A Study on the Sensitivity of Dynamic Behavior of

Jacket Type Offshore Structure

Choong-Yul Son, Kang-Su Lee, Jung-Tak Lee, Keon-Hoon Kim

(INHA UNIVERSITY Department of Naval Architecture & Ocean Engineering Inchon 402-751, Korea)

Abstract : Unlike strucutres in the air, the vibration analysis of a submerged or floating structure such as offshore structures is possibly only when the fluid-structures is understood, as the whole or part of the structure is in contact with water. Through the comparision between the experimental result and the finite element analysis result for a simple cylindrical model, it was verified that an added mass effects on the structure. Using the commercial FEA program ANSYS(v.11.0), the stress matrix considering an load and underwater added mass was superposed on the stiffness matrix of the structure. A frequency response analysis of forced vibration in the frequency considered the dynamic load was also performed. It was proposed to find the several important modes of resonance peak for these fixed type structures. Furthermore, it is expected that the analysis method and the data in this study can be applied to a dynamic design and dynamic performance evaluation for the ground and marine purpose of power generator by wind. Key words: Natural Frequency, Wind Turbine Jacket, Finite Element Method, Beam Theory, The static

analysis

(email : soncy@inha.ac.kr)

1. INTRODUCTION

Because of unlimited resources, cleanness of energy

and advantage of technical commonness, Wind

Turbine System is one of the future oriented

techniques as spotlighted alternative energy technique

converting wind energy into electrical energy.

Modal test which is one of the examination

assessments is the method to analyze the dynamic

characteristics. . Its purpose is to avoid the resonance

which, finding the natural frequency of the wind tower

and forecasting the vibration phenomenon for mode

shape. In case of domestic, study for Wind Turbine

System has been preceded actively in some big

corporation, small-medium enterprises and national

researcher. But it was impossible to obtain systematic

data. Today, the research field is very numerous

unlike an advanced country oversea. Therefore, it is

necessary to study the Wind Turbine System as stated

above.

Based on this design we calculated the complex

load on the tower off- and onshore. The onshore load

is calculated using aerodynamic load(caused by wind)

and gravity load(caused by the upper structure).

Calculations in the offshore case have to take into

account aerodynamic load, wave load(caused by

waves) and current load(caused by the current).

However, since current load is insignificant compared

to wave load, it can be ignored

2. ENVIRONMENTAL LOADS The external loads include hydrostatic pressure, wind,

wave, current, tide, ice, earthquake, temperature,

fouling, marine growth and scouring.

2-1. The load calculation in on shore We calculated the gravity load of the upper structure,

which consists of the wind turbine system (i.e. blade,

nacelle and generator). In order to carry out the

structural analysis of the tower we first divided it into

sections of height 3m each. Then the feasibility of the

load was determined and the resulting stress and

deflection analysed. For the purpose of calculating the

section loads in the tower the tower can be viewed as

a cantilever beam as shown in figure 1.

Fig. 1 Cantilever beam model of Tubular tower

When the tower is analysed structurally, the following three main loads have to be considered: 2-1-1. Impellent force The impellent force caused by a rotating blade can be

calculated using the dynamic pressure of a rotating

blade or the drag force affecting the tower.

2-1-2. Distribution force The tower is of a cylindrical shell type. Assuming a

maximum wind speed of 23m/s and the tower being

divided into 3m spacing sections, the load that affects

the tower can be obtained by evaluating each section

area.

2-1-3. Gravity force The gravity force can be calculated as follows.

(The weight of nacelle + blade + generator) × 9.8m/s2

2-2 The load calculation in off shore. To calculate wave load we assume the water to be on

average 5m deep, maximum wave height of 10m and

maximum wind speed 23m/s. Because the ratio of

horizontal dimension (D) to wave length (L) is smaller

than 0.05, we can calculate the wave load with

Morrison’s Formula.

Wave load depends on the form of the structure (here :

the tower), the form of the current, Inertia force due to

wave particle velocity, the roughness of the surface

and Drag force depending on Reynold’s number.

Wave load per unit length is as follows:

F = 0.5ρCDAu2 + ρCmVdu/dt

Cm and Cd are a coefficients determined by shape, condition of the surface and Reynold’s number. They are calculated using the ABS rule; Cd is 0.5 and Cm is 1.5

2-3. Wind Load Since the wind acts as an external force to the upper

structure, above sea level, the wind velocity is

determined to estimate the wind generated force (Lee,

1989). The sustained wind speed is the average

velocity during 1 min and that is used to determine the

wind force acting on the whole structure. The gust

wind speed is the average velocity during 3 sec and is

applied on planning deck facilities.

The wind force, acting on the structure, is largely

divided into drag force and lift force. The drag force is

a force that is created in the flow direction by pressure

difference and lift force created in the vertical flow

direction by shape or orientation of object. Total drag

force from seabed to height z above the surface is

(1)

Total life force from sea bottom to height z above the surface of ocean is

(2)

The wind force can be applied to upper structure

above M.W.L. The length of a pile for wind force

calculation can be determined by considering the

maximum wave elevation and the clearance under the

super structure. Therefore, the buoyancy uplift and

direct wave force that could occur on the deck

structure can be avoided. The air gap is also

considered in determining fixed platform height.

Commonly 1.5m of air gap and 1/10 wave height is

applied.

2-4. Wave Load A number of wave theories such as Airy, Stoke,

Stream Function, Cnoidal and Solitary Wave Theory,

enable a suitable wave theory to be applied for the

estimation of wave load. The appropriate wave theory

can be determined by water depth, wave length and

wave period. Stoke wave theories are valid for

d/L>0.039, and Cnoidal or Solitary wave theories for

shallow sea of d/L>0.04. After selecting the

approximate wave theory, the wave force can be

calculated by the Morrison equation (Sarpkaya and

Issacson, 1981). Considering the energy conservation

law, boundary conditions, initial conditions and

Bernoulli equation, the following expressing for wave elevation, can be obtained.

(3)

From the above equation, the following relationship

can be obtained

+

(4)

Representing wave and potential as power series:

(5)

(6)

Each potential has to satisfy Laplace’s

equation and the boundary conditions. If the potential

is represented as a Taylor-series of still water surface

in the free surface then,

(7)

The wave force is approximated by using stokes wave

theory which can resolve the non-linear wave

motion(Dawson, 1983). To simulated the actual ocean

wave, this theory is applied in the study. Wave celerity,

can be calculated as

(8)

Surface elevation, is

(9)

Horizontal particle velocity, is

(10)

Vertical particle velocity, is

(11)

Horizontal particle acceleration, is

(12)

Vertical particle acceleration, is

(13)

Wave force in the horizontal direction on the vertical

pile can be classified as an inertia force by

acceleration and drag force caused by the boundary

layer effect (Clasuss,et. Al., 1988). The inertia force

can be expressed as

(14)

Where, = Mass Coefficient, determinated by

experiment.

The maximum inertia force is

(15)

The inertia force is generated between the boundary

layer and the fluid layer with the assumption that an

infinitely thin fluid layer is stuck on the cylinder side

and the velocity is exponential is increased by the

distance from the cylinder. Fig. 2 shows the schematic

diagram of the wave force on a pile.

Fig. 2

Wave

load

for pile

The

drag

force

can be

expres

sed as

(16)

Where, = Drag Coefficient, determined by

experiment.

The unit area of a member is dA which is projected on

the vertical plane of force direction. Therefore the

maximum drag force is

(17)

The total wave force on a pile can be represented as

+ (18)

The calculation of the wave force on a cylindrical

object can differ by the ratio of member diameter/wave

length, D/L. When this value is lower than 0.05, the

pile does not effect the wave property, thus Morrison

equation can be applied. However, The Morrison

equation can be utilized up to ratio of 0.2. For a large

body in the calculation of the wave force. The

and vary as the pile roughness, degree of fouling,

aspect ration(the ratio of width length), cross-sectional

shape, body orientation, relative flow velocity, and

Reynolds number etc.. In offshore steel structures

= 0.1 and = 2.0 are recommended. These

values consider marine roughness.

2-5. Current load Because the actual current is composed of the various

sums of currents coming from multi-directions, it is

common to measure the current speeds at several

depths of the region (Lee, 1989). Should this data be

unavailable, the following equations are used to

estimate the current speed;

(19)

and for 0 ≤ z ≤ h

for 0 ≤ z ≤

for and z

2-6. The load calculation in off shore. To calculate wave load we assume the water to be on

average 5m deep, maximum wave height of 10m and

maximum wind speed 23m/s. Because the ratio of

horizontal dimension (D) to wave length (L) is smaller

than 0.05, we can calculate the wave load with

Morrison’s Formula.

Wave load depends on the form of the structure (here :

the tower), the form of the current, Inertia force due to

wave particle velocity, the roughness of the surface

and Drag force depending on Reynold’s number.

Wave load per unit length is as follows:

(20)

and are a coefficients determined by shape,

condition of the surface and Reynold’s number. They

are calculated using the ABS rule;

= 1.5 and = 0.5

3. The analysis of Finite Element In this paper the finite element method (ANSYS) was

used for the purpose of modal analysis. The 4-leg steel jacket is numerically modeled with the

fixed boundary condition at the sea bottom. The

principal specification of the model is described below:

3-1. Principal characteristics of analyzed model

Table 1. Jacket Type Tower of Analysis Model

Top diameter [m] 0.5

Thickness [m] 0.05

Water Depth [m] 10

Jacket Type Tower total length

[m] 58.665

Number of leg [pieces] 4

Top dimension [m] 10 × 10

Bottom dimension [m] 21.36 × 21.36

Table 2. Jacket Type Tower Property of leg

Out diameter [cm] 50

Wall thickness [cm] 5

Shear area modulus 0.5

E(Young's modulus) [Kg/sq cm] 2100×1000

G(Shear modulus) [Kg/sq cm] 840×1000

Yield strength [Kg/sq cm] 2450

Density [ton/�] 7.85

K factor 1.0

Tower wall thickness[cm] 2.5

3-2. The analysis of Finite Element In this paper the finite element method(ANSYS) was

used for the purpose of modal analysis.

Fig. 3 1st Modal analysis of Jacket Type Tower

Fig. 4 2nd modal analysis Jacket Type Tower

Fig. 5 3rd modal analysis Jacket Type Tower

Fig. 6 4th modal analysis of Jacket Type Tower

3-3. The result of Finite Element Method

Table 4. Natural frequency of Jacket Type Tower

Mode

2MW

(Added

Mass :

20m)

2MW

(Added

Mass :

30m)

3.5MW

(Added

Mass :

20m)

3.5MW

(Added

Mass :

30m)

1 0.2833 0.2833 0.2793 0.2793

2 0.2840 0.2840 0.2800 0.2800

3 1.8596 1.8596 1.8596 1.8596

4 1.8625 1.8625 1.8625 1.8625

Fig. 7 Natural frequency of Jacket Type Tower 3-4. Result of Forced Vibration The Forced Vibration Analysis is executed using

harmonic analysis function of ANSYS(harmonic

force → exciting force) The responced sympathetic

vibrations modes are 4,8,9,10th form

Table 3. Result Comparison of Frequency response & Natural Frequency

Mode Natural Frequency Response frequency

1 3.108 -

2 4.491 -

3 5.570 -

4 8.720 8.500

5 9.644 -

6 10.076 -

7 11.055 -

8 14.543 13.250

9 17.431 17.250

10 19.051 19.000

You can check the Peak Point after forced vibration

analysis at Fig. 8, and Fig. 9 is the result of transformation

to log scale through Fig. 8

Fig. 8 Forced vibration of Jacket Type Tower

Fig. 9 Forced vibration of Jacket Type Tower

First of all, in case of Tubular Type Tower, Peak

frequency is occurred at 2,3,4th when forced vibration.

It express that sympathetic vibrations will be occurred

at 2,3,4th mode as like Table. 2. Next, in case of

Jacket Type Tower, If you watch to 10th mode shape,

you will find that sympathetic vibrations will be

occurred at 4,8,9,10th mode.

To restrict vibration controls, size of vibration

response added-vibration stress below allowance, We

must execute protection way of design process,

analysis of measurement result.

4. CONCLUSION

This research compared the result of forced vibration

analysis that applied the periodic load to exciting force

expressed by natural frequency result and rotating

blades. We design the structure that avoids

sympathetic vibration through reinforcing the materials

or installation the damper between blade and tower.

Also, when we design the control-part, consider that

Tubular Type Tower does not be operated at 2,3,4th

response frequency, Jacket Type Tower does not be

operated at 4,8,9,10th response frequency. This

control is able to restrict the blade velocity through

generator control.

This research can show you the concept of dynamic

design about two type wind energy generator.

Therefore, considering the annual wind map and other

data, must design sympathetic vibration frequency

band of generator and research using the real

response through exciting signal data acquired by

impellent[driving] force.

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