l17-wave loading on risers [compatibility mode]
TRANSCRIPT
-
7/28/2019 L17-Wave Loading on Risers [Compatibility Mode]
1/19
u : u u Riser Design
Arun S ChandelAssistant Professor
09997200339
-
7/28/2019 L17-Wave Loading on Risers [Compatibility Mode]
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 =
-
7/28/2019 L17-Wave Loading on Risers [Compatibility Mode]
3/19
Figure shows drag and lift coefficient for a
-
7/28/2019 L17-Wave Loading on Risers [Compatibility Mode]
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.
-
7/28/2019 L17-Wave Loading on Risers [Compatibility Mode]
5/19
Members lying within the wakes of otherscauses problem in Cd estimation
Shielding effects:-
Typically windtunnel tests will berequired
-
7/28/2019 L17-Wave Loading on Risers [Compatibility Mode]
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
-
7/28/2019 L17-Wave Loading on Risers [Compatibility Mode]
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
-
7/28/2019 L17-Wave Loading on Risers [Compatibility Mode]
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
-
7/28/2019 L17-Wave Loading on Risers [Compatibility Mode]
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
-
7/28/2019 L17-Wave Loading on Risers [Compatibility Mode]
10/19
The Morrison OBrian Equation has been
v u w v
Useful for small structural elements
where 2.0/
-
7/28/2019 L17-Wave Loading on Risers [Compatibility Mode]
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
-
7/28/2019 L17-Wave Loading on Risers [Compatibility Mode]
12/19
the total force on the cylinder is the sum of all
r
==dFFORdFF
infinitesimal dy
r yyr ==
+=0 0
2
nm UdyUrCdyUrCF &
-
7/28/2019 L17-Wave Loading on Risers [Compatibility Mode]
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 &
-
7/28/2019 L17-Wave Loading on Risers [Compatibility Mode]
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
-
7/28/2019 L17-Wave Loading on Risers [Compatibility Mode]
15/19
At the surface the element displacementscan be described for a regular wave as
H==
msin0Horizontal
2
tHD
V
== 2
-
7/28/2019 L17-Wave Loading on Risers [Compatibility Mode]
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
, =
-
7/28/2019 L17-Wave Loading on Risers [Compatibility Mode]
17/19
-
7/28/2019 L17-Wave Loading on Risers [Compatibility Mode]
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
-
7/28/2019 L17-Wave Loading on Risers [Compatibility Mode]
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.