Data-driven prediction and study of vortex induced vibrations by leveraging hydrodynamic coefficient databases learned from sparse sensors

Marine risers may experience a complex vortex-induced vibration (VIV) owing to the enhanced nonlinear effects from structural curved shapes versus sheared flows. Many studies have focused on VIV of straight risers in sheared flows or curved risers in uniform flows. In this study, a numerical prediction model is advanced to investigate the multidirectional VIV of a catenary riser subjected to linearly sheared flow. The prediction model is described by equations of three-dimensional responses of the catenary riser coupled with the spatially distributed nonlinear wake oscillators calibrated against experimentally observed VIV responses of curved cylinders. Hydrodynamic lift and drag forces are mathematically modelled based on fluid-structural variables accounting for effects of space-varying riser local inclinations, vortex excitation frequencies and relative flow-cylinder velocities following the Independence Principle. The coupled VIV system is discretized in space by a second order finite difference scheme and integrated in time. To validate the model, simulations are performed based on a flexible curved cylinder under the concave sheared flow and compared with experimental results in the literature. By varying the relative directions between the riser equilibrium and the incoming flow in planar and non-planar configurations, VIV responses of a long flexible catenary riser in a uniform free stream flow versus a linearly sheared flow are compared and analysed in terms of amplitudes, resonant frequencies, lock-in conditions, and energy transfer mechanisms under perpendicular, convex and concave flows. Typical VIV features are captured alongside travelling wave responses, modulated amplitudes and frequency switching caused by sheared flows. Overall results highlight the influence of sheared flows on multidirectional VIV features.

Three-dimensional VIV prediction model for a long flexible cylinder with axial dynamics and mean drag magnifications

The STRIDE JIP has performed test initiatives into several areas considered to be crucial to the design of steel catenary risers for harsh, deepwater environments. The following investigations are described:Water-tank testing of a ¼" diameter × 100ft long catenary riser model, looking at response to production vessel motions, in particular the response in the touch-down region for rigid and elastic seabed simulations.Vortex induced vibration tests on riser models 20ft long, 6" in diameter, in simulated currents up to 16.5 ft/s (5m/s - Reynolds 6.7x105). Helical straked and bare pipe models were towed at angles of up to 45° to the flow, simulating current flow over non-vertical riser sections of simple catenary and buoyant wave risers. The requirement and effectiveness of strakes on inclined sections was investigated.Vortex induced vibration tests on riser strings 650ft long, 10.75" diameter in simulated currents up to 5.8 knots (3m/s - Reynolds 6x105). Helical straked and bare pipe models were towed at angles of up to 75° to the vertical in a Norwegian Fjord between two tugs, continuing the investigation into non-vertical riser response to high currents. Introduction Phase II of the STRIDE JIP was initiated by 2H Offshore in March 1998, and is sponsored by 15 operators and 5 engineering contractors. During Phase I of the project, 2 areas were identified as being of prime importance to the design of deepwater steel catenary risers: the touch down point (TDP) and vortex induced vibration (VIV)1. TDP - A deepwater catenary riser TDP can actually involve a wide region of possible contact between different parts of the riser and different areas of the seabed, as dictated by the environmental loading on the floating production vessel and riser system. STRIDE Phase I identified this area of a catenary riser as critical with regards to the strength and fatigue life of the whole system. Confidence in analysis techniques was considered to be of paramount importance to such developments, and this lead to the proposed test program. VIV - Lack of empirical data on VIV of inclined and curved structures required a conservative design approach in STRIDE Phase I. In particular, it had to be assumed that VIV suppression strakes would be required over most of the riser length. The increase in riser drag due to such heavy straking produces a succession of technical and commercial knock-on effects. A high drag catenary riser needs extra ballast in the vertical section to accommodate the current loading, otherwise the riser can be pushed into shapes that overstress the TDP - Figure 1. Within the analysis, ballast was assumed to be most effectively applied as increased riser pipe wall thickness, and resulted in an increase of +40% on that required for pressure considerations alone. Increased wall thickness was shown to have a major impact on installation costs, particularly the amount of temporary buoyancy required for what was found to be the leading installation method at the time, controlled depth tow out. At the kick-off meeting for STRIDE Phase II, it was agreed by all participants that VIV and TDP be top of the list for further investigations. TDP Testing Program The main objective of these tests was to benchmark the ability of industry software to predict the response of a riser pipe catenary at its TDP, particularly as it is put into compressive loading or buckling as a result of extreme motions at the top end, for instance due to extreme storm motions on the floating production vessel.

This study presents an advanced numerical prediction model based on nonlinear wake oscillators for the investigation of multidirectional vortex-induced vibration (VIV) responses of a long catenary riser depending on the structural curved configuration versus the incoming flow direction. By considering a uniform free-stream flow aligned with the initial curvature plane of the catenary riser in a convex or concave shape, the normal flow velocity component is nonlinearly sheared owing to the spanwise variation of inclination angles. This is different from the perpendicular flow case in which the normal flow velocity is spatially constant. To capture the influence of flow direction on the three-dimensionally coupled cross-flow and in-line VIV, distributed wake oscillators are introduced and applied to simulate the fluctuating hydrodynamic lift and drag forces that account for the important effects of cylinder inclination, variable vortex excitation frequencies, global–local​ displacement relationships, and relative flow-cylinder velocities. The amplified mean drag force and the axial force depending on the tangential flow velocity are also considered. These empirical hydrodynamic effects are nonlinearly coupled with the equations of riser three-dimensional motion, and the overall governing equations are numerically solved to assess the multimode, multi-frequency and multi-degree-of-freedom responses. Validation of the model is carried out for VIV of flexible straight and curved cylinders based on experimental results in the literature. Parametric investigations are performed by varying the incoming flow velocities in perpendicular, convex and concave configurations for a long catenary riser with a low mass-damping ratio. In-plane (horizontal and vertical) and out-of-plane VIV features are presented and discussed in terms of space–time varying amplitudes, drag-amplified shape reconfigurations, oscillation frequencies, lock-in occurrences, dual resonances, orbital motion trajectories, fluid–structure energy transfer, and multimodal contributions. Overall prediction results highlight the influence of the cylinder geometric configuration versus the incoming flow orientation on multidirectional VIV characteristics that should be recognised and incorporated into practical analysis tools.

Numerical simulation of vortex-induced vibration of a full-scale flexible riser at supercritical Reynolds number in uniform and linear shear flow

Three-dimensional nonlinear vortex-induced vibrations of risers under internal gas-liquid and external shear flows

This paper presents the initial results from VIV (Vortex-Induced Vibration) field testing of a long, flexible, model riser at high mode number. The experiments were designed to better understand the dynamic behavior of a long riser in uniform flow responding at mode numbers from 10 to 25 in cross-flow vibration. The 1.31 inch, (0.0333 m), diameter riser model was made from fiberglass line pipe, manufactured by Fiberspar Corp. Two model configurations with length of 201 feet (61.26m) and 401 feet (122.23m) were towed behind a vessel in a deep lake in upstate New York. Motion was recorded with twenty four evenly spaced internal tri-axial accelerometers. Observed reduced velocity and RMS displacement response levels are reported. Mean drag coefficients and hydrodynamic damping derived from measured data are compared to calculated values from formulas commonly used in engineering design of offshore systems. Introduction The Experiments at Lake Seneca, New York took place in the summer of 2004. They are part of a larger testing program developed by DEEPSTAR (A joint industry technology development project) aimed at improving the ability to model and mitigate VIV. While these particular tests were focused on investigating uniform flow conditions, a second set of tests designed for shear flow conditions was subsequently performed in November 2004 and will be reported on in the future. The initial motivation for this uniform flow VIV field experiment was to improve the understanding of VIV at high mode number. Most model testing has been conducted at low mode numbers (<10). As a consequence, low mode number VIV is quite well understood. There have been numerous tests conducted on very long cables as well, Reference [1]. In such experiments the dynamic behavior can be represented by cables of infinite length. Traveling waves dominate the response and standing wave modal behavior is not observed. Current drilling and production in 1000 to 3000 meters depths has brought on the need to understand VIV behavior at higher mode number, but still short of infinite length behavior. The principal objectives, of the MIT towed pipe experiments were:To gather vortex-induced vibration response data on a densely instrumented circular pipe at high mode number,To investigate mean drag coefficient (CD) at high mode number,To validate or improve drag coefficient prediction formulas,To test the efficacy of helical strakes at high mode numbers,To obtain statistics on the distribution of single-mode vs. multi-mode response of a pipe at high mode number,To determine the relative contribution to damage rate from the in-line and cross-flow VIV,To improve knowledge of damping factors. In this paper, RMS response, reduced velocities, drag coefficients and damping factors are presented. Experiment Description The Lake Seneca test facility was selected as the testing site, because it is a fully equipped field test station moored in calm, deep water. It was ideal for conducting a controlled test on a long circular pipe in uniform flow. This was accomplished by towing a vertical, composite pipe with a suspended bottom weight to produce the desired tension.

Numerical simulations of vortex-induced vibration of a three-dimensional flexible Cylinder under uniform turbulent flow are calculated when Reynolds number is 1.35×104. In order to achieve the vortex-induced vibration, the three-dimensional unsteady, viscous, incompressible Navier-Stokes equation and LES turbulence model are solved with the finite volume approach, the Cylinder is discretized according to the finite element theory, and its dynamic equilibrium equations are solved by the Newmark method. The fluid-Cylinder interaction is realized by utilizing the diffusion-based smooth dynamic mesh method. Considering VIV system, the variety trends of lift coefficient, drag coefficient, displacement, vertex shedding frequency, phase difference angle of Cylinder are analyzed under different frequency ratios. The nonlinear phenomena of locked-in, phase-switch are captured successfully. Meanwhile, the limit cycle and bifurcation of lift coefficient and displacement are analyzed using trajectory, phase portrait and Poincare sections. The results reveal that: when drag coefficient reaches its minimum value, the transverse amplitude reaches its maximum and the “lock-in” begins simultaneously. In the range of “lock-in”, amplitude decreases gradually with increasing of frequency ratio. When lift coefficient reaches its minimum value, the phase difference, between lift coefficient and lateral displacement, undergoes a suddenly change from the “out-of-phase” to the “in-phase” mode. There is no bifurcation of lift coefficient and lateral displacement occurred in three dimensional flexible Cylinder submitted to uniform turbulent flow.

Fatigue life calculations have been made for suspended spans of offshore pipelines exposed to steady flow and undergoing vortex-induced vibrations. The effect of the proximity of the sea bottom was taken into account by utilizing the results of related model tests. It was found that the effect of the sea-bottom proximity is to increase the fatigue life of a suspended span of given length or equivalently to increase the safe length of a suspended span for a given fatigue life. Furthermore, the effect of the pipe-to-wall gap to pipe diameter ratio on the fatigue life of such spans has been determined. INTRODUCTION A steady flow about a bluff body, such as a pipeline with a circular cross section, will separate and form a wake. Because of the instability and mutual interaction of the separated shear layers, vortices form and periodically shed from alternate sides of the body. The result is steady and unsteady drag forces in line with the flow and unsteady lift forces? in the transverse, or cross flow direction. If the pipeline is flexible and/or flexibly supported, it begins to vibrate under the action of these periodic forces. The vibrations of the pipeline modify the flow and lead to a nonlinear interaction between the elastic and the fluid systems. The maximum amplitude of inline vortex-induced vibrations is much smaller than the maximum amplitude of transverse vortex induced vibrations, so their contribution to the fatigue life of a pipeline is small. Consequently, attention is focused on the transverse vibrations which will be referred to as "vortex induced vibrations" hereafter. In the last ten years a number of comprehensive overviews of this important class of fluid-structure interaction problems have appeared [1-4]. Experience with unburied offshore pipelines laid in strong current areas has shown that such pipelines may develop unsupported spans due to sea bottom being scoured out from under the pipe due to current action. In turn such unsupported spans exposed to currents may undergo vortex induced vibrations which may affect the fatigue life of the pipeline. Due to lack of data for the vortex-induced vibrations of a flexible cylinder in close proximity to a plane boundary, fatigue life calculations of suspended pipeline spans that determine the maximum safe length of such spans have been based, out of necessity, on data for the vortex-induced vibrations of an isolated flexible cylinder, i.e., no wall effect. In a recent experimental study, Tsahalis and Jones [5] determined the effect of the proximity of a plane boundary on the vortex-induced vibrations of a flexible pipe. They found that the proximity of the plane boundary has the following effects on the response of the pipe as compared to the response of the isolated pipe, i.e., no wall effect (see also Figure 1). First, the increase of the response frequency with the flow velocity is less steep. Second, the first perceptible vibrations take place at a higher flow velocity. Fourth, the maximum amplitude is achieved at a higher flow velocity. Fifth, the maximum amplitude is reduced. Sixth, once the maximum amplitude is achieved it appears that it remains constant for higher flow velocities.

Vortex-induced vibration response characteristics of catenary riser conveying two-phase internal flow

Drilling and production risers experiencing vortex-induced vibrations (VIV) may adversely impact operations in two ways: by increasing deflection due to amplified drag and causing structural fatigue damage due to VIV induced dynamic stresses. Complex hydrodynamic mechanisms controlling correlation length and force dependence on motion and frequency of response are major obstacles in predicting the VIV response, except for a limited number of cases for which extensive experimental calibrations were carried out. A pragmatic VIV analysis methodology has been developed based on correlation length measurements, and riser specific experimental tests to establish basic CD and CL databases for realistic riser configurations with auxiliary lines and buoyancy modules. Correlation length properties are established using flow visualization methods, in particular Digital Particle Image Velocimetry (DPIV), which allows whole-field quantitative information on the velocity and vorticity fields to be obtained. Identification of the role of two basic VIV mechanisms, the formation of braid vortices and the impact of vortex splitting, has provided a robust correlation length model. A VIV analysis program has evolved from these experimental tests in conjunction with extensive research in structural and hydrodynamic riser responses. Introduction The design of drilling risers for mobile offshore drilling units (MODUs) is governed by operational considerations, specifically, the need to keep the riser deflection angle within 1° to 2° during normal drilling operations. This necessitates stringent measures:keep the rig within a tight watch radius of around 0.5% to 2.0% water depth,maintaining high riser top tension, andminimizing riser net in-water weight by the use of buoyancy modules. The occurrence of VIV may adversely impact drilling operability because VIV causes an apparent increase in hydrodynamic drag, resulting in increased riser deflection angles. In addition, fatigue damages appear to be a second concern, however less so since it is feasible to frequently inspect risers. In the event of strong current, the need to keep riser deflection angles at a minimum may dictate the use of faired riser sections. This is, however, a very costly option and must be avoided if at all possible. For example, increased tensioner capability may prove to be just as effective without encountering the same handling difficulties. As for production rigid risers and steel catenary risers for permanently installed platforms, they are much more tolerant of riser deflections and require minimal riser tensions. As a result of low top tension these risers become much more compliant and VIV responsive than rigid drilling risers. Fatigue considerations may dictate that these risers be protected with VIV suppression devices, such as strakes, in ections exposed to strong current. This paper highlights a pragmatic VIV analysis tool (VIVA) based on riser-specific experimental tests and mathematical models. This is followed by a review of VIV analyses for representative rigid drilling and production risers for 3000-foot water depth. VIV response sensitivity is investigated for 1.5-knot slab, linear, and reverse current profiles that are indicative of the 1-year extremes West of Shetland and Brazil. A Pragmatic VIV Analysis Methodology VIVA is a computational tool developed to predict the vortex-induced vibrations and fatigue damage of marine risers in shear flows based on strip theory and an extensive database of hydrodynamic data on sectional force coefficients and correlation length (Reference 1). The program is generically written to allow the input of additional hydrodynam

Vortex-induced vibrations of flexible cylinders predicted by wake oscillator model with random components of mean drag coefficient and lift coefficient

Optimum acoustic impedance in circular ducts with inviscid sheared flow: Application to turbofan engine intake

This paper presents experimental results of vortex-induced vibrations (VIV), concomitantly carried out in water with a flexible cylinder, rigidly fixed, and with a ‘rigid’ cylinder, mounted on an elastic apparatus. The experiments were run at IPT towing tank facility, in a side-by-side arrangement. The flexible cylinder is simply fixed at the upper end. For the flexible cylinder, two degrees of freedom (2DOF) are implied for each vibration mode: crosswise and aligned with respect to the incident flow. The elastic support to which the ‘rigid’ cylinder is mounted is made of two vertical leaf-springs, fixed to two thick horizontal plates, conferring to the cylinder a single degree of freedom (SDOF) to oscillate transversally with respect to the incident flow. The mass ratios of the cylinders are almost the same, around 1.2 and 1.4, respectively, very low values, typical of long ocean pipe structures, as risers and pipelines. The structural damping ratio is also typically low and such as to guarantee high-amplitude responses. Besides usual spectral and statistical analysis, the Hilbert–Huang spectral analysis technique is applied, as, strictly, VIV is a non-stationary oscillation emerged from a nonlinear dynamic system. A discussion is made on the distinct VIV behaviors of the SDOF and the 2DOF systems.

Modelling and prediction of vortex-induced vibrations (VIV) of marine risers is a challenging task due to the associated multi degrees of freedom in both cross-flow/in-line directions and the multi-mode fluid-structure interactions. In addition, the axial motion and its geometrically nonlinear coupling with lateral responses can be significant, especially at higher-order modes. Nevertheless, several papers in the literature dealing with VIV predictions have often overlooked such aspects. Therefore, this study aims to investigate and understand the effect of axial or longitudinal motion through a theoretical model and numerical approach in time domain. Attention is paid to VIV of vertical risers subjected to linearly sheared currents. To capture a three-dimensional aspect of the flexible cylinder experiencing VIV, a semi-empirical model is developed consisting of nonlinear equations of cross-flow, in-line and axial structural oscillations which are coupled with the distributed van der Pol-type wake-oscillators modelling the fluctuating fluid lift/drag forces. The mean drag force is also taken into account. These model equations are numerically solved via a space-time finite difference scheme, and the obtained numerical results highlight several aspects of VIV of elastic cylinders along with the axial motion effects. Apart from the validation of the numerical model with published experimental results, this study reveals how the effect of axial motion and its nonlinear coupling with the two lateral cross-flow/in-line motions can be very important. These depend on the flow velocity, the fluid-structure parameters, the single or multi-mode lock-in condition, and the standing-wave or travelling-wave feature. We recommend that the axial response should be accounted for in VIV analysis and prediction model.