Vortex Induced Vibration of a Rotating Blade

2017 ◽  
Author(s):  
Lokanna Hoskoti ◽  
Ajay Misra ◽  
Mahesh Manchakattil Sucheendran
Keyword(s):  
Vortex Shedding ◽  
Coupling Parameter ◽  
Coupled System ◽  
Beam Equation ◽  
Vortex Induced Vibration ◽  
Coupled Equations ◽  
Rotating Blade ◽  
Response Equation ◽  
The Stability ◽  
Lock In

The vortex-induced vibration (VIV) of a rotating blade is studied in this paper. Euler-Bernoulli beam equation and the nonlinear oscillator satisfying Van der Pol equation are used to model the rotating blade and vortex shedding, respectively. While the fluctuating lift due to vortex shedding acts on the blade and the blade is coupled with fluid through a linear inertial coupling, resulting in a fluid-structure interaction problem. The coupled equations are discretized by using modes which satisfy the Eigenvalue problem. The work attempts to understand the instabilities associated with the frequency lock-in phenomenon. The method of multiscale is used to obtain the frequency response equation and frequency bifurcation diagrams of the coupled system. They are obtained for the primary (1:1) resonance for different values of the coupling parameter. The stability of the solution is presented by examining the nature of the Eigenvalues of the Jacobian matrix.

An Analytical/Computational Approach in Assessing Vortex-Induced Vibration of a Variable Tension Riser

2010 ◽  
Vol 132 (3) ◽  
Author(s):  
Per M. Josefsson ◽  
Charles Dalton
Keyword(s):  
Fluid Flow ◽  
Flow Field ◽  
Natural Frequency ◽  
Vortex Shedding ◽  
Beam Equation ◽  
Vortex Induced Vibration ◽  
Forcing Function ◽  
Strip Theory ◽  
Constant Tension ◽  
Variable Tension

The transverse vibratory response of a long, slender vertical top tension riser, subject to an ocean current, is studied. The problem is treated as a coupled fluid flow/vibration problem, which is solved numerically. The fluid flow part is represented by the 2D Navier–Stokes equations, with large-eddy simulation turbulence modeling and strip theory, which are solved numerically to obtain the flow field and determine the vortex-shedding behavior in the flow. The approach flow is a shear flow ranging in Reynolds number from 8000 to 10,000. Given the flow field and vortex-shedding behavior, the transverse fluid forcing function can be determined at a given instant, which becomes the input to the Euler–Bernoulli beam equation to calculate the displacement of the riser, using a technique that involves the Wentzel–Kramers–Brillouin (WKB) method and modal decomposition. The boundary conditions for the fluid flow equations are updated each time step as the cylinder moves. The natural frequency of the riser is tension dominated, not bending-stiffness dominated. With the decrease in tension with increasing depth, the natural frequency is affected. Therefore, the solution will be influenced by the depth-dependent tension. This study has indicated some interesting features regarding the vortex-induced vibration of a variable-tension riser. The vibrational response is greater for a variable-tension riser than for a constant-tension riser, when the variable-tension riser is assumed to have the same top tension as the constant-tension riser. Thus, this is one reason why it is important to take into account the variable tension when estimating fatigue failures of marine risers.

scholarly journals Design and Analysis of A Vortex Induced Vibration Based Oscillating Free Stream Energy Converter

2021 ◽  
pp. 112-117
Author(s):  
Ratan Kumar Das ◽  
Muhammad Taharat Galib
Keyword(s):  
Vortex Shedding ◽  
Large Scale ◽  
Bluff Body ◽  
Free Stream ◽  
Theoretical Formula ◽  
Pendulum Motion ◽  
Ansys Fluent ◽  
Vortex Induced Vibration ◽  
Karman Vortex ◽  
Lock In

The Kármán Vortex Shedding is one of the special types of vortex that is generated from asymmetric flow separation. For many years engineers tried to suppress the vortex shedding as it brings unnecessary motion to the static members inside the flow field. A converter model is designed and studied to harness the energy associated with this vortex shedding and convert it into usable form rather than suppressing it. It is a bluff body placed on the free stream incurring vortex-induced vibration and giving out a swinging pendulum motion. This motion is utilized to produce electricity. The model is analyzed on the free stream of water and conversion efficiency of 8.9% is achieved. A theoretical formula is derived regarding the force acting on the bluff body during the motion. Various parameters such as aspect ratio, flow velocity, lock-in delay, frequency of oscillation, etc. as well as their relations are studied by simulating the model in ANSYS FLUENT 18.1 for different configurations. From the simulated results it is obvious that as the lift force on the bluff body increases, more power generation is possible. Also, the experimental results paved the way for further study for practical large-scale implementation of the converter.

Vortex-Induced Vibration of a Tall Bridge Tower with Four Columns and the Wake Effects on the Nearby Suspenders

2020 ◽  
Vol 20 (09) ◽  
pp. 2050105
Author(s):  
Chen Fang ◽  
Zewen Wang ◽  
Haojun Tang ◽  
Yongle Li ◽  
Zhouquan Deng
Keyword(s):  
Cross Sections ◽  
Vortex Shedding ◽  
Wake Flow ◽  
Suspension Bridges ◽  
Aerodynamic Forces ◽  
Vortex Induced Vibration ◽  
Wake Effects ◽  
Lock In ◽  
Bridge Tower ◽  
Dominant Frequencies

With the increasing span of suspension bridges, the towers have higher heights and have become more flexible, and so do the nearby suspenders. Not only are the towers easy to be affected by winds, but also the nearby suspenders by the wake flow of the towers. To enhance the structural stiffness, a bridge tower may be designed with more columns, but this design may lead to strong aerodynamic interference among the columns, complicating the wind-induced behaviors of the tower and nearby suspenders. In this paper, wind tunnel tests and numerical simulations were carried out to investigate the vortex-induced vibration of a tall bridge tower with four columns, and the wake effects on nearby suspenders. The results show that the displacement response at the tower top increases with the increasing wind speed. No obvious lock-in region is observed, as different cross-sections of the tower show different vortex shedding characteristics. The vortex shedding characteristics are determined mainly by the aerodynamic forces acting on the leeward columns. In the wake of the tower, the aerodynamic forces of the suspenders have the same dominant frequencies as the shedding frequencies of the vortices from the tower. The frequencies may approach the natural frequencies of the suspenders, causing possible wake-induced vibration that should be avoided for a good design.

Frequency lock-in during vortex induced vibration of a rotating blade

2018 ◽  
Vol 80 ◽  
pp. 145-164 ◽  
Author(s):  
Lokanna Hoskoti ◽  
Ajay Misra ◽  
Mahesh M. Sucheendran
Keyword(s):  
Vortex Induced Vibration ◽  
Rotating Blade ◽  
Lock In

Nonlinear Dynamics of a Fluid–Structure Coupling Model for Vortex-Induced Vibration

2019 ◽  
Vol 19 (07) ◽  
pp. 1950071 ◽  
Author(s):  
Jie Chen ◽  
Qiu-Sheng Li
Keyword(s):  
Vortex Shedding ◽  
Multiple Scales ◽  
Coupled Model ◽  
Coupling Model ◽  
Motion Equation ◽  
Multiple Scales Method ◽  
Modulation Equation ◽  
Fluid Structure ◽  
Vortex Induced Vibration ◽  
Lock In

This paper presents a fluid–structure coupling model to investigate the vortex-induced vibration of a circular cylinder subjected to a uniform cross-flow. A modified van der Pol nonlinear equation is employed to represent the fluctuating nature of vortex shedding. The wake oscillator is coupled with the motion equation of the cylinder by applying coupling terms in modeling the fluid–structure interaction. The transient responses of the fluid–structure coupled model are presented and discussed by numerical simulations. The results demonstrate the main features of the vortex-induced vibration, such as lock-in phenomenon, i.e. resonant oscillation of the cylinder occurs when the vortex shedding frequency is near to the natural frequency of the cylinder. The resonant responses of the fluid–structure coupled model in the lock-in region are determined by the multiple scales method. The accuracy of the asymptotic solution by the multiple scales method is verified by comparing with the numerical solution from the motion equation. The effects of different parameters on the steady state amplitude of oscillation are investigated for a given set of parameters. Frequency–response curves obtained from the modulation equation demonstrate the existence of jump phenomena.

scholarly journals A Theoretical Model for the Transmission Dynamics of the Buruli Ulcer with Saturated Treatment

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Ebenezer Bonyah ◽  
Isaac Dontwi ◽  
Farai Nyabadza
Keyword(s):  
Human Population ◽  
Reproduction Number ◽  
Buruli Ulcer ◽  
Coupled System ◽  
Model Parameters ◽  
The Public ◽  
Treatment Function ◽  
Medical Facilities ◽  
The Stability ◽  
Saturated Treatment

The management of the Buruli ulcer (BU) in Africa is often accompanied by limited resources, delays in treatment, and macilent capacity in medical facilities. These challenges limit the number of infected individuals that access medical facilities. While most of the mathematical models with treatment assume a treatment function proportional to the number of infected individuals, in settings with such limitations, this assumption may not be valid. To capture these challenges, a mathematical model of the Buruli ulcer with a saturated treatment function is developed and studied. The model is a coupled system of two submodels for the human population and the environment. We examine the stability of the submodels and carry out numerical simulations. The model analysis is carried out in terms of the reproduction number of the submodel of environmental dynamics. The dynamics of the human population submodel, are found to occur at the steady states of the submodel of environmental dynamics. Sensitivity analysis is carried out on the model parameters and it is observed that the BU epidemic is driven by the dynamics of the environment. The model suggests that more effort should be focused on environmental management. The paper is concluded by discussing the public implications of the results.

scholarly journals Vortex-induced vibrations of a long flexible cylinder in shear flow

2011 ◽  
Vol 677 ◽  
pp. 342-382 ◽  
Author(s):  
REMI BOURGUET ◽  
GEORGE E. KARNIADAKIS ◽  
MICHAEL S. TRIANTAFYLLOU
Keyword(s):  
Shear Flow ◽  
Vortex Shedding ◽  
Cross Flow ◽  
Maximum Velocity ◽  
Travelling Wave ◽  
Transition To Turbulence ◽  
Wave Component ◽  
Flexible Cylinder ◽  
Vortex Induced Vibrations ◽  
Lock In

We investigate the in-line and cross-flow vortex-induced vibrations of a long cylindrical tensioned beam, with length to diameter ratio L/D = 200, placed within a linearly sheared oncoming flow, using three-dimensional direct numerical simulation. The study is conducted at three Reynolds numbers, from 110 to 1100 based on maximum velocity, so as to include the transition to turbulence in the wake. The selected tension and bending stiffness lead to high-wavenumber vibrations, similar to those encountered in long ocean structures. The resulting vortex-induced vibrations consist of a mixture of standing and travelling wave patterns in both the in-line and cross-flow directions; the travelling wave component is preferentially oriented from high to low velocity regions. The in-line and cross-flow vibrations have a frequency ratio approximately equal to 2. Lock-in, the phenomenon of self-excited vibrations accompanied by synchronization between the vortex shedding and cross-flow vibration frequencies, occurs in the high-velocity region, extending across 30% or more of the beam length. The occurrence of lock-in disrupts the spanwise regularity of the cellular patterns observed in the wake of stationary cylinders in shear flow. The wake exhibits an oblique vortex shedding pattern, inclined in the direction of the travelling wave component of the cylinder vibrations. Vortex splittings occur between spanwise cells of constant vortex shedding frequency. The flow excites the cylinder under the lock-in condition with a preferential in-line versus cross-flow motion phase difference corresponding to counter-clockwise, figure-eight orbits; but it damps cylinder vibrations in the non-lock-in region. Both mono-frequency and multi-frequency responses may be excited. In the case of multi-frequency response and within the lock-in region, the wake can lock in to different frequencies at various spanwise locations; however, lock-in is a locally mono-frequency event, and hence the flow supplies energy to the structure mainly at the local lock-in frequency.

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