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.

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.

The Cross-Flow Response of a Tube Array in Water—A Comparison With the Same Array in Air

1982 ◽  
Vol 104 (3) ◽  
pp. 139-146 ◽  
Author(s):  
D. S. Weaver ◽  
D. Koroyannakis
Keyword(s):  
Cross Flow ◽  
Added Mass ◽  
Response Curves ◽  
Flow Response ◽  
Tube Arrays ◽  
Mass Coefficient ◽  
Pitch Ratio ◽  
Added Mass Coefficient ◽  
The Stability ◽  
Wind Tunnel Study

A water tunnel study was conducted on a parallel triangular array of tubes with a pitch ratio of 1.375. The array was geometrically identical to that used previously in a wind tunnel study so that the tube response to cross flow could be compared. It was seen that the response curves for tube arrays in water are much less regular than those in air, creating ambiguity in defining the stability threshold. The irregularities are seen to be associated with shifts in relative tube mode and frequency. Arrays in water apparently first become unstable in one of the lowest frequencies of the band of frequencies associated with a given structural mode. The added mass coefficient computed from the observed frequency at instability is a little larger than the largest added mass coefficient obtained from existing theory for tube arrays in quiescent fluid.

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.

Response of Pipelines Under VIV: An Experimental Investigation

2010 ◽  
Author(s):  
Prashant K. Soni ◽  
Carl M. Larsen
Keyword(s):  
Response Pattern ◽  
Dynamic Properties ◽  
Cross Flow ◽  
Flexible Beam ◽  
Hydrodynamic Coefficients ◽  
Response Model ◽  
Flexible Pipe ◽  
Damping Force ◽  
Robust Response ◽  
A Current

Pipelines laid on an uneven bottom often have free spans. For cases with long spans, one may have several modes and eigenfrequencies that can be excited by vortex shedding. Furthermore, due to the sag effect of a long free-span, the dynamic properties are different in vertical and in horizontal directions. This causes a complex response pattern in the cross-flow (CF) and in-line (IL) directions. From previous research we know that pure IL response at relatively low current velocities may significantly contribute to fatigue damage. This response type must be studied in addition to the combined IL and CF response. The objective of this paper is to present experimental results from flexible beam experiments where both response types are studied, as well as to present results from an empirical response model for the same cases. The empirical model is based on two types of experiments. The first set of experiments were conducted with a flexible pipe for both single and double span configuration. Pure IL and combined IL and CF motions were observed. In the second set of experiments, forces on a rigid cylinder were measured under forced motions in a current. The motions were found from measurements of cross section in the flexible pipe tests. Hydrodynamic coefficients such as drag, added mass, excitation and damping force coefficients were found and then applied in the empirical response model. In the present paper the results from the flexible beam experiments are presented and also compared with the results from the empirical response model. The results so far are encouraging, but further work and more data are needed in order to have a general and robust response model for combined CF and IL VIV.

Reynolds Number Effects on Hydrodynamic Coefficients for Pure In-Line and Pure Cross-Flow Forced Vortex Induced Vibrations

2009 ◽  
Author(s):  
Jamison L. Szwalek ◽  
Carl M. Larsen
Keyword(s):  
Reynolds Number ◽  
Prediction Models ◽  
Current Knowledge ◽  
Cross Flow ◽  
Reynolds Numbers ◽  
Added Mass ◽  
Hydrodynamic Coefficients ◽  
Vortex Induced Vibrations ◽  
Reynolds Number Effects ◽  
Sinusoidal Oscillations

In-line vibrations have been noted to have an important contribution to the fatigue of free spanning pipelines. Still, in-line contributions are not usually accounted for in current VIV prediction models. The present study seeks to broaden the current knowledge regarding in-line vibrations by expanding the work of Aronsen (2007) to include possible Reynolds number effects on pure in-line forced, sinusoidal oscillations for four Reynolds numbers ranging from 9,000 to 36,200. Similar tests were performed for pure cross-flow forced motion as well, mostly to confirm findings from previous research. When experimental uncertainties are accounted for, there appears to be little dependence on Reynolds number for all three hydrodynamic coefficients considered: the force in phase with velocity, the force in phase with acceleration, and the mean drag coefficient. However, trends can still be observed for the in-line added mass in the first instability region and for the transition between the two instability regions for in-line oscillations, and also between the low and high cross-flow added mass regimes. For Re = 9,000, the hydrodynamic coefficients do not appear to be stable and can be regarded as highly Reynolds number dependent.

Interference in a three-dimensional array of jets

2015 ◽  
Vol 26 (5) ◽  
pp. 795-819
Author(s):  
P. E. WESTWOOD ◽  
F. T. SMITH
Keyword(s):  
Cross Sections ◽  
Flow Direction ◽  
Three Dimensional ◽  
Cross Flow ◽  
Longitudinal Vortex ◽  
Cross Sectional ◽  
Dimensional Array ◽  
Unsteady Jets ◽  
The Cross ◽  
Jet Cross Sections

The theoretical investigation here of a three-dimensional array of jets of fluid (air guns) and their interference is motivated by applications to the food sorting industry especially. Three-dimensional motion without symmetry is addressed for arbitrary jet cross-sections and incident velocity profiles. Asymptotic analysis based on the comparatively long axial length scale of the configuration leads to a reduced longitudinal vortex system providing a slender flow model for the complete array response. Analytical and numerical studies, along with comparisons and asymptotic limits or checks, are presented for various cross-sectional shapes of nozzle and velocity inputs. The influences of swirl and of unsteady jets are examined. Substantial cross-flows are found to occur due to the interference. The flow solution is non-periodic in the cross-plane even if the nozzle array itself is periodic. The analysis shows that in general the bulk of the three-dimensional motion can be described simply in a cross-plane problem but the induced flow in the cross-plane is sensitively controlled by edge effects and incident conditions, a feature which applies to any of the array configurations examined. Interference readily alters the cross-flow direction and misdirects the jets. Design considerations centre on target positioning and jet swirling.

Wall Proximity and Curvature Effect on Added Mass Forces in Two-Phase Cross-Flow

2014 ◽  
Author(s):  
C. Béguin ◽  
T. Plagnard ◽  
S. Étienne
Keyword(s):  
Cross Flow ◽  
Added Mass ◽  
Two Phase ◽  
Averaged Equations ◽  
Flow Potential ◽  
Mass Coefficient ◽  
Added Mass Coefficient ◽  
A New Technique ◽  
Infinite Wall ◽  
Wall Proximity

This paper studies the effect of wall proximity and wall curvature on the added mass coefficient of a spherical bubble. Results are based on a semi-analytical method. This information is essential to completely characterize finely dispersed bubbly flows in two-phase cross flow. In such flows small spherical gas bubbles are present in a continuous liquid phase close to a cylinder. This paper uses solid harmonics to solve 3D potential flow around a bubble and a wall. A new technique is developed to calculate the flow potential around a sphere and a cylinder using solid harmonics. Several configurations were calculated: one bubble close to an infinite wall, one bubble close to a cylinder and one bubble close to a spherical wall. Our results are compared with previous studies. As expected added mass forces increase in the vicinity of the wall and for lower curvature. The main purpose of this work is to understand the effect of wall curvature and proximity on added mass. These results are suitable for further use, particularly as added mass models for multiphase flow averaged equations.

First-principle study on electronic structure and optical properties of GaN nanowires with different cross-sections

2016 ◽  
Vol 30 (22) ◽  
pp. 1650136
Author(s):  
Yike Kong ◽  
Lei Liu ◽  
Sihao Xia ◽  
Honggang Wang ◽  
Meishan Wang
Keyword(s):  
Optical Properties ◽  
Cross Sections ◽  
Formation Energy ◽  
Comparative Investigation ◽  
Dielectric Constants ◽  
Cross Sectional ◽  
Gan Nanowires ◽  
Bulk Gan ◽  
Structure Density ◽  
The Stability

This paper explores the properties of intrinsic gallium nitride (GaN) nanowires (NWs) in terms of formation energy, band structure, density of state (DOS) and optical properties with plane-wave ultrasoft pseudopotential method based on first-principles. Results show that after relaxation, N atoms of the outer layers move outwards, while Ga atoms move inwards, and the relaxation of surface atomic structure appears less obvious with the increasing cross-sectional area. Comparing different cross-sections of GaN NWs, it is found that the formation energy decreases and the stability goes stronger with the increasing size. With the increasing cross-section, the bandgap is decreased. Moreover, through comparative investigation in optical properties between GaN NWs and bulk GaN, a valuable phenomenom is found that the static dielectric constants of GaN NWs are notably lower, which contributes remarkably to the excellent absorbing performance of GaN NWs.

Calculation of In-Line Vortex Induced Vibrations of Free Spanning Pipelines

2007 ◽  
Author(s):  
Carl M. Larsen ◽  
Rune Yttervik ◽  
Kristoffer Aronsen
Keyword(s):  
Cross Flow ◽  
Added Mass ◽  
Response Analysis ◽  
Hydrodynamic Coefficients ◽  
Response Model ◽  
Analysis Method ◽  
Vortex Induced Vibrations ◽  
Long Time ◽  
General Response

Pure in-line (IL) vibrations will in many cases contribute significantly to fatigue damage for free spanning pipelines. This might be the case even if IL amplitudes are smaller than cross-flow (CF). While CF response has been subjected to research for a long time, little attention has so far been given to the pure IL VIV case. The hydrodynamic coefficients needed for response calculation have in fact not been available until recently, but results from forced IL oscillations have improved this situation. Data for added mass and force in IL direction has been used to establish a general response model along the same lines as for traditional CF response analysis. This has made it possible to calculate stresses from IL VIV in free spanning pipelines, and include the influence from interaction with the seafloor at the span shoulders. A brief presentation of the analysis method is given, but the main part of the paper gives results from a case study that illustrates important effects and the significance of IL response as compared to CF.

Translational Added Mass of Axisymmetric Underwater Vehicles with Forward Speed Using Computational Fluid Dynamics

2011 ◽  
Vol 55 (03) ◽  
pp. 185-195
Author(s):  
Virag Mishra ◽  
S. Vengadesan
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Cross Flow ◽  
Added Mass ◽  
Navier Stokes ◽  
Inertia Force ◽  
Mass Coefficient ◽  
Computational Fluid Dynamics Cfd ◽  
Accelerated Flow ◽  
Axisymmetric Bodies

This paper presents a computational fluid dynamics (CFD) approach to the calculation of translational added mass coefficient of axisymmetric underwater bodies in both longitudinal and transverse directions. The proposed method involves CFD simulations of accelerated as well as uniform flows past axisymmetric bodies based on Reynolds averaged Navier-Stokes (RANS) equations and makes use of the results of these simulations to obtain the inertia force acting on a body as a function of time. The translational added mass can be obtained from this inertia force history. Validation of the methodology is presented for the benchmark case of accelerated flow past sphere and infinitely long circular cylinder in cross-flow for which analytical solutions of the added mass problem are well known.

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