Hydrodynamic Coefficients for Calculation of ... - Science Direct

Marine Structures 9 (1996) 745-758 © 1996 Elsevier Science Limited Printed in Great Britain. All rights reserved

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Hydrodynamic Coefficients for Calculation of Hydrodynamic Loads on Offshore Truss Structures O v e T. G u d m e s t a d a & Geir M o e b

aStatoil A/S, Forus, N-4035, Stavanger, Norway bNTH, Trondheim, Norway (Received 14 December 1994; accepted 24 June 1995)

ABSTRACT The ctwrent American Petroleum Institute's recipe [API RP 2A WSD, Recommended practice for planning, designing and constructing fixed offshore platforms, working stress design. AP1, USA, 1993.]for calculation of hydrodynamic loads on offshore truss structures is compared with the corresponding North Sea Design Practice, as given by the rules of Det Norske Veritas. Most emphasis is put on the hydrodynamic coefficients and the estimation of design current as these issues are identified to be particularly critical Use of the updated AP1 (1993) recommendations in which the drag coefficient for roughened cylinders is increased from a minimum of O.6 (AP11991) to 1.05 (AP! 1993) and where current is included, could lead to a general increase in the estimated load level on slender offshore structures [Petrauskas, C., Heideman, J.C. & Berek, E.P., Extreme waveforce calculation procedure for the 20th edition of AP1 RP 2A. OTC paper 7153, In Proc. OTC 1993, Houston, Texas, 1993, pp. 201'-211]. The main emphasis with regard to the impact of the new API recommendations, howew,r, is that a consistent approach is provided to the calculation of lO0-yr directhmal loads. This includes taking into account the effect of marine growth on force coefficients, modifying the wave kinematics for directional spreading, and considering current blockage effects, conductor shielding effects, and joint occurrence of wave height and current (i.e., using the associated current as being representative of the current that would lead to the lO0-yr load). It is concluded that a consistent approach, such as that underlying the new API RP 2A (1993) re&'pe, is preferable to the current North Sea Design Practice [Det Norske Veritas, Environmental conditions and environmental loads. D N V classification notes 30.5,1991. ] in thisfield, and thus that the North Sea Design Practice should.be updated. This relates in particular to selection of hydrodynamic coeffi745

O. T. Gudmestad, G. Moe

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cients. Measurement programmes to obtain full scale global force data simultaneously with wave and current data are furthermore recommended. © 1996 Elsevier Science Limited.

Key words: wave forces, hydrodynamic coefficients, offshore truss structures, API Recommended practice.

1 INTRODUCTION The International Organisation for Standardisation (ISO) is developing a new world-wide code for offshore structures, supported by USA (API), U K (Health and Safety Executive, HSE), Norway (Norwegian Petroleum Directorate, NPD) as well as other countries, w Part 1 (General principles) of this code has already been completed. Currently extensive work on steel jacket structures is underway. In connection with this effort, it is necessary to select the load recipe to use for the calculation of environmental loads. The state-of-the-art for estimating hydrodynamic loads on truss structures (jackets), assuming quasi-static behaviour, is to use a regular design wave and Morison's equation, 13 involving the following features: height and corresponding period, and a current velocity; particle kinematics and current velocity profile; --values of hydrodynamic coefficients. --wave --wave

Since the first API RP 2A appeared in 1969, and the first NPD Regulations and DNV Rules were issued a few years later, design guidelines have undergone changes. However, the state-of-the-art, sea load calculation recipe for jacket structures has remained practically the same over the last 10-15 years. The API approach introduced in 19771 and the so-called standard North Sea Practice for jackets 6 were relatively close until API introduced its 20th ed., 3 with substantial changes in the recommended design practice. In view of this, it is seen prudent to summarise the API changes, to discuss the background for these changes, and to point to the need for harmonisation of the API RP 2A recommendations and North Sea Design Practice, see Table 1. 2 THE API CHOICE OF H Y D R O D Y N A M I C COEFFICIENTS The present API procedure for the calculation of hydrodynamic loads on slender offshore structures is described in API RP 2A. 3'4'17 The main differences between the present and the previous API procedures 2 are given in Table 2.17 It should be noted that the previous versions of API RP 2A 2 refer to DNV 6 for determination of hydrodynamic coefficients for noncircular cross-sections and for vertical forces on conductor guide frames

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Calculation o f hydrodynamic loads

TABLE 1 Parameters for Calculation of Deterministic Hydrodynamic Loading 1tern

AP1 (1993) 3,4

North Sea Design Practicez

Wave kinematics

Stokes/Stream function

As API

Wave kinematics factor

Include, if directional spreading

Normally not included

Shielding filctor

To be calculated

To be calculated

Current velocity

100 year wave + current load

100 year wave in comb with 10 year current

Hydrodyn. coefficients

High drag coeff, value Lower inertia coeff, value

Low drag coeff, value Higher inertia coeff, value

Wave hei#tt

About 1 m lower than for previous API recommendations 2

TABLE 2 20th vs 19th Edition of API RP 2A Wave Force Procedures 2' 3,4 and Gulf of Mexico Metocean Criteria 17 Consideration

19th ed. 2

20th ed. 3' ~

Wave force procedure Current

Not included

Included

Current blockage factor

Not applicable

Factor of 0.7-1.0 applied to current. Value depends on number of legs and wave direction

Wave period

Unmodified

Doppler effect used

Wave kinematics factor

Not applied

Factor is 0.88 for hurricanes and 0.95-1.0 for extratropical storms

Force coefficients

Ca = 0"6--1-2 Cm = 1.3-2.0

For drag dominated forces Ca (smooth) = 0.65 Ca (rough) = 1.05 Cm (smooth) = 1.6 Cm (rough) = 1.2

Conductor shielding factor

Not applied (Factor = 1.0)

Function of spacing/diameter ratio

Marine growth

Mentioned

Value of 1-5in used to 150ft depth for Gulf of Mexico

Gulf of Mexico metocean criteria

Omnidirectional wave

Directional with current, function of longitude and water depth

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O. T. Gudraestad, G. Moe

(Sections 2.3-16.2 and 4, respectively). For global horizontal forces it was required that a platform in the Gulf of Mexico or other US waters was designed for a certain minimum force level, the reference force level (Section 2.3.4g2). This force level was to be achieved by using the reference level wave height, Morison equation with Ca = 0.6 and Cm = 1-5 (for 6 ft outer diameter, and larger Cm for larger outer diameter), zero storm current, and appropriate wave theory. Consequently, if one believed that a lower wave height was appropriate, then it was still required that the same force level be achieved by increasing Ca, using a storm current, etc. The updated API Recommended Practice is based on a consistent treatment of all variables involved in calculating hydrodynamic load. For a review of selection of wave kinematics models, see Ref. 9. A considerable increase in hydrodynamic loads results from the use of updated hydrodynamic coefficients and inclusion of current, especially if load reducing factors, such as shielding, blockage, etc. 17 are not considered. It should be noted that API 3'4 now assumes that the wave and current loading are based on a joint probability assessment aiming at obtaining the 10 -2 per year environmental loading. 1° Since real ocean waves are directional and irregular, the selection of the regular wave to use in such analyses may still, however, be a matter of some controversy. Quantification of load differences found by utilizing the 1993 vs the 1991 edition of API RP 2A (i.e., 20th vs. 19th) has been discussed by the API Task Group on Wave Force Commentary. 18 Whether or not the new API recommendations lead to higher or lower forces depends on previous practice and the wave direction. Impact on steel weight for Gulf of Mexico jackets depends on the amount of optimization one might perform with respect to directional criteria. Also, for every one % increase in force, the increase in steel weight is about 0.25-0-20%. For the Gulf of Mexico, the Task Group 3'4 also came up with revised wave heights which were on the order of 1 m lower (for depths > 150 ft) than those determined in accordance with the 19th ed. 2 The net effect on forces was a significant increase in the principal wave direction in deep water, but in some cases broadside forces were lower than found from the 19th ed. For shallow water, the effect is dependent on structure location because the current is spatially variable. For the North Sea, sensitivity studies indicate that the 100-yr force can be significantly lower depending on the choice of wave kinematics factor and associated current than that determined using current U K practice utilizing the 50-yr wave height and 50-yr current criteria. 18 For static regular wave analysis, global platform wave forces can, according to API, 3'4 be calculated by the Morison's formula with particle kinematics taken from a so-called design wave, in combination with prescribed force coefficients. The design wave is usually determined in two steps. In the

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first step (called long term statistics) the highest significant wave height and its associated period are predicted from field data, usually based on averages of 20 rain periods, registered at 3 hour intervals. The use of individual storms may be a better strategy, however, since these may be assumed to be statistically independent events. 15'21 In the second step (short term statistics), the expected amplitude al of the highest wave for such an extreme seastate is estimated, assuming linearity, so that the higher peaks will be Rayleigh distributed. For predictions of surface geometry, second order terms may be added, increasing the peaks and decreasing the depths of the troughs, relative to the linear estimate, but the particle velocities seem to be better predicted on basis of the linear amplitude al. An adjustment factor to account for wave directionality is a useful concept and is included in the API recipe which, however, also recommends the use of a regular nonlinear design wave, e.g., a Stokes 5th order wave. An approach that may prove more advantageous is to predict the wave form and the particle kinematics from the statistically based new-wave. 2°' 12 API recommends the following drag and inertia values for unshielded circular cylinders: Smoot]~ cylinders: Rough cylinders:

Ca = 0.65, C,, = 1.6 Ca = 1.05, C,n = 1.2.

These values are said to be appropriate for - - the case of a steady current with negligible waves; or

- - t h e case of large waves with UmoTapp/D > 30 where

Umo = maximum horizontal particle velocity at storm mean water level under the wave crest from a two-dimensional wave kinematics theory 9 Tapp = apparent wave period D = platform leg diameter at storm mean water level. For wave dominant cases with UmoTapp/D < 30, the hydrodynamic coefficients for nearly vertical members are modified by 'wake encounter'. Such situations may arise with large diameter caissons in extreme seas or ordinary platform members in lower seastates (typically considered in fatigue analysis). Further details as to selection of Ca and Cm in accordance with the recent API recommended practices are given in Refs 3 and 4, comm. C3.2.7. For dynamic analysis, the API procedure 3'4 recommends time history methods based on simulated random waves. Frequency domain methods

o. T. Gudmestad,G. Moe

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may be used for the global dynamic analysis, provided the linearization of the drag force can be justified. The hydrodynamic coefficients developed for use with individual deterministic waves can, according to API, also be used for random wave analysis (either time or frequency domain) of fixed platforms by using:

--significant wave height and --spectral peak period to calculate K, the Keulegan-Carpenter Number. 3'4

3 H Y D R O D Y N A M I C C O E F F I C I E N T S R E C O M M E N D E D BY D N V The DNV rules 6' 7 represent North Sea Design Practice for the calculation of hydrodynamic loads on offshore truss structures. These suggest tentative values of Cm for different cross-sectional shapes. For circular cylinders the value amounts to 2-0. It is in particular noted that DNV call for use of the selected Cm value in 'Conjunction with the acceleration of water particles as calculated using an appropriate wave theory' (see also Ref. 23). The selection of Ca values should, according to Ref. 6, take into account the variation of Ca as a function of: - - Reynold's number, Re; --Keulegan-Carpenter number, Kc; - - r o u g h n e s s number kr/D where kr is the effective roughness height and D the diameter of member, kr/D = 10 -2 in the absence of more reliable data for marine growth); - - v a r i a t i o n of cross-sectional geometry. Tentative values for the drag coefficient for a circular cylinder of varying roughness in steady flow are shown in Fig. 1, while tentative values in the supercritical regime in steady flow for some in-service marine roughnesses are given in Fig. 2. Note that the following values of surface roughness k, could be used in the determination of the drag coefficient: Steel, new uncoated Steel, painted Steel, highly rusted Concrete Marine growth

k, (metres) 5 x 10-5 5 x 10-6 3 x 10-3 3 x 10-3 5 x 10-3-5 x 10-2

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1.4 1.2 1.0 o= 0.s ~ 0.6

[kdDxl0-3f 3.1 V I 2/" ~ 0.4 L L z.

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°-"°"

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0.2 ~

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I II I1

I

105

SIm~ltil(kr/D"~';) 106 Reynold's number (Re) I

,

,

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Fig. 1. The drag of sand-roughened cylindersin steady uniform flow. D N V 6 finally state that 'hydrodynamic drag coefficients for a rough cylinder in oscillating flow are subject to approval in each case'. For a smooth cylinder in oscillating flow, Ref. 6 states that the drag coefficient should not be less than 0.7. It should be noted that the marine growth should be included in the estimate of the member diameter. In order to reduce the outer diameter and to use the drag coefficient applicable for smooth members, Statoil decided to use antimarine growth coating on their Veslefrikk jacket which was installed in the Northern North Sea. 5 D N V updated their relevant document in 1991. 7 The updated document 1.4 :

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0.8 o 0.6

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Range of 'in service' marine roughness

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