Transcript

OTC 6438

Hydrodynamic Aspects of Flexible Risers H.J.J. van den Boom and F. van Walree, MARIN

Copyright 1990, Offshore Technology Conference

This paper was presented at the 22nd Annual OTC in Houston. Texas, May 7-10. 1990.

This paper was selected for presentation by the OTC Program Committee following review of information contained in an abstract submitted by the author(s). Contents of the paper, as presented, have not been revlewed by the Offshore Technology Conference and are subject to correction by the author@). The material, as presented, does not necessarily reflect any position of the Offshore Technology Conference or its officers. Permission to copy is restricted to an abstract of not more than 300 words. Illustrations may not be copied. The abstract should contain conspicuous acknowledgment of where and by whom the paper is presented.

ABSTRACT

For the evaluation of extreme loads and the assessment of the fatigue life of flex risers, use is made of discrete element models. Most of the models describe the fluid forces by means of empirical formulations using coefficients from 2-D cylinder tests. Recent research has shown that the fluid force modelling should incorporate lift forces perpendicular to the incoming flow. More- over, model tests on typical flex riser sections have proven that the 2-D cylinder formulations are not applicable and may lead to significant errors.

In this paper a new fluid model formulation is presented. This formulation is derived from both model tests and theoretical vortex simulations. Results of systematic drag tests for riser sec- tions are discussed. Capabilities of vortex simu- lation~ are evaluated.

INTRODUCTION

Flexible risers have proven to be a key item for cost effective floating production systems. Most problems involved with the application of rigid risers, such as restricted horizontal floater motions and heavy and costly heave compen- sators, can be eliminated with the application of flexibles. Many flow lines have already been used in mild environments and for limited exposure times .

In harsh environments such as the North Sea, the large diameter and relatively stiff flexible risers for permanent floating production (Fig. l ) , require extensive design and engineering analysis.

Riser systems have to be evaluated for extreme conditions as well as fatigue life. To this end analysis of the dynamic behaviour of the riser system is of prime importance. Typical items of investigation are:

- extreme motions; - interference with mooring or other risers; - minimum bending radii; - end-connector loading; - dynamic tension; - dynamic torsion; - flow induced vibrations.

The motions of the riser and the fortes are primarily excited by floater motions, direct wave forces on the riser and by current. These exciting forces are counteracted by the riser-end fortes, the internal forces (bending, stretch and torsion) and the fluid reactive forces due to the riser motions relative to the water.

During the last four years several tomputa- tional methods have been developed for the analy- sis of the dynamic behaviour of riser systems. Discrete element techniques such as the Finite Element Method (FEM) and the Lumped Mass Method (LMM) are nowadays available for the design, engineering and operation of flexibles (see amongst others refs. [l] and [ 2 ] ) . These tech- niques utilize a spacewise discretization of the riser (Fig. 2) describing the relevant fortes on each of the elements and nodes. Knowing the forces and mass properties of each section the accefera- tions can be solved and numerically integrated to velocities and excursions.

Although in reality the fluid force-riser motion mechanism is both complicated and impor- tant, the fluid load models used in the discrete

References and illustrations at end of paper.

2 hYDRODYNAMIC ASPECTS OF FLEXIBLE RISERS OTC 6438

element methods are normally rather simple and in- accurate. The models are generally based on the well-known Morison approach using relative fluid velocities. Constant drag and inertia coefficients are derived from 2-D cylinder tests.

Flexible risers, though slender in overall dimensions, comprise 3-D curvature, subsea buoys, tethers and buoyancy beads in various shapes. These features provide 3-D flow ensuing not only large in-line drag forces but also lift forces perpendicular to the incident flow. Correlation studies [ 3 ] have clearly demonstrated that use of conventional 2-D cylinder data may lead to e.g. significant under estimation of tensions.

For slender pipe sections it is also well known that vortex shedding from the boundary layer around the cylinder results in non-stationary forces and hydroelastic response.

The Maritime Research Institute Netherlands (MARIN) at Wageningen is involved in the develop- ment of riser analysis tools such as DYNFLX [ 4 ] . As part of this R&D-work much attention has been paid to the mechanism and numerical modelling of the dominant fluid loads on flexible risers. In this paper a general review of the hydromechanic aspects of flexible risers is given. Furthermore an accurate description of drag forces on buoyancy bead sections as well as a practical model of non- stationary vortex induced forces are presented.

HYDROMECHANICS OF FLEXIBLE RISERS

Flow Field

Flexible risers are subjected to a complicated flow field generated by directionally spread ir- regular seas and current. The top-motions of the riser system can normally be considered as forced motions due to the large displacement of the floater (e.g. Floating Production and/or Storage Vessel). The riser is normally free to deploy large amplitude 3-D motions.

Such motions typically feature the following components: - Low frequency (period > 30 S) due to horizontal floater motions, changes in current etc.

- Wave frequency (2 < period < 30 S) due to wave induced floater motions at the top and the direct wave forces on the riser components.

- High frequency (period < wave period) due to vortex shedding, instabilities, production oper- ations etc.

The riser always operates in the vicinity of a floater such as an FPS. The floater disturbs the flow field due to the current flow around the vessel as well as wave diffraction by the vessel. Detailed diffraction analyses, however, have indicated that these disturbances are normally not relevant for the riser response.

The generally accepted description of the local flow along the riser is based on linear wave theory. Using direct summation, FFT or impulse response techniques [2] the orbital fluid veloci- ties and acceleration can be derived from the given wave elevation. Current velocity may be summed to the local orbital velocity components taking into account current profile and direction.

Relative fluid velocities are then derived by subtracting the local riser ('nodet) velocities from the absolute fluid velocities at that loca- tion.

Fluid Forces

The most widely used method to compute fluid forces on risers are based on the well-known Morison approach. This approach distinguishes an force component which is proportional to the fluid acceleration ('inertiat) and a component propor- tional to the relative velocity squared ('drag').

For stationary (e.g. current only) and for quasi-static (e.g. low frequency motions) the con- tribution of inertia components is negligible. The dynamic behaviour in these frequency ranges is often approximated by using damping terms only.

When looking to responses in the wave frequen- cy region, the inertia contribution in the fluid forces is often of minor importance. In survival conditions the wave energy is concentrated in the lower frequency region (periods > 10 S). Floater motion response normally also peaks in this region. Furthermore it should be noticed that the fluid inertia is often smaller than the inertia of the riser itself. Drag forces are therefore con- sidered to be dominant for the response of riser systems to extreme wave conditions.

Flexible risers are slender when compared to the water depth and the wave lengths of interest. When using a discrete element model for the analy- sis of such risers it can also be assumed that element length/wave length and element length/ water depth ratio's are small. This implicates that the dynamic drag forces may be approximated by stationary methods.

This evaluation clearly indicates that for the analysis of flexible risers in extreme wave condi- tions, a major obstacle of the Morison approach viz. a proper choice of the drag and inertia coefficient, can be by passed. Costly large scale forced oscillation tests with riser sections can be replaced by straightforward drag tests. In the following section this approach will be presented in detail.

For the dynamic response in the high frequency regions the above method is invalid, Though small in amplitude this type of response is of im- portance for fatigue analysis, flutterfstrumming

OTC 6438 VAN DEN BOOM AND VAN WALREE 3

vibrations and it may also be responsible for a significant increase of low frequency in-line drag.

Since the basic assumptions made for the description of the low frequency fluid forces are not valid, a more detailed evaluation is required here.

Time varying forces are caused by the periodic shedding of vortices from the boundary layer of cylindrical blunt bodies. Hydroelastic body oscil- lations can result from these non-stationary forces provided the internal structural damping is sufficiently low. The vortex shedding frequency then locks on to the natural frequency of the system. Motion amplitudes may increase to values of once to twice the characteristic body length. An important issue is the increased drag force and risk of fatigue due to the high frequency oscilla- tions of the structure.

Several semi-empirical formulae exist for the prediction of drag and lift forces. These models all have in common that details of the flow field are not taken into account, i.e. they are chiefly based on mechanical and electrical analogons. More advanced models contain tuning parameters to fit the model to experimental observations. Again, these parameters have no physical interpretation other than their analogons in other fields. On the contrary, very advanced numerical schemes exist for solving the instationary viscous Navier-Stokes equations. These methods certainly take into account the flow field, but even with present-day computing power such complex simulations will impose an economical limit on their use for prac- tical problems.

These latter methods are indispensable for research purposes such as knowledge of the details of complex vortex flows, Attempts have been made to couple the direct flow simulation to a struc- tural code by e.g. Hansen et al. [5]. The limita- tions on computer power require many simplifica- tions and heuristic arguments in the model. The predictive abilities of this approach are there- fore limited. For practical cases such as hydro- elastic oscillations, simplified models must be developed, drawing on the results and insights obtained from large scale, systematic computations and experiments. As a first step in this direc- tion, a wake oscillator model (e.g. Griffin [6,7,8]) is tuned to the results obtained by performing a number of simulations using a vortex blob method for solving the Navier-Stokes method. The calculations were conducted for a two-dimen- sional flow around a spring mounted cylinder. The tuned model was subsequently used in the structur- al analysis code of DYNFLX to simulate the hydro- dynamic loading and structural response of a marine riser, a pipe and a cable in current. This work is described into detail by Dercksen and Van Walree [ 9 ] . In this paper the practical implica- tions of the empirical wake oscillator model are presented. --

STATIONARY APPROACH

General

In the Lumped Mass Method a spacewise discre- tization of the flexible riser is obtained by lumping the mass and all forces to a finite number of nodes (Fig. 2). The governing equations of motions are obtained by Newton's law in global coordinates:

(Mj + m.(t)) K (t) = F.(t) 3 j J

. . . . . . a . S . . (1)

where j is the node index and t is time.

It is normally assumed that the fluid reactive forces due to the motions of the flexible riser in water may be described by an inertia ('added massf) component in-phase with the oscillation and a quadrature phase ('damping') component. The inertia component of the fluid reactive forces m is directly accounted for in the left-hand side 04 equation (1). Assuming circular riser cross sec- tions and slender elements it is convenient to express all fluid forces in normal components transverse to the riser and tangential components along the riser (see Fig. 3).

[Anj] and [A . l : directional transformation matrices.

where a and a represent the normal and tan- nj t j

gential added mass:

To solve the accelerations (and by means of numerical integration the velocities and excur- sions) of each node, the right-hand side of equa- tion (1) should be evaluated. This nodal force vector F.(t) contains all internal and external riser foJces such as tension, shear forces, nett weight as well as all fluid forces.

The fluid forces acting on the submerged part of the flexible originate from water particle motions due to waves and current as well as motions of the flexible itself (fluid reactive forces). These forces are approximated by the Morison formulation with velocity (drag) and acceleration (inertia) contributions:

F = K p C D L. u.(t) luj(t)( + D j j J J 2 e . . . . . . . . . . ( 4 )

n p C .D. L i . ( t ) I J J j J

Since the inertia part of the fluid reactive forces is already accounted for in the left-hand side of equation (1) and the current velocity is

4 HYDRODYNAMIC ASPECTS OF FLEXIBLE RISERS OTC 6438

assumed to be constant, ; only consists of the orbital water acceleration due to wave action.

The relative fluid velocity U can be obtained from summation of the velocity components due to waves, current and structure velocity:

To calculate the instantaneous orbital veloc- ities and accelerations of the water particles due to irregular waves use can be made of direct sum- mation, FFT or impulse response techniques.

Riser Sections

Flexible risers normally have circular cross sections with diameters from 4 to 20 inch (0.11 to 0.50 m). Flexibility with respect to floater ex- cursions and wave induced motions is normally ensured by a S-layout obtained by a tethered buoy or so-called buoyancy beads in the lower region of the riser (see Fig. 1). In this region the riser is strongly curved. Due to cross-current even the steady state configuration may be strongly three- dimensional.

To model the fluid forces on the riser cor- rectly special attention should be given to the 3-D curvature as well as to the buoyancy region.

Assuming a discretization with a sufficient number (30 - 60) of straight elements, the fluid forces on each element are normally approximated with equation (4) using coefficients for 2-D cylinders. Taking advantage of the circular cross sections and the large length/diarneter ratio's the forces are divided in normal and tangential compo- nents (Fig. 3). These components can be presented as functions of velocity and acceleration compo- nents in the normal and tangential direction respectively (Fig. 3).

For the damping/drag term this leads to the well-known pressure drag formulation:

/ = H p cDn D L (U cos a)L

It should be noted that in equation ( I ) the added mass m of the riser section is normally small when compared to its structural mass H and is therefore often of minor importance. Assuming that the wave length is large when compared with the element diameter and length, coefficients can be determined from the S ationary and resistance tests with the riser section.

Buoyancy Bead Sections

The hydromechanic characteristics of buoyancy bead sections can certainly not be described by the 2-D cylinder approach described above. Depend- ing on the diameter, the length and the spacing, the beads provide significant cross-flow (lift) forces when the flow makes small angles with the circular plane of the bead. When more oriented in the direction of the riser, the beads are sub- jected to shielding effects.

As part of the DYNFLX development project extensive drag tests with full scale riser bead sections have been carried out in February 1990. The test program comprised systematic variations of bead diameter, length and spacing. The main particulars of the configurations are given in Fig. 4 and illustrated by the photo graphs. The sections were towed in MARINts Deep Water Basin, which measures 220 X 10 X 5.5 m in length, width and depth respectively. The test set-up consisted of a universal joint at the top of the riser section which enables the riser section to rotate freely. The universal joint was instrumented with a 2-component strain gauge force transducer mea- suring the vertical and horizontal components of the towing force.

Based on the results of these tests new formu- lations for the fluid force component were de- rived. Both the tangential and the normal force coefficients were defined as functions of the total flow velocity, the angle of incidence, the volumetric diameter and the length of the section:

2 FDt = % p CDt D L (U sin a)

- - *........, The CDtb and CDnb-coefficients are functions

The coefficients CDn, CDt, CIn and CI can be

derived from forced oscillation tests with a full scale riser section. Alternatively the coeffi- cients may be deducted from captive tests with a section fixed in waves. The coefficients are func- tions of the velocity (Reynolds number) and the frequency of oscillation (Keulegan-Carpenter num- ber).

where a is the angle of incidence of flow, (Fig.

show that at small angles the tangential forces are proportional to the the angle of incidence. This means that the beads produce considerable lift forces. At angles between 30 and 60 degrees the lift forces are negligible due to flow separation and vortex shedding. The tangential drag forces are maximum in the 40 to 60 degree region. At large angles the drag decreases due to shielding effects of the beads.

of angle of incidence and bead configuration and bead shape. Typical results of the model tests are presented in Figs. 5 and 6. These results clearly

OTC 6438 VAN DEN BOOM AND VAN WALREE 5

The normal drag coefficients (Fig. 6) as defined in equation (7), show an almost propor- tional decrement with the angle of incidence of the flow.

On the basis of the described experiments, equation (7) in relation with the following formulations for the drag coefficients are pro- posed for use in flexible riser analysis programs:

CDtb = Ctl 2n sina/(4 .c n sina) + Ct2 sin(2 a)

CDnb = Cnl 2n cosd(4 + n sina)

where Ctl, Ct2 and Cnl are functions of bead shape and spacing. These coefficients can be derived from drag tests with full scale riser sections.

It should be noted that the above formulations are based on the assumptions of stationary flow. Forced oscillation tests in still water and waves with full scale buoyancy bead sections will pro- vide data to validate this approach and to derive the inertia (added mass) coefficients of such sect ions.

Results

Results of riser analysis using the described fluid loading model have been compared with those from conventional analysis. The case study con- cerned a turret moored 40,000 dwt tanker with a steep wave flexible riser on 80 m water depth, (Fig. 2). In Fig. 7 characteristic DYNFLX results are presented for the cross wave/cross current situation.

The tanker was headed perpendicular to the vertical plane through the riser end terminals. The riser itself experienced out-of plane excita- tion due to surge of the tanker as well as direct cross wave and current forces. Fig. 7 shows some results for a regular wave with a height of 10 m at a period of 15 seconds and a constant current of 2 knots over the entire water depth. Selected results are given using the conventional buoyancy bead fluid load model and the fluid load model based on equations (7) and (8) using drag coeffi- cients from Figs. 5 and 6.

As illustrated by the geometry snap shot the fluid loading on the buoyancy bead has a pro- nounced effects on the transverse (out of plane) motions. The envelope plots show significant dif- ferences in tension and torsion in the lower part of the riser.

NON-STATIONARY HYDROMECHANfCS

Vortex Induced Cylinder Oscillations

The wake of a bluff body is comprised of an alternating vortex street. The shedding frequency f of the vortices is a function of the ambient flow velocity U, cylinder diameter D and Reynolds number. This relation was first discovered by Strouhal. The non-dimensional Strouhal number S is defined as:

and is more or less constant over a wide range of Reynolds numbers (100 < Re < 100000): S = 0.2, for smooth cylinders. If the cylinder is flexibly mounted, there are non-linear interactions between the shedding frequency and the cylinder motion. Provided the damping is sufficiently low, the cylinder can extract energy from the flow, exciting sustained oscillations at a frequency close to, or coincident with, its natural fre- quency. In water both cross-flow and in-line excitation occurs. The in-line oscillations are excited at much lower velocities than required for cross-flow excitation.

Two dimensionless numbers which are often used in analyzing experimental data are the reduced velocity:

and the stability parameter:

where fn is the natural frequency of the spring mounted cylinder, M is the virtual mass, S is the logarithmic decrement of damping, p is the fluid density and L the cylinder length. Experiments have shown that the cross-flow excitation range extends over 4.5 < Vr < 10 with a maximum ampli- tude of 1.5 diameters. For in-line oscillations there are two instability regions within 1.25 < V, < 3.8 with a maximum amplitude of 0.20 diameters. More details on experimental results can be found in the review of Sarpkaya [10].

Wake Oscillator Model

As an attempt to collect all observed phenom- ena in a compact model, several semi-empirical approaches exist [10]. One of the models is the wake oscillator model, in which a non-linear oscillator for the lift force is coupled to the equation of motion of the cylinder. The response 2 parameter S 2nS KS is the main parameter of importance. G ~ h e governing equations of the so- called Griffin Model are:

for the lift coefficient;

6 HYDRODYNAMIC ASPECTS OF FLEXIBLE RISERS OTC 6438

and for the equation of motion in the direction normal to the onset flow;

The shedding frequency % follows from the Strouhal relation and the natural frequency w m, where k is the spring stiffness. The d~mensionless coefficients F, G and H are to be determined from experimental results. The used coordinate system is shown in Fig. 8.

The major drawbacks of the model are the facts that it is based on fluid damping in still water and that there is a continuous phase angle varia- tion between the exciting force and the response of the cylinder. Additional damping has therefore been added to the Griffin model. This damping is a function of the cross-flow displacement and is given for ay > 0.25 by:

This is a slightly modified form of the empirical equation as proposed by Skop et al., see e.g. Sarpkaya 1101.

For the drag coefficient of the oscillating cylinder, the following empirical formulation is used :

CD = CD e J sin (2wt) .......... (15) where:

where w is the frequency of cross-flow motion, ay is the standard deviation of the cross-flow motion and I and J are constants to be determined from numerical results obtained with the vortex blob method. CDo is the mean drag coefficient for a 2 stationary cylinder, Re = wnD / v is the Reynolds number based on the oscir)lation.

This wake oscillator model was incorporated in the computer code of DYNFLX. At each time step the velocity and acceleration vectors of the structur- al elements are known. From these vectors, the cross-flow velocity and acceleration components are determined. Using these quantities, equation (12) is solved using a fifth order Runge-Kutta method. The cross-flow hydrodynamic lift force is then known. The drag force is derived from equa- tion (15) and the time history of the structural

response. The lift and drag forces are then evenly distributed along each element. From the excita- tion forces and reaction forces, the program computes the kinematics for the next time step. This process is repeated each time step,

A circular cross section is assumed in this approach, i.e. element rotation is assumed to be perpendicular to the flow. The flow along each element is further assumed to be fully correlated, i.e. two-dimensional. This assumption is valid as the amplitude of motion increases jlO]. Although the fluid loading is thus essentially two-dimen- sional on each element, the structural response computational scheme allows for three-dimensional responses.

In this section some practical results obtained from calculations with the structural code will be presented. The cases concern a verti- cal marine riser subjected to a uniform incoming flow. For this application, results obtained from another computer program are also available, see Hansen et al. 151. The main parameters are shown in Table 1, while Fig. 9 shows a general arrange- ment.

1

The first case shows the riser behaviour for the condition that its natural frequency is close to the vortex shedding frequency. Some statistical results are shown in Table 2.

Practical Results

Relatively large displacements are shown which are not unusual for lightly damped structures. The resemblance with results obtained from Hansen et al. 151 is good, although their maximum cross-flow and in-line displacements are larger. This may be caused by the fact that they use no structural damping at all. Using the present structural code this is not possible due to numerical instabili- ties for very lightly damped structures.

Fig. 10 shows the extreme in-line and cross- flow displacements. The in-line displacement is dominated by a static part due to the mean drag force. The dynamic in-line displacement is domi- nated by a second mode vibration. This is due to the frequency of the drag force which is twice the cross-flow force frequency. The cross-flow fre- quency is pronounced and vibrates in the first excitation mode at a frequency close to the natu- ral frequency.

The second case shows the riser behaviour for the condition that its natural frequency is close to twice the vortex shedding frequency. This will cause second mode cross-flow displacements. Table 3 shows some statistical results.

In comparison to the first case, the maximum in-line displacement is larger here due to the higher current velocity. Despite this higher cur- rent velocity, the minimum in-line displacement is clearly more directed against the current veloc-

OTC 6438 VAN DEN BOOM AND VAN WALREE

ity. The cross-flow displacement is smaller compared to the case 1 results. This is due to the occurrence of second mode vibrations. This be- haviour also results in high drag coefficients and corresponding high tension variations,

Figure 11 shows typical riser motions. Both first and second mode vibrations are shown for the in-line and cross-flow motions. Although not shown here, low amplitude fourth mode vibrations occur occasionalLy in the in-line direction.

CONCLUSIONS

In this paper a concise outline of the model- ling of fluid loads on flexible riser systems is given. An integrated numerical approach combining vortex simulation with global motion analysis is still prohibited by computational performance.

Application of Morisonfs approximative method can be combined with the use of tangential and normal fluid force coefficients derived from drag tests with full scale riser sections.

The presented wake oscillator model can be used to simulate non-stationary cross-flow effects.

Incorporation of these fluid load models in flexible riser analysis models may contribute significantly to the overall reliability and accuracy of the analysis.

NOMENCLATURE

Added mass vector

Hydrodynamic drag coefficient

Hydrodynamic inertia coefficient

Hydrodynamic lift coefficient

Riser diameter

Force (vector)

Vortex shedding frequency

Natural frequency

Empirical constant

Empirical constant

Empirical constant

Empirical constant

Stability parameter

Riser element length

Mass (matrix)

Added mass (matrix)

Reynolds number

Strouhal number

Response parameter

Tension

Time

Ambient flow velocity

Relative fluid velocity

Reduced velocity

Current velocity

Wave induced velocity

Excursion vector

Cross flow displacement

Flow incidence

Logarithmic decrement of damping

Wave elevation

Transformation matrix

Fluid density

Standard deviation

Kinematic viscosity

Angular frequency

Superscript

Differentation with respect to time

Subscripts

b Buoyancy bead j node number n normal, natural o mean value t tangential

ACKNOWLEDGEMENT

The authors are indebted to the following sponsors of the DYNFLX89 research program for their kind permission to make use of the results of the program: - AMOCO Netherlands Production Company - Bluewater Engineering - Heerema Engineering Service - MARLN - Shell Internationale Petroleum Maatschappij - Smit Engineering - IRO-Research/Dutch Ministry of Economic Affairs.

REFERENCES . .

1. OfBrien, P.J. and McNamara, J.F.: "Analysis of Flexible Riser Systems Subject to Three-Dimen- sional Sea State Loading," BOSS Conference, Trondheim, June 2988.

2. Boom, H.J.J. van den, Dekker, J . N . and Elsacker, A.W. van: "Dynamic Aspects of Off- shore Riser and Mooring ConceptsIu Proceedings of Offshore Technology Conference, Paper 5531, Houston, May 1987.

8 HYDRODYNAMIC ASPECTS OF FLEXIBLE RISERS OTC 6438

3. Elsiicker, A.W. van: "The Behaviour of Flexible Risers in Waves," Proceedings of Offshore Technology Conference, Paper 6168, Houston, May 1989.

4. Boef, W.J.C., Lange F.C. and Boom, B.J.J. van den: "Analysis of Flexible Riser Systems," Fifth Conference on Floating Production Systems, London, December 1989.

5. Hansen, H.T., Skomedal, N.G. and Vada, T.: "Computation of Vortex Induced Fluid Loading and Response Interaction of Marine Risers," Proceedings of Eighth International Conference on Offshore Mechanics and Arctic Engineering, The Hague, 1989.

6. Griffin, O.M., Skop, R.A. and Ramberg, E.R.: "The Resonant, Vortex-Excited Vibration of Structures and Cable Systems," Proceedings of Offshore Technology Conference, Paper 2319, Houston, 1975.

7. Skop, R.A. and Griffin, O.M.: '*An Eeurfstic Model, for Determining Flow-Induced Vibrations of Offshore construction^,^^ Proceedings of Offshore Technology Conference, Houston, Paper 1843, 1975.

8. Griffin, O.M., Skop, R.A. and Koopmann, G.H.: "Measurements of the Response of Bluff Cylinders to Flow Induced Vortex Shedding,'$ Preprints of Proceedings of Offshore Technology Conference, Houston 1973.

9. Dercksen, A. and Walree, F. van: gtSimulation of the Hydrodynamic Loading and Structural Response of a Marine Riser," 5th International Conference on Numerical Ship Hydrodynamics, Tokyo, 1989.

10. Sarpkaya, T.: "Vortex-Induced Oscillations, a Selective Review", Journal of Applied Me- chanics, Vol. 46, pp. 241-258, 1979.

Table 1

Vertical riser properties

Table 2 Table 3

Comparison between calculated Calculated results for vertical riser, case 2 results for vertical riser, case 1

160

Quantity

Length

Diameter

Mass

Natural frequency

Flow velocity

Pre-tension

Response parameter

Unit

m

m

kg/m tad/s

m/s N -

Value

Quantity

Xmin X ma X

Ymin

ymax

?D

Tmean

ATmax

Case 1

10 0 2

3220

0.71

1.0

1.6~10

0.15

Quantity

Xmin

'max

ymin

Yma X

E , Tmean

ATmax

Unit

m

m

m

m - N

N

Calculated

1.05

2.60

-3.05 3.05

1.75

1.7~10 6

8.5x104

Case 2

10 0 2

4130

1.42

2.0

1.6~10 6

0.15

Nansen

1.35

2.80

-3.40

3.40

1.60

1.7~10 6

8.0x104

Unit

m m m m - N N

Calculated

-0.42

4.11

-2.26

2.20 -

2.7x106

1.4~10 6

TANGENTIAL DRAG / LIFT COEFFICIENTS FOR VARIOUS BUOYANCY CONFIGURATIONS b e a d c o n f i g m o d e l test CDtb= C t l ( 2 n s i n a / ( 4 + x s i n a ) ) + Ct2 s i n ( 2 a )

C t l et2 I1 0 0 111 A - - - - -- -

0.0 30.0 ~ 0 . 0 ANGLE OF INCIDENCE

Fig. 5 Tangential drag force o n buoyancy bead s e c t i o n s

NORMAL DRAG / LIFT COEFFICIENTS FOR VARIOUS BUOYANCY CONFIGURATIONS

I b e a d c o n f i e 1 m o d e l t e s t I CDnb= C n l ' (2ncosa / ( 4 + ~ r s i n a l ) I C n l

I I l l I A l

NEW FLUID LOAD MODEL - - - - - -- CONVENTIONAL FLUID LOAD MODEL

SNAPSHOT O F RISER MOTIONS ENVELOPES O F TORSION. TRANSVERSE D EPLECTION AND TENSION

8 0 . 0

- E .d

4 0 . 0 m ;:::E] N

E0.O 5 -1.0

E --- --- --- 0.0

D.0 40.D 1 0 . 0 ILO.0 0 .0 4 0 . 0 1 0 . 0 120 .0 -3 .0

X ( m ) LENGTH ALONG RISER ( m )

0.0 40.0 n o o 1 l . o LENGTH ALONG RISER ( m )

Fig. 7 Influence of bead f l u i d load modelling on r e s u l t s o f f l e x r i s e r ana lys i s

F i g . 6 N o m l drag force c o e f f i c i e n t on buoyancy bead s e c t i o n s


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