Lec4_Wave Loads on Structures

8/8/2019 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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Lec4_Wave Loads on Structures

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