Hydrodynamic Coefficients for Vortex Induced Vibrations of Slender Beams

2009 ◽  
Author(s):  
Prashant K. Soni ◽  
Carl M. Larsen ◽  
Jie Wu
Keyword(s):  
Cross Section ◽  
Amplitude Ratio ◽  
Higher Order ◽  
Reliable Data ◽  
Flexible Beam ◽  
Hydrodynamic Coefficients ◽  
Rigid Cylinder ◽  
Vortex Induced Vibrations ◽  
Slender Beams ◽  
Frequency Components

Empirical codes for prediction of vortex induced vibrations need reliable data for hydrodynamic coefficients. Such data are almost exclusively based on measured forces on rigid cylinders that have forced harmonic motions in cross-flow (CF) or in-line (IL) directions. This type of experiment is not able to capture all effects that could be important for realistic cross section motions of slender beams due to two reasons: 1. Slender beams will normally have combined IL and CF oscillations. 2. Higher order frequency components will normally be present for vibrating beams. It is difficult to measure local forces on short segments of flexible beams in laboratory tests due to the small diameters. The most convenient instrumentation is to use a large number of strain gauges or accelerometers along the beam. Proper data processing will then give reliable data for the motions, which means that the trajectory of cross sections can be found. Hence, the following set of experiments can be carried out in order to find hydrodynamic coefficients under realistic VIV conditions: 1. Experiments with a slender flexible beam and processing of recorded strains or accelerometers to identify cross section trajectories. 2. Measurement of forces on a rigid cylinder section with forced motions. Reynolds number, amplitude ratio, orbit shape and non-dimensional frequency must be identical in the flexible beam and rigid cylinder tests. Such experiments have been carried out, and the results are presented in terms of hydrodynamic coefficients for combined CF and IL oscillations. Coefficients are found for the primary CF and IL frequencies, but also for higher order frequency components. Results are presented and discussed in relation to well known results from pure CF and IL oscillations. One way of verifying that the coefficients have been correctly identified, is to apply the coefficients in an empirical response model and compare analysis results to the observation. This step has, however, not been carried out so far.

On Determination of VIV Coefficients Under Shear Flow Condition

2010 ◽  
Author(s):  
Decao Yin ◽  
Carl M. Larsen
Keyword(s):  
Amplitude Ratio ◽  
Cross Flow ◽  
Flexible Beam ◽  
Hydrodynamic Coefficients ◽  
Periodic Patterns ◽  
Research Activity ◽  
Severe Fatigue ◽  
Vortex Induced Vibrations ◽  
Load Effects ◽  
Offshore Oil Industry

Long marine risers exposed to ocean currents will experience vortex induced vibrations (VIV), which may cause severe fatigue damage. VIV is, however, generally less understood than other load effects. The offshore oil industry has therefore supported an intensive research activity on VIV during the last two decades. High mode VIV model tests with long flexible riser models were initiated by the Norwegian Deepwater Programme (NDP). A 38 m horizontally towed instrumented riser was tested in uniform and linearly sheared current profiles with varying towing speed. A second series of experiments has been conducted with a motion-controlled rigid cylinder in order to find the hydrodynamic coefficients for realistic cross-section trajectories. The pipe was forced to follow periodic patterns found from the NDP tests with flexible beam. The Reynolds’ number and the non-dimensional frequency, as well the amplitude ratio was kept identical for both types of tests, ensuring that the flow conditions for these two experiments remain the same. The hydrodynamic coefficients calculated from natural trajectories show a general agreement with pure harmonic forced motion tests. A slight change of excitation regions was, however, found for cross-flow response. Another observation is that in-line excitation force coefficients have much higher values than found from pure in-line test.

Experimental and Numerical Analysis of Forced Motion of a Circular Cylinder

2011 ◽  
Author(s):  
Decao Yin ◽  
Carl M. Larsen
Keyword(s):  
Influence Factor ◽  
Amplitude Ratio ◽  
Cross Flow ◽  
Flexible Beam ◽  
Hydrodynamic Coefficients ◽  
Forced Motion ◽  
Vortex Pattern ◽  
Severe Fatigue ◽  
Vortex Induced Vibrations ◽  
Uniform Current

Vortex induced vibrations (VIV) of long, slender marine structures may cause severe fatigue damage. However, VIV is still not fully understood, which calls for further research on this topic. This paper discusses results from experimental and numerical investigations of forces on rigid cylinders subjected to combined in-line (IL) and cross-flow (CF) motions, and it aims at improving the understanding of the interaction between IL and CF response components. Model tests with a long flexible beam were conducted at MARINTEK for the Norwegian Deepwater Programme (NDP). The model was 38 m long and it was towed horizontally so that both uniform and linear sheared current profiles could be obtained. Orbits for cross section motions at selected positions along the beam were identified in these tests. Forced motion experiments using these orbits were later carried out in the Marine Cybernetic Laboratory at Norwegian University of Science and Technology (NTNU). A 2 m long rigid cylinder was towed horizontally and forced to follow the measured orbits with identical amplitude ratio, non-dimensional frequency and Reynolds number as for the flexible beam tests. Parts of the results from these tests were published by Yin & Larsen in 2010. In this paper results from an investigation of trajectories for six positions along the beam in a uniform current condition will be shown. Three orbits have nearly the same CF amplitude ratio at the primary CF frequency, and the other three have similar IL amplitude ratio at the primary IL frequency, which is twice the CF frequency. Hydrodynamic coefficients have been found from experiments and numerical computations were carried out to find vortex shedding patterns for these cases. The main conclusions are that the IL motion component is a significant influence factor, and that higher order displacement components are more pronounced in IL direction than CF. Significant displacements in IL direction at 6 times the primary CF frequency were also observed, the ‘2T’ vortex pattern was captured when strong IL motion components were present. It is also seen that hydrodynamic coefficients should be found for combined CF and IL orbits and thereby improve the empirical models for prediction of VIV.

Importance of Added Mass for the Interaction Between IL and CF Vibrations of Free Spanning Pipelines

2011 ◽  
Author(s):  
Ida M. Aglen ◽  
Carl M. Larsen
Keyword(s):  
Cross Sections ◽  
Amplitude Ratio ◽  
Large Diameter ◽  
Cross Flow ◽  
Added Mass ◽  
Flexible Beam ◽  
Hydrodynamic Coefficients ◽  
Cross Sectional ◽  
Mass Coefficient ◽  
The Stability

The importance of cross-flow (CF) response generated by vortex induced vibrations (VIV) of free spanning pipelines has long been recognised. The significance of in-line (IL) vibrations has recently been understood and hence also been subjected to research. The combined effect of CF and IL vibrations is, however, still not fully described. This paper highlights the CF-IL interaction with focus on the transition zone from pure IL to CF dominated response, giving special attention to how the added mass influences the interaction. Results from extensive flexible beam tests connected to the Ormen Lange (OL) development have been used as a basis for this study. Trajectories for cross sectional motions from the flexible beam test were identified, and then used as forced motions of a large diameter rigid cylinder exposed to uniform flow. Non-dimensional parameters like Reynolds number (Re), amplitude ratio and reduced frequency were identical for the two tests. Hence, forces found from the forced motion test could be used to find hydrodynamic coefficients valid for the flexible beam case. This paper discusses the results from the flexible beam tests with a relatively short length to diameter ratio (L/D) of 145. Modal analyses by Nielsen et al. (2002) show that the first mode dominates in both directions for these particular tests, even though the IL response frequency is twice the CF frequency. In this paper the added mass variations along the OL flexible beam is studied. Forces acting on 4 different cross sections along the beam are measured for 7 different prototype velocities. For each test the hydrodynamic coefficients are calculated, and the results show how the added mass changes along the beam for increasing velocities, and thereby creates resonance for both IL and CF response. The stability of the added mass coefficient throughout the time series is also evaluated.

Investigating the Relevance of Strip-Theory for Pipelines Subjected to Vortex Induced Vibration

2008 ◽  
Author(s):  
Prashant K. Soni ◽  
Carl M. Larsen
Keyword(s):  
Cross Section ◽  
Numerical Solutions ◽  
Classical Method ◽  
Response Analysis ◽  
Flexible Beam ◽  
Navier Stokes Equation ◽  
Rigid Cylinder ◽  
Strip Theory ◽  
Hydrodynamic Effects ◽  
Force Calculation

Empirical models for prediction of vortex induced vibrations (VIV) apply hydrodynamic coefficients to represent the fluid forces on the structure. The coefficients are found by measuring forces on a rigid cylinder under harmonic pure inline (IL) and pure cross flow (CF) forced motions, and presented as functions of non-dimensional motion amplitude and frequency. In the response analysis the forces at a specific cross-section are assumed to be defined by the motion of this cross-section, which implies that possible three-dimensional (3D) hydrodynamic effects are neglected. The approach is often referred to as ‘strip-theory’, which is a term originally used in ship hydrodynamics. Here, a classical method for calculation of motions and beam forces is based on the same type of simplification. The strip-theory has been used for VIV analysis both in combination with empirical coefficients but also combined with 2D numerical solutions of the Navier-Stokes equation for force calculation. The approach as such has never been verified and the loss of accuracy from neglecting 3D hydrodynamic effects has never been quantified. The purpose of the present work is to contribute to such verification. The investigation reported herein consists of three steps. – Experiments with a flexible beam subjected to VIV. Response amplitudes on CF and IL directions were measured so that the trajectories for several cross-sections along the beam could be found; – Measurement for hydrodynamic forces on a rigid cylinder that was forced to follow the same trajectories as found from the beam experiments; – Use of a finite element program to calculate the dynamic response of a flexible beam with the same properties as for the first test and subjected to forces from the second test. If the calculated response is found to be identified to the measured the verification exercise could be accepted as successful. Discrepancies between measured and calculated response might be caused by 3D hydrodynamic effects or poor quality of the experiments. The present study is a first attempt and the reported results do not lead to a firm conclusion.

Forced Motion Experiments With Measured Motions From Flexible Beam Tests Under Uniform and Sheared Flows

2012 ◽  
Author(s):  
Decao Yin ◽  
Carl M. Larsen
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Amplitude Modulation ◽  
Cross Flow ◽  
Hydrodynamic Forces ◽  
Flexible Beam ◽  
Forced Motion ◽  
Vortex Induced Vibrations ◽  
Time Histories ◽  
Orbit Types

Hydrodynamic forces on a cylinder under realistic combinations of in-line (IL) and cross-flow (CF) vortex induced vibrations (VIV) have been investigated. Signals of strain gauges and accelerometers from the Norwegian Deepwater Programme (NDP) tests with a long, slender beam were used to identify cross section orbits. 19 cross sections almost evenly distributed along the pipe were selected, and their motions were applied in controlled motion experiments with a rigid cylinder. Dimensionless parameters like Reynolds number and non-dimensional frequency were identical for the two sets of experiments. Comparison between hydrodynamic coefficients found from forced motion tests with observed motion time histories and periodic approximations are presented. Force histories are also investigated in detail. Orbit types for combined IL and CF VIV are categorized based on relative amplitude and phase, and it is shown that IL motions exhibit chaotic character more easily than CF. Amplitude modulation is observed frequently. Cases where cross section motions are close to periodic have similar hydrodynamic forces as for periodic motion, implying that periodic forced motion tests are relevant to get valid force information. Many cases have amplitude modulated IL motions, while CF motions are quasi-steady. In such cases, IL amplitude modulation can cause abrupt change of IL forces and also 3rd order CF forces, which can accumulate large fatigue damage. When both IL and CF motions are chaotic, the force-motion relationship is impossible to describe by constant coefficients.

Vortex Pattern Comparison for Periodic and Harmonic Combined Cross-Flow and In-Line Forced Oscillations

2009 ◽  
Author(s):  
Prashant K. Soni ◽  
Carl M. Larsen
Keyword(s):  
Vortex Shedding ◽  
Cross Flow ◽  
Periodic Trajectory ◽  
Empirical Models ◽  
Forced Oscillations ◽  
Flexible Beam ◽  
Hydrodynamic Coefficients ◽  
Cylinder Wake ◽  
Rigid Cylinder ◽  
Vortex Pattern

For prediction of vortex-induced vibrations (VIV) the empirical models apply hydrodynamic coefficients to represent the fluid forces on the slender structures. The coefficients are in most cases found by measuring forces on a rigid cylinder under harmonic pure in-line (IL) or pure cross-flow (CF) forced motions, and are generally presented as functions of non-dimensional motion amplitude and frequency. The objective of the present work has been to find hydrodynamic coefficients for realistic combinations of CF and IL motions. Such trajectories were found from measured VIV of a flexible beam, and then used as forced motions of a rigid cylinder in uniform flow. Hydrodynamic forces were measured and used for calculation of hydrodynamic coefficients. The diameter of the rigid cylinder was larger than for the flexible beam in order to obtain optimum conditions for both experiments. However, both Reynolds number and non-dimensional frequency were identical for the two test types. The flexible beam oscillations were not perfectly periodic, but close to. More than one periodic trajectory could hence be identified as representative for the observed response, and these were used as forced motions in order to study the variability of the hydrodynamic coefficients. Alternative harmonic loops were also constructed in order to investigate the potential for using coefficients from harmonic tests as basis for empirical models. The vortex shedding process behind the cylinder has been mapped using Particle Image Velocimetry (PIV). PIV planes can picture the difference in cylinder wake for these trajectories and thus help to understand the process. The vorticity patterns at instantaneous positions for both periodic and harmonic trajectories are obtained. The vortices were mapped and the forces were measured simultaneously. Higher order harmonic components of the force are seen for all types of trajectories, and a correlation between these components and the vortex shedding pattern is observed.

On the Prediction of Fatigue Damage From VIV

2014 ◽  
Author(s):  
Elizabeth Passano ◽  
Carl M. Larsen ◽  
Jie Wu
Keyword(s):  
Vortex Shedding ◽  
Inverse Analysis ◽  
Flexible Beam ◽  
Hydrodynamic Coefficients ◽  
Response Behavior ◽  
Empirical Methods ◽  
New Methods ◽  
New Information ◽  
Vortex Induced Vibrations ◽  
Excitation Force

Empirical methods for calculation of response from vortex shedding are based on a set of coefficients that determines response frequencies, excitation force and damping, but also how competing frequencies will appear in time and along a structure. It is easy to formulate a mathematical model for Vortex Induced Vibrations (VIV), but the key challenges are to find the necessary hydrodynamic coefficients and a model for how the active frequencies appear in time and space. Since the original version of VIVANA was released more than ten years ago, new information has been become available through new test techniques, as well as from new methods for analysis of old tests. In this study, recent re-examination of the results of the NDP 38 m tests is presented. The observed response behavior is compared to predicted VIV response and fatigue. The consequences of assuming that response frequencies will be active concurrently or consecutively are investigated and predicted response and fatigue are compared to results based on the measurements. Another method that has provided valuable information has been inverse analysis, by which forces on a flexible beam are estimated from measured strains and/or accelerations. When forces are known, the underlying coefficients can be calculated from the standard equations. Inverse analysis has been carried out from a set of experiments, and a new set of coefficients has been estimated for use in coefficient based programs such as VIVANA. Initial comparisons between measured and predicted response show that the new coefficients give an improved agreement with regard to amplitudes and frequency composition.

Carrier Redistribution Analysis of Gate-Biased SiC Power-MOSFET Using Super-Higher-Order Scanning Nonlinear Dielectric Microscopy

2015 ◽  
Author(s):  
Norimichi Chinone ◽  
Yasuo Cho
Keyword(s):  
Cross Section ◽  
Measurement System ◽  
Higher Order ◽  
Depletion Layer ◽  
Gate Bias ◽  
Power Mosfet ◽  
Nonlinear Dielectric ◽  
Voltage Dependent ◽  
Carrier Redistribution ◽  
Source Voltage

Abstract Gate-bias dependent depletion layer distribution and carrier distributions in cross-section of SiC power MOSFET were measured by newly developed measurement system based on super-higher-order scanning nonlinear dielectric microscope. The results visualized gate-source voltage dependent redistribution of depletion layer and carrier.

Accuracy of Cotton-Mouton polarimetry in sheared toroidal plasma of circular cross-section

Open Physics ◽  
2011 ◽  
Vol 9 (1) ◽  
Author(s):  
Yury Kravtsov ◽  
Janusz Chrzanowski
Keyword(s):  
Simple Model ◽  
Phase Shift ◽  
Perturbation Method ◽  
Cross Section ◽  
Amplitude Ratio ◽  
Circular Cross Section ◽  
Shear Angle ◽  
Tokamak Plasma ◽  
Toroidal Plasma ◽  
Small Shear

AbstractThe Cotton-Mouton effect in sheared plasma with helical magnetic lines is studied on the basis of the equation for complex amplitude ratio (CAR). A simple model for helical magnetic lines in sheared plasma of toroidal configuration is suggested. The equation for CAR in the sheared plasma is solved by perturbation method, using the small shear angle deviations as is characteristic for tokamak plasma. It is shown that the inaccuracy in polarization measurements caused by deviations of the sheared angle amounts to some percentage of the shearless Cotton-Mouton phase shift. One suggested method is to subtract the “sheared” term, which may improve the accuracy of the Cotton-Mouton measurements in the sheared plasma.

Sign in / Sign up

Export Citation Format

Share Document