Proceedings of OMAE02 21st International Conference on Offshore Mechanics and Arctic Engineering

June 23-28, 2002, Oslo, Norway

TS

TrianIT huse, MA

Offshore risers that hang off a floating oil drilling and production vessel in deep water must be designed for fatigue. Fatigue damage is calculated from the stress cycle history of the risers that resustates. The stron the risers. Tdamage from both the stroccurrence ahydrodynamicequation and alow sea statescurrent.

In generaderived fromstrakes can bhydrodynamicRecent tests a

was 200 cm and the cylinder diameter was 7.62 cm. The cylinder had triple-start strakes. The strake height was 22 % of the cylinder diameter, and the strake pitch was 1 to 17 diameters, i.e., the strake raps around the cylinder over 360

Proceedings of OMAE02 21st International Conference on Offshore Mechanics

and Artic Engineering 1 Copyright 2002 by ASME

lts from the motions of the vessel in different sea ess history depends on the hydrodynamic loading ypically, the fatigue damage is dominated by the

low sea states (low KCs) since for these sea states ess cycle frequency and the probability of re relatively higher. The estimates of the loads are made on the basis of Morisons ppropriate hydrodynamic coefficients, i.e., for the , coefficients for low KC and different levels of

l, hydrodynamic coefficients (drag and inertia) are experiments. Coefficients for risers without e found in the literature [1]. However, data on coefficients for risers with strakes are lacking. t MIT [2] have provided data on straked risers for

degrees for every cylinder length of 17 diameters.

The recorded channels included the force components inthe direction of tow and transverse to the direction of tow. Theforce components were measured on both ends of the cylinder.The transverse oscillatory motion amplitude and frequency werealso recorded. The sampling rate was 100 Hz. DATA COLLECTED

There were 32 test runs made with and without tow for thesmooth cylinder. The forced transverse oscillations varied fromamplitude to diameter ratio (= DA / ) of 0.16 to 0.80, and froma period of 0.55 seconds to 1.84 seconds. The tow speed(current) varied from zero to 0.80 m/sec. HYDRODYNAMIC COEFFICIEN

Kostas F. Lambrakos CSO-AKER

11700 Old Katy Road Houston, TX 77079

Michael S. M

77 MassacCambridge

ABSTRACT Drag and inertia coefficients for offshore risers with strakes

have been derived from model tests, and are reported in this paper. The coefficients correspond to flow conditions of forced oscillations with tow in the transverse direction, and without tow. For the forced oscillations the Keulegan-Carpenter (KC) range was 1 to 5. The drag coefficients are higher than generally assumed, and decrease monotonically with KC in the absence of current. In the presence of current the drag coefficient becomes dependent on the ratio of current velocity to wave velocity. Low KC numbers strongly affect the calculated riser fatigue damage caused by vessel motions in storms. The present data fill an important need in riser design since in many situations fatigue damage governs riser design, and frequently the assumed coefficients are overly conservative.

INTRODUCTION OMAE2002/ OFT-28221

FOR RISERS WITH STRAKES

tafyllou

tts Ave. 02139

Thanos Moros BP America, Inc.

501 Westlake Drive Houston, TX 77079

the case of oscillatory motion without current. The hydrodynamic coefficient data reported in this paper are for low KC number sea states with and without current.

The experiments for these coefficients were performed at MIT with a short cylinder that simulates a section of the riser. The paper includes discussion on (1) the experimental set-up, (2) the data analysis approach, and (3) the summarized results on the drag and inertia coefficients. EXPERIMENTAL SET-UP AND INSTRUMENTATION

The tests were performed in the main tank of the MIT Testing Tank Facility. The dimensions of the tank are 120-ft long, 8-ft wide, and 4-ft deep. The experimental apparatus is shown in Figure 1. The carriage includes a device that oscillates the cylinder in the vertical direction while it is towed down the tank at constant speed to simulate current. The cylinder length

June 23-28, 2002,Oslo, Norway

OMAE2002-28221

3. The data window selected for data analysis included 20 to The data can be scaled on the basis of three dimensionless

parameters (excluding the cylinder roughness). The parameters are: 1. The Keulegan-Carpenter (KC ) number defined on the

basis of the oscillatory motion:

DAKC 2 (1)

where A is the amplitude of the oscillatory motion, and

D is the cylinder diameter.

2. The Reynolds number defined on the basis of the oscillatory motion plus the current:

DVUm2

122

Re (2)

where

mU is the amplitude of the oscillatory velocity, V is the tow speed or current, and is the kinematic viscosity of the water.

3. The ratio of the current to the oscillatory velocity amplitude:

mU

Vr (3)

The KC number in the tests was 1, 2, 3, or 5; the Reynolds

number varied from about 7000 to 90000; and the current to wave velocity ratio varied from zero to 5.5. DATA PROCESSING

The steps followed to ensure high accuracy in the derived coefficients are: 1. Force transducer calibration was carried out daily and

whenever a cylinder was re-installed in the apparatus. 2. The four force channels and the transverse motion channel

were low-pass filtered forward and backward at 30 rad/sec, and then the oscillatory motion was further filtered to match the phase loss induced by the analog filters. 40 oscillatory cycles. These cycles followed 10 to 20 cycles at the beginning of each run that were removed in order to ensure no transients in the data analysis.

4. The in-line force data were detrended using measurements from before towing starts and after towing ends. The transverse force data were detrended and the mean component was removed using polynomial fitting.

5. The transverse force data were corrected for the weight of the cylinder. Also, there were tests made without the cylinder to quantify any parasitic loads in the data channels.

6. The dominant frequency of the oscillatory motion was used to split the data of a particular test run into bins of approximately one cycle. Coefficients were calculated for each cycle and average values over all cycles in the run were determined. These average values of the coefficients are reported in this paper. The number of bins used was in the range of 20 to 40 per test.

DATA ANALYSIS

The drag and inertia coefficients are calculated by using Morisons equation based on the resultant flow velocity impinging on the cylinder. The two-dimensional Morisons equation for a moving cylinder is given by

WaC

DWW

dCDF

4

2

2

1 (4)

where F

is the load per unit length, is the water density, D is the cylinder diameter, dC is the drag coefficient,

W

is the relative velocity,

aC is the added mass coefficient, and

W

is the relative acceleration. The resultant velocity is made up of a time varying oscillatory component and a current component

VUW

(5) where

U

is the oscillatory (wave) velocity, and

V

is the current velocity. 2 Copyright 2002 by ASME

effect of the current on the drag coefficient is consistent with what is prescribed in API RP2A [3]. CONCLUSIONS

The drag coefficient of the straked cylinder decreases monotonically with KC in the absence of current, and is considerably higher than the drag coefficient for steady flow. In the presence of current, the drag coefficient decreases linearly to its steady flow value at a threshold current ratio of about 1.25, and stays constant for greater current ratios. The mean added mass coefficient is double the added mass coefficient of the bare cylinder, and can be assumed as independent of KC.

It should be noted that the present findings refer to the KC

range of 1 to 5, and to the particular strakes tested, which had a height of 22% of the cylinder diameter, and a pitch of 1:17 diameters. The relative acceleration of the flow is given by

UW

(6)

The drag and inertia coefficients are derived by taking the dot product of the force with the velocity and acceleration, respectively, and integrating over one cycle. The calculated coefficients are scaled appropriately and are given in terms of the KC number and the ratio of current to wave velocity amplitude. The drag coefficient is scaled by the corresponding drag coefficient in steady flow ( 0dC ), which was measured to be near 2, and the added mass coefficient is scaled by the added mass coefficient of a bare cylinder in potential flow ( apC ), which is 1. Also, it is implicitly assumed that the coefficients are independent of the Reynolds number. This is a reasonable assumption considering that flow separation is dominated by separation on the strake edges. RESULTS

The scaled drag coefficient for zero current is shown versus KC in Figure 2. The ratio varies from a value of about 3.25 for KC=1 to a value of 2.5 for KC=5. The mean values for each KC number show a slight trend to decrease as KC increases, and for this small range in KC this trend can be assumed linear. Unlike the drag coefficient for a smooth cylinder that shows a dip in the variation with KC at these low KC numbers, the drag coefficient for the cylinder with strakes appears to decrease linearly with KC.

The scaled drag coefficient for the cases of force

oscillations with tow (current) is shown versus the ratio of the current (tow speed) to the oscillatory velocity amplitude in Figure 3. The figure indicates a consistent trend for all KC numbers and Reynolds numbers. From the zero current ratio to a current ratio of about 1.25, the scaled drag coefficient decreases approximately linearly from a value of about 3 to a value of 1. For current ratios greater than 1.25 the scaled drag coefficient is constant at 1, i.e., it attains its steady flow value for current ratios greater than 1.25.

The scaled added mass coefficient is shown versus KC in

Figure 4. The figure shows the coefficients for all current ratios and Reynolds numbers. Considering the inherent scatter in the data, it is reasonable to assume that the scaled added mass coefficient for this range of KC could be approximated with a mean value of about 2. Some dependence on the KC number and the current ratio was found, but the typical variation of the maximum load due to the variation of the added mass coefficient from the mean value is less than about 10%.

The present results for the case without current are

consistent with the results from similar tests at MIT [2]. The ACKNOWLEDGEMENTS

The authors would like to thank BP America for allowing the publication of these data, and Dr. Franz Hover, and Mr. Joshua Davis who conducted the experiments at MIT. REFERENCES 1. Sarpkaya, T., Forces on a Circular Cylinder in Viscous

Oscillatory Flow at Low Keulegan-Carpenter Numbers, Journal of Fluid Mechanics, Vol. 165, 1986.

2. Imas, L., Triantafyllou, M.S., Thompson, H.M., Hsu, T.,

and Young R., Sensitivity of SCR Response and Fatigue Life to Variations in Hydrodynamic Loading at Low Keulegan-Carpenter Numbers, Proceeding of the Offshore Technology Conference, OTC 13109, May 2001.

3. API RP 2A-LRFD, Recommended Practice for Planning,

Designing and Constructing Fixed Offshore Platforms Load Resistance Factor Design, First Addition, July 1, 1993.

3 Copyright 2002 by ASME

Figure 1. Experimental Apparatus

Figure 2. Drag Coefficient for Zero Current

0

0.5

1

1.5

2

2.5

3

3.5

4

0 1 2 3 4 5 6

KC

Cd/

Cd 0

KC=1

KC=2

KC=3

KC=5

Ave

Approx.4 Copyright 2002 by ASME

Figure 3. Drag Coefficient vs. Current Ratio

Figure 4. Added Mass Coefficient vs. KC

0.0

1.0

2.0

3.0

4.0

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6

Current Ratio

Cd/C

d 0

KC=2

KC=5

KC=1

KC=3

Model

0

0.5

1

1.5

2

2.5

3

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5

KC

Ca/C

ap5 Copyright 2002 by ASME

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