phd student, uis - norcowe · 2014-09-25 · introduction •conventional methods, such as a...

Breaking Wave Impact Forces on an Offshore Structure

Sung-Jin ChoiPhD student, UiS

PhD thesis Defense, UiS, 21st August 2014

Advisor, UiS: Prof. Ove T. Gudmestad

Contents

1 Introduction

2 Validation of 3D numerical analysis model

3 The effect of dynamic amplification on breaking wave impact

4 Dynamic behavior of OWT structures under breaking waves

and wind forces

5 Conclusions

Introduction

• Until now, many offshore structures, consisting of vertical and inclined members, have been developed.

The stability of such structures is dependent upon the wave forces acting on them.

• In the case where an offshore structure is installed in a shallow-water region, the nonlinear waves

can give rise to higher local pressures and impulsive forces on the structure.

1 / 46

Fig. 1 Breaking wave impact forces on an offshore structure (copyright www.flyingfocus.nl)

Introduction

• Conventional methods, such as a combination of a wave model and a structural model, have mainly

been used for estimating the breaking wave impact forces.

• Such methods have several problems with respect to accurate estimation of the wave forces.

• Most of wave analysis models are based on the shallow water equations.

• Even though the wave models can simulate the undisturbed wave kinematics at the structural

position, they are unlikely to be sufficient for simulating nonlinear interactions between waves

and the structure.

Stokes

Wave

theory

Deep water

Shallow water

HHWL

Fig. 2 Wave theories used in deep water and shallow water

Boussinesq

Equation

Problems

Problem 1

/ 0.5d L / 0.05d L

2 / 46

Introduction Problems

• Most of structural analysis models use Morison equation.

• Drag and inertia coefficients involve uncertainties in their applications (different experimental studies).

• Estimated coefficients show differences depending on the wave theories used in the experiments.

• If the foundation shape is complex, the coefficients have to be estimated for each member on

the basis of additional experimental studies instead of the use of data from technical reports.

Fig. 4 Drag coefficients depend on structural shapes

(DnV-RP-C205, 2010)

Problem 2

Fig. 3 Experimentally determined values of Cd

(CERC, 1984)

3 / 46

• Most of structural analysis models use the slamming equation.

Problems

T M D IF F F F (1)

2

I b s bF R C C

Morison Slamming

(2)

Where, is the water density, is the radius of the pile, is the wave celerity at breaking point, is the slamming coefficient,

is the curling factor, and is the maximum surface elevation at the breaking point.

R bCsC

b

Fig. 5 Time variation for typical breaking wave forces calculated by eqn.1

t (sec)

Wave f

orc

e (

N)

= ?

= ?sC

= ?

• Slamming coefficient ( ), impact duration ( ), and curling factor ( ) need to be determined

in advance on the basis of values presented in technical reports or additional experiments.

sC

Problem 3

Introduction

4 / 46

• A number of theoretical and experimental studies have been performed to establish appropriate values

of the slamming coefficient ( ) and the curling factor ( ).

• Empirical coefficients obtained in the previous experiments show a considerable degree of scatter.

(ranged from 3.14 to 6.28).

Problems

Table 1 Comparison of the breaking wave factors estimated by different studies

2

b

R

C

1

2 b

R

C

13

32 b

R

C

sC

Where, is the radius and is the wave celerity at breaking pointR bC

von Karman

(1929)

Wagner

(1932)

Goda et al.

(1966)

Tanimoto

(1986)

Wienke and

Oumeraci

(2005)

- -

- -0.3~0.4 (1/10)

0.07~0.1(1/100)0.5 0.46

2

sC

Introduction

5 / 46

• Interestingly, there is a great variation in the maximum breaking wave forces from impact to impact,

even when all waves are nominally identical.

• Even if one of the suggested coefficients is taken, the use of the coefficient would be significantly

restricted because the coefficients are experimentally determined under the influence of various

external parameters.

Problems

Fig. 6 Breaking wave forces measured in the total time series (H = 1.3 m and T = 4 sec)

0.0 40.0 80.0 120.0 160.0

t (sec)

-10000.0

0.0

10000.0

20000.0

30000.0

F (

N)

-10000.0

0.0

10000.0

20000.0

30000.0

Introduction

6 / 46

• To sum up, it is not possible to accurately estimate breaking wave impact forces on an offshore

structure using the combined model.

Research questions

1. Are there 3D numerical models which can predict well breaking wave impact forces without the

use of empirical coefficients and additional wave analysis models?

2. Why did the slamming coefficients obtained in previous experiments show a considerable degree of

scatter?

3. Why did the maximum values of the breaking wave forces measured in the total time series show a

great variation from impact to impact, even when all waves were nominally identical?

Research questions

Introduction

7 / 46

Literature review (Q1)

Fig. 7 A model structure (inclined pile) installed in Numerical Wave Tank (NWT)

• A Navier-Stokes solver can simulate nonlinear characteristics of the waves occurring in the vicinity of

a structure and can as well calculate the wave forces by direct integration of the pressure distribution

over the wetted surface of the pile.

• There is thus no need to use an empirical formula and an additional wave analysis model for

calculating the breaking wave impact forces on the structure.

Introduction

8 / 46

• Bottom geometry and breaking wave shapes (when the breaking waves act on the structure)

- Peregrine et al. (2004) : magnitude of maximum breaking wave impact can be dramatically changed with a slight

variation of the incident wave height and the bottom geometry.

• Little information is currently available in the literature on the effect of the dynamic

amplification due to the structural vibration caused by the breaking wave impact.

• Effect of the entrained air bubbles in the breaker (large amounts of air bubbles change rise-time).

- Hattori et al. (1994) : the highest impact is induced when the smallest air bubbles are entrained in the breaker.

• Dynamic amplification of the structure (large dynamic response)

- Tanimoto et al. (1986) : measured data in the force transducers show a larger response at the beginning of

the impact, and subsequent oscillations due to the structure’s vibration in its natural frequency.

Literature review (Q2 and Q3)Introduction

9 / 46

Objectives

The objectives of this study is to

• Study the effect of dynamic amplification due to the structural vibration caused by the breaking

wave impact.

• Develop a 3D numerical model which can predict well the breaking wave impact forces on vertical

and inclined piles without the use of the empirical coefficients and an additional wave model.

• Gain a better understanding of the breaking wave induced vibrations.

Introduction

10 / 46

Research approach

Fig. 8 Overall research approach used in this study

Introduction

11 / 46

Verification

Sloping bottom case

(Experimental data by DHI (2008))

Choi, S.J., Lee, K.H., Hong, K., Shin, S.H. & Gudmestad, O.T., Nonlinear wave forces on an offshore wind turbine

foundation in shallow waters. International Journal of Ocean System Engineering, 3 (2), pp. 68-76, 2013.

The 3D Navier-Stokes solver was firstly validated by using the results of several hydraulic model tests.

12 / 46

• NWT dimension : 14.0 m (L), 0.45 m (W), and 1.2 m (H)

• Wave height : 0.14 m, wave period : 1.57 sec (Stokes 1st)

• Water depths : 0.53 m (offshore), 0.17 m (shallow)

• Bottom slope : 1 / 25.

• Diameter of cylindrical pile : 0.075 m (located over the sloping bottom)

H = 1.2 m

(b) Plane view of Numerical Wave Tank (NWT)

(a) Cross section of Numerical Wave Tank (NWT)

W = 0.45 m

Y

X

Open boundary

Wave generator

X

Z

Added dissipation zone D=0.075 m

14.0 m

Cylinder

2L

Wave

d1=0.53 m

slope = 1 / 25

d2=0.17 m

4.0 m9.0 m1.0 m

2L7.75 m 6.25 m

Fig. 9 Cross section (a) and plane view (b) of the Numerical Wave Tank (not to scale).

Model description, DHI experimentsVerification

13 / 46

Y

X

Slope zone

WG1 WG2WG3

VG1WG4

0.0 0.5 1.0 1.5 2.0 2.5 3.0

t / T

-0.8

-0.4

0.0

0.4

0.8

1.2

/ H

i

EXP.

CAL.

0.0 0.5 1.0 1.5 2.0 2.5 3.0

t / T

-0.8

-0.4

0.0

0.4

0.8

1.2

/ H

i

EXP.

CAL.

• As the waves move over the sloping bottom, the wave profiles are transformed into typical shallow

water waves such that the wave crests are steeper and narrower with increased wave heights and the

wave troughs are longer and flatter.

• At locations WG 2 and 3, the slight ripples in the wave trough are reproduced fairly well in the

numerical results, even though a slight phase discrepancy is observed.

Fig. 10 Comparison of free-surface elevations between experimental data and the numerical results

at WG 2 and 3.

Sloping bottom - Free surface elevation

WG 3WG 2

Verification

14 / 46

Y

X

Slope zone

WG1 WG2WG3

VG1WG4

0.0 0.5 1.0 1.5 2.0 2.5 3.0

t / T

-0.4

-0.2

0.0

0.2

0.4

0.6

u / (

gH

i)1/2

EXP.

CAL.

0.0 0.5 1.0 1.5 2.0 2.5 3.0

t / T

-0.4

-0.2

0.0

0.2

0.4

0.6

w / (

gH

i)1/2

EXP.

CAL.

•The calculated velocities agreed well with the measured velocities.

• Several characteristic ripples are estimated fairly well in the computed velocities.

• For the vertical water particle velocities, the calculated results at both the crest and trough are slightly

(6 to 7 %) overestimated compared with the experimental data.

Fig. 11 Comparison of the time variations for horizontal and vertical water particle velocities (VG1) between

experimental data and numerical results

Sloping bottom - Velocities

VG 1_Vertical velocityVG 1_Horizontal velocity

Verification

15 / 46

• The computed nonlinear wave forces are obtained by integrating the dynamic pressures on the

wetted surface of the cylindrical pile.

• The measured wave forces are obtained by a 3D forces gauge located underneath the cylindrical pile.

• Calculated wave forces are quite similar to the measured wave forces, even though there is a

slight discrepancy at the troughs of the wave forces.

Fig. 12 Comparison of the time variations for inline wave forces on the cylindrical pile between

experimental data and numerical results

Sloping bottom – Wave forces

0.0 0.5 1.0 1.5 2.0 2.5 3.0

t / T

-1.0

-0.5

0.0

0.5

1.0

1.5F

x / g

HiD

2 EXP.

CAL.

Verification

16 / 46

• The cylinder and the sloping bottom are embodied by the new application based on the cut-cell method.

• The free surface elevation is simulated relatively well in the vicinity of the structure.

Fig. 13 Snapshots of the spatiotemporal variations of the instantaneous water levels (time =12.15 s, 12.35 s,

12.55 s, and 12.75 s)

Sloping bottom, free surface elevationVerification

17 / 46

Breaking wave impact


(Experimental data by TU Braunschweig (2002))

Choi, S.J., Lee, K.H. & Gudmestad, O.T., The effect of dynamic amplification due to a structure’s vibration on

breaking wave impact. In review: Ocean Engineering Journal.

The validated numerical model was used for predicting the breaking wave impact forces on a vertical

and on inclined piles installed in a shallow water region.

18 / 46

• NWT dimension : 54.0 m (L), 5.0 m (W), and 11.4 m (H)

• Wave height : 1.3-1.4 m , wave period : 4.0 sec (Steam function theory)

• Water depths : 3.8-3.92 m (offshore), 1.5-1.62 m (shallow)

• Bottom slope : 1 / 10. (weekly plunging breaker (Surf similarity parameter : 0.42-0.44))

• Diameter of cylindrical pile : 0.7 m (located at the edge of the slope)

• Inclination of cylinder : -22.5 degree, 0 degree, and +45 degree

Fig. 14 Cross section (a) and plane view (b) of the Numerical Wave Tank (not to scale).

Model description, TU Braunschweig

H = 11.4 m

(b) Plane view of Numerical Wave Tank (NWT)


W = 5.0 m

Y

X

Open boundary

Wave generator

X

Z

Added dissipation zone D=0.7 m

54.0 m

0 Degree

2L

Wave

d1=3.8 ~ 3.92 m

slope = 1 / 10

d2=1.5 ~ 1.62 m

16.0 m23.0 m15.0 m

2L38.0 m 16.0 m

WG 11

+45.0 Degree

- 22.5 Degree


19 / 46

• A reasonable agreement between the measured and the calculated free surface elevations is observed.

• To some details, the slight ripples in the wave trough are reproduced fairly well in the numerical

results.

Fig. 15 Comparison of free surface elevations between experimental data and the CFD results at WG

11 for Vertical pile (a) : Vertical pile, b): Inclined pile

Free surface elevation

Locations of wave gauge

y

x

WG 11

26.0 28.0 30.0 32.0 34.0 36.0 38.0

t (sec)

-0.8

-0.4

0.0

0.4

0.8

1.2

1.6

m

EXP.

CAL.


26.0 28.0 30.0 32.0 34.0 36.0 38.0

t (sec)

-0.8

-0.4

0.0

0.4

0.8

1.2

1.6

m

EXP.

CAL.

a) Vertical pile (0 dgree)

b) Inclined pile (-22.5 degree)

20 / 46

• On the whole, the breaking wave process was simulated reasonably well in front of the vertical cylinder.

• It is observed that the wave front was approximately parallel to the vertical cylinder.

Fig. 16 Snapshots of the spatiotemporal variations of an instantaneous water level for the vertical pile

(time = 31.06 sec, 31.26 sec, 31.47 sec, 31.67 sec, 31.87 sec, and 32.07 sec)

Free surface elevation (vertical)Breaking wave impact

21 / 46

• Breaking wave process is reproduced reasonably well in the vicinity of the inclined cylinder.

Fig. 17 Snapshots of the spatiotemporal variations of an instantaneous water level for the inclined pile

(-22.5 degree) : (time =30.63 sec, 30.83 sec, 31.03 sec, 31.23 sec, 31.43 sec, and 31.63 sec)

Free surface elevation (Inclined piles)Breaking wave impact

22 / 46

animation/NWT_Enlarge_10.avi

animation/NWT_Enlarge_10.avi

• A grid refinement test was performed in order to check the sensitivity of the grid spacing.

• Three grid sizes are tested to check the convergence of the results from the NWT, which are

a coarse grid, a medium grid, and a fine grid.

Grid refinement test

Table. 2 Grid sizes

Table. 3 Computational conditions

Coarse Medium Fine

Number of grid 1,338,444 3,212,900 3,815,238

Run time 40 sec 40 sec 40 sec

Time increment Automatically adjust Automatically adjust Automatically adjust

Total

Computational time2 days 8 days 10 days


Coarse Medium Fine

Nearby cylindrical pile 0.1 m x 0.1 m x 0.1 m 0.06 m x 0.05 m x 0.08 m 0.05 m x 0.04 m x 0.05 m

At wave generator 0.2 m x 0.2 m x 0.4 m 0.2 m x 0.2 m x 0.2 m 0.2 m x 0.2 m x 0.2 m

23 / 46

• The mean values of the measured pressures are used for making a comparison with the CFD results.

• The peak values calculated using the fine grid show a good agreement with measured peak values.

• Even though slight deviations can be observed between the fine grid and the medium grid results,

there are good overall agreement.

Fig. 18 Comparison of dynamic pressures using the coarse grid, the medium grid, and the fine grid, and

the measured dynamic pressures at P5 and P7 for vertical pile

Dynamic pressures (vertical)

Cylinder zone

d2=1.5 m

P 7 = 4.632 m

P 6 = 4.432 m

P 5 = 4.232 m

Locations of pressure gauges

y

x

z

xEL. = 2.3 m

EL. = 3.8 m 31.05 31.10 31.15 31.20 31.25 31.30 31.35

t (sec)

-20000.0

0.0

20000.0

40000.0

60000.0

80000.0

P (

N/m

2)

EXP.

CAL. (Fine)

CAL. (Medium)

CAL. (Coarse)

31.05 31.10 31.15 31.20 31.25 31.30 31.35

t (sec)

-20000.0

0.0

20000.0

40000.0

60000.0

80000.0

P (

N/m

2)

EXP.

CAL. (Fine)

CAL. (Medium)

CAL. (Coarse)


24 / 46

• Calculated dynamic pressures agree very well with the measured pressures.

• Computed rise-time is somewhat delayed compared with the measured rise-time.

• Because the CFD model is based on incompressible momentum equations and because the cylinders

are modeled as rigid objects in the NWT, the rise-time could not be correctly calculated.

Fig. 19 Comparison of the calculated dynamic pressures and the measured dynamic pressures at P6

for Inclined pile

Dynamic pressures (Inclined)

30.75 30.80 30.85 30.90 30.95 31.00 31.05 31.10

t (sec)

-20000.0

0.0

20000.0

40000.0

60000.0

80000.0

P (

N/m

2)

EXP.

CAL.

Cylinder zone

d2=1.52 m

P 6 = 4.432 m

Locations of pressure gauges

y

x

z

xEL. = 2.3 m

EL. = 3.82 m


25 / 46

Fig. 20 Comparison of breaking wave force measurement methods

Breaking wave force

(a) CFD (b) Experiment

Rigid object Moving object

• Vertical and inclined piles are modeled as rigid objects in the CFD model.

• In the experiment, the piles are installed as moving objects, which can induce dynamic amplification

due to the structures’ vibration.

• It is not possible to make a direct comparison between CFD results and experimental data because

the effects of the motions of the structures must be analyzed.

X


26 / 46

Fig. 21 Force separation procedure

Force separation procedure

Unfiltered breaking wave force

(EXP.)

Filtered breaking wave force

(Cut-off : 14 - 20 Hz)

Low pass filter

Net breaking wave force

(i.e., The effect of dynamic amplification

due to structure’s vibration is removed)

Breaking wave force

by CFD Comparison

EMD

• In order to make quantitative comparison between CFD and EXP., a force separation procedure is used.

• A Low pass filter and EMD (Empirical Mode Decomposition) are used for completely removing the effect

of the dynamic amplification in Experimental data.


27 / 46

Fig. 22 Comparison of unfiltered breaking wave forces (EXP.) and calculated breaking wave forces

CFD VS Unfiltered EXP.

• Calculated breaking wave forces are greatly underestimated compared with the unfiltered breaking

wave forces (EXP.).

• Unlike the CFD results, unfiltered breaking wave forces show large response at the beginning of the

impact, and subsequent oscillations in its natural frequency.

30.4 30.6 30.8 31.0 31.2 31.4 31.6 31.8 32.0

t (sec)

-5000.0

0.0

5000.0

10000.0

15000.0

20000.0

25000.0

F (

N)

Force by CFD

Unfiltered force (EXP.)

30.4 30.6 30.8 31.0 31.2 31.4 31.6 31.8 32.0

t (sec)

-5000.0

0.0

5000.0

10000.0

15000.0

20000.0

25000.0

F (

N)

Force by CFD

Unfiltered force (EXP.)

(b) Case 2 (Inclined pile : -22.5 degree)

(a) Case 1 (Vertical pile : 0 degree)


28 / 46

Natural frequency of structure

peak

• Unfiltered experimental data are converted into frequency domain, and a peak that corresponds to

the natural frequency of the structure ( 17.8 Hz and 20.0 Hz) is observed.

• This implied that the measured results contained a considerable amount of energy induced by the

structure’s response.

Fig. 23 Comparison of the unfiltered forces and the forces cut-off by a FFT low pass filter in frequency

domain (EXP.)

0.0 5.0 10.0 15.0 20.0 25.0

f (Hz)

0.0

200.0

400.0

600.0

800.0

1000.0

S (

f)_N

2-

sec

Unfiltered force

Filtered force_Cut-off : 20 Hz

0.0 5.0 10.0 15.0 20.0 25.0

f (Hz)

0.0

200.0

400.0

600.0

800.0

1000.0

1200.0

S (

f)_N

2-

sec

Unfiltered force

Filtered force_Cut-off : 17.8 Hz




29 / 46

CFD VS filtered EXP. (by low pass filter)

• A FFT low pass filter is used (Cut-off frequency : 20 Hz and 17.8 Hz) in order to remove the effect of

dynamic amplification in the experimental data.

• However, in sprite of the use of the FFT low pass filter, residual responses still exist in the filtered

breaking wave forces.

Fig. 24 Comparison of the forces filtered by a FFT low pass filter (EXP.) and the forces computed by the CFD

model

Residual response

30.4 30.6 30.8 31.0 31.2 31.4 31.6 31.8 32.0

t (sec)

-5000.0

0.0

5000.0

10000.0

15000.0

20000.0

F (

N)

Force by CFD

Filtered force (EXP.)

30.4 30.6 30.8 31.0 31.2 31.4 31.6 31.8 32.0

t (sec)

-5000.0

0.0

5000.0

10000.0

15000.0

20000.0

F (

N)

Force by CFD

Filtered force (EXP.)

(b) Case 2 (inclined pile : -22.5 degree)



30 / 46

Fig. 25 Net breaking wave force calculated by low pass filter and EMD.

EMD (Empirical mode decomposition)

• EMD (Empirical mode decomposition) is used in order to completely remove the residual responses

in the filtered breaking wave force.

- Step 1 : The local extremes on the filtered wave force (gray line) are extracted.

- Step 2 : The upper envelop (black line) and lower envelop (blue line) are made by connecting

the extracted local extremes.

- Step 3 : The mean (red dash line) is calculated based on the two envelops.

• High frequency oscillation in the measured wave force is completely removed by the use of the

low pass filter and the EMD.

30.4 30.6 30.8 31.0 31.2 31.4 31.6 31.8 32.0

t (sec)

-5000.0

0.0

5000.0

10000.0

15000.0

20000.0

F (

N)

Upper_envelope

Lower_envelope

Filtered Force(EXP.)_Cut-off : 17.8 Hz

Filtered Force (EXP.)+EMD


31 / 46

Fig. 26 Comparison of the CFD results and the breaking wave impact forces filtered by the FFT low pass

filter and EMD (EXP.) for inclined pile

30.4 30.6 30.8 31.0 31.2 31.4 31.6 31.8 32.0

t (sec)

-5000.0

0.0

5000.0

10000.0

15000.0

20000.0

F (

N)

Force by CFD

Filtered force (EXP.)+EMD


• CFD results show reasonable agreement with the filtered experimental data.

• Calculated peak is rather overestimated compared with the filtered peak, and the computed rise-times

are rather delayed compared with the filtered rise-times.

• Measured values have a finite rise-time, during the breaking wave forces increase from zero to a peak.

• Several factors, such as entrained air bubbles in the water, compressibility of water, inclination,

roughness, and motion of cylinder, would account for the finite rise-time.

• Due to the incompressibility assumption, the computed rise-times are rather delayed, and a changed

rise-time can result in a variation in the magnitudes of the breaking wave impact.

(CFD VS filtered EXP. (by low pass filter and EMD, Final results)Breaking wave impact

32 / 46

(CFD VS filtered EXP. (by low pass filter and EMD, Final results)

• Calculated wave forces on fall-time are somewhat overestimated compared with the filtered breaking

wave forces (EXP.).

• A large amount of air bubbles can decrease the effective density of the water and the corresponding

velocity of sound in the water, and these can lead to reduced wave forces during the fall-times.

• The discrepancy could be improved by using a 3D numerical model for compressible flow.

• Despite these discrepancies, the overall results show a reasonable agreement with the filtered data.

Fig. 27 Comparison of the CFD results and the breaking wave impact forces filtered by the FFT low pass

filter and EMD (EXP.) for the vertical pile

30.4 30.6 30.8 31.0 31.2 31.4 31.6 31.8 32.0

t (sec)

-5000.0

0.0

5000.0

10000.0

15000.0

20000.0

F (

N)

Force by CFD

Filtered force (EXP.)+EMD



33 / 46

Separated force time series

• In this part, we look at the two components of the measured force time history.

Fig. 28 Measured breaking wave force and separated force time series


30.4 30.6 30.8 31.0 31.2 31.4 31.6 31.8 32.0

t (sec)

-5000.0

0.0

5000.0

10000.0

15000.0

20000.0

25000.0

F (

N)

30.4 30.6 30.8 31.0 31.2 31.4 31.6 31.8 32.0

t (sec)

-5000.0

0.0

5000.0

10000.0

15000.0

F (

N)

30.4 30.6 30.8 31.0 31.2 31.4 31.6 31.8 32.0

t (sec)

-10000.0

-5000.0

0.0

5000.0

10000.0

F (

N)


Measured breaking wave force

Low Pass filter

+ EMD

Amplified force component due to the structure’s vibration

34 / 46

Separated force time series, explanation

• Large structural responses take place if the breaking wave impact force duration is close to the

natural frequency of the structure.

• Unlike the unfiltered data, each peak value of the filtered breaking wave forces have almost the same

magnitude in the total time series for all cases.

• The amplified force component can give rise to a significant variation in the magnitude of breaking

wave impact if the breaking wave impact duration is close to the natural frequency of the structure.

• In the case that the slamming coefficients are estimated using experimental data, the amplified force

component must be removed in the experimental data.

Fig. 28 Measured breaking wave force and separated force time series

30.4 30.6 30.8 31.0 31.2 31.4 31.6 31.8 32.0

t (sec)

-5000.0

0.0

5000.0

10000.0

15000.0

20000.0

25000.0

F (

N)

30.4 30.6 30.8 31.0 31.2 31.4 31.6 31.8 32.0

t (sec)

-5000.0

0.0

5000.0

10000.0

15000.0

F (

N)

30.4 30.6 30.8 31.0 31.2 31.4 31.6 31.8 32.0

t (sec)

-10000.0

-5000.0

0.0

5000.0

10000.0

F (

N)

Amplified force component due to the structure’s vibration


Measured breaking wave force

Low Pass filter

+ EMD


35 / 46

Fig. 29 Verification procedure

Unfiltered breaking

wave force (EXP.)

Breaking wave Force

by CFD

Comparison

Duhamel integral

Dynamic breaking

wave force

Verification

• A Duhamel integral is used to reproduce the dynamic breaking wave forces based on the breaking wave

forces calculated by the CFD model.

• Reproduced dynamic breaking wave forces are compared with unfiltered breaking wave forces (EXP.) .


36 / 46

Duhamel integral

• The Duhamel integral can be used to evaluate the response of a damped SDOF system to any form

of dynamic loading ( ).

• Total response ( ) can be obtained by the integration of all the differential responses

developed during the loading history, See eqn. 3.

( )

0

( ) ( ) sin ( )

t

t

dyn d

d

kF t p e t d

m

(3)

: Stiffness

: Breaking wave impact applied for an extremely short time

: Damped natural frequency of the system

: Damping coefficient

( )p

( )dynF t

k

( )p

d

( )


37 / 46

Fig. 30 Comparison of dynamic breaking wave force (CFD) reproduced by using Duhamel integral and

unfiltered breaking wave force (EXP.) in the time domain for the vertical pile

• Diameter, thickness, and length : 0.7 m, 0.01 m, 5.0 m, respectively

• Natural frequency : 20 Hz (125.66 rad/s)

• Mass : 1442 kg

• Stiffness : 2.24 E+07 N/m

• Damping coefficient : 0.05

• The reproduced total forces including the amplified force component agree reasonably well with the

unfiltered experimental data, even though there is a small gap at the crest and trough of the forces.

Wave direction

Verification_Vertical pile

30.9 31.0 31.1 31.2 31.3 31.4 31.5

t (sec)

0.0

5000.0

10000.0

15000.0

20000.0

25000.0

F (

N)

Reproduced_force (CFD)

Unfiltered_force (EXP.)


38 / 46


unfiltered breaking wave force (EXP.) in the frequency domain for the vertical pile


• Natural frequency : 20 Hz (125.66 rad/s)

• Mass : 1442 kg



• The maximum energy calculated in the numerical model is somewhat overestimated compared with

the unfiltered experimental data because of the overestimated wave forces on the fall-time.

Wave direction

Verification_Vertical pile

0.0 5.0 10.0 15.0 20.0 25.0

f (Hz)

0.0

200.0

400.0

600.0

800.0

1000.0

1200.0

1400.0

S (

f)_N

2-

sec




39 / 46

1.7 1.8 1.9 2.0 2.1 2.2 2.3

t (sec)

-5000.0

0.0

5000.0

10000.0

15000.0

20000.0

25000.0

F (

N)




unfiltered breaking wave force (EXP.) in the time domain for the inclined pile (-22.5 degree)

Wave direction

• An very good agreement between the reproduced dynamic breaking wave forces and the unfiltered

breaking wave forces (EXP.) is observed.

Inclined pile (-22.5 deg)


• Natural frequency : 17.8 Hz (111.84 rad/s)

• Mass : 1528 kg




40 / 46


• Natural frequency : 17.8 Hz (111.84 rad/s)

• Mass : 1528 kg




unfiltered breaking wave force (EXP.) in the frequency domain for the inclined pile (-22.5 degree)

Wave direction

• Due to the delay of the rise-time, the peak value of energy calculated in the frequency domain is

underestimated compared with the unfiltered experimental data.

Inclined pile (-22.5 deg)

0.0 5.0 10.0 15.0 20.0 25.0

f (Hz)

0.0

200.0

400.0

600.0

800.0

1000.0

1200.0

1400.0

S (

f)_N

2-

sec




41 / 46

Breaking wave induced vibration

Breaking wave induced vibration

Choi, S.J. & Sarkar, A., Dynamic characteristics of an offshore wind turbine with breaking wave and wind load.

International Journal of Computational Methods and Experimental Measurements, 2 (3), pp. 280-297, 2014.

(CFD model + HAWC2)

In order to gain a better understanding of the breaking wave induced vibrations, the general dynamic

behavior of an OWT structure under the actions of breaking wave forces and wind forces was studied.

42 / 46

Model descriptionBreaking wave induced vibration

• In the hydrodynamic part of this paper, breaking wave impact forces on an OWT structure (6.0 m

diameter mono-pile) are calculated, and the computed results are applied on the OWT structure

modeled in a structural analysis model.

H = 91.2 m


Wave generator

X

Z

432.0 m

Mono-pile (6.0 m)

Wave (H=10.4 m, T=11.3 sec)

d1=30.4 m

slope = 1 / 10

d2=12.0 m

128.0 m184.0 m120.0 m

Table 4 Major properties of the OWT structure

Fig. 34 Bottom geometry and mono-pile structure used in the study

• In the structural part of this paper, HAWC2 is employed to predict the dynamic responses induced by

the breaking wave forces and wind forces (Contribution from Dr. Sarkar).

43 / 46

Higher harmonicsBreaking wave induced vibration

• When the total breaking wave force time series is converted into frequency domain, it show the

presence of higher harmonics.

• The first three higher harmonics not only exist in the vicinity of the structure’s natural frequency,

but also contain a significant amount of energy.

• If the three higher harmonics are close to the natural frequency of the structure, these would cause

a large structural response.

0.0 20.0 40.0 60.0 80.0 100.0 120.0

t (sec)

-2000.0

0.0

2000.0

4000.0

6000.0

8000.0

10000.0

F (

kN

)Total breaking wave force

0.0 0.2 0.4 0.6 0.8 1.0

f (Hz)

0.0

100.0

200.0

300.0

400.0

500.0

600.0

Am

plitu

de (

kN

) Total breaking wave force

Higher harmonics

Fig. 35 Total breaking wave force on 6.0m diameter mono-pile ((a) time domain and (b) frequency domain)

(a) Time domain

(b) Frequency domain

44 / 46

Foundation flexibility

Aerodynamic dampingBreaking wave induced vibration

• The response of the mono-pile installed on a flexible foundation is larger than the response of the

structure installed on a fixed foundation because the foundation flexibility allows some rotation

of the tower at the seabed level.

• The effect of the aerodynamic damping on the structure’s response was found to be negligible.

Fig. 37 Nacelle acceleration with aerodynamic damping

132.0 134.0 136.0 138.0 140.0 142.0 144.0

t (sec)

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

Na

ce

lle

ac

ce

lera

tio

n

(m/s

2)

Flexible foundation

Fixed foundation at 2 x dia.

Fixed foundation at mudline

132.0 134.0 136.0 138.0 140.0 142.0 144.0

t (sec)

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

Na

ce

lle

ac

ce

lera

tio

n

(m/s

2)

Flexible foundation

Fixed foundation at 2 x dia.

Fixed foundation at mudline

Fig. 36 Nacelle acceleration without aerodynamic damping

45 / 46

1. The CFD results show good agreement with the filtered experimental data, even though the computed

rise-time is somewhat delayed.

2. Unlike the unfiltered data, each peak value of the filtered breaking wave forces had almost the same

magnitude in the total time series for all cases.

3. Breaking wave impact forces measured in the experiments comprise of two force components;

the net breaking wave force and the amplified force component due to the structure’s vibration.

4. The amplified force component can give rise to a significant variation in the magnitude of the breaking

wave impact if the breaking wave impact duration coincides with the natural frequency of the structure.

5. In the case that the slamming coefficient is estimated using experimental data, the amplified force

component must be removed in the experimental data to obtain the accurate slamming coefficient.

6. Higher harmonics in the breaking wave impact forces can cause a large structural response.

7. The foundation flexibility plays an important role in determining the magnitude of the structure’s

response.

8. The proposed 3D numerical model is a useful tool which can predict the breaking wave forces on

offshore structures without the use of an empirical formula and additional wave analysis models.

Conclusion

46 / 46

1. Prof. Ove Tobias Gudmestad (UiS)

2. Prof. Hocine Oumarachi (TU Braunschwieg)

3. Mr. Lisham Bonakdar (TU Braunschwieg)

4. Dr. Henrik Kofored-Hansen (DHI)

5. Prof. Kwang-Ho Lee (Kwandong Univ.)

6. Dr. A. Sarkar (Subsea 7)

Acknowledgements

46 / 46

Thank you

phd student, uis - norcowe · 2014-09-25 · introduction •conventional methods, such as a...

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