annex1 dynamic analysis results

Annex 1: Dynamic analysis results

1


In this annex, calculations from ANSYS Aqwa regarding with chapter 7 are shown:

Morison

It has been checked for loads obtained in chapter 8, therefore 6 design load cases are

shown and one survival case:

Wind speed= 6 m/s; Hs = 0,5 m; Tp = 5 s

Maximum value= 2838,6 N/mm

2; Minimum value= -785,18 N/mm

2

Figure 1: Pressures over platform in N/mm

2

A basic check of diffraction absence is shown:

Figure 2: Wave height in m. Figure 3: Amplitude of waves in m

Maximum=0,67 m ; minimum=-0,57 m Maximum=0,42 m; minimum=0m


2

Wind speed= 10 m/s; Hs = 1,48 m; Tp = 5,74 s

Maximum value= 8564 N/mm


2


2

A basic check of diffraction importance is shown:




3




2


2





4

Wind speed= 18 m/s & 22 m/s; Hs = 2,5 m; Tp = 7 s



2


2





5

Wind speed= 24 m/s; Hs = 3,5 m; Tp = 8 s



2)


2



Maximum=2,46 m ; minimum=-2 m Maximum=2,62 m; minimum=0m


6



2; Minimum value= -7470 N/mm

2)


2


Figure 17: Wave height in m. Maximum=5,88 m ; minimum=-3,23 m


7

Summary:

Pressures calculated over platform show how bigger waves with longer periods creates

increase pressure loads over platform. The maximum is obtained for the survival case

and due to wind forces over rotor on survival conditions are relatively low, the wave

importance on structure motions acquires the main influence over it.

Added mass

It has been studied for a wave period between 2,6 to 125 seconds. The

directions of incidence have no influence because structure the structure is

symmetric.

Surge (A11)

0,0E+00

5,0E+06

1,0E+07

1,5E+07

2,0E+07

2,5E+07

3,0E+07

3,5E+07

125,728,416,011,18,56,95,85,04,43,93,63,23,02,82,6

Wave period [s]

Ad

de

d m

ass [K

g]

Figure 18: “Added Mass on Surge”

On surge maximum added mass is reached at 15 seconds meanwhile that the minimum

is reached around 8 seconds. The difference between both of them shows how

depending of the wave period the added mass can be twice bigger than minimum.

Sway (A22)

0,0E+00

5,0E+06

1,0E+07

1,5E+07

2,0E+07

2,5E+07

3,0E+07

3,5E+07

125,728,416,011,18,56,95,85,04,43,93,63,23,02,82,6

Wave period [s]

Ad

de

d m

ass [K

g]

Figure 19: “Added Mass on Sway”

Because of structure symmetry the effects in Sway, figure 19 are the same than in surge.


8

Heave (A33)

0,0E+00

2,0E+07

4,0E+07

6,0E+07

8,0E+07

1,0E+08

125,728,416,011,18,56,95,85,04,43,93,63,23,02,82,6

Wave period [s]

Ad

de

d m

ass [K

g]

Figure 20: “Added Mass on Heave”

On heave added mass is more variable than in surge, it reach the peak at 15 seconds and

a minimum in 7,5 seconds. This big variation in a short range of periods may create

instability.

Roll (A44)

4,0E+09

4,4E+09

4,8E+09

5,2E+09

5,6E+09

6,0E+09

125,728,416,011,18,56,95,85,04,43,93,63,23,02,82,6

Wave period [s]

Ad

de

d m

ass [K

g·m

2/r

ad

]

Figure 21: “Added Mass on Roll”

On roll, added mass shows a double peak of similar values for 5 and 9 seconds

meanwhile the minimum is in very low periods.

Pitch (A55)

4,0E+09

4,4E+09

4,8E+09

5,2E+09

5,6E+09

6,0E+09

125,728,416,011,18,56,95,85,04,43,93,63,23,02,82,6

Wave period [s]

Ad

de

d m

ass [K

g·m

2/r

ad

]

Figure 22: “Added Mass on Pitch”


9

On pitch the same added mass than for roll is obtained because of platform symmetry

Yaw (A66)

6,5022

6,5024

6,5026

6,5028

6,5030

125,728,416,011,18,56,95,85,04,43,93,63,23,02,82,6

Wave period [s]

Add

ed m

ass [K

g·m

2/r

ad]

Figure 23: “Added Mass on Yaw”

Finally for yaw, added mass maintains constant because waves doesn’t affects to this

degree of freedom. The apparently big step for short periods looking to the scale can be

observed that it is insignificant

Summary:

It can be seen how the added mass increases several tonnes the system mass in all

degrees of freedoms. These added masses help to a get a bigger mxx component value

increasing the excitation period of structure and therefore moving it away from most

common waves natural periods.

Radiation damping It has been studied for a wave period between 2,6 to 125 seconds. The directions of

incidence have no influence because structure the structure is symmetric.

Surge (B11)

0,0E+00

2,0E+06

4,0E+06

6,0E+06

8,0E+06

1,0E+07

125,728,416,011,18,56,95,85,04,43,93,63,23,02,82,6

Wave period [s]

Radia

tion D

am

pin

g [N

/m/s

]

Figure 24: “Radiation damping on Surge”

Figure 24 shows how radiation damping has a peak at 9 seconds being for the rest of

periods 4 times smaller.


10

Sway (B22)

0,0E+00

2,0E+06

4,0E+06

6,0E+06

8,0E+06

1,0E+07

125,728,416,011,18,56,95,85,04,43,93,63,23,02,82,6

Wave period [s]

Radia

tion D

am

pin

g [N

/m/s

]

Figure 25: “Radiation damping on Sway”

Because of structure symmetry the effects in sway, figure 25 are the same than in surge.

Heave (B33)

0,0E+00

5,0E+06

1,0E+07

1,5E+07

2,0E+07

2,5E+07

3,0E+07

125,728,416,011,18,56,95,85,04,43,93,63,23,02,82,6

Wave period [s]

Radia

tion D

am

pin

g [N

/m/s

]

Figure 26: “Radiation damping on Heave”

Figure 26 shows a peak for a similar period. Between 2,6 to 5 seconds period there is no

radiation damping.

Roll (B44)

0,0E+00

2,0E+08

4,0E+08

6,0E+08

8,0E+08

1,0E+09

125,728,416,011,18,56,95,85,04,43,93,63,23,02,82,6

Wave period [s]

Radia

tion D

am

pin

g

[N·m

/(ra

d/s

)]

Figure 27: “Radiation damping on Roll”


11

Radiation damping in roll, figure 27, shows a peak in 4 seconds

Pitch (B55)

0,0E+00

2,0E+08

4,0E+08

6,0E+08

8,0E+08

1,0E+09

125,728,416,011,18,56,95,85,04,43,93,63,23,02,82,6

Wave period [s]

Radia

tion D

am

pin

g

[N·m

/(ra

d/s

)]

Figure 28: “Radiation damping on Pitch”

Because of structure symmetry the effects in pitch, figure 28 are the same than in roll.

Summary:

Biggest radiation damping is located on roll and pitch tilting movements because they

are the most sensitive degrees of motion against waves. Waves induced movements is

mostly seen in these tilting movements, therefore for a structure with such a big

hydrostatic stiffness it can be expected to find these great values.

Response amplitude operators

In this study RAOs have been obtained using ANSYS Aqwa module and a study range

from 2,5 seconds to 125,5 seconds.

Surge

,00

2,00

4,00

6,00

8,00

10,00

125,66415,9948,5405,8254,4203,5612,9822,565

Period [s]

RA

O X

[m

/m]

Figure 29: “Response amplitude operator in surge” Figure 29 shows how for surge, excitation starts to become significant after

16 seconds. These periods are over design load cases here studied.


12

Heave

0,0

0,3

0,6

0,9

1,2

1,5

125,66415,9948,5405,8254,4203,5612,9822,565

Wave period [s]

RA

O X

[m

/m]

Figure 30: “Response amplitude operator in heave”

Figure 30 shows how heave excitation is importat for periods grater than 6 seconds.

Natural period of waves can have also that value therefore excitation on heave can be

expected.

Pitch

0,00

0,05

0,10

0,15

0,20

0,25

125,66415,9948,5405,8254,4203,5612,9822,565

Period [s]R

AO

RY

[ra

d/m

]

Figure 31: “Response amplitude operator in pitch”

Pitch excitation for pitch is clearly situated between 22,5 and 30 seconds with the

maximum value in 29 seconds. That period is on the upper limit of natural waves

periods and excitation can appear specially during storms.

Summary:

Periods of excitation change widely for the different degrees of freedom analysed

meaning that the structure could not be stablile for diferent periods, mostly of them in

the natural waves period. Therefore specific solutions for each case should be

developed.

annex1 dynamic analysis results

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