Wind Loads on Offshore Structures

. van Walree Maritime Research Institute Netherlands (MARIN), P.O. Box 28, 6700 AA Wageni,ngen, The Netherlands . Willemsen National Aerospace Laboratories NLR, P.O. Box 153, 8300 AD Emmeloord, The Netherlands

SUMMARY

A new computational model for determining the wind loads on off-

shore structures is described. This model aims to bridge the gap

between calculation procedures provided by the classification

societies and wind tunnel testing. The new model is based on the

so-called building block approach, whereby the structure is thought

to be composed of standard components with known force characteris-

tics. Special attention is given to the modelling of the wind flow

field, component interaction and lift forces on elevated and in-

clined main decks. Three comparisons between experimental and cal-

culated results are given for typical offshore structures. These

comparisons show that the results obtained by using the new compu-

tational model are much closer to the experimental values than

those obtained from the classification society rules.

1. INTRODUCTION

Wind forces contribute significantly to the total environmental

loads on offshore structures. Drag forces are of importance for

moori.ng, dynamic positioning and manoeuvring of floating struc-

tures. Stability of floating and fixed structures may be affected

by overturning moments due to drag and lift forces. Knowledge of

these loads is therefore indispensable for the design and operation

of such structures.

From the point of view of the wind flow field and wind induced

pressures, offshore platforms and vessels are rather complex. Semi-

submersible drilling rigs, jack-ups with huge cantilever legs,

floating production and storage units and crane vessels, to mention

only a few, display a large variety of columns, work decks, super-

structures, derricks, heli decks etcetera. -

Commonly followed routes to obtain the wind force data for such

complicated shapes are:

- simple calculation methods as provided by classification

societies ( see ABS [ l] and DnV [ 21 ) ;

- wind tunnel tests. The first method is easily applicable and requires little time but

the accuracy is limited, primarily because lift effects on decks

and interaction effects between adjacent members are neglected.

Wind tunnel tests, when performed correctly, provide realistic re-

sults but are rather time-consuming and expensive. For further in-

sight into these matters reference is made to Boonstra and Leynse

[3] and Macha and Reid [4] . - l,

In order to bridge the gap between the methods outlined above, in

1987 a joint industry development study was carried out. This study

aimed at the development of an advanced computational model for de-

termining wind forces on arbitrary offshore structures. The project

was carried out by MARIN in close cooperation with NLR as part of

the Netherlands Marine Technological Research (MaTS) program. The

project was sponsored and supervised by the following companies:

De Hoop (~obith);

GUSTO Engineering;

Maritime Project Engineering;

Rijkswaterstaat;

Shell Internationale Petroleum Maatschappij;

Verolme Trust;

WijsmulLer Engineering.

In an early stage of the study, detailed requirements as to the

computational mode1 were derived. ~pplications of the mode1 as

foreseen, required the validity of the method for arbitrary off-

shore structures. Wind loads in 6 degrees of freedom for arbitrary

orientations (wind directions) and heel angles up to 20 degrees had

to be calculated. Furthermore the accuracy of the model had to be

improved significantly when compared with existing calculation pro-

cedures.

Since the resulting computer program had to be used in various

design and engineering studies at small offshore engineering of-

fices, the program had to run on mini- and personal computers with

a reasonable performance. : Based on these requirements a new computational model has been de- >

veloped, whereby the physical model was derived from classical

aerodynamics and empirical formulations. Data bases with additional

information completed the computational model.

0-

The computational model developed in this study has been imple-

mented in a Fortran 77 computer program by MARIN.

Extensive wind tunnel experiments have been carried out in the low

speed wind tunnel (3.0 X 2.25 m) of NLR. The experimental program

was carried out, to provide data for derivation of empirical formu-

lations, to complete relevant data bases and in order to verify the

overall model..

2. COMPUTATIONAL CONCEPT

The various project demands set the trend of alternative approaches

to the computational model. Possible approaches are:

- theoretical methods; - correction methods; - fully empirical methods: - building block methods (as applied by ABS and DnV).

Theoretical methods for flows around complex bluff bodies like off-

shore structures are not available, although programs for single

bluff bodies have appeared recently, see Van Oortmerssen et al.

[5]. These programs can only run on large and very fast mainframe

units. As such, application of these methods is out of the ques-

tion.

The correction method is based on wind tunnel test data of struc-

tures similar to the proposed design. By adding and subtracting

certain parts of the construction, and at the same time correcting

the wind load, one can obtain the wind loads on the structure. This

method is based on the availability of suitable test data which may

form a problem especially for new designs. Furthermore, interaction

effects will not be proper1,y accounted for.

Empirical, formulations also need a set of wind tunnel data for each

type of offshore structure. The more data available the higher the

accuracy of empirical relations. Again, a good prediction for an

unusual or new type of construction is not possible. Also, a com-

parison based on wind loads of a series of prototypes with the same

main dimensions but with for example alternative deck lay outs,

will in general not be possible.

The building block method does not rely on data of similar designs;

it can be applied to any structure provided the characteristics of

its components are known. The accuracy of this method however, is

strongly related to a proper inclusion of several physical flow

phenomena.

Considering these methods, it was thought that the building block

method would be the most promising one. Its flexibility and

physical correctness play an important role. The following items

form the fundamentals of the physical model:

- force characteristics of the standard components; - wind velocity field; - determination of component interaction; - forces on inclined structures. These topics will be discussed in detail in the next section.

3 . PHYSICAL MODEL

3.1 Standard Components

The basis of the calculation method is formed by a set of three-

dimensional geometrical components with known force characteris-

tics. These characteristics are reflected by three force coeffi-

cients (for the drag, side and lift force) and the centre of effort

of each force component. The characteristics of the components are

mainly obtained from published results of model experiments. By

means of the following five types of standard components, an ade-

quate description of offshore structures can be given:

- circular cyli.nders ; - rectangular prisms; - flat plates; - lattice structures; - ship hulls.

The description of the force characteristics of circular cylinders

includes effects due to the Reynolds number (flow separation), sur-

face roughness, flow turbulence, cylinder inclination, aspect ratio

and taper. Fig. 1 shows the drag coefficient for two-dimensional

(infinite aspect ratio) circular cylinders. The horizontal axis I

represents the effective Reynolds number which is corrected for t flow turbulence and surface roughness.

- . - - - . -

R,, = Reynolds nunber v E/O = relative surface roughness

Fig. 1. Drag Coeffici.ents for Circular Cylinders

Drag, side and lift force coefficients for rectangular prisms were

derived as a function of the prisms relative dimensions and

inclination angle. The side force may be comparable in magnitude

with the drag force and may therefore add substantially to the

total overturning moment on offshore structures. Surface mounted

prisms may experience an appreciable lift force due to the acceler-

ated flow and accompanying reduced pressure over the top face. As

the boundary layer separation points are fixed at the sharp cor-

ners, no significant Reynolds number effects occur. Also, since the

forces are predominantly determined by pressure forces and not by

skin friction, the surface roughness of the prism's sides is irrel-

evant.

For flat plates normal to the flow, only a drag force arises. At

incidence, a lift and a side force are introduced which are depen-

dent on the incidence angle and the aspect ratio, see Fig. 2. The

tangential force is negligible and Reynolds number effects for full

scale conditi.ons may be neglected. The centre of effort positi.on of

the force component is also dependent on incidence and aspect ra-

tio. The lifting characteristics of flat plates may be of partic-

ular interest for the prediction of the forces due to helicopter

decks subjected to a platform induced upflow.

A = DYIDX DY = PLATE WIDTH

For the prediction

of forces on lattice

structures, a bulk

method is used where

the forces are ob-

tained from empiri-

cal data relating

C the force coeffi- 1.6

cient for a single 0.25

framework to it S 2.00 overall shape and

solidity ratio. An

allowance is pro-

vided for the effect 111, o 10 20 3: 4 Ib Qo 70 80 PO (d*J. i of shielding for

downstream frames.

Fig. 2. Normal Force Coefficients for

Flat Plates

The data base provides force coefficients for a wide variety of

Lattice structures. Three basic arrangements of chord members are

considered: a triangular, a square and a rectangular arrangement.

The bracing configuration is arbitrary since the solidity ratio of

the configuration is the main variable. The structural. members may

either be of the angular (flat faced) or the circular type.

Wind load coefficients for ship hulls were again derived from wind-

tunnel tests. The contribution of the several superstructure compo-

nents was subtracted from the total measured wind loads. In this

way, the corrected force coefficients may be used for ships with an

arbitrary superstructure configuration.

3.2 Wind Velocity Field and Component Interaction

For the transfer of a force coefficient for a specific component to

an actual force, knowledge is required of the component area and

mean dynamic pressure. The first follows from the model descrip-

tion; the latter is determined from the mean value over the wind

area A of the component. An component-bounded effective wind speed

ve is defined:

V: = & v2(y,z) dydz (1

For the undisturbed atmospheric boundary layer the wind velocity

increase with height is commonly expressed in t.he power-law repre-

sentation:

where V, denotes the reference wind speed at the reference height

zr. The exponent value p will range between 0.10 and 0.15 for most

practical purposes.

Local windspeeds may deviate from the power-law profile due to

various effects like the occurrence of separated flow regions, t.he

circulation around a lift generating main deck and the presence of

other deck components. The combined effect of these disturbances

will lead to a highly complex velocity field. For the flow along an

elevated main deck the following equations were derived from Hess

C61 :

where t is the body thickness and X and z are the local coordi-

nates, see Fig. 3.

These formulations, basically valid for the potential flow around

flat nosed bodies, agree for the flow outside the separation zone,

along the main deck centre line. Experimental data were used for

corrections of the velocity components V, and V, accounting for

flow separation and three-dimensional effects (near the deck

edges). Fig. 3 shows the computed streamlines for two main deck

types.

To account for the reduced velocities in an elements wake, the

following description was taken from Schlichting [ 7 ] :

where b is the wake

width, CD is the upstream

component drag coeffi-

cient, dw is the upstream

component width and X and

y denote a local coordi-

nate system, see Figure

4. The exponents pl and ' p2 have a value dependent

on the aspect ratio of

the upstream member.

The equations (4) and (5)

may only be used for not

too short distances be-

_U_J- tween the two bodies. For

short distances the wake

e of the upstream body is

Fig. 3. Flow Fields along Elevated too much affected by the

Main Decks presence of the down-

stream one. In that case

data obtained from literature and from special wind tunnel experi-

ments were used. These data also account for effects due to the

bodies aspect ratio, flow enhancement and multiple interaction.

3.3 Forces on Inclined Structures

For the discussion of the various principles, column-supported

structures will be taken as starting point. Surface vessels then

form a group with the limiting condition of a zero airgap. The

basic ideas are drawn from classical aerodynamic theories on lif-

ting bodies, like the wing theory. The features for a specific

platform are a rather linear lift curve with a positive lift in

level condition, a lift induced drag increase at inclined condi-

tions and a lift increase due to the proximity of the sea surface.

As pointed out by various investigators the lift may be rather high

and important because of its contribution to the overturning moment

[8,9]

The present work demonstrates an increased importance of the lift

because of its contribution to the drag. Physically, the lift gene-

rating entity of a platform is the main deck. To compare t.he test

results of various platforms as available in open literature and at

NLR, the presented drag and lift coefficients were re-cal.culated

with appropriate reference values for area and dynamic pressure.

The applied reference values were the main deck area and the mean

dynamic pressure over the height range of the main deck boundaries. 2 In general the test results showed rather linear CL(a) and C (C )

D L relations for inclination angles up to, say 15 degrees.

-- I V(Y)

Fig. 4. Velocity Reduction due to Shielding

The lift curves also showed a posi.tive lift at a = 0 degrees (level

condition), indicating that a platform is subjected to an upflow

angle aO, caused by the presence of platform columns and sea boun-

dary. Therefore, an effective pitch angle aeff is defined:

a eff = a + a

0

where a is the main deck pitch angle with respect to the wind axes

system.

The relation between CL and oreff is calculated from literature,

accounting for the thickness ratio t/c and aspect ratio A ( = b2/~)

of the main deck thickness, excluding the contribution of large

protruding elements.

The definitions of b and c, i.e. platform main deck dimensions in

the wind axes system, imply that for a non-circular main deck A and

t/c vary with the wind direction 8 .

For t/c < 0.05 the lift curve is assumed to be linear, with a lift

curve slope C calculated by applying the Jones edge-velocity La

correction to Anderson's formula on basic and additional lift dis-

tribution [l01 :

For larger values of t/c this thickness parameter will affect the

lift curve slope in a non-linear way, i.e. also dependent on the

value of aeff. Experimental data [l11 were used to modify the above

relation accordingly.

The upflow angle a. is estimated from the calculated drag distribu-

tion along the platform and the airgap geometry by means of an

empirical relation.

For a wide variety of platforms the typical value of a. was 5 to 10

degrees.

Wind tunnel experiments showed that with decreasing airgap between

main deck and simulated sea surface the lift is increasing, without

significantly affecting the drag. This indicates that the main deck

is subjected to a "ground induced" upflow angle and that the dynam-

ic pressure remains unaffected. Ground effects on a lifting wing,

which are represented by a bound vortex along the span and trailing

vortices from the tips, result in a dynamic pressure increase from

the plane-imaged bound vortex and in an induced upflow angle from

the plane-imaged trailing vortices. Apparently, for a platform only

the imaged trailing vortices play a significant role. To correct

for this phenomenon the following correction formula, valid for a

wing with eliiptic Lift distribution along the span [12], is ap-

plied:

2zeff) 0.768 with 5 = e x p ( - 2 . 4 8 ( ~ 1

where zeff is the height halfway the wing trailing edge and the

wing aerodynamic centre. Similarly, w e define:

It will be clear that. this procedure may be considerably improved

when more is known about the actually non-elliptic lift distribu-

tion and corresponding vortex system of main decks at various

thickness ratios, particularly for the relatively thick main decks

(t/c greater than approximately 0.35).

With t h e above descr ibed procedure t h e l i f t curve of a s p e c i f i c

pla t form i s ca lcu la t ed , whereby a l s o drag at . aeff = 0 i s de te r -

mined.

The e a r l i e r mentioned v a l i d i t y of 0.1 - 2 l i n e a r C ( C ) curves po in t s t o

D L k=( l - t /c )a /2

CL: t h e c l a s s i c a l induced drag con-

cep t :

- 1 2 ACD - . CL (1 1) a

From c l a s s i c a l aerodynamics it i s

known t h a t t h e parameter k i s de-

pendent on t h e aspec t r a t i o A .

For an e l l i p t i c d i s t r i b u t i o n

along t h e span k is equal t o n .

Hoerner [ l31 r e p o r t s fo r l i f t i n g

su r faces with small aspec t r a t i o s

a value of k equal t o n / 2 . The

wind tunnel t e s t r e s u l t s , d i s -

cussed e a r l i e r , showed t h a t k

should be cor rec ted f o r t.he main

deck th ickness . The following

c o r r e c t i o n was appl ied:

t . / c 0.75: k = ( l - t / c ) r / 2

Fig. 5. Induced Drag Coef f i c i en t s t / c 0.75: k = 0.393 (12)

Fig. 5 shows t h e t e s t r e s u l t s f o r a rec tangular main deck (RMD)

with dimensions b = 500 mm, c = 750 mm ( a t B = 0 degrees) and t =

300 mm. The induced drag concept and t h e modified k-value agree

w e l l wi th t h e t e s t r e s u l t s f o r t h e two t e s t e d wind d i r e c t i o n s and

var ied a i r g a p va lues . The v a l i d i t y of k = 0.393 a t t / c > 0.75 could

not be v e r i f i e d , a s no s u f f i c i e n t d a t a a r e a v a i l a b l e f o r those re-

l a t i v e l y t h i c k types of platform.

For t h e c a l c u l a t i o n of t h e over turning moment, not only t h e drag

a r e a s of t h e var ious plat form components and t h e main deck l i f t

must be ca l cu la t ed , b u t a l s o the var ious c e n t r e s of e f f o r t .

The working l i n e of t h e drag on a s p e c i f i c pla t form component i s

determined by t h e h e i g h t of t he mean dynamic pressure over t h a t

component. The l i f t induced drag i s added t o t h e main deck drag.

The working l i n e of t h e l i f t i s ca l cu la t ed from t h e well-described

flat plate data [14], with a correction for the main deck thickness

as deduced from wind tunnel tests:

* where X /c denotes the centre of effort of a flat plate.

c P Analysis of the tests showed that for a platform with a smooth main

deck an aerodynamic torque is present. This torque decreases with

increasing ratio of deck thickness and streamwise platform length,

with increasing airgap between main deck and sea surface and with

increasing deck arrangement. The origin of this torque is believed

to be due to the formation of a separation bubble at the main deck

leading edge. Enlargement of this bubble up to even bursting re-

sults in a decreasing torque, increasing lift and a forward shift

of the lift working line. This process il.lustrates the importance

of a properly modelled platform in wind tunnel testing.

4. CORRELATION OF WINDOS WITH EXPERIMENTAL RESULTS

4.1 Introduction

A computer program (WINDOS) has been developed based on the phy-

sical model discussed. For the correlation between calculated and

experimental results, three comparisons will be given here which

are thought to be representative for typical WINDOS applications.

The comparisons concern:

- a semi-submersible consisting of a rectangular main deck, four circular columns and a helicopter deck located at the main deck's ,

leading edge. The experimental data are obtained from the NLR

wind tunnel tests;

- a so called semi-spar platform, consisting of a circular main deck and circular columns. The experimental data are obtained

from Willemsen et al. [ 91 ;

- a jack-up platform consisting of a triangular main deck, three square legs and several superstructure components. The experi-

mental data are obtained from Norton [l51 . In the several comparative figures, the calculated results by using

the ABS or DnV method are given too. These methods do not account

for lift effects.

4.2 Semi-submersible with Helicopter Deck

Fig. 6 shows the results for this structure in terms of a drag co-

efficient CD, a lift coefficient CL and an overturning moment CO-

aOnV, a = 0 efficient CM. Four wind headings 0 WT, a = 0

WT. a = 10 ( 8 ) and two platform inclination WINDOS, a = - 0 angles (a) are given. The corre-

9 WINDOS; a = 1 0 lation between WINDOS and the

HELIDECK

0 0

30 B 60 9 0

wind tunnel data is both qualita-

tively and quantitatively good

for the lift and drag coeffi-

cients. The overturning moment

coefficient is somewhat underpre-

dicted (a = 0 degrees) or over-

predicted (a = 10 degrees, 0 = 0

and 30 degrees) by WINDOS, al-

though the trends with the incli-

nat.ion and wind angle are well

predicted. The gap effect on the

overturning moment needs probably

t.o be extended in the physical

model of WINDOS.

The greater overturning moment

for the inclined platform at a

Fig. 6. Semi-submersib4e with Helideck

zero degree wind angle is caused by the lift forces on the main-

and helicopter decks. Apart from the flow inclination due to the

structure's pitch angle, the main deck induced velocity field acts

as an inclined flow (see Fig. 3) to this helicopter deck. This

deck, modelled as a flat plate in WINDOS, experiences then a sig-

nificant lift force, which adds to the overturning moment by the

long lever arm.The DnV prediction for the drag at even keel is too

conservative. This overprediction is less pronounced for the , overturning moment.

4.3 Semi-spar Platform

Fig. 7 shows the re- Wind

sults for this case.

'-D WINDOS

WT o

DnV o

C~ WINDOS A

WT A

DnV A

The correlation between

WINDOS and the experi-

ments for the drag and

overturning moment co-

efficients is good.

This indicates a proper

modelling of interac-

tion effects between

circular cylinders in

WINDOS. The resemblance

for the lift coeffi-

cients is not satisfac-

tory. This is due to

the circular shaped

main deck which is not

Fig. 7. Semi-Spar Platform modelled in WINDOS.

The DnV results for this structure are reasonably good, compared

with the previous case. WINDOS results are more close to the expe-

rimental values than the DnV results due to a better treatment of

Reynolds number and interaction effects on the circular cylinders. I i , 1

4.4 Jack-up Platform 1 5

The drag and overturning moment coefficients are shown in Fig. 8. I Lift coefficients are not shown as the experimental arrangement is

judged to be inadequate for a good prediction of the lift forces. I f;

The comparison between the WINDOS and experimental results is again f! I

reasonably good. The ABS predictions are too conservative, espe- 'i

cially for the drag coefficients.

i 5. CONCLUDING REMARKS

Fig. 8. Jack-up Platform

* The new developed method for the computation of

wind loads on offshore

structures is based on

physical principles, expe-

rimental data and computer

capabilities.

* The main physical princi- ples used, are based on

classical aerodynamic the-

ories on lifting bodies.

* An extensive wind tunnel

test program validated the

basic principles, enabled

the derivation of empiri-

cal formulations and pro-

vided new data sets.

* The final computer program WINDOS has been verified

with results of several

wind tunnel tests. A sig-

ni fi.cant improvement of

the correlation was found

when compared with the re-

sults from classification

society rules.

NOMENCLATURE

A main deck area; component wind area

b cross main deck dimension; wake width

C longitudinal main deck dimension

dw component width

CD drag coefficient

lift coef fici.ent

lift curve slope

CM overturning moment coefficient

90 mean airgap between main deck and sea surface

k variable in the induced drag relation

P exponent

main deck thickness

velocity

effective velocity

reference velocity

coordinate system

distance from main deck leading edge to the lift

working line

roughness height

reference height

wind axis pitch angle of main deck

platform induced upflow angle

effective platform inclination angle

wind heading

aspect ratio; A = b 2 / ~

variable in ground effect formula

REFERENCES

[l] American Bureau of Shipping, Rules for Building and Classing Mobile Offshore Units, 1985.

[2] Det n o r s w ~ u l e s for Classification of Mobile Off- shore Units, 1985.

[ 31 BOONSTRA, H. and LEYNSE, C., "Windtunnel Tests on a Model of a Semi.submersible Platform and Comparison of the Results with - Full Scale Data", OTC Paper 4285, 1982. MACHA, J.M. and REID, D.F., "Semisubmersible Wi.nd Loads and Wind Effects", Transactions SNAME, Vol. 92, 1984. OORTMERSSEN, G. VAN, VEGT, J.J.W. VAN DER and WALREE, F. VAN, "Forces on cylinders in oscillatory flow: a comparison of the results of numerical and physical -modelsN, 3rd-PRADS Confer- ence, Trondheim, 1987. HESS, J.L., "Analytical Solutions for Potential Fl.ow over a Class of semi-1nf inite Two-Dimensional Bodies having Ci.rcular Arc Noses", Journal of Fluid Mechanics, Vol 60, Part 2, 1973, pp. 225-239. SCHLICHTING, H., Boundary Layer Theory, MC Graw-Hill, 7th Edition, New York. BJERREGAARD, E. T . D. and SORENSEN, E. G., "Wind Overturning Effects obtained from Wind Tunnel Tests with various Semisub- mersible Models", OTC Paper No. 4124, 1981. WILLEMSEN, E., LEYNSE, C. and GRAAF, G., "Analysis of High- Reynolds Number Wind Tunnel Tests of the Semi-Spar", = Paper No. 4956, 1985. ABBOTT, J.H. and DOENHOFF, A.E., Theory of Wing Sections, Dover Publications Inc., New York, 1959. "Mean Fluid Forces and Moments on Rectangular Prisms", Engi- neerinq Sciences Data Unit, Item Number 80003, Dec. 1979. TORENBEEK, E., Synthesis of Subsonic Airplane Design, Delft University Press, 1986. HOERNER, .F. and BORST, H.V., Fluid-Dynamic Lift, published by Mrs. L.A. Hoerner, 1955. "Fluid Forces and Moments on Flat Plates", Engineerinq Sciences Data Unit, Item Number 70015, Sept. 1970. NORTON, D.J., Mobile Offshore Platform Wind Loads; Jack-ug Design, Report TEES-TR-83-10450-1, Oct. 1983.