whereas drag enhancement happens when the vortex shedding is inhibited.     

The vibrational behaviour of bladed disks with multiple coupling devices

In turbomachinery applications turbine blades are subjected to high static and dynamic loads. Static loads are due to centrifugal stresses and thermal strains. Especially the dynamic excitation caused by fluctuating gas forces results in high vibration amplitudes which can lead to high cycle fatigue failures (HCF). Therefore, in practical applications, coupling devices like underplatform dampers, lacing wires and tip shrouds are installed to the structure. In case of blade vibrations the relative displacements between these coupling devices and the blades generate friction forces. The resulting energy dissipation provides additional damping to the structure. Furthermore, coupling devices, in particular tip shrouds, snubbers and lacing wires, increase the stiffness of the structure. Hence, they lead to a shift of the resonance frequencies. So far, only effects of single coupling devices and the influencing properties have been examined. Within this paper the effect of multiple couplings is determined and compared with single couplings. The forced response of turbine bladings with multiple couplings is calculated under consideration of geometrical and mechanical parameters of the blading and contacts, respectively. The results are compared with the single coupled blading. Furthermore, a multiple coupled device with under-platform damper and connecting pin is compared with respect to his effectiveness. Especially the influence on the resonance frequency and the achievable damping is analysed. The results of the simulation are verified by measurements at a two-blade non-rotating test rig with an underplatform damper and connecting pin. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical exploration of new features on three-dimensional transition of a cylinder wake

The three-dimensional transition of the wake flow behind a circular cylinder is studied in detail by direct numerical simulations using 3D incompressible N-S equations for Reynolds number ranging from 200 to 300. New features and vortex dynamics of the 3D transition of the wake are found and investigated. At Re = 200, the flow pattern is characterized by mode A instability. However, the spanwise characteristic length of the cylinder determines the transition features. Particularly for the specific spanwise charac-     

MILU-CG方法和绕旋转圆柱流动的数值研究

本文采用以修正的不完全LU分解作预处理器的共轭梯度法(MILU-CG),结合高阶隐式差分格式,改进了作者(1992)提出的基于区域分解、有限差分法与涡法杂交的数值方法(HDV).系统地研究了雷诺数Re=1000,200,旋转速度比α∈(0.5,3.25)范围内,绕旋转圆柱从突然起动到充分发展,长时间内尾流旋涡结构和阻力、升力系数的变化规律.计算所得流线与实验流场显示相比,完全吻合.首次揭示了临界状态时的旋涡结构特性,并指出最佳升阻比就在该状态附近得到.     

速度-涡量法数值求解具有表面吹吸圆柱的绕流问题

用速度-涡量法数值求解了具有表面吹吸圆柱的绕流问题.所得高阶隐式差分方程,采用以修正的不完全LU分解作预处理器的共轭梯度法(MILU-CG),高效解出.研究了雷诺数Re=100时,各种吹吸位置、吹吸强度对圆柱尾流涡旋结构和阻力、升力系数的影响规律.指出,在圆柱肩部的吸气和在圆柱尾部的吹气,可有效地抑制尾流涡旋结构在垂直来流方向上的非对称性,达到减小升力的目的.对在圆柱肩部吸气的情形,合适选择吸气强度,还可有效减小圆柱在来流方向上所受的阻力.     

Dynamics of a Sea Platform Interacting with the Seabed and the Water Medium

Transient vibrations of the system {structure–seabed–water layer} are investigated. The schematic representation of the structure consists of a rigid circular foundation slab and a superstructure in the form of a vertical viscoelastic cylinder with lumped masses. The interaction of the foundation with a viscoelastic half-space (the seabed) is taken into account by using the method of orthogonal polynomials to solve the dynamical contact boundary-value problem. A procedure is developed for including in the analysis the interaction of a cylindrical foundation-supported structure with the water layer (to simulate the dynamics of an oil-drilling platform). The assumed load is seismic action specified by an analog accelerogram of the local area. A computational system is developed for numerical simulation of the vibrations and for determining the forces, displacements, accelerations, and contact stresses.     

On stability and self-excited vibrations in fluid-structure-interaction

In flexible channels conveying fluid the steady state may loose stability by divergence or flutter. The aim of this contribution is to investigate the basic excitation mechanisms of flow-induced vibrations and to evaluate the influence of various parameters on the stability behaviour of the coupled problem. Therefore, a simple, yet general model is proposed. The fluid is assumed to be inviscid and irrotational and both incompressible and compressible flow is considered. It is guided by a planar, rectangular channel with a rigid wall and a thin, flexible wall. The latter is modelled as a one-parametric continuum on an elastic foundation, which exhibits bending and extensional stiffness. By examining the energy balance over one oscillation circle it is possible to reveal the mechanisms of energy transfer between the coupled components of the system. Based on this analysis a physical explanation of the arising instabilities is possible. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Steady-state vibrations of a compound isotropic cylinder under a plane strain

We solve the problem of two-dimensional strain of a compound isotropic cylinder deformed by distributed pulsing forces. We study the influence of the geometric and elastic characteristics of the layers on the magnitude of the stresses and the lowest natural frequency of radial-symmetric vibrations of a three-component cylinder. Two figures Bibliography: 3 titles Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 25, 1995, pp. 103–108.     

Numerical exploration of new features on three-dimensional transition of a cylinder wake

The three-dimensional transition of the wake flow behind a circular cylinder is studied in detail by direct numerical simulations using 3D incompressible N-S equations for Reynolds number ranging from 200 to 300. New features and vortex dynamics of the 3D transition of the wake are found and investigated. At Re = 200, the flow pattern is characterized by mode A instability. However, the spanwise characteristic length of the cylinder determines the transition features. Particularly for the specific spanwise characteristic length linear stable mode may dominate the wake in place of mode A and determine the spanwise phase difference of the primary vortices shedding. At Re = 250 and 300 it is found that the streamwise vortices evolve into a new type of mode’“dual vortex pair mode” downstream. The streamwise vortex structures switch among mode A, mode B and dual vortex pair mode from near wake to downstream wake. At Re = 250, an independent low frequency f _m in addition to the vortex shedding frequency f _s is identified. Frequency coupling between f _m and f _s occurs. These result in the irregularity of the temporal signals and become a key feature in the transition of the wake. Based on the formation analysis of the streamwise vorticity in the vicinity of cylinder, it is suggested that mode A is caused by the emergence of the spanwise velocity due to three dimensionality of the incoming flow past the cylinder. Energy distribution on various wave numbers and the frequency variation in the wake are also described.     

Aerodynamic characteristics of propeller in non-axial flow

Flow on running propellers installed on aircraft in general case is not axial what results in off-axis forces and moments at the propeller. Lifting line method is applied for propeller blade model using set of discrete vortex filaments. Propeller wake defined by vortex sheet of discrete vortex filaments is modelled with application of free-wake method. Presented propeller model combines the blade and the wake model and with its low computational cost realization it is suitable for preliminary prediction of propeller contribution to the aircraft aerodynamic characteristics. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Dynamic contact problem for a bridge modeled by a viscoelastic full von Kármán system

The existence of solutions is proved for a full system of dynamic von Kármán equations expressing vibrations of geometrically nonlinear viscoelastic plate, the viscosity of which has the character of a short memory. The system models the behaviour of a bridge. The in-plane acceleration terms are taken into account. The boundary contact conditions for plane displacements and possibly the contact with the rigid support are considered.     

Dynamic contact problem for a bridge modeled by a viscoelastic full von Kármán system

The existence of solutions is proved for a full system of dynamic von Kármán equations expressing vibrations of geometrically nonlinear viscoelastic plate, the viscosity of which has the character of a short memory. The system models the behaviour of a bridge. The in-plane acceleration terms are taken into account. The boundary contact conditions for plane displacements and possibly the contact with the rigid support are considered.