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Proceedings Papers

Publisher: Offshore Technology Conference

Paper presented at the Offshore Technology Conference, April 30–May 3, 2018

Paper Number: OTC-28813-MS

... and established a methodology. The established methods were then used to predict VIM for Malikai TLP and combined motion of TLP-TAD. The drag and

**lift****coefficient**for the lab scale TLP at reduced velocity of 10 and heading of 22.5° was 1.33 and 0.13 respectively. The nominal surge, sway and yaw amplitude...
Abstract

The operating environment for the Malikai project is strong and persistent current with speed up to 2 m/s for even a return period of 50 years. This could lead to vortex induced vibration (VIV) of the risers and vortex induced motion (VIM) of the floating systems such as Tension Leg Platform (TLP) or Tender Assisted Drilling (TAD) vessel. The VIV and VIM could affect the riser and mooring system strength and subsequent failure. This could lead to unplanned production deferment and riser maintenance. Therefore, the current study investigated the VIV and VIM phenomenon for Malikai riser and floating system respectively. The Malikai project used U shaped AIMS fairing to suppress VIV of the risers. These fairings have low drag, provide operational advantage and faster installation compared to traditional VIV suppression methods. Computational Fluid Dynamics (CFD) simulations were performed for the fairing and riser system and confirmed low drag coefficient (0.4) in Malikai environment. Experiments verified it further. The second part of the study was focussed on investigating VIM of TLP and TAD. The CFD simulations were first carried out to validate the motion of TLP at the lab-scale and established a methodology. The established methods were then used to predict VIM for Malikai TLP and combined motion of TLP-TAD. The drag and lift coefficient for the lab scale TLP at reduced velocity of 10 and heading of 22.5° was 1.33 and 0.13 respectively. The nominal surge, sway and yaw amplitude at this condition was 0.05, 0.12, and 1.8 respectively. These predictions were in well agreement with the experimental data obtained from the University Technology Malaysia (UTM). The sway and yaw frequencies were twice of surge indicating VIM. The motion amplitudes for the Malikai TLP were smaller than the lab scale experimental data at reduced velocity of 5. This could be attributed to difference in Reynolds number and tendon arrangement. There was no evident dominating frequency of motion. It was more of a flow induced motion. The drag and lift coefficients for TLP/TAD at heading of 0° was 1.1/0.28 and 0.014/.001 respectively. The drag and lift coefficients are lower for TAD as it is in the wake of TLP (lower currents around TAD). The motion amplitude for TAD were higher than TLP due to more fluctuations in the drag and lift forces. This could be attributed to TAD having only two pontoons. The motion amplitudes were overall small for all the cases and could be due smaller submersed height of columns above the pontoons. The motion and drag predictions can be directly used in the design of hull, riser and mooring line systems and can be further integrated with structural analysis to obtain the fatigue life. This was an attempt to capture the VIM and has indicated promising results. An exhaustive validation can aid in standardization of CFD methods and make it a potential tool to predict VIM. Accurate predictions can help in lowering and building confidence in design parameters.

Proceedings Papers

Publisher: Offshore Technology Conference

Paper presented at the Offshore Technology Conference, May 5–8, 2008

Paper Number: OTC-19289-MS

... cylinder upstream oil & gas contact load hydrodynamic test

**lift****coefficient**installation roller test strake drag coefficient otc 19289 coefficient vertical oscillation bare pipe polyethylene strake reynolds number deformation pipe helical strake OTC 19289 Effectiveness...
Abstract

Abstract Helical strakes are an important Vortex Induced Vibration (VIV) suppression device for Steel Catenary Risers (SCR's). This paper presents the results of two sets of hydrodynamic tests performed at MARIN, on a 12?? pipe fitted with 16D Helical Polyethylene strakes. The first set of tests established the suppression efficiency of the strakes for the Intact Configuration (no deformation). The second set of tests established the performance of the same strakes after undergoing a roller test in which the fins and the body of the strakes have sustained permanent deformations due to a simulated high contact load on the roller of a stinger during an S-lay installation. The type of permanent deformations sustained by the strakes can be described as bulging of the strake body, and permanent folding of the fins. Both configurations of the strakes (Intact and Deformed) were tested at high and low Reynolds numbers (velocities of 2.5 m/s and 0.5 m/s) and at different reduced velocities Vr. The results show that for the Deformed strakes configuration, there was no appreciable decrease in the VIV suppression efficiency of the strakes from a design consideration. The test results indicated that both Intact and Deformed strakes were at least 90% efficient in suppressing VIV. Therefore, based on the tests reported in this paper, the Polyethylene strakes were deemed acceptable to use on the SCR's even when using the S-Lay installation method.

Proceedings Papers

Publisher: Offshore Technology Conference

Paper presented at the Offshore Technology Conference, April 30–May 3, 2007

Paper Number: OTC-18973-MS

... contribute to the overall drag of the riser or drill string and must be carried by the floating platform and its mooring or positioning system.

**lift****coefficient**drag coefficient viv response amplitude ratio amplitude reynolds number upstream oil & gas frequency riser pipe experiment...
Abstract

Abstract This paper presents the developments and key findings of a comprehensive test program executed by AIMS International, Inc. to predict the effectiveness of various Vortex-Induced-Vibration (VIV) suppression devices for riser systems. In addition, the test results were fully integrated into a widely-used riser analysis numerical code, whereby the suppression characteristics of the test devices were compared with standard design practices for a typical riser concept. This paper will discuss the (1) extensive testing of conventional and ROV deployable VIV suppression systems; (2) development of stable, low-drag fairing designs that are not subject to galloping; (3) implementation of these systems in the empirical models such as SHEAR7 and; (4) evaluation of the impact of such suppression devices. Introduction The search for, and production of, hydrocarbon has been relentlessly moving into deeper and deeper water. In the Gulf of Mexico where much of this deep water activity has been pioneered, slender and flexible components are used to moor floating platforms or to transport fluids to and from the seabed. The Loop Current and its associated eddies interact with these relatively bluff bodies causing the shedding of von Karmen vortices. Under certain conditions, the interaction of the vortices with the body produces VIV. This phenomenon can significantly increase the drag of the body and the vibration can lead to shortened life through fatigue. In the Gulf of Mexico, the problem is compounded by several factors: as production moves into deeper water the Loop Current and its associated eddies become stronger and more prevalent, the risers need more external buoyancy to support their weight hence their diameter increases and, of course, the risers are longer. All of these factors contribute to the overall drag of the riser or drill string and must be carried by the floating platform and its mooring or positioning system.

Proceedings Papers

Publisher: Offshore Technology Conference

Paper presented at the Offshore Technology Conference, May 1–4, 2006

Paper Number: OTC-18348-MS

... industry-accepted tools for frequency domain VIV analysis (Shear7). upstream oil & gas turbulence model configuration marine riser

**lift****coefficient**cross-section cfd boundary engineering accuracy viscosity eddy viscosity boundary layer otc 18348 reynolds equation calculation...
Abstract

Abstract The application of CFD (Computational Fluid Dynamics) to the issue of vortex induced vibration (VIV) of marine risers is a rapidly developing area of engineering which offers the potential to improve design capability whilst reducing associated testing costs. However, the tools and processes to achieve this are still being developed, tested and validated by a number of groups within the offshore industry and as yet only sporadic project application has been made of CFD for VIV analysis of marine risers. This paper discusses the key issues associated with the application of CFD to projects followed by a case study illustrating a suitable area of application given the current level of maturity of the numerical tools and the timeframes required to perform the work. The first part of the paper includes a review of the available turbulence models comparing their benefits and drawbacks as well as the important issue of validation and benchmarking with recommendation on acceptable levels of accuracy given the application objectives and requirements. The case study is based on a deepwater drilling riser and the assessment of understanding the VIV performance differences obtained when using staggered bare and buoyant joints along the riser. It is a generally accepted view that staggering bare joints improves riser VIV response however current analysis techniques do not provide the capability to evaluate the staggering and no hard evidence exists (e.g. testdata) in support of a staggering philosophy. Through the use of CFD the influence of the non-cylindrical bare joints is captured in the analysis process permitting at least a qualitative evaluation of particular staggered configurations. This application and the stated objectives of the work are used to highlight the main points of the preceding discussion. Introduction The last years have seen an increasing interest in the use of Computational Fluid Dynamics for the assessment of the Vortex-Induced-Vibration (VIV) behaviour of marine risers. This is still an on-going process where CFD methods are undergoing rigorous testing to prove their applicability in marine riser design. CFD is widely used in other industries (automotive, aerospace, energy) but investment has been made to achieve sufficiently good accuracy in the models for the various industryspecific flow regimes encountered. The offshore/subsea industry is now starting to do the same in realising the potential for CFD application to VIV, process simulation, splash zone loading etc. Currently, projectapplication of CFD is mainly in complimentary role. Deepsea uses CFD for several types of projects such as workover riserVIV, strake and fairing design/analysis, as well as riser tower VIV analysis and drilling riser configuration development. This paper aims to outline the procedure used for the development of the configuration of a drilling riser using CFD analysis for the assessment of the hydrodynamic behaviour of the drilling riser components which is being used as input to standard industry-accepted tools for frequency domain VIV analysis (Shear7).

Proceedings Papers

#### Development of SHEAR 7 Lift Curves For VIV Analysis And Application To Single Pipe And Bundle Risers

Publisher: Offshore Technology Conference

Paper presented at the Offshore Technology Conference, May 2–5, 2005

Paper Number: OTC-17533-MS

... a strategy for both single pipe and the non-symmetric riser bundle tests. 2H managed the tests for BP and provided post analysis. The objectives of this paper is to present:

**Lift****coefficients**obtained from the large scale single rough pipe tests Parabolic lift curves created from the single rough pipe...
Abstract

Abstract In late 2003 BP contracted 2H to manage and run a series of forced oscillation tests at the Marin test basin, Netherlands. The tests examined the effect of vortex induced vibration (VIV) and galloping response on a full size section model of a single pipe riser and a non-symmetric riser bundle. The tests used a 200mm diameter pipe at a Reynolds number of 39,600. This paper presents the results (lift and added mass coefficient with increasing amplitude and reduced velocity) from the single pipe forced oscillation tests. A method is developed to convert the test data into parabolic lift curves and damping coefficients for Shear7 VIV analysis. The parabolic life curves created from the single pipe forced oscillation test data are shown. The method is then extended for use with the test data from the non-symmetric riser bundle forced oscillation tests, and accounts for differences in peak reduced velocity in the test data by calculating effective vortex shedding diameters. Sensitivity analysis is conducted using the parabolic lift curves with Shear7 on an example deepwater riser. This shows that the fatigue lives predicted using the parabolic lift curves are generally lower than the default Shear7 lift curves. Introduction Forced oscillation VIV tests on a 200mm diameter single rough pipe were conducted using the MARIN forced oscillation test rig. Further tests were conducted using a nonsymmetric riser bundle. 2H Offshore worked with BP and MARIN to establish a strategy for both single pipe and the non-symmetric riser bundle tests. 2H managed the tests for BP and provided post analysis. The objectives of this paper is to present: Lift coefficients obtained from the large scale single rough pipe tests Parabolic lift curves created from the single rough pipe test data. The method used to convert test data into lift curves accounting for the non-symmetric riser bundle. Sensitivity of VIV fatigue life to the different lift curves. Further tests using the single pipe at a range of critical and trans-critical Reynolds numbers with and without the rough coating were conducted. These are not detailed in this paper. In this paper the term 'lift coefficient' refers to the lift coefficient in phase with velocity, C LV , which indicates the flow induced lift (vortex induced lift) as opposed to the lift coefficient in phase with acceleration. Forced Oscillation Tests for VIV Forces Forced Oscillation Test Rig The tests were conducted using a 200mm diameter × 3.4m long aluminium pipe that was artificially roughened by coating the pipe with 500 micron sand grains. The roughness is greater than may be seen on real risers, but was chosen to provide a definite rough pipe benchmark. Moreover ocean conditions would be more turbulent than would be the case in the tank, and the higher roughness would make up for this by forcing laminar-turbulent boundary layer transition. The test rig used was able to test in both forwards and reverse directions at speeds of up to 2m/s.

Proceedings Papers

Publisher: Offshore Technology Conference

Paper presented at the Offshore Technology Conference, May 5–8, 2003

Paper Number: OTC-15386-MS

..., and a wake model for the drag and

**lift****coefficients**of the downstream riser. The methodology has been benchmarked with blind comparison of predictions and measurements of the threshold velocity from long-riser tests at Marintek and NDP. The wake model has been benchmarked with BP data on the drag and**lift**...
Abstract

Abstract Riser interference has become a critical issue in riser design with the progression of oil production into deep water. This is particularly the case in the Gulf of Mexico due to strong loop and submerged currents. The generally accepted philosophy for riser interference or clashing is to prevent occurrence in extreme current conditions. In special cases limited clashing under these environmental conditions could be allowed provided no damage on the risers can be demonstrated. Regardless of the design philosophy, the need exists for accurate prediction of the threshold current above which clashing could occur. A comprehensive methodology has been developed to estimate the potential for interference between two risers, one in the wake of the other. The computational procedure involves the use of ABAQUS as a core time domain solver in conjunction with SHEAR7 for VIV and drag amplification, and a wake model for the drag and lift coefficients of the downstream riser. The methodology has been benchmarked with blind comparison of predictions and measurements of the threshold velocity from long-riser tests at Marintek and NDP. The wake model has been benchmarked with BP data on the drag and lift coefficients of the downstream cylinder in two-cylinder tests. The paper presents a discussion of the methodology, and the results from the benchmarking. Introduction Riser interference governs the riser layout, and is of greater importance for field development in deep water. Thus, for the design of riser layouts, it is critical to have an analytical capability which captures all the important physics of riser interference and has been validated with test data. The interference between two risers is governed by drag and lift forces which include wake and shielding from upstream risers, and vortex-induced-vibration (VIV). This paper discusses an interference analysis tool, and the verification of aspects of this tool with model test data from the Norwegian Deepwater Program (NDP). The verification is carried out on (1) drag and lift coefficients for the downstream riser of two risers in tandem, and (2) threshold current (minimum current) that can cause clashing of the two risers. Interference Methodology The methodology for riser interference is based on a time domain analysis with the code ABAQUS. The methodology is applicable to both top tensioned risers (TTR), and steel catenary risers (SCR). The analysis iterates on the two riser configurations as indicated in the flow chart in Figure 1. The steps in the analysis are: Specification in ABAQUS of the properties of the two risers, riser coordinates, appropriate hydrodynamic parameters, current profile, and possible vessel offset. ABAQUS calls ABAFER for the hydrodynamic loads on the risers for each time step. ABAFER calculates the loads on the upstream riser on the basis of (1) the free stream current at each elevation, the free stream drag coefficient given in the input, (3) the amplification in the drag coefficient due to VIV, and (4) the adjustment in the drag coefficient because of the proximity of the downstream riser.

Proceedings Papers

Publisher: Offshore Technology Conference

Paper presented at the Offshore Technology Conference, May 1–4, 2000

Paper Number: OTC-11998-MS

... conference flow velocity otc 11998 frequency experiment

**lift****coefficient**larsen drag coefficient upstream oil & gas vikestad cylinder amplitude vortex-induced vibration kyrre vikestad Copyright 2000, Offshore Technology Conference This paper was prepared for presentation at the 2000...
Abstract

Abstract Vortex-induced vibration (VIV) of a long riser in sheared current is oftenconsidered as an energy balance problem: Excitation forces in the power-inregion add an equal amount of energy to the system as is dissipated by dampingforces outside this region and by structural damping. A riser may havedifferent excitation and damping regions depending on the actual oscillationfrequency, cross-section properties and local flow velocity. A damping modelmust hence be able to handle higher and lower flow velocities than theexcitation velocity range. In this paper the fluid damping models proposed by Venugopal [1] are compared with the experiments conducted by Gopalkrishnan [2]and Vikestad [3]. The results show that the models are conservative at high andlow reduced velocities. Introduction VIV is dependent on many factors such as the Reynolds number, flow velocity andturbulence of the incident current, surface roughness, cross-section shape, inclination, motion of the structure, etc. No solutions or models exist whichcan account for all these factors. The solution has therefore been to simplify the interaction problem as muchas possible hopefully without loosing the information important for theprediction of the resulting VIV and fatigue life of the riser. One suchsimplification is to assume that each cross-section along the riser isoscillating harmonically in the cross-flow direction only and that the incidentflow is constant in time. Then the fluid forces can be split into two parts; the inertia part in phase with the acceleration and the excitation/damping partin phase with the velocity of the cross-section. If the force in phase withvelocity has the same sign as the velocity it is excitation, if it has oppositesign it is damping. In this paper we compare the damping model presented by Venugopal [1] toother experiments. The model predicts the damping force for oscillations instill water, at velocities lower than the excitation velocity range, and athigher. The Venugopal model was based on published empirical damping data fromsub-critical flow experiments. In this paper the Venugopal model is furthertested against the experimental data gathered by Vikestad [3]. The model wasfound to be slightly conservative in that it tends to underestimate thedamping, but not overly so.

Proceedings Papers

Publisher: Offshore Technology Conference

Paper presented at the Offshore Technology Conference, May 4–7, 1992

Paper Number: OTC-6817-MS

... circular cylinder transverse motion

**lift****coefficient**frequency vortex-induced loading bearman transverse force cylinder experiment OTe 6817 Vortex-Induced Loading on Offshore Structures: A Selective Review of Experimental Work D.M. Sheppard and A.F. Omar, U. of Florida Copyright 1992. Offshore...
Abstract

ABSTRACT: This paper is a review of experimental research on vortex-induced transverse forces on smooth, rigid, fixed and elastically mounted circular cylinders, subjected to a variety of steady and periodic flows. The salient flow and geometric parameters influencing the vortex shedding process and thus the transverse force are outlined and discussed. Using data from a number of investigators', attempts are made to illustrate both accepted findings and behavioral trends in the available data. Experimental work by the authors presently underway with oscillatory, nonplanar flows is described and some preliminary results discussed. Areas where information is sparse or nonexistent or where there is significant scatter in existing data-are outlined as topics for future work. INTRODUCTION: When a viscous fluid such as water or air flows past a blunt body with sufficient velocity, flow separation occurs and a wake region is formed. Over a wide range of flow and structure parameters of interest, vortices are observed to form near the points of flow separation. For symmetric structure shapes, void of sharp edges, such as right circular cylinders, vortices are formed on both sides of the body. Under certain conditions these vortices remain attaclled to the body while under other conditions they are shed from the body in or out of phase with each other. The net effect of this phenomenon is a fluctuation in the points of flow separation, which in turn causes a time varying distribution of normal and tangential stresses over the body. This results in time dependent inline and transverse loads on the structure, even when the flow is steady and planar (uniform). The processes associated with flow separation are complex and difficult to predict. Yet minor changes in the separation point can result in relatively large changes in both the inline and the transverse forces on the structure. This flow instability problem is sensitive to perturbations such as those introduced by surface roughness, motion of the body, free stream turbulence, flow orientation relative to the structure, flow around the ends of the structure, etc. In an attempt to understand and model this phenomenon, researchers have isolated various aspects of the problem starting with the (seemingly) simplest case and moving toward the more complex flow and structure situations. The processes are of course nonlinear and thus their individual effects cannot be simply superimposed to obtain the combined effect. However, much can be learned about the mechanisms involved and some guidance for the design engineer can be achieved by such a process. Vortex induced loads are of interest in a number of engineering disciplines, and of particular importance in the design of offshore structures. Structural elements are constantly subjected to loading due to wind and/or ocean currents and waves. Most flow situations encountered in nature are turbulent, nonplanar (nonuniform), and unsteady. To further complicate matters the structural element of interest is often in close proximity to other members, compliant, and perhaps partially covered with biofouling.

Proceedings Papers

Publisher: Offshore Technology Conference

Paper presented at the Offshore Technology Conference, May 4–7, 1992

Paper Number: OTC-6902-MS

... currently uncertain parameters, such as dynamic

**lift****coefficient**and spanwise correlation [6]. The Brown & Root simplified design procedure [5] was a compromise between DnV(1991) and ESDU 85038. It adopted K. in its formulation and yet allowed for a variation of the**lift****coefficient**in different...
Abstract

Abstract Wind-induced vibration of long slender members of offshore structures may lead to fatigue damage. A review of a wide variety of design codes revealed gaps in the essential knowledge base and led to a series of wind tunnel experiments in which a flexible cylinder with pinned ends was excited by vortex shedding. The experiment results and a recommended design procedure are presented. A lack of information regarding the probability of occurrence of the necessary wind conditions is identified as the probable explanation of the disparity between predicted and observed failures in the field. 1 Introduction In recent years there have been a number of well publicized incidence of vortex-induced vibration (VIV) in flare booms [I] [2]. In addition to these cases, significant dynamic response has also been seen in sections of elevated overland pipeline, and in jacket members, during construction and when under tow to the installation site. The initial purpose of this research was to review the currently available procedures, assess strengths and weaknesses, and recommend a "best" one for possible adopt ion by the American Petroleum Institute for possible inclusion in API-RP2A. Several design codes, assessing the vortex-induced vibration response of structural members, can be found in the literature [3] [4] [5]. These design codes have been reviewed recently [6] [5]. DnV(1991) [3], like most other empirical methods, stated that the response was primarily dependent on the stability parameter, Ks. This method was simple and explicit, but seems to result in excessively high response predictions and hence stress levels [7]. ESDU 85038 [4] proposed a random vibration model, taking many empirical parameters into account. This method is too complicated, and requires knowledge of several currently uncertain parameters, such as dynamic lift coefficient and spanwise correlation [6]. The Brown & Root simplified design procedure [5] was a compromise between DnV(1991) and ESDU 85038. It adopted K. in its formulation and yet allowed for a variation of the lift coefficient in different Reynolds number regimes. However, the relation between lift coefficient and Reynolds number, as adopted from ESDU 85038, needs to be further verified. The unsatisfactory performance of the existing design codes, indicates that there exist important gaps in our knowledge of aerodynamic coefficients and lock-in mechanisms, particularly with respect to the single span, dynamic, flexible cylinders in air in which our interest lies. The uncertainties in the literature regarding essential parameters led us to conduct a series of simple wind tunnel tests on a 1.903 inch outer diameter carbon fiber tube with pinned-pinned supports. The results are discussed first in this paper, revealing the following conclusions: response at Ka values greater than 20 is capable of producing fatigue. resonant oscillation with lock-in characteristics is observable at RMS response amplitudes of as little as 1% of a diameter. large response amplitudes, comparable to that predicted by many K. based empirical methods, can be achieved at lock-in, under ideal circumstances in the wind tunnel.

Proceedings Papers

Publisher: Offshore Technology Conference

Paper presented at the Offshore Technology Conference, April 27–30, 1987

Paper Number: OTC-5521-MS

... range of test parameters allows the cables to be well characterized. cable drag data cable geometry drag coefficient reynolds number characteristic coefficient drag force

**lift****coefficient**hydrodynamic force cable model equation yaw angle hydrodynamic characteristic otc 5521...
Abstract

ABSTRACT The Naval Coastal Systems Center performed a series of cable tests in the high speed tow basin at the David Taylor Naval Ship Research and Development Center. The test program was intended to provide data to aid in the design of marine cable systems and the development of predictive methods. Lift and drag characteristics and strum responses were measured for five stranded cables. Cable samples 14 feet long were tensioned between two struts and towed over a velocity range of 2 to 10 knots with yaw angles varying from 20 to 90 degrees. Lift and drag loading functions were developed from the mean steady force data. The force and strum characteristics of the cables were compared with results from previous tests of yawed cables. INTRODUCTION A wide variety of marine systems use stranded cables, also referred to as wire ropes. Moored platforms and oceanographic buoys are examples of stationary systems using cables. Ship and helicopter towed systems consist of cables and hydrodynamic bodies. Such systems are used for naval defense purposes, underwater environmental tests, and seabed mapping. The performance of stationary and towed cable systems can be significantly affected by the lift, drag, and strum properties of the cables. Yet the stranding geometry of a cable is rarely chosen to optimize the system's performance. This is due to the lack of analytic methods for arbitrary cablegeometries and to the relatively small data base available for cable hydrodynamic properties. The placement of a mine sweep device is one technology issue illustrating the need for improved understanding of cable hydrodynamics. The capability to position accurately a mine sweep device requires the design of a sweep wire that produces a specific lift component allowing it to remain in the horizontal plane while under tow. Analytic methods to predict the force and strum characteristics of arbitrary cable geometries have not been developed. Therefore, experimental measurements are relied upon for the design of cable systems. Various tests have been conducted on stranded cables to characterize their hydrodynamic properties. The three-dimensional forces developed by several cables at yaw angles were measured in a wind tunnel at the David Taylor Model Basin in 1945 and 1962. Other wind tunnel measurements of cable forces have been performed at Imperial College of Science and Technology in the United Kingdom. 3 The strum properties of stranded cables have been measured by several investigators. The unique aspect of the present test program is that both the hydrodynamic forces and the strum properties have been measured for several stranded cables over a range of incidence angles and towspeeds. This wide range of test parameters allows the cables to be well characterized.

Proceedings Papers

Publisher: Offshore Technology Conference

Paper presented at the Offshore Technology Conference, April 27–30, 1987

Paper Number: OTC-5503-MS

... ambient (undisturbed) water particle velocity and acceleration, and C D , C M and C G are timeinvariant drag, inertia and

**lift****coefficients**. Equation (1) is commonly referred to as the Morison equation. The hydrodynamic force coefficients, C D , C M and C L are often taken from the 1976 or 1981 DnV...
Abstract

ABSTRACT A new hydrodynamic force model for the prediction of forces on marine pipelines has been verified as described in this paper. Comparisons of forces predicted by the new model with those measured in full-scale laboratory and field investigations demonstrate the accuracy of the model, in terms of general force characteristics, peak force values and spectral energy content, for both regular and irregular waves, with or without superimposed currents pipeline motions calculated from predicted forces are in good agreement with motions calculated from measured forces. Similar comparisons using the conventional Morison equation show it to have deficiencies and demonstrate the considerable improvements attained by the new model. Two effects included explicitly in the new force model, related to the wake behind the pipeline and the time dependence of the force coefficients, are supported by the measurements. It is also shown that forces cannot be described accurately by the conventional Morison equation using constant coefficients and ambient velocity. INTRODUCTION The calculation of the hydrodynamic forces associated with wave and current action is crucial to pipeline horizontal stability calculations. Present industry practice is based on the following simple formulae for the calculation of horizontal and vertical forces, F x and F z for a pipe of diameter D submersed in water of mass density Q. (mathematical equation) (available in full paper) where U and Ú are the time-dependent total ambient (undisturbed) water particle velocity and acceleration, and C D , C M and C G are timeinvariant drag, inertia and lift coefficients. Equation (1) is commonly referred to as the Morison equation. The hydrodynamic force coefficients, C D , C M and C L are often taken from the 1976 or 1981 DnV rules, [1] and [2]. Coefficient data has also been reported in [3J and [4], from the field, and [5], [6] and [7] from the laboratory. That the conventional force models above, equation (1) and, in particular, (2), do not describe force time-series for combined flow with accuracy has been known for some time, [6] and [8]. For the case of regular waves with a reasonably large steady current component, measured forces are not found to exhibit the large differences between maximum forces in the two halfcycles expected from equation (2). For the most realistic situation of irregular waves with a superimposed current, equation (2) is certainly inadequate as demonstrated for example in [6]. Concerns with equations (1) and (2) and the lack of comprehensive large scale field data motivated Exxon Production Research (EPR) to carry out the Pipeline Field Measurement Program (PFMP) in 1980 with Esso Norge and Statoil participation. In these tests force measurements were conducted on an instrumented section of a 24" pipeline placed offshore. From the test results an improved force model was developed [9]. The new model, referred to as the wake model, includes two effects; the modification of the ambient velocity approaching the pipe due to the wake being swept back and forth over the pipe (the "wake" effect), and the time dependence of drag and lift coefficients due to "start-up" amplification following flow-reversal. The need to modify the ambient flow velocity due to the wake effect has been recognised for some time, [10], [11] and [8].

Proceedings Papers

Publisher: Offshore Technology Conference

Paper presented at the Offshore Technology Conference, May 6–9, 1985

Paper Number: OTC-5007-MS

... rectangular horizontal flume, 0.3 m wide, 0.3 m high. The working section was situated at a distance of about 1 m from the upstream end of the flume. downstream body hydrodynamic force diameter bokaian coefficient downstream cylinder drag coefficient cylinder lateral geoola

**lift****coefficient**...
Abstract

ABSTRACT Measurements are presented of forces on a pair of identical parallel circular cylinders with a scotch surface under a steady uniform flow. The drag coefficient of the cylinders was found to be a continuous function of the cylinders' spacing. With increasing the stream wise separation, whereas the transverse extent of the force field on the downstream cylinder indicated an increase, that on the upstream one showed a decrease. In the near wake, the lift forces attained peak values while the drag forces remained lower than the single cylinder value. The forces on the upstream body differed from those on an isolated body only if the two cylinders were as close as two diameters. Mutual interference effects were observed to be most significant at small separations. INTRODUCTION The resistance to fluid flow around a body is strongly affected by the presence of other nearby bodies. When two cylinders are in close proximity, the flow around the downstream body can affect that about the stream one and vice versa. Adjacent structural members subjected to fluid flow may generate an interaction which can cause the force on individual members to increase or decrease over the single cylinder value. Examples include members of the jacket type drilling platforms, semi-submersibles, floating tubular structures, risers, and other tubular structures in offshore engineering; cooling towers and transmission lines in civil engineering and so on. Characteristics of the flow around two interfering circular cylinders are a research topic much more complex than that concerning isolated bluff bodies. When two parallel cylinders are far apart and the rear (downstream) body is well outside the wake of the front (upstream) one there is no interference between them. The flows around both cylinders are the same as that around a single cylinder. The interference between the two bodies will start either when they are sufficiently close to each other or when the downstream cylinder is adjacent to or within the wake of the upstream one. A careful review of flow interference between two parallel circular cylinders in various arrangements in a cross-flow has been presented by Zdravkovich 12 . The quantification of the interference effects in terms of static forces on individual members, and vortex shedding frequency in terms of the governing flow parameters constitute the essence of the problem. This paper describes a series of experiments aimed at determining the lift and drag forces on two parallel and closely spaced circular cylinders with a smooth surface positioned at right angle to approaching flow direction. EXPERIMENTAL ARRANGEMENT AND PROCEDURE The investigation was conducted in a long rectangular horizontal flume, 0.3 m wide, 0.3 m high. The working section was situated at a distance of about 1 m from the upstream end of the flume.

Proceedings Papers

Publisher: Offshore Technology Conference

Paper presented at the Offshore Technology Conference, May 3–6, 1982

Paper Number: OTC-4227-MS

... and Trytten8 The drag, inertia, and the

**lift****coefficients**for a smooth cylinder (~ = DL/vT = 4000) are shown in Figs. 1 through 3. Clearly, the independence principle does not hold true for sinusoidally-oscillating flow about yawed smooth cylinders. Both the drag and inertia coefficients increase...
Abstract

Abstract The forces acting on yawed smooth and rough circular cylinders in a sinusoid ally oscillating planar flow have been investigated experimentally and the force transfer coefficients have been evaluated. The results have shown that the so-called "independence principle" does not hold true over the range of Reynolds numbers and Keulegan-Carpenter numbers covered by the investigation. It has further been shown that the Morison equation predicts the measured force with the same degree of accuracy as that for the normal cylinder provided that the force coefficients appropriate to each yaw angle, Reynolds number, and Keulegan-Carpenter number are used. Introduction The effect of body orientation on resistance particularly for bodies of finite length has been the subject of extensive investigation in steady flow (for a critical review see e.g., Sarpkaya and Isaacson). It has not been possible to correlate the in-plane normal force and the out-of-plane transverse force with a single Reynolds number. Hoerner 2 proposed the "independence principle", which stated that the normal pressure forces are independent of the tangential velocity for sub critical values of Re n , where Re n is the Reynolds number based upon the flow velocity normal to the cylinder. This principle allowed the decomposition of forces and velocities into normal and tangential components and the neglecting of the tangential components. Bushnell and Loftin 3 found that the independence principle does not apply to the critical and Tran critical flow regimes. Norton, Heideman, and Mallard 4 found that the independence principle does apply to post-critical as well as sub critical flow, but not to the critical and Trancritical" regions in between. Thus, recent research has shown that the independence principle applies to steady ambient flow about yawed cylinders when the boundary layer is wholly laminar or wholly turbulent, i.e., when the drag coefficient is nearly constant, but its use in the critical and Tran critical regions is uncertain, i.e., when C d varies rapidly with the Reynolds number. In oscillatory or wave flow the Reynolds number varies from zero to Re max during a half cycle. Thus it could be postulated the boundary layer would, at times, be fully laminar; at other times fully turbulent; and the rest of the time be in transition. In light of this, it is rather doubtful that the independence principle applies at all to oscillating or wave flow. Furthermore, C d and C m are really never constant. The primary objective of this investigation was to study the forces exerted by a sinusoid ally oscillating planar flow on yawed circular cylinders to determine whether the independence principle is applicable or not. If so, the force-transfer coefficients calculated by Fourier analysis using the normal velocity component should reduce identically to the normal cylinder case at corresponding values of the Keulegan Carpenter number (K=U mn T/D), Reynolds number (Re = U mn D/v), and the relative roughness k/D. If the independence principle does not apply, it is desired to determine what the coefficients are as functions of yaw angle, roughness ratio k/D, Re, and K. It would also be necessary to determine how well Morison's equation works with the new coefficients.

Proceedings Papers

Publisher: Offshore Technology Conference

Paper presented at the Offshore Technology Conference, May 4–7, 1981

Paper Number: OTC-3992-MS

...

**lift****coefficient**valve amplitude upstream oil & gas projector OTC 3992 HYDROELASTIC RESPONSE OF CYLINDERS IN HARMONIC AND WAVE FLOW by Turgut Sarpkaya, Naval Postgraduate School; Farhad Rajabi, Mohamed F. Zedan, Brown &Root, Inc. and F. Joseph Fischer, Shell Development Company ©Copyright...
Abstract

ABSTRACT This paper presents the results of two related investigations regarding the vortex-induced oscillations of circular cylinders. The first concerns the dynamic response of spring-mounted, smooth and rough, rigid cylinders in a sinusoidally-oscillating two-dimensional flow. The second concerns the in-line and transverse oscillations of cantilevered piles at or near resonance conditions in regular laboratory waves at intermediate- and deep-water conditions. The results of both studies have shown that the test bodies undergo hydroelastic oscillations in a relatively well defined region of the reduced velocity U r = U m /f n D and that the local as well as the average of the lift force is considerably amplified due to nonlinear interactions between the body and the separated fluid motion. The difficulties arising from the quantification of the correlation length; variation of the fluid velocity with depth, time, and direction; orbital motion of the fluid particles; shear; upstream turbulence; the link between the hydrodynamical behavior of the cylinder and its surface characteristics; and the effect of Reynolds number (particularly at critical and super-critical Reynolds numbers appropriate to the prevailing body and fluid motions) remain unresolved. INTRODUCTION Vortex-induced oscillations of risers, cables, and other offshore structures can give rise to serious operational and structural problems. In recent years, the need to install and operate structures in deeper waters under relatively more severe and uncertain environmental conditions has tended to aggravate the dynamic response problems. The determination of the effect of the major parameters controlling the phenomenon became even more difficult. It is not yet possible to quantify the mitigating effects of the variation of the current direction along a pile, the cellular structure of the vortices and their non-stationary character in shear flow, the relationship between the local and total transverse forces, etc. Where engineering considerations permit, it is possible to modify the structure to reduce the vortex shedding and/or its consequences. Strumming suppression devices are a typical example. These devices are designed, not only to minimize or reduce oscillations, but also to give rise to very little or no additional in-line force. For a specific structure, it is possible to model many of the parameters in a large enough wave channel .or water tunnel designed for this purpose. Nevertheless, for scientific understanding and for developing design methods, it is necessary to try to examine the various effects separately in relatively simple, idealized situations. One such idealization is the study of the dynamic response of elastically-mounted cylinders in sinusoidally oscillating uniform flow. Subsequently, the investigation of the same phenomenon may be brought one step closer to the prototype conditions by carrying out the experiments with flexible cantilevered cylinders in a wave tank. Ultimately, the results of the oscillating-flow and wave-flow experiments may be compared with those obtained from the instrumented prototypes and the effect of the additional environmental conditions be assessed. The present paper is a systematic effort along these lines. RELATED STUDIES The nonlinear vibration of elastic structures in oscillating and wave flows has not been sufficiently explored.

Proceedings Papers

Publisher: Offshore Technology Conference

Paper presented at the Offshore Technology Conference, May 5–8, 1980

Paper Number: OTC-3761-MS

... provided that the boundary" layer remains laminar. transverse force machine learning fraction inline inertia coefficient oscillation

**lift****coefficient**roughened cylinder artificial intelligence evidently cylinder smooth cylinder sarpkaya rough cylinder boundary reynolds number tunnel...
Abstract

ABSTRACT The in-line and transverse forces acting on smooth and sand-roughened circular cylinders placed on a plane boundary (with no gap) in a sinusoidally oscillating flow in a U-shaped vertical water tunnel have been measured. The drag and inertia coefficients for the in-line force have been determined through the use of the Morison's equation and the Fourier analysis. The transverse force has been analyzed in terms of its maximum and minimum values, root-mean-square values, and the time it remains above a fraction of its maximum. The results have been presented as a function of the Keulegan-Carpenter number and the frequency parameter (available in full paper). INTRODUCTION The design of unburied pipelines laid on or near the ocean bottom requires an understanding of the external fluid forces acting on them and an appreciation of the complexities stemming from all other environmental conditions. Numerous studies have been conducted both in laboratory and in the field on the determination of the forces acting on submerged pipelines. l -10 In spite of these past efforts, however, there still remains much to be learned about the fluid forces acting on smooth and rough cylinders resting on a plane boundary. Recently Yomamot, Nath, and Slotta 7 and Wright and Yamamoto 10 investigated the wave forces on cylinders near a plane boundary for small values of the Reynolds number and the Keulegan-Carpenter number. It is a well known fact that for small values of the period parameter the flow about the cylinder does not quite separate, the wake-dependent drag force is very small or negligible, and the in-line as well as the transverse forces are essentially from the wave temporal accelerator. Under such circumstances, the appropriate coefficients may be evaluated from the potential theory. The results of such a study show that 7 when the cylinder touches the boundary a net force exists away from the wall. However, if even a very small gap exists between the cylinder and the wall, then a large net force exists toward the wall. The inertial forces alone do not usually give rise to the maximum load situation for small structures, such as pipelines located on or near bottom, and the separation effects become extremely important not only in the determination of the magnitude but also the direction of the forces. Sarpkaya 8,9 determined the drag, inertia, and lift coefficients for circular cylinders placed near a plane boundary in oscillatory flow at high Reynolds numbers and Keulegan-Carpenter numbers for various relative gaps of e/D. He has shown that the drag and inertia coefficients for the in-line force acting on a cylinder in the vicinity of a plane wall are increased by the presence of the wall. This increase is most evident in the range of e/D values smaller than about 0.5. Both coefficients depend on the Reynolds number, Keulegan-Carpenter number, and the relative gap. The effect of the boundary layer or the penetration depth of the viscous wave is small provided that the boundary" layer remains laminar.

Proceedings Papers

Publisher: Offshore Technology Conference

Paper presented at the Offshore Technology Conference, April 30–May 3, 1979

Paper Number: OTC-3647-MS

... experiment oscillation rms value circular cylinder transverse oscillation harmonic flow cylinder sarpkaya frequency coefficient relative displacement reynolds number

**lift****coefficient**amplitude dynamic response displacement vibration natural frequency synchronization rough...
Abstract

ABSTRACT An elastically-mounted cylinder may undergo hydroelastic transverse oscillations in harmonic flow when the reduced velocity, U r = U m /f n D, is about 5.5. At perfect synchronization, the Strouhal number remains constant throughout the cycle and the vortex-shedding frequency locks on to the natural frequency of the cylinder. The lift coefficient is amplified by a factor of about two relative to that for a stationary cylinder in harmonic flow. The relative amplitude of oscillation for both smooth and rough cylinders is a unique function of the response parameter R p . INTRODUCTION The individual members or small groups of members of a deep-water steel platform structure are seldom, if ever, designed to preclude the occurrence of hydroelastic oscillations under the action of waves and/orcurrents. The dynamic magnification of relatively small loads as a consequence of synchronized oscillations rather than statically-applied design-wave loads can give rise to critical stresses and fatigue. Thus, the prediction of the dynamic behavior of individual members as well as that of the entire structure is important. This, in turn, requires the determination of the critical values of the governing parameters and of the amplification factors for the corresponding force-transfer coefficients. The non-linear vibration of elastically-mounted structures in oscillating flows have not been sufficiently explored. While much progress has been made regarding the in-line and transverse forces acting on stationary structures and regarding the oscillations of elastic structures in steady flows 1 , there has been relatively little work on the complex dynamic response of elastic structures to oscillating flows. Laird 2 explored the effects of support flexibility by oscillating a vertical cylinder through still water. He found that (i) the forces acting on a flexibly supported oscillating cylinder can exceed 4.5 times the drag force of the cylinder rigidly-mounted while moving at a uniform velocity equal to the maximum velocity during the oscillation; and that (ii) a cylinder, flexible enough to have transverse oscillations with amplitudes more than half the diameter, while performing large amplitude oscillations in water, tends to oscillate transversely at the eddy frequency and to vibrate at twice the eddy frequency in the in-line direction. Vaicaitis 3 investigated the response of deepwater piles due to cross-flow forces generated by wind induced ocean waves. The resulting cross-flow forces were treated as random processes in time-space domain and are assumed to be dependent on fluid velocities and vortex shedding processes. Verly and Every 4 measured wave-induced stress on similar rigid and flexible vertical cylinders in a wave channel at relatively low Keulegan-Carpenter numbers. Even though they were unable to correlate their data with any suitable parameter governing the motion, they concluded that the vibration is caused by the cylinder's response to eddy shedding and that there is no fluid-structure interaction. They found that the vibration occurs if Ur is greater than about unity for any natural frequency, wave frequency, and damping. The reduced velocity U never reached high enough values in Verly and Every?s experiments for the cylinder to undergo self-excited oscillations, as the present investigation has shown.

Proceedings Papers

Publisher: Offshore Technology Conference

Paper presented at the Offshore Technology Conference, May 1–4, 1977

Paper Number: OTC-2897-MS

..., and roughness effects on the in-line and transverse force coefficients (i.e., drag, inertia, and the

**lift****coefficients**have recently been carried out by Sarpkaya. These studies were prompted by the need for systematic data and partly by the controversy concerning the influence of Reynolds number and surface...
Abstract

ABSTRACT Transverse oscillations of a flexibly-mounted rigid cylinder in harmonic flow have been investigated through the use of a U-shaped vertical water tunnel. The results have shown that the largest amplitudes of oscillation for a given damping ratio, Keulegan-Carpenter number, and the Reynolds number occur when the vortex-shedding frequency is nearly in tune with the natural frequency of the cylinder. It has also been found that the amplitude of oscillations is proportional to the square of the reduced velocity defined by U m /f n D. INTRODUCTION The investigation of the nonlinear deterministic or statistical response of an offshore structure is of considerable interest and may be carried out through mathematical modeling, small-scale experiments, and prototype testing or through a combination of these three techniques. Much of what is known about the wave forces and moments acting on bodies and complex structures of various shapes came from field data and experiments in wave channels. To extrapolate from these to the prediction of forces on new structures in natural waves is often very uncertain, due to difficulty or impossibility of modeling all the parameters that might have an effect. For example, there is considerable uncertainty as to how to account for the effect of currents which may be superposed on waves, for the elasticity and flow-induced oscillations of the members of the structure, for the roughness and diametral increase of the connecting members, for the effects of ambient flow with shear, etc., not to mention the two most commonly discussed dimensionless parameters, namely, the Reynolds number and the relative amplitude. For a specific structure, it is possible to model many of the parameters in a large enough wave channel or water tunnel designed for this purpose. Nevertheless, for scientific understanding and for developing design methods, it is necessary to try to understand the various effects separately in relatively simple, idealized situations. The analogy with other branches of mechanics is obvious - the research on basic elements under controlled conditions and testing of replica models both play necessary roles. Although some progress has been made in recent years in determining the force-transfer coefficients for sinusoidally oscillating and wavy flows about circular cylinders and piles, a complete understanding of them is still lacking at present. This is due in part to the limited availability of model and especially prototype data, and in part due to theoretical limitations. Much work still needs to be done to determine quantitatively the relative significance of the various factors enumerated above. Studies of Reynolds number, relative amplitude, and roughness effects on the in-line and transverse force coefficients (i.e., drag, inertia, and the lift coefficients have recently been carried out by Sarpkaya. These studies were prompted by the need for systematic data and partly by the controversy concerning the influence of Reynolds number and surface roughness on the time-dependent loads on circular cylinders in harmonic flow.

Proceedings Papers

Publisher: Offshore Technology Conference

Paper presented at the Offshore Technology Conference, May 1–4, 1977

Paper Number: OTC-2898-MS

... of the Morison's equation. The transverse force has been expressed in terms of a single

**lift****coefficient**. The results have shown that the effect of wall-proximity is to increase the force coefficients for-relative gaps of e/D less than about 0.5. In this range of e/D values (0<e/D?0.5) the non-linear...
Abstract

ABSTRACT The in-line and transverse forces acting on circular cylinders placed near a plane boundary in a sinusoidally oscillating fluid in a U-shaped vertical water tunnel have been measured. The drag and inertia coefficients for the in-line force have been determined through the use of the Morison's equation. The transverse force has been expressed in terms of a single lift coefficient. The results have shown that the effect of wall-proximity is to increase the force coefficients for-relative gaps of e/D less than about 0.5. In this range of e/D values (0<e/D?0.5) the non-linear interaction between the shear layers emanating from the top and bottom of the cylinder is reduced and the frequency of oscillations in the shear layers is a synchronised. For e/D larger than about 0.5, the regular vortex shedding resumes, more or less unimpeded by the presence of the wall, and the lift, drag and inertia coefficients nearly assume their free-cylinder values. INTRODUCTION There are numerous problems associated with the design and installation of pipelines in deepwater offshore. The results such as the ones presented herein touch upon only one facet of the submerged pipeline design and do not deal with the consequences of pipeline forces due to temperature, pressure, seabed friction, buckling, scour, hydroelastic oscillations, etc. Suffice it to say that the reliable design information is most likely to come from a combination of laboratory studies, field experience, and careful documentation of the causes of failures. The present investigation is fn extension of that previously reported by this writer 1 and was undertaken for the purpose of determining the in-line and transverse forces un cylinders near a wall at relatively higher Reynolds numbers. It is a well-known fact that for very small values of the period parameter U m T/D, the flow about the cylinder does not separate, the wake-dependent drag force is very small or negligible and the in-line as well as the transverse forces are essentially from the wave temporal acceleration. Under such circumstances, the appropriate coefficients may be easily evaluated from the potential theory. When the cylinder touches the boundary, a net force exists away from the wall. However, if even a very small gap exists between the cylinder and the wall, then a large net force exists toward the wall. The inertial forces alone do not usually give rise to the maximum load situation for small structures, such as pipelines located on or near ocean bottom, and the separation effects become extremely important not only in the determination of the magnitude but also the direction of the forces. It is important to recognize that the separation effects are not free from the effects of the boundary layer which forms on the bottom plane.

Proceedings Papers

Publisher: Offshore Technology Conference

Paper presented at the Offshore Technology Conference, May 1–4, 1977

Paper Number: OTC-2901-MS

... number drag coefficient roughened cylinder

**lift****coefficient**variation smooth cylinder evidently circular cylinder keulegan-carpenter number roughness element harmonic flow rough cylinder coherence steady flow cylinder relative roughness coefficient OTe 2901 WAVE FORCES ON ROUGH-WALLED...
Abstract

ABSTRACT This paper presents the results of an extensive experimental investigation of the in-line and transverse forces acting on sand-roughened circular cylinders placed in oscillatory flow at Reynolds numbers up to 1,500,000; Keulegan-Carpenter numbers up to 100; and relative roughnesses from 1/800 to 1/50. The drag and inertia coefficients have been determined through the use of the Fourier analysis and the least squares method. The transverse force (lift) has been analysed in terms of its maximum and root-mean-square values. In addition, the frequency of vortex shedding and the Strouhal number have been determined. The results have shown that all of the coefficients cited above are functions of the Reynolds number, Keulegan-Carpenter number, and the relative roughness height. The results have also shown that the effect of roughness is quite profound and that the drag coefficients obtained from tests in steady flow are not applicable to harmonic flows even when the fluid loading is predominantly drag. INTRODUCTI ON Of the scores of papers dealing with fluid loading on offshore structures none seems to have treated the effect of roughness on the force-transfer coefficients. Yet it is a fact that the structures in the marine environment become gradually covered with rigid as well as soft excrescences. (see Fig. 1). Thus, the fluid loading due to identical ambient flow conditions may be significantly different from that experienced when the structure was clean partly because of the 'roughness effect' of the excrescences on the flow and partly because of the increase of the 'effective diameter' of the elements of the structure. In the absence of any data appropriate to the harmonic or wavy flows. it has been assumed that "the drag coefficients obtained from tests in steady flow" over artificially - or marine-roughened cylinders "are applicable to wave flows at least when the loading is predominantly drag". Even for large amplitudes of oscillations. there is only a finite vortex street comprised of vortices of nearly equal As the flow reverses, the situation is not that of a uniform flow (with or without free-stream turbulence) approaching a roughened cylinder but rather that of a finite vortex street approaching a rough-walled cylinder. Such a flow cannot be regarded identical to steady flow with some turbulence of fairly uniform intensity and scale as the present results show. It is a well-known fact that organized, uniform roughness in steady flow about a cylinder precipitates the occurrence of the critical regime and gives rise to a minimum drag coefficient which is larger than that obtained with a smooth cylinder. This is partly because of the transition to turbulence of the free shear layers at relatively lower Reynolds numbers due to disturbances brought about by the roughness elements and partly because of the retardation of the boundary-layer flow by roughness (higher skin friction) and, hence, earlier separation.

Proceedings Papers

Publisher: Offshore Technology Conference

Paper presented at the Offshore Technology Conference, May 4–7, 1975

Paper Number: OTC-2320-MS

... validation. Mathematical modeling and numerical techniques have been used by l 2 3 many investigations. cable system oscillator model

**lift****coefficient**engineer differential equation bond graph method experimental data excitation cylinder frequency energy flow upstream oil & gas...
Abstract

A methodology is developed to analyze the vortex-induced vibration of moored or towed cable systems. The fluctuating forces are considered as sources of energy which generate waves propagating through the cable-body system with dissipation and scattering in the process. Because of its emphasis on energy flow, this method facilitates the incorporation of various vortex models into dynamic cable analysis. INTRODUCTION Cables exposed to current in deep-ocean moors or used for towing bodies or arrays for ocean survey are subject to transverse oscillations from vortex-induced forces. This phenomenon, called strumming, has been under investigation for many years because it affects the fatigue life of the structure and the noise of any attached sensors. Experiments conducted in water channels indicate that the vortex-induced vibration can be substantially reduced by introducing hydrodynamic disturbances to the flow near the structure. For example, mechanical devices, such as splitter vanes, trailing ribbons and fairings, have been used to disturb the formation of the vortex flow, while spiral wrappings have been used to disturb their spanwise coherence. Other investigations have been made concerning the nature of the vortex flow and to model the vortex-induced cable vibrations. Wind tunnel and water channel experiments were carried out to measure the characteristics of vortex formation and cable responses. However, due to limitations of the experimental equipment, the motion of a full-scale system cannot easily be modeled experimentally. Thus, numerical modeling is probably the best way to analyze the dynamic motion of a cable system under strumming excitation. To this end, empirical models have been developed recently in which the fluid oscillation near the cable is represented by a non-linear, self-excited oscillator that is dynamically coupled to the structural member. These models can reproduce the synchronization effect as the shedding frequency approaches the natural frequencies of the structure. The models have been used to simulate the motion of an elastically mounted circular cylinder. The results are in good agreement with experimental data of the maximum amplitude in the resonant or entrained state when the vortex shedding frequency is equal to the natural frequencies of the vibrating cylinder. Studies are underway to couple the models to the equations of motion of a flexible cable to simulate the motion of a cable under vortex excitation. The purpose of this paper is to present the bond graph method as a modeling technique that can incorporate a dynamic model of vortex-induced forces in models of cable systems. Using this method, the response of a complete cable system under various environmental conditions is simulated. In the next section this modeling technique is compared with other cable dynamic modeling techniques. A review of oscillator models then is presented with some examples given to demonstrate the feasibility of the bond graph method as a modeling technique for vortex-induced cable system vibrations. DYNAMIC ANALYSIS OF CABLE-BODY SYSTEMS Since cable-body systems are being used in more and more ocean facilities, there is a strong interest in valid analytical tools which require development of analytical approaches supported by experimental validation. Mathematical modeling and numerical techniques have been used by l 2 3 many investigations.