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

Concept of wave loading calculation

MATLAB

Morison

Equation

Wave Loading Calculation

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

ntal wave loading per unit

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!

Wave loading is divided into three directional components

with respect to Cartesian reference system

Radius (D) 1.2192 m

Water depth (h) of 24.38 m

Wave heading of 30°

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

Elemental wave loadings per unit length

Elemental wave loadings

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 10. MATLAB code algorithm for wave loading calculation

Figure 11. Elemental and total wave loadings with respect to ωt from the wave loading calculation MATLAB code

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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