OrcaFlex Manual - Orcina

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Theory, Vessel Theory
separate 1-dimensional interpolations, the first being according to period τ (or frequency ω=2π/τ if τ is larger
than the longest period specified in the data), and then the second according to direction β.
� For bi-directional full QTFs (wave drift or sum frequency), the interpolation is needed for a QTF Q(β1,β2,τ1,τ2)
that is a function of 4 variables. This interpolation is done using a 4-dimensional linear interpolation in the
space whose coordinates are β1, β2, τ1 and τ2.
� For uni-directional full QTFs (wave drift or sum frequency), the interpolation is only needed for a QTF function
Q(βmean,βmean,τ1,τ2) that is a function of only 3 variables, since the QTF is only needed for wave component pairs
with equal directions, βmean. So in this case the interpolation is done using a 3-dimensional linear interpolation
space whose coordinates are βmean, τ1 and τ2.
Default Limiting Values
The default limiting value at τ=Infinity is Q=0. The effect of this is that if the user does not specify the QTF limit for
τ=Infinity then for periods greater than the longest period specified in the data the user data will be linearly
extrapolated (on frequency) towards zero QTF at infinite period (zero frequency). This default long period QTF limit
is theoretically correct for a freely floating body, since the body behaves like a cork and does not disturb the
propagating wave, so the second order wave load tends to zero for long periods (low frequencies).
The default limiting value at τ=0 is taken to be equal to the Q value for the lowest period specified in the data. The
effect of this is that if the user does not specify the QTF limit for τ=0 then the QTF given for the shortest period
specified in the data will be used for all periods less than that shortest specified period.
Warning: QTF extrapolation could introduce significant errors if a significant amount of wave energy is
outside the range of wave periods specified in the QTF data. In addition, the default zero QTF value
for long period waves is only theoretically valid for a free-floating vessel. It could be poor for a fixed
or moored vessel (especially if firmly moored). The limiting QTFs for zero and Infinity periods
should therefore be specified in the data if the default limits are not suitable.
Wave Drift Damping Theory
OrcaFlex will calculate the wave drift damping effect on the wave drift load if both Wave Drift Load and Wave Drift
Damping are in the included effects.
The wave drift damping is calculated using an encounter effects approach developed by Molin from Aranha's
original analysis in deep water, but extended according to the results of Malenica et al to be applicable to all water
depths. The velocity used in this calculation is the vessel low frequency velocity relative to the current, so the wave
drift damping includes both the current effect on wave drift load and the damping effect on vessel low frequency
motion.
Note: These encounter effects are only applied to the wave drift load, not to the sum frequency load.
OrcaFlex also only applies wave drift damping in the surge and sway directions, since there is not
normally significant slow drift motion in heave, roll or pitch, and there is not yet a widely accepted
method of modelling yaw wave drift damping.
Wave Drift Damping with Newman Approximation Method
Molin uses the same form of Newman's approximation as OrcaFlex. The effect of wave drift damping is implemented
by using modified wave drift QTF values, Qde(β,β,τ,τ), where the extra subscript 'e' has been added to denote that
they allow for the encounter effects. The modified diagonal QTF values are given by:
where
Qde(β,β,τ,τ) = Ae . Qd(βe,βe,τe,τe)
Ae = 1 + (ω ∂α/∂ω - 2)UL/Cg = Aranha scaling factor
βe = β + UT/Cg = encounter heading
τe = 2π/ωe = encounter period
ωe = ω(1 - UL/Cp) = encounter frequency
Cp = ω/k = wave phase velocity
Cg = ∂ω/∂k = wave group velocity
k = wave number