Simultaneous Wake- and Vortex-Induced Vibrations of a Cylinder With Two Degrees of Freedom in Each Direction

2014 ◽  
Vol 136 (3) ◽  
Author(s):  
J. R. Chaplin ◽  
W. M. J. Batten
Keyword(s):  
Degrees Of Freedom ◽  
Natural Frequencies ◽  
Elastic System ◽  
Cross Flow ◽  
Structural Response ◽  
Flow Induced Vibration ◽  
Vortex Induced Vibrations ◽  
Complicated Process ◽  
The Subject ◽  
Flow Directions

The flow-induced vibration of one cylinder in the wake of another is the subject of continuing interest in connection with interactions between vertical tension risers in deep water. When one riser is downstream of another, it is likely to be subject to wake-induced and vortex-induced excitations at different frequencies simultaneously. Both are complex mechanisms, and it is reasonable to assume that they interact. To begin to understand this complicated process, it is desirable that any modeling should incorporate some features of a multidegree-of-freedom structural response. With this aim, this paper describes experiments in which one cylinder was free to undergo simultaneous wake- and vortex-induced vibrations downstream of a similar but stationary cylinder in a steady flow. The downstream cylinder was mounted on an elastic system that had two natural frequencies in both the in-line and cross-flow directions. Mass ratios were almost the same in all four modes. Measurements are presented of simultaneous wake- and vortex-induced vibrations for cylinder separations of 5 and 10 diameters in the in-line direction, and up to 4 diameters transversely. At a reduced velocity of 83 (based on the cylinder's lower submerged natural frequency) and a separation of 5 diameters, excursions of wake-induced vibrations peaked at almost 5 diameters, when the downstream cylinder was near the edge of the upstream cylinder's wake.

Modal Frequency Response of a Four-Pad Tilting Pad Bearing With Spherical Pivots, Finite Pivot Stiffness and Different Pad Preloads

2010 ◽  
Author(s):  
Timothy W. Dimond ◽  
Amir A. Younan ◽  
Paul E. Allaire ◽  
John C. Nicholas
Keyword(s):  
Frequency Response ◽  
High Speed ◽  
Degrees Of Freedom ◽  
Natural Frequencies ◽  
Theoretical Calculations ◽  
Leading Edge ◽  
Damping Coefficients ◽  
Tilting Pad ◽  
The Subject ◽  
Stiffness And Damping

Tilting pad journal bearings (TPJBs) provide radial support for rotors in high-speed machinery. Since the tilting pads cannot support a moment about the pivot, self-excited cross-coupled forces due to fluid-structure interactions are greatly reduced or eliminated. However, the rotation of the tilting pads about the pivots introduces additional degrees of freedom into the system. When the flexibility of the pivot results in pivot stiffness that is comparable to the equivalent stiffness of the oil film, then pad translations as well as pad rotations have to be considered in the overall bearing frequency response. There is significant disagreement in the literature over the nature of the frequency response of TPJBs due to non-synchronous rotor perturbations. In this paper, a bearing model that explicitly considers pad translations and pad rotations is presented. This model is transformed to modal coordinates using state-space analysis to determine the natural frequencies and damping ratios for a four-pad tilting pad bearing. Experimental static and dynamic results were previously reported in the literature for the subject bearing. The bearing characteristics as tested are considered using a thermoelastohydrodynamic (TEHD) model. The subject bearing was reported as having an elliptical bearing bore and varying pad clearances for loaded and unloaded pads during the test. The TEHD analysis assumes a circular bearing bore, so the average bearing clearance was considered. Because of the ellipticity of the bearing bore, each pad has its own effective preload, which was considered in the analysis. The unloaded top pads have a leading edge taper. The loaded bottom pads have finned backs and secondary cooling oil flow. The bearing pad cooling features are considered by modeling equivalent convective coefficients for each pad back. The calculated bearing full stiffness and damping coefficients are also reduced non-synchronously to the eight stiffness and damping coefficients typically used in rotordynamic analyses and are expressed as bearing complex impedances referenced to shaft motion. Results of the modal analysis are compared to a two degree-of-freedom second-order model obtained via a frequency-domain system identification procedure. Theoretical calculations are compared to previously published experimental results for a four-pad tilting pad bearing. Comparisons to the previously published static and dynamic bearing characteristics are considered for model validation. Differences in natural frequencies and damping ratios resulting from the various models are compared, and the implications for rotordynamic analyses are considered.

The Numerical Research of Two-Degrees-of-Freedom Vortex-Induced Vibrations of Circular Cylinders

2012 ◽  
Vol 204-208 ◽  
pp. 4598-4601
Author(s):  
Jie Li Fan ◽  
Wei Ping Huang
Keyword(s):  
Degrees Of Freedom ◽  
Amplitude Ratio ◽  
Flow Direction ◽  
Cross Flow ◽  
Circular Cylinders ◽  
Two Degrees Of Freedom ◽  
Line Frequency ◽  
Ansys Cfx ◽  
Vortex Induced Vibrations ◽  
Lock In

The two-degrees-of-freedom of vortex-induced vibration of circular cylinders is numerically simulated with the software ANSYS/CFX. The VIV characteristic, in the two different conditions (A/D=0.07 and A/D=1.0), is analyzed. When A/D is around 0.07, the amplitude ratio of the cylinder’s VIV between in-line and cross-flow direction in the lock-in is lower than that in the lock-out. The in-line frequency is twice of that in cross-flow direction in the lock-out, but in the lock-in, it is the same as that in cross-flow direction and the same as that of lift force. When A/D is around 1.0, the amplitude ratio of the VIV between in-line and cross-flow in the lock-in is obviously larger than that in the lock-out. Both in the lock-in and in the lock-out, the in-line frequency is twice of that in cross-flow direction.

POD Analysis of the Wake Development of a Pivoted Circular Cylinder Undergoing Vortex Induced Vibrations

2017 ◽  
Author(s):  
E. Marble ◽  
C. Morton ◽  
S. Yarusevych
Keyword(s):  
Circular Cylinder ◽  
Degrees Of Freedom ◽  
Structural Response ◽  
Cylinder Wake ◽  
Time Resolved ◽  
Vortex Induced Vibrations ◽  
Image Velocimetry ◽  
Pod Analysis ◽  
Component Particle ◽  
Proper Orthogonal

Vortex Induced Vibrations (VIV) of a pivoted circular cylinder with two degrees of freedom are investigated experimentally, focusing on quantifying the wake topology. Experiments are performed in a water tunnel for a pivoted cylinder with a fixed mass ratio of 10.8, moment of inertia ratio of 87.0–109.5, and a diameter-based Reynolds number of 3100. The reduced velocity was varied from 4.42 to 9.05 by varying the natural frequency of the structure. Velocity measurements were performed via time-resolved, two-component Particle Image Velocimetry (PIV), synchronized with cylinder displacement measurements. Time and phase-averaging are employed to analyze the wake development and relate it to the structural response. Proper Orthogonal Decomposition (POD) is utilized to gain insight into the development of coherent structures in the cylinder wake. The observed shedding patterns agree well with the Morse & Williamson [1] shedding map except for the cases at the boundary between 2P and non-synchronized shedding. The results show that the cylinder follows an elliptical trajectory with equal frequency of oscillation in streamwise and transverse directions. For the 2P regime, the tilt and direction of trajectory affect the formation and development of vortices in the wake. This results in a distinct asymmetry about the wake centerline in time-averaged statistics.

Structural Response of Pipeline Free Spans Based on Beam Theory

2002 ◽  
Author(s):  
Olav Fyrileiv ◽  
Kim Mo̸rk
Keyword(s):  
Natural Frequencies ◽  
Structural Response ◽  
Beam Theory ◽  
Vertical Vibration ◽  
Mode Shapes ◽  
Ocean Current ◽  
Vibration Modes ◽  
Wave Loading ◽  
Vortex Induced Vibrations ◽  
Subsea Pipelines

One of the main risk factors for subsea pipelines exposed on the seabed is fatigue failure of free spans due to ocean current or wave loading. This paper describes how the structural response of a free span, as input to the fatigue analyses, can be assessed in a simple and still accurate way by using improved beam theory formulations. In connection with the release of the DNV Recommended Practice, DNV-RP-F105 “Free Spanning Pipelines”, the simplified structural response quantities have been improved compared to previous codes. The boundary condition coefficients for the beam theory formulations have been updated based an effective span length concept. This concept is partly based on theoretical studies and partly on a large number of FE analyses. The updated expressions are general and fit all types of soil and pipe dimensions for lower lateral and vertical vibration modes. The present paper focus on estimation of simplified response quantities such as lower natural frequencies and associated mode shapes. Hydrodynamical aspects of Vortex Induced Vibrations (VIV) are outside the scope of this paper.

On Cross Flow-Induced Vibration of a Flexible Cylinder

2014 ◽  
Author(s):  
H. Cen ◽  
D. S-K. Ting ◽  
R. Carriveau
Keyword(s):  
Reynolds Number ◽  
Degrees Of Freedom ◽  
Cross Flow ◽  
Mass Ratio ◽  
Flexible Cylinder ◽  
Flow Induced Vibration ◽  
Slowing Down ◽  
Mode Vibration ◽  
Inner Diameter ◽  
Multi Mode

An experiment study on the cross flow-induced vibration of a flexible cylinder with two degrees of freedom had been conducted in a towing tank. The test cylinder was a 45 cm long Tygon tubing with outer and inner diameter of 7.9 mm (5/16 in) and 4.8 mm (3/16 in), giving a mass ratio of 0.77 and an aspect ratio of 56. It was towed from rest up to 1.6 m/s before slowing down to rest again over a distance of 1.6 m in still water, covering the range of Reynolds number from 1500 to 13000 and reduced velocity from 4 to 35. Multi-mode vibration and sudden shift between different modes were observed. The vibration amplitude, frequency and mode were quantified. The results obtained during the brief constant towing speed were expressed in term of the corresponding Reynolds number or reduced velocity. These findings were cast with respect to the existing knowledge in the literature.

A Model Experiment Investigation on Two Degrees of Freedom VIV of Cylinder

2014 ◽  
Author(s):  
Yunhe Zhai ◽  
Ruxin Song ◽  
Zh. Kang ◽  
Liping Sun ◽  
Peng Li
Keyword(s):  
Degrees Of Freedom ◽  
Cross Flow ◽  
Natural Vibration Frequency ◽  
Mass Ratio ◽  
Response Characteristics ◽  
Line Flow ◽  
Flow Directions ◽  
The Cross ◽  
Spring Constants ◽  
Two Degree Of Freedom

An experimental investigation on vortex-induced vibration (VIV) response characteristics of a rigid cylinder was conducted at the Towing Tank Lab in Harbin Engineering University. The Reynolds Number based on proposed diameter ranged from 6×104 to 2.4×105, with the cross-flow mass ratio my* = 1.127 and the in-line mass ratio mx* = 1.363. In the experiment, the spring constants of the cross-flow and in-line flow directions were regulated to change the natural vibration frequency of the model system. One- and two-degree-of-freedom VIV experiment was respectively carried out to analyze the vibration characteristic and trajectory. It was found that the non-dimension in-line and cross-flow natural frequency ratio fx/fy, is an important parameter which not only affects cross-flow vibration peak but also affects the forms of vibration trajectory except the reduced velocity.

Two-Phase Flow Induced Vibration of an Array of Tubes Preferentially Flexible in the Flow Direction

2005 ◽  
Author(s):  
R. Violette ◽  
N. W. Mureithi ◽  
M. J. Pettigrew
Keyword(s):  
Natural Frequencies ◽  
Flow Direction ◽  
Cross Flow ◽  
Diameter Ratio ◽  
Phase Flow ◽  
Flow Induced Vibration ◽  
Two Phase ◽  
Array Configuration ◽  
Fluidelastic Instability ◽  
Existing Data

Tests were done to study the fluidelastic instability of a cluster of seven cylinders much more flexible in the flow direction than in the lift direction. The array configuration is rotated triangular with a pitch to diameter ratio of 1.5. The array was subjected to two-phase (air-water) cross flow. Cylinder natural frequencies of 14 and 28 Hz were tested. Fluidelastic instabilities were observed at 65, 80, 90 and 95% void fraction albeit at a somewhat higher flow velocity than that expected for axisymetrically flexible arrays. These results and additional wind tunnel results are compared to existing data on fluidelastic instability.

Modal Frequency Response of a Four-Pad Tilting Pad Bearing With Spherical Pivots, Finite Pivot Stiffness, and Different Pad Preloads

2013 ◽  
Vol 135 (4) ◽  
Author(s):  
Timothy Dimond ◽  
Amir A. Younan ◽  
Paul Allaire ◽  
John Nicholas
Keyword(s):  
Frequency Response ◽  
High Speed ◽  
Degrees Of Freedom ◽  
Natural Frequencies ◽  
Theoretical Calculations ◽  
Leading Edge ◽  
Damping Coefficients ◽  
Tilting Pad ◽  
The Subject ◽  
Stiffness And Damping

Tilting pad journal bearings (TPJBs) provide radial support for rotors in high-speed machinery. Since the tilting pads cannot support a moment about the pivot, self-excited cross-coupled forces due to fluid-structure interactions are greatly reduced or eliminated. However, the rotation of the tilting pads about the pivots introduces additional degrees of freedom into the system. When the flexibility of the pivot results in pivot stiffness that is comparable to the equivalent stiffness of the oil film, then pad translations as well as pad rotations have to be considered in the overall bearing frequency response. There is significant disagreement in the literature over the nature of the frequency response of TPJBs due to nonsynchronous rotor perturbations. In this paper, a bearing model that explicitly considers pad translations and pad rotations is presented. This model is transformed to modal coordinates using state-space analysis to determine the natural frequencies and damping ratios for a four-pad tilting pad bearing. Experimental static and dynamic results were previously reported in the literature for the subject bearing. The bearing characteristics as tested are compared to a thermoelastohydrodynamic (TEHD) model. The subject bearing was reported as having an elliptical bearing bore and varying pad clearances for loaded and unloaded pads during the test. The TEHD analysis assumes a circular bearing bore, so the average bearing clearance was considered. Because of the ellipticity of the bearing bore, each pad has its own effective preload, which was considered in the analysis. The unloaded top pads have a leading edge taper. The loaded bottom pads have finned backs and secondary cooling oil flow. The bearing pad cooling features are considered by modeling equivalent convective coefficients for each pad back. The calculated bearing full stiffness and damping coefficients are also reduced nonsynchronously to the eight stiffness and damping coefficients typically used in rotordynamic analyses and are expressed as bearing complex impedances referenced to shaft motion. Results of the modal analysis are compared to a two-degree-of-freedom second-order model obtained via a frequency-domain system identification procedure. Theoretical calculations are compared to previously published experimental results for a four-pad tilting pad bearing. Comparisons to the previously published static and dynamic bearing characteristics are considered for model validation. Differences in natural frequencies and damping ratios resulting from the various models are compared, and the implications for rotordynamic analyses are considered.

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