INTRODUCTION

METHODOLOGY

Wave load is the most important aspect in designing of offshore structures, i.e.offshore wind turbines (OWT), oil platforms, etc. This has been discussedextensively in previuos studies e.g Sarpkaya & Isaacson (1981); Sumer et al.(2006); Heideman et al. (1979) and Davies et al. (1990). Generally,estimations of the wave loads are mainly based on the Morison equation(Morison et al., 1950). By applying the Morison approach, the importantparameters are the loading coefficients, i.e. the drag and inertia coefficients.There are available methods to estimate these coefficients, i.e.: the least-squares method with fitting on time domain and/or frequency domain; wave-by-wave fitting the method of moments (Isaacson et al., 1991).The accuracy of methods in estimating the force coefficients (C and C ) are

discussed in Isaacson (1991). The first approach seems to be the mostaccurate.Heideman et al. (1979) and Davies et al. (1990) determined the drag andinertia coefficients in random wave conditions as a function of Keulegan-Carpenter number (KC = UT/D, where U is the horizontal velocity, T is the waveperiod and D is the cylinder diameter), see . The drag coefficient isconsiderably scatterred at low KC number.

In this paper available methods are used to estimate the force coefficients.Those are the max-min method and least-squares method (simplified by fit onwave-by-wave basis). According to the method of max-min values of wavekinematics are determined only at the crest, trough and still water level for eachindividual wave. The least-squares method in time domain is simplified byDavies (1990) by applying a wave-by-wave basis.

D M

Figure 1

COMPARISON OF DRAG AND INERTIA COEFFICIENTS FOR A CIRCULARCYLINDER IN RANDOM WAVES DERIVED FROM DIFFERENT METHODS

STUDYAPPROACH

In this study, a combination of analytical approaches and interpreting results ofphysical model tests is applied. Series of physical model experiments areconducted by fixing a cylinder with a diameter of 30 cm in the wave flume of theFranzius-Institute (Germany), see . Sets of random waves areapplied in combination with varying water depths. For each test pressuresaround the cylinder induced by waves are measured at different elevations.Measured data are used to estimate the coefficients derived from analyticalapproaches in combination with different wave theories (Airy, Stokes 2 and 5order).

nd th

Figure 2 & 3

Franzius-Institute for Hydraulic, Waterways andCoastal EngineeringLeibniz University Hannover.Nienburger Str. 4, 30167 Hannover, Germany.

Tri Cao Mai , Mayumi Wilms , Arndt Hildebrandt , Torsten Schlurman1 2 3 4

SUMMARY OF THE RESULTS

- Applying different wave theories results in an variation of ~10 % in estimatingthe wave force coefficients.- Relations of drag and/or inertia coefficients, and the Reynolds- and/or KC-numbers are established. The force coefficients are correlated to the KCnumber, however the drag coefficient is rather scattered at low KC number( ). This agrees well with previous studies in Davies (1990), Heideman(1979) and Isaacson (1991).Figure 4

1

2

3

4

M.Sc., (corr. author)Dipl.-Ing.,Dipl.-Ing.,Prof. & Director,

mai@fi.uni-hannover.dewilms@fi.uni-hannover.dehildebrandt@fi.uni-hannover.de

schlurmann@fi.uni-hannover.de

(a) Heideman 1979 (b) Davies 1990

Figure 1: The correlations of the force coefficients and Keulegen-Carpenter number

MWL

Cylinder

Pressure tranducers

Figure 2: Setting up experiments (units in cm) Figure 3: Physical model in the wave flume

(t)uDCρπ

u(t)u(t)DCρF(t) MD������������ 2

42

1

Figure 4: C , C & KC-number at level z= -0.1mD M Figure 5: Wave surface & force at z= -0.1m

1.133.911.422.64Stokes 5th

1.093.851.352.47Stokes 2nd

1.114.101.382.55Airy

z = -0.1m

1.253.161.482.16Stokes 5th

1.213.071.432.03Stokes 2nd

1.243.211.452.30Airy

z = -0.4m

CCDCMC

Max-minLeast-squaresWave theoryLevel

1.133.911.422.64Stokes 5th

1.093.851.352.47Stokes 2nd

1.114.101.382.55Airy

z = -0.1m

1.253.161.482.16Stokes 5th

1.213.071.432.03Stokes 2nd

1.243.211.452.30Airy

z = -0.4m

CMCCD

Max-minLeast-squaresWave theoryLevel

1.273.801.412.66Stokes 5th

1.203.681.342.63Stokes 2nd

1.243.491.392.56Airy

z = -0.1m

1.502.621.532.00Stokes 5th

1.422.521.462.05Stokes 2nd

1.502.801.512.29Airy

z = -0.4m

CMCDCMCD

Max-minLeast-squaresWave theoryLevel

1.273.801.412.66Stokes 5th

1.203.681.342.63Stokes 2nd

1.243.491.392.56Airy

z = -0.1m

1.502.621.532.00Stokes 5th

1.422.521.462.05Stokes 2nd

1.502.801.512.29Airy

z = -0.4m

CC

Max-minLeast-squaresWave theoryLevel

Table 1: The mean values of C & C (H = 0.2 m,

T = 2.5 s, d = 0.95 m)D M s

p

Table 2: The mean values of C & C (H = 0.25 m,

T = 3.0 s, d = 0.95 m)D M s

p

Figure 5

Table 1 & 2

Figure 6

presents the estimated force at a level of 0.1m below mean water level(MWL) on the cylinder. It appears that the estimation of Stokes 5 order agreeswell with the measured data.

show the mean values of C and C at different levels of the cylinder

under two wave conditions.shows the water surface, wave forces and wave kinematics at level of

0.4 m below MWLfor a random wave condition.

th

D M

MAIN REFERENCES

Davies, M. J. S., Graham, J. M. R., Bearman, P. W., “ ”. In Conf. onenvironmental forces on offshore structures and their prediction, pages 113 – 136, 101 Philip Drive, Norwell, MA 02061,1990.

Heideman, J. C., Olsen, O.A., Johansson, P. I., “ ”. Volume IV, 1979.Henderson,A. R., Zaaijer, M. B., “ ”. Engineering Integrity

Society, Volume 25, pp24-31, 2008.Isaacson, M., Baldwin, J., Niwinski, C., “ ”. Journal of

Offshore Mechanics andArctic Engineering, 113 (2), pp. 128-136, 1991Morison, J. R., O’Brien, M. P., Johnson, J. W. and Schaaf, S. A., “The Force Exerted by Surface Wave on Piles”, Petroleum

Transactions,American Institute of Mining Engineers 189: 149-154, 1950.Sarpkaya, T., Isaacson, M., “ ”. Van Nostrand Reinhold Company, New York,

1981.Sumer, B. M., Fredsøe, J., “ ” (Revised Edition). World Scientific Publishing Co.

Pte. Ltd., Denmark, 2006.

In-line forces on fixed cylinders in regular and random waves

Local wave force coefficientsHydrodynamic Loading on Offshore Wind Turbine Support Structures

Estimation of drag and inertia coefficients from random wave data

Mechanics of wave forces on offshore structure

Hydrodynamics around cylindrical structures

Figure 6: Wave surface, force and kinematics at z= -0.4m

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