CROSS SECTION VIV MODEL TEST FOR NOVEL RISER GEOMETRIES

Transcription

1 CROSS SECTION VIV MODEL TEST FOR NOVEL RISER GEOMETRIES Abstract Jaap de Wilde MARIN (Maritime Research Institute Netherlands) Haagsteeg 2 / P.O. Box AA WAGENINGEN, The Netherlands A. Sworn and H. Cook BP N. Willis and C. Bridge 2H Offshore The global loads and fatigue life of deepwater risers or riser bundies in current are often dominated by Vortex Induced Vibrations (VIV). Semi-empirical prediction program such as Shear7 and VIVARRAY are still the most commonly used tools for analyzing the VlV response of such systems. These programs rely on large databases with experimentally determined hydrodynamic coefficients. A new test apparatus has been developed for measuring the hydrodynamic VIV coefflcients on an oscillating model of the riser in uniform and steady current. A 3.4 m long section of the riser can be tested at full scale dimensions and real current speeds. Tests are carried out at different tow speeds, oscillation frequencies and amplitudes. Tests at full scale Reynolds numbers reveal new insights in the Reynolds scale effects and reduce uncertainties of such effects in the design process. An efficiënt test strategy has been developed for finding the peak lift loads of a new riser geometry or configuration. About 50 tests are needed for each flow onentation. A non-ctrcular riser bundie can be tested for 8 flow angles between 0 and 360 degrees, using steps of 45 degrees. Over 400 tests can be conducted in about 2 weeks time. Symbols A Cd CLV Cu Cm D f n : amplitude of oscillation : drag coëfficiënt : lift coëfficiënt in phase with velocity : lift coëfficiënt in phase with acceleration : added mass coëfficiënt : cylinder diameter : natural frequency of riser mode shape n 1

2 f 0 f s Re St U U r : oscillation frequency : vortex-shedding frequency : Reynolds number : Strouhal number : flow velocity : reduced velocity 1. Introduction One of the great challenges in the offshore industry is still the assessment of the motions of a circular cylinder in waves and current for application to risers or riser bundies in water depths up to 3,000 m (10,000 feet). Here the global loads and the fatigue life are often dominated by Vortex Induced Vibrations (VIV). VIV can be of major concern because of the increase in drag loads and the high fatigue damage means high investment and maintenance costs of the risers. In ocean currents, alternating vortices will develop on the riser which can excite the riser in one or more of its natural frequencies. Resonant type VIV happens when the vortex shedding frequency gets close to one of the natural frequencies. Due to the so-called "lock-in" effect, the correlation length increases as well as the vortex strength. Lock-in also leads to vortex induced vibrations over a much wider range of oscillation frequencies than would be expected for normal resonance. At lock-in the vortex shedding somehow adapts itself to the oscillation frequency. Vortex induced vibrations are self-limiting at amplitudes around one times the cylinder diameter (A/D = 1). The fatigue damage can still be large due to the high frequency and concentration of the stress variations in the anti-nodes of one or more excited modes. Figure 1: MARIN High Reynolds VIV test apparatus 2

3 2. Vortex shedding and lock-in VIV A cylinder in a steady cross flow develops a flow field that depends on the flow velocity, the geometry and the surface roughness. The flow regimes can be classified into several Reynolds regimes. The Reynolds number denotes the ratio between the inertial and viscous forces in the flow: V For Reynolds numbers above 40 a classical von Karman vortex street develops in the downstream wake. Two opposite vortices are generated every cycle and are transported downstream with nearly the free flow velocity. «O 0 VO Figure 2: Von Karman type vortex street. Offshore riser systems operate at Reynolds numbers well above 10,000, where the following Reynolds regimes can be distinguished [1]: Sub-critical regime: 2,000 < Re < The turbulent vortex street has an almost constant vortex shedding frequency (St «0.20). The boundary layer is laminar up to the separation point at about 80 from the upstream stagnation point. The drag coëfficiënt of a smooth circular cylinder in the sub-critical Reynolds regime is very constant with a value close to 1.2. Critical regime: 200,000 < Re < The boundary layer becomes unstable, but separates before becoming turbulent. The width of the wake decreases and the drag coëfficiënt drops to a value near 0.3. The vortex shedding frequency is very variable. Supercritical regime: < Re < 3, There is first a laminar separation at about 100 from the stagnation point. The flow becomes turbulent and then re-attaches, forming a separation bubble before finally separating from the body near 140. The regime is recognised with a drag coëfficiënt increasing from 0.5 to 0.7. The wake is disorganised and the shedding frequency is very variable. 3

4 The ïn-line drag of a cylinder is proportionai to its diameter and the square of the flow velocity: c F " d - D*pv* The vortex shedding frequency is proportionai to the free flow velocity and inverseiy proportionai to the diameter. The Strouhal number denotes the proportionality constant: st=i U The drop of the drag coëfficiënt in the critical Reynolds regime is known as "drag crises" or "drag bucket". The drag coëfficiënt of a very smooth cylinder can drop from about 1.2 to as low as 0.3, as shown in the next figure based on NACA wind tunnel measurements [2]. Sub-critical Super-critical '»* s 3 4.e a io* e 3 4 e e /o*' z 3 ' Re Figure 3: Drag coëfficiënt and Strouhal number for Reynolds l&to 2 x l(f 3. Lock-in VIV The VIV phenomenon happens in the so-cal!ed "lock-in" region, where the vortex shedding frequency collapses onto the natural frequency. Lock-in VIV has been widely explored, and it is known to be associated with: increase of the correlation length, increase of vortex strength, 4

5 increase of response bandwidth, self-limiting nature at approximately 1 diameter, and increase of the in-line drag. The lock-in phenomena is clearly demonstrated with the experimental Feng data [3]: Ofif - O.0OH5 i O STATIOMARY %n< CYLINDER 0 r - SHE00ING rreque«cy--y^ 1J> W^^^iltft^ te OJ ^ AO FENG DATA + 02 (M u 0 : ^ A?\ * S 6 f0 Figure 4: Frequency and amplitude response in the lock-in regime Two regions can be distinguished in the lock-in region (5 < Ur < 8): f s < f n f 8 > f n The vortex shedding frequency is lower than the natural frequency. The added mass coëfficiënt in this regime is usually larger than 1. The lock-in results in a downward shift of the natural frequency, thereby adapting the natural frequency to the vortex shedding frequency. The vortex shedding frequency is higher than the natural frequency. The added mass coëfficiënt is usually smaller than 1. The lock-in results in a downward shift of the vortex shedding frequency. The vortex shedding frequency now adapts to the natural frequency. Outside the lock-in regime (U r < 5 or U, > 8) the response follows the vortex shedding frequency, but the response is very small. Often a figure-of-eight type response is found for 2 degrees of freedom pipe motions. 5

6 i i.oodi- y 0.50* / A J - \ -looov n Figure 5: Figure-of-eight VIVresponse 4. Modal response in sheared current The VIV analysis of a deepwater riser in sheared current is still a major challenge. Specialised groups work on improving and calibrating existing prediction tools, developing new numerical tools using computational fluid dynamics (CFD), new model tests techniques or performing full scale measurements. A deepwater riser can be excited at different locations along it length, in different modes and at different frequenties, resulting in interesting phenomena such as: mode interference, multi-mode response mode switching. The response may even not consist of true modes, but rather of travelling waves that carry energy from one area of the riser to others. The mode response in sheared current can be demonstrated with the following simplified example. A vertical riser in a linear shear is considered, with zero current speed at the seabed and maximum speed at the water surface. 6

7 Figure 6: Simplified riser in sheared current In the next graph, the lock-in regions (5 < Ur < 8) are highlighted for the first seven modes. It is however unlikely that all these modes will participate simultaneously, because of the selflimiting nature of the VIV and the limited amount of energy that can be extracted from the vortex shedding process. In fact, the more powerful modes tend to dominate. In this example the more energetic modes are excited at the top of the riser, where the flow velocity is the highest. The largest excitation region can de observed for modes 4 and 5. WO 1.0 max PP K / / f4 sïl / n V 5 8 Ur ' D Figure 7: Example ofmodal response in sheared current 5. Fatigue damage The fatigue damage is one of the major concerns for the design of deepwater riser systems. The stress fluctuations cause small defects in the pipe material to grow, which in the long term can 7

8 lead to riser damage or even failure. The fatigue capacity of a material can be expressed in the number of stress cycles to failure (S-N curve): In which N is the number of cycles to failure and AS is the amplitude of the stress fluctuations. The power m and the constant C depend on the material properties, the mean tension and the stress range. S-N relations are determined empirically. The fatigue analysis requires accurate predictions of the modes, amplitudes and frequencies. The importance of the response amplitude is evident, reducing the fatigue life with the m 01 power (m is typically 3 to 5). The importance of the mode number can be understood when comparing the fatigue damage of a single mode response with that of several participating modes. In the first case the damage is always accumulating at the same locations in the anti-nodes, whereas the in the Iatter case the damage tends to be more distributed over the riser. An example of the large variation in predicted fatigue life is presented in the next table. Table 1: Variation in predicted fatigue life Current Speed U [m/s] Mode No. n H Fatigue Life for A/D = years 133 days 8 days 5.8 years 17 days 36 hours 1.7 years 5 days 11 hours 265 days 2 days 5 hours 136 days 1 day 2 hours 6. Riser VIV analysis VIV prediction tools, such as Shear7 or VIVARRAY, have been developed for the analysing the VIV response of deepwater risers, [4] and [5]. The semi-empirical approach has been in use for a few decades and has faced a lot of criticism. In spite of this, it survived and it is still the most commonly used approach in the industry. The phenomenological approach is based on the assumption that the fluid forces can be locally described by a non-linear oscillator, which describes the excitation of vortex shedding process in terms of oscillating lift forces at the Strouhal frequency or as so-called negative damping. The self-limiting nature of the oscillation amplitude is taken care of by the non-linear description of these forces. This approach has survived for a long time because it is adjustable to experimental results and describes the known phenomena quite well. The mathematical core of the programs basically involves a generalised equation of motion describing the riser oscillations around the global shape: d 2 Z DdZ d 2 L.Ö 2 zl d [ T ÖZ] _,.v öt 2 öt öx 2 \ öx 2 J öx\ dxj ' V ; 8

9 Most programs solve this equation mode-by-mode in the frequency domain. Finite element methods (FEM) are used for analysing the structural part, on the left hand side of the equation. Strip theory is used to describe the alternating vortex shedding loads on the right hand side of the equation. An extensive database is used with non-dimensional lift and added mass coefficients, which have been obtained from experiments. Solutions are found in an iterative process to deal with the strongly non-linear behaviour of the lift coefficients. This part represents in fact the true nature of the hydro-structural VIV problem, in which the motions are excited by the fluid flow but the fluid flow itself depends again on the structural motions. Figure 8: Strip theory approachfor a slender riser Figure 9: Fluidstructure interaction for VIV 9

10 The program returns for each individual mode: oscillation amplitudes, oscillation frequency, drag loads, fatigue life. The interpretation of the multi-mode response is mostly left to the user. 7. High Reynolds test apparatus A new test apparatus has been developed for measuring the vortex shedding loads on an oscillating cylinder at full scale Reynolds numbers, [6] and [7]. A 3.4 m section of the riser is towed while being oscillated at the same time. The forces on the cylinder are measured and can be processed to obtain the dimensionless coefficients for calibration of the VIV prediction programs. The measurements at full scale Reynolds numbers provide new insights in the scale effects when entering the critical regime. The existing lift coëfficiënt databases are mostly populated with data from sub-critical experiments. The new apparatus may also be used for testing new and non-symmetrical riser geometries and configurations, including straked risers, riser bundies, piggy-back risers, risers with staggered buoyancy, drilling risers with kill and choke lines, etc. In 2002 the set-up was used for testing a dual pipe riser system for Conoco Phillips [8]. The test up has also been used for testing the efficiency of various strake geometries. The development of the set-up started in 1999 as an in-house research activity and continued afterwards for the VIVARRAY JIP. The set-up, pictured below, consists of: (1) vertical struts arrangement, (2) linear bearings, (3) test pipe, (4) large circular end plates, (5) vertical drive shafts, (6) oscillator with gearing and crank wheels (7) 30 kw electric motor. 10

11 Figure 10: High Reynolds VIVtest apparatus The test pipe is horizontally suspended at mid depth from the carriage on two streamlined struts with linear bearings. The oscillation is forced by the oscillator using a crank-shaft mechanism. The oscillation frequency and amplitude can be accuratejy adjusted from test to test. The overhead carriage runs on rails over the 210 m long towing tank of 4 m width and 4 m depth. The 165 kw engine can deal with over 10 kn of drag loads at tow speeds up to 4 m/s. The carriage can run in both forward and backward direction, which means that the cylinder is either pushed or pulled trough the tank. Both directions show a uniform flow field with low turbulence. The apparatus is capable of: - maximum cylinder drag load of 10 kn. - maximum vertical cylinder loads of 10 kn - maximum tow speed of 4 m/s maximum oscillation frequency of 3 Hz - maximum oscillation amplitude of 330 mm An example of the measured forces is presented in the next graph and shows the cylinder motion, velocity, acceleration, the in-line drag force, the total cross flow force, the cross flow lift force after inertia removal and the instantaneous energy transfer from the fluid to the pipe. A positive mean value of this signal over an integer number of cycles means a nett excitation. 11

12 TEST NO. locooe ZMOT m "D DJ»-. W\AAA/W\AA/WWVWW\A/VWW\AAA/\A/m 1.00-j toac "3 100 FL N *D 2*00-1 Figure 11: Example ofmeasured time traces 8. Data analysis In general, the oscillating lift forces of the vortex shedding process show a phase shift with the cylinder motions, which can for harmonie signals be expressed as follows: z(t) = Asin(ü)t) FL(t) = FLsin(cot+4>o) or FL(t) = FLsin <t»o cos{(üt) + FL COS <J»0 sirt(cot^) The in-phase and the out-of-phase lift forces relate respectively to the added mass and the power transfer from the fluid to the cylinder respectively. The power transfer can be either positive (exciting) or negative (damping). The lift coëfficiënt in-phase with the velocity and the lift coëfficiënt in-phase with the acceleration can be defined as follows: -^ % and Cu=^ k DL^pU 2 DL±pU 2 The added mass coëfficiënt can be calculated from the in-phase lift forces: p f D 2 L(27tf 0 ) z A 12

13 Usïng the same sign conventions as Gopalkrishnan [9], a positive Clv coëfficiënt denotes power transfer from the fluid to the cylinder oscillation and a positive Cla coëfficiënt denotes a negative added mass. 9. Test strategy An efficiënt test strategy has been developed in collaboration with 2H Offshore and BP, for finding the non-dimensional input coefficients for Shear7 calculations on an asymmetrie riser configuration. The difficulty here is to find the input coefficients in such a way that sufficiënt resolution is guaranteed, without expanding the test matrix too much. The three independent test parameters are: tow velocity (Reynolds number) oscillation frequency (reduced velocity) oscillation amplitude (amplitude ratio) We needed about 50 individual tests for every flow angle. Eight flow angles were tested: 0, 45, 90, 135, 180, 225, 270 and 315. Over 400 tests were conducted in about 2 weeks. Series A: 6 non-oscillating tests. Series B: 10 reduced velocity sweep tests at 0.75 A/D * Series C: 10 reduced velocity sweep tests at 0.25 A/D Series D: 4 reduced velocity sweep tests at 0.50 or 1.2 A/D Series E: 2 tests at the peak reduced velocity Series F: 4 Reynolds sweep tests at 0.75 A/D Series G: 4 Reynolds sweep tests at 0.25 A/D Series H: 4 Reynolds sweep tests at 0.5 or 1.2 A/D Series I: 6 spare tests A pictorial plot of the above test matrix is presented in Figure 12 with the sub-critical Gopalkrishnan data for a circular cylinder in the background. The lock-in area is scanned in two directions. A reduced velocity sweep (horizontal traverse) was executed to find the location of the peak in the bell curve, which appears not to be trivial for a non circular riser geometry. The amplitude sweep (vertical traverse) yielded the onset lift coëfficiënt, the maximum lift coëfficiënt and the zero crossing A/D value. 13

14 Single Smooth Pipe Test Matrix Superimposed onto Gopalkrishnan (1993) Data Strouhal Numbor. St f D/V (-) I o Re o Re a Re x Re Figure 12: Pictorial summary of test matrix The lift and added mass coefficients obtained from our recent experiments on a smooth circular cylinder are plotted in Figure 13 as a function of the reduced velocity. The osciuation amplitude and Reynolds number were kept constant at respectively 0.5 A/D and Reynolds 40,000. It can be observed that the lift coëfficiënt peaks at a reduced velocity of 6, with a maximum value of 0.9. It can also be observed that the added mass coëfficiënt rapidly crosses the Cm = 1 line at the same peak value. This phenomenon is associated with a distinct transition from one vortex shedding system to another (i.e. lp to 2p transition). For our bundie tests we used this transition to localize the peak lift coefficients from initial tests at a coarse reduced velocity grid. 14

15 Smooth Bare Pipe, Lift Coëfficiënt and Added Maas with Reduced Velocity l ' ' ' s Jl s fi / \ / f / i ƒ """ *" 'T "' \ \ i» \ i E 1! 0.5 -g < Reduced Velocity, V/fD (-) A/D 0.5, Re * A/D 0.5, Re *- Cm, A/D 0.5, Re *- Cm, A/D 0.5, Re Figure 13: Reduced velocity sweep on smooth pipe An example of the Reynolds sensitivity for the smooth pipe is presented in Figure 14. Similarly as for a non-oscillating cylinder, the drag coëfficiënt drops when entering the critical Reynolds regime. The sensitivity for the amplitude ratio and the reduced velocity can also be observed from the graph. For the oscillating smooth cylinder we measured drag coefficients between 0.5 and 2.0. The non-oscillating drag coëfficiënt of this cylinder dropped from 1.2 in the sub-critical regime to 0.3 in the critical regime. 15

16 Smooth Pipe, Drag Coëfficiënt with Reynolds Number A ^ ^ ^ ^» --- ^-~-^, """"-^^._ Reynolds Number, Re (x10 3 )» A/D 0.5, Vr 6.0 a A/DO-S, Vr *- A/D 0.5, Vr * - A/D 0.5, Vr 10.0 Figure 14: Reynolds sensitivity for smooth pipe 10. Results bare pipe Contour plots of the measured lift force coëfficiënt in-phase with the velocity are presented in Figure 15 and 16. Figure 15 shows our new data for a roughened cylinder at Reynolds 40,000. The other figure was derived from Gopalkrishnan [9] data for a smooth cylinder data at Reynolds 10,000. The figures reveal a complex dependence of the lift coëfficiënt as a function of the reduced velocity and the amplitude. A similarly complex dependency can be observed for the added mass and the drag coëfficiënt (not presented here). This type of lift coëfficiënt contour plots forms the bases of the databases in semi-empirical VIV prediction tools. Both figures show a clear peak of the lift coëfficiënt in the "lock-in" region for reduced velocities between 5 and 7 and amplitude of about 0.5 diameter. The highest lift coëfficiënt is about 1. The Clv = 0 line denotes the boundary between positive and negative energy transfer or positive and negative damping. Negative damping means excitation by the vortex shedding process. The highest amplitude crossing from positive to negative lift coefficients occurs at about one diameter, in agreement with the self-limiting nature of the VIV phenomenon. Recent results for a smooth and rough cylinder at sub-critical and critical Reynolds numbers were reported by Ding et. al. [10]. 16

17 Contor Plot of Lift Coëfficiënt with Vr and A/D. Single Pipe Tests )2H O * O. < Reduced Velocity, Vr Figure 15: Lift coëfficiënt in phase with velocity, Contour plot Clv with Ur and A/D Single rough pipe, Reynolds 40,000, MARIN new test apparatus, 2004 Lift coëfficiënt in phase with velocity: Clv [-] 'jm^^r^r^^s^, i i! -^r\* s* ^^^^3^*" w ' r -1 s* >^ss3^ ^il X 7 *- > *" S N ^ ;.»* m. ^ / / \ r\ / v \ ( / V ^N ' ^ / ) \ \ \ / N ^ / 1 \ \ / V S s \ i \ ) N r i j \ J \ Reduced velocity Ur [-] --/ A/D [-1 D D D D D G D D D D G D D Figure 16: Lift coëfficiënt in phase with velocity, Contour plot Clv wüh Ur and A/D Smooth circular pipe, Reynolds 10,000, Gopalkrishnan, MIT,

18 11. Conclusions and recommendations A new test apparatus has been developed for measuring the hydrodynamic input coefticients for calibration of semi-empirical VIV prediction programs such as Shear7 or VIVARRAY. A 3.4 m long section of the riser or the riser bundie can be tested at full scale dimensions and real current speeds. The tests at full scale Reynolds numbers reveal new insights in the Reynolds scale effects and reduce uncertainties in the design process. Based on the results presented in this paper and recent experience with the new set-up, the following conclusions and recommendations seem justified: 1. The hydrodynamic input coefficients for calibration of semi-empirical VIV prediction programs can be tested with the new apparatus, using a 3.4 m long model. 2. The new test apparatus has been successfully calibrated for a smooth and a rough circular cylinder at Reynolds 40,000. Comparison with existing sub-critical data is good. 3. Distinct scale effects can be observed when comparing results from critical with sub-critical Reynolds experiments. For oscillating circular cylinders this has been reported before, but for non-circular oscillating cylinders such data is very scarce. 4. An efficiënt test strategy has been developed for finding the peak lift loads of a riser bundie geometry. About 50 tests are needed for each flow orientation. A non-circular riser bundie can be tested for 8 flow angles between 0 and 360 degrees, using steps of 45 degrees. Over 400 tests can be conducted in about 2 weeks time. 5. Experiments were carried out with one degree of freedom oscillations in cross flow direction. It seems worthwhile however, to explore further on two degrees of freedom oscillations with combined in-line and cross flow motions, including figure-of-eight type motions. 6. Non-circular riser geometries can show a large sensitivity of the mean lift load coëfficiënt for the flow angle. In those cases it is recommended to check the potential for galloping type dc. (ar. \ instabilities. The instability criterion - = C can be used as a first check. da l da /a=q 12. Acknowledgement The authors would like to thank the BP management for their support in development of the new test set-up and for the permission to publish some of the results presented in this paper. 18

19 13. References [1] Blevins, R.D., Flow induced vibrations, Krieger publishing company, Malabar, Florida, second edition, [2] Delany, N.K.. and Sorensen N.E., Low speed drag of cylinders ofvarious shapes, NACA technical note 30338, Washington, [3] Feng, CC, The Measurements of Vortex-Induced Effects in Flow Past Stationary and Oscillating Circular and D-section Cylinders, M.A.Sc. Thesis, University of British Columbia, [4] Vandiver, J.K. and Li,. L., Shear7 V4.3program theoretical manual, MIT, Cambridge, USA, [5] Triantafyllou, M.S., VIVARRAY user manual, David Tein Consulting Engineers, Houston, USA, [6] de Wilde, J.J. & Huijsmans, R.H.M., Experiments for High Reynolds Numbers VJVon Risers, ISOPE, Paper 200 l-jsc-285, [7] de Wilde, J.J., Huijsmans, R.H.M. & Triantafyllou, M.S., Experimental Investigation of the Sensitivity to In-line Motions and Magnus-like Lift Production on Vortex-Induced Vibrations, ISOPE, Paper 2003-JSC-270, [8]" Gu, G.Z. et. al., Technical feasibility of tubing risers, Offshore Technology Conference, OTC paper 15100, Houston, USA, [9] Gopalkrishnan, R., Vortex-Induced Forces on Oscillating Bluff Cylinders, D.Sc. thesis, Department of Ocean Engineering, MIT, Cambridge, USA, [10] Ding, Z.J., et. al., Lift and damping characteristics of bare and straked cylinders at riser scale Reynolds numbers, Offshore Technology Conference, OTC paper 16341, Houston, USA,