lec4_wave loads on structures
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structure primary tasks! most difficult! complexity of the interaction b/t waves &
structures inadequacy of wave theories to describe randomocean waves
Reasonable prediction of wave loads on a variety of offshorestructures based on the theories available coupled with ourunderstanding of the interaction phenomenon through: ana y ca s u es, laboratory experiments and
at-sea measurements ase on e ype an s ze o e mem ers n a o s ore
structure, different formulations for wave forces areapplicable. (depending on the flow regime in the vicinity of
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e s ruc ure
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Morison Equation
Small structures
Empirical method
Wave diffraction theory
Large structures
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Due to regular wave
Inline force
Appropriate design values of coefficients
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Keulegan-Carpenter (KC) number
DDKC
Frequency parameter ()2
Re KC
Reynolds number (Re)
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Combining the effects of
water particle velocityandaccelerationon thestructure
uuCuD
C 12
DM
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Inertia force dra force
Morison force on a vertical ile
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M, D
determined experimentally by scaled
model testin Held the structure model in waves
,water particle velocity (u, v) for each constant, .
Compute C , CD using Morison Eq. Establish relationship: CM, CD ~ KC, Re
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-Small
-multiple frequencies
-Inertia dominant
-Same frequency
as wave
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easure n ne an ransverse orce me s ory on a ver ca cy n er
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modified form of the Morison equation to
describe the force experienced by the structure inmotion
xxCxD
CxmfDA
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Inertia force drag force
the values of the coefficients CA and CD are determined
.invariantover a cycle for a given frequency ofoscillation.
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A D
Two methods:
Structure oscillatinin calm water
Inertia coefficients for an oscillating vertical cylinder
oscillatory fluid
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Drag coefficients for an oscillating vertical cylinder
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cylinder due to asymmetric
shedding of vortices
Lift force frequency
as a function of KC,
having multiple frequencies Unlike the drag and inertia
coefficients a lift coefficient
,1976]
over one cycle may NOT bedetermined
enerall C resented as
an rms or a maximum value.
12Lift coefficients from an oscillation test [Sarpkaya (1976)]
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mo e or son equa on:
UuUuCuDC 12
recommended method [API-RP2A (2000) ] -
loading is based on the design approach in whicha single wave height and period are selected to
sea. Wave kinematics are computed by the wave
theory based on wave height, apparent wave periodan wa er ep . urren oes no en er n o scalculation except for the altered wave period.
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Uur
0
,is based on the maximum velocityincluding the current. In order tocompensate for the current in the CD value
,
following correction factor:
2
**12where21 rrATANrC
When r> 0.4, current is strong, so that the
drag coefficient for all practical purposes is
r
CD o t e stea y-current va ue. ere s noneed to compute KCand hence thecorrection factor, Crin these cases.
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a D
1. Field tests
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a D
2. Guidelines of certifying agencies
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Example design procedures from API
(2000) ompu e e ec ve mem er ame er: = + ;
- DS . .
Calculate C fi . 4.15b for KC12
For non-circular members, CDS independent of roughness
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S
C
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Steady drag coefficient vs. surface roughness [API, 2000)
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C /C (KC12) D DS
Drag coefficient vs. KC[API, 2000)
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