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## Seung Hyeon Yoo

on 6 May 2014

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#### Transcript of Stoke's 5th order wave loading on a jacket structure

Seunghyeon Yoo

Professor G.E. Hearn
Professor Zhimin Chen
Aims and objectives
Using Stoke's 5th order wave theory, calculate wave loadings on a member of a jacket structure
Concept of Stoke's 5th order wave parameter calculation
MATLAB
CODE
WAVE
THEORY
WAVE
PARAMETER CALCULATION
TWO CASES ARE ASSUMED
WATER DEPTH (h), WAVE HEIGHT (H) and WAVE LENGTH (λ) is given
WATER DEPTH (h), WAVE HEIGHT (H) and WAVE PERIOD (T) is given
Requires one phase of iteration
Requires two phases of iterations
Case
Case
Acceleration
required
For Case 1, an acceleration factor 'm' is incorporated based on
'Accelerated Newton's method'
For Case 2, an acceleration factor 'r' is incorporated
Case 2, without acceleration
Case 2, with acceleration
Number of iteration : 273 times
Number of iteration : 7 times
Reduced to 1/40
The values of acceleration factor 'm' for Case 1, which yield the least number of iteration are found with respect to the given condition: wave height (H), water depth (h) and wave length (λ)
The values of acceleration factor 'r' for Case 2, which yield the least number of iteration are found with respect to the given condition: wave height (H), water depth (h) and wave period (T)
Plotting 'm' value for optimum iteration with respect to wave height (H) and wave length (λ)
Plotting 'r' value for optimum iteration with respect to wave height (H) and wave period (T)
These 'm' and 'r' data are incorporated into the MATLAB codes for calculating Stoke's 5th order wave parameters and referenced automatically for faster iteration!
Stoke's 5th order wave parameter calculation
Wave loading calculation on a member of a jacket structure by using Morison Equation
Vertical Cylindrical Member
Horizontal Cyl
indrical Member
45˚ Inclin
ed

Cylin
drical Member
Last dissertations only covered simple orientations of cylindrical members on a jacket structure as below:
The application of Morison equation is generalised to any arbitrary oriented cylindrical members of a jacket structure
MATLAB
Morison
Equation
θ
φ
The orientation of an arbitrary oriented cylindrical member is defined by the angle between y axis and the member as phi (φ) and the angle between x axis and the projection of the member on the x-z plane as theta (θ)
Two cases are assumed:
Water depth (h), Wave height (H) and Wave length (λ) are given
Water depth (h), Wave height (H) and Wave period (T) are given
Case
Case
Eleme
length
with respect to different
incom
ing waves
Cylindrical mem
ber of a jacket structure
Different incoming waves
A format of expressing elemental wave loading distribution per unit length on a cylindrical member with respect to different angles of incoming waves
y
x
z
Wave height (H) = 10.668m
Water depth (h) = 22.860m
Wave period (T) = 8.8831sec
Case
A simulation is conducted with following conditions by the generated MATLAB code
Acceleration factor r = 0.623
Acceleration factor m = 0.590
are incorporated!
with respect to Cartesian reference system
Water depth (h) of 24.38 m
φ = 15°
θ = 15°
CD = 1
CM =2
Frequency (ω) 0.793 sec-1
Wave length (λ) 91.44 m
Wave number (k) 0.06856 m-1
Wave height parameter (γ) 0.1896
A simulation was conducted with following conditions by the generated MATLAB code
Total wave force in x-axis
Total wave force in y-axis
Total wave force in z-axis
The modulus of total wave force
A result from the wave load calculation MATLAB code
Wave load calculation MATLAB Code algorithm
Case 1 MATLAB code algorithm
Case 2 MATLAB code algorithm
The first phase of iteration
The second phase of iteration
From the previous simulation,
it is proved that:
The acceleration factors have critical roles on reducing the number of iterations
Optimum values of the acceleration factors need to be found with respect to the given wave properties
Therefore,
Other simulations were conducted with the same foregoing conditions to find the effect of inclination of a cylindrical member on a wave loading
Water line
φ
Each simulation was conducted by changing the angle of φ, which indicates the angle between the
y axis and the member, from 0° to 20°
Figure 16. Comparison of the maximum mean wave forces with respect to the angle of incoming wave depending on different inclination angles of phi (φ)
A
&
The greater angle of phi (φ), the greater polarisation on the wave forces occurs
Not only total and elemental wave loading with respect to Cartesian reference system, but also elemental wave loadings per unit length are calculated by the generated MATLAB code
It enables to plot elemental wave loading distributions along a member of a jacket structure
Generate MATLAB code for determining associated parameters of Stoke’s 5th order theory

Find a measure to accelerate the Stoke’s 5th order wave parameter determination process and apply within the wave loading MATLAB code

Generate MATLAB code for calculating wave loading on a single arbitrary oriented member of a jacket structure with the Stoke’s 5th order wave theory and Morison’s wave loading equation
Objectives
Aims
Thank you!
One phase of iteration is required in Case 1
Contents
Aims and objectives
Stoke's 5th order wave parameter calculation
Wave loading calculation on a member of a jacket structure by using Morison Equation
Figure 1. Deep water jacket structures configuration
Figure 2. MATLAB code algorithm for Case 1 Stoke's 5th order wave parameter calculation
Figure 3. MATLAB code algorithm for Case 2 Stoke's 5th order wave parameter calculation
Figure 4. The results of Stoke's 5th order wave parameter calculation without acceleration factors (above)
Figure 5. The results of Stoke's 5th order wave parameter calculation with acceleration factors (below)
Figure 6. The optimum values of the acceleration factor 'm' with respect to wave height (H) and wave length (λ) (above)
Figure 7. The optimum values of the acceleration factor 'r' with respect to wave height (H) and wave period (T) (below)
Figure 8. The orientations which were covered by last dissertations
Figure 9. Definition of the angles phi (φ) and theta (θ)
Figure 12. Format of plotting wave loading distribution results by the MATLAB code
Figure 13. The result of the wave load distribution calculation by the MATLAB code, from 0° to 180°
Figure 14. The result of the wave load distribution calculation by the MATLAB code, from 180° to 360°
Figure 15. Variation of the angle phi (φ) from 0° to 20°
Summary
The MATLAB codes for Stoke's 5th order wave parameter calculation is generated
The acceleration methods for accelerating Stoke's 5th order wave parameter calculation iteration processes are investigated

Optimum acceleration factors for any given wave properties can be found by the generated MATLAB code
The MATLAB code for calculating wave loading on any arbitrarily oriented cylindrical members of a jacket structure is generated
The effect of the inclination of a member with respect to y axis on wave loading is investigated
Summary
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