L17-Wave Loading on Risers [Compatibility Mode]

7/28/2019 L17-Wave Loading on Risers [Compatibility Mode]

1/19

u : u u Riser Design

Arun S ChandelAssistant Professor

[email protected]

09997200339


2/19

Offshore risers or platform legs can berepresented by a very long cylinder

The drag force (inNewtons) on the

indicated is:

SUCF DD =2

2

1

LS =


3/19

Figure shows drag and lift coefficient for a


4/19

The CD

for a short section can be gainedfrom:

DLDCCDDshort 10),

.

5.0( +=

DDshort >=

we assume that the Reynolds number isknown and that the CD is known from

ublished data or from ex erimentation.


5/19

Members lying within the wakes of otherscauses problem in Cd estimation

Shielding effects:-

Typically windtunnel tests will berequired


6/19

Waves represent the dominant forcemechanism on offshore systems

r r r y r u -

linearity can give rise to mean and lowfrequency drift forces

Non linearity can also induce superarmon c g requency orces

they excite system resonances


7/19

Wave loading on a offshore structure is an

r r

y y, y r

towards the influence of:

Wave height

D ameter o

structural elements

Wave length


8/19

It is usual to characterise wave loadingaccording to non-dimensionalcoefficients

)/( D=Structural member diameter

Wave length

)/( DH=Wave height

Structura mem er ameter


9/19

The Keulegan-Carpenter Number (KC) is a

r r r r y w v

TU

D=

=mU

maximum fluid flow speed underthe waves m s

=T wave period (s)

= cylinder diameter (m)KC5; drag dominated


10/19

The Morrison OBrian Equation has been

v u w v

Useful for small structural elements

where 2.0/


11/19

The force on the short section of length dyis given by

nnDnm UUdSCUdVCdF 1

+= &

=nU instantaneous wave fluid velocity=U& instantaneous wave fluid acceleration

= water density

=CC , inertial and drag coefficient


12/19

the total force on the cylinder is the sum of all

r

==dFFORdFF

infinitesimal dy

r yyr ==

+=0 0

2

nm UdyUrCdyUrCF &


13/19

Moments about the Sea Bed is moreimportant than force

(in Newtons) and its perpendicular distance(metres) from, in this case, the sea bed

+++=0 0

2 )()()()(d d

DM UdyyUydrCdyyUydrCF &


14/19

Linear wave theory relationship is neededto predict forces

Surface displacement

)cos(),( xtAxt =As our cylinder is vertical, we can assume aconstant value of x=0m

)cos(2

),( tH

xt = is the water height (m)

Using the equations for Ux etc. earlier in thecourse it is possible to calculate the total forcean t e tota moment


15/19

At the surface the element displacementscan be described for a regular wave as

H==

msin0Horizontal

2

tHD

V

== 2


16/19

Linear theory predicts that fluid elementsunder a regular wave travel in circles

acceleration

path of a fluid

element

( ) ( )teH

ty y cos,D

DeepwaterAssume

V =

T

2and

2==

( ) ( )teH

tyD y

H

sin2

, =


17/19


18/19

Inertial & Drag Forces on a Riser

2Inertia force:

24

2

LCF mi =

12

2 H=

rag orce:

42

Force ratios:

where= Di FRF

1;2;2 == Dm CCH

R


19/19

A riser analysis is conducted to assesseffects of environmental loadings

A riser is designed based on previous design orspec ca on

Mathematical model of hydrodynamics forces based onenv ronmen a an opera ng con ons s app e orload calculation

as c r ser ana ys s s en carr e ou o eva ua ethe risers structural response to the hydrodynamicloadings

The response is compared to the design requirements andthe design is refined as necessary.

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L17-Wave Loading on Risers [Compatibility Mode]