wave run-up on monopiles. an engineering model
TRANSCRIPT
© Det Norske Veritas AS. All rights reserved Slide 318 April 2023
Numerical & Physical Models
Numerical simulation using DHI refined flow code, NS3, of wave run-up on a circular wind turbine, with a scour protection(copy from Offshore Center Denmark Annual report)
DHI Wave Run-up Test (EOW(2007)
© Det Norske Veritas AS. All rights reserved Slide 418 April 2023
Run-Up Formula by De Vos et al 2007
Based on experiments carried out at AUC DE Vos et all have made a run-up formula for
irregular waves: The 2% highest run-up can be determined as
For monopile fundations: m=2.72
For cone fundations: m=4.45
Crest velocity and crest elevation from second wave order theorya) H2% b) The Peak Period Tpc) The Water Depth
%2max,
2%2
%2 2
g
umRu
© Det Norske Veritas AS. All rights reserved Slide 518 April 2023
Run-Up Tests by De Vos et al. 2007
Water depth=0.35m-0.5m
pile diameter=0.12m
Bed Slope in front of pile 1:100
Non-dimensional Properties
Water depth to pile diameter ratio (h/D = 3 and 4).
Significant Wave height to water depth ratio (Hs / h =0.23-0.39).
Wave steepness (s0p = 0.018 - 0.06)
Both regular and irregular tests.
© Det Norske Veritas AS. All rights reserved Slide 618 April 2023
AUC Model Tests 2006(completed after De Vos et al. 2007 tests)
AUC, Horns Rev II, 2-D Model TestsWave Run-Up on Pile. 2006 (Downloaded from the internet from AUC homepage)
Water depth=0.2m 0.3m and 0.4m
Pile diameter=0.1m
Bed Slope in front of pile 1:100
Water depth to pile diameter ratio (h/D = 2,3 and 4).
Wave height to water depth ratio (Hs / h = 0.35, 0.40, 0.43 and 0.46).
Deep water wave steepness (s0p = 0.02 and 0.035)
© Det Norske Veritas AS. All rights reserved Slide 718 April 2023
Results of experiments: AUC Model Tests 2006
Max Run-Up
2% Run-Up
© Det Norske Veritas AS. All rights reserved Slide 818 April 2023
Effect of wave Steepness, AUC Model Tests 2006
AUC, Horns Rev II, 2-D Model TestsWave Run-Up on Pile. 2006(Downloaded from the internet)
%2max,
2%2
%2 2
g
umRu
© Det Norske Veritas AS. All rights reserved Slide 918 April 2023
Results of experiments: AUC Model Tests 2006
Wave slope= 0.02: m=4
Wave slope=0.035: m=3
Crest velocity and crest elevation and are calculated
by stream function waves theory based on
a) H2%
b) the Peak Period Tp and
c) the Water Depth
g
umRu
2
2%2
%2max,%2
© Det Norske Veritas AS. All rights reserved Slide 1018 April 2023
Measurements carried out at DHI. With Focussing waves. (copy from EOW 2007)
D=0.164 m
Water depth =0.4 m.
© Det Norske Veritas AS. All rights reserved Slide 1118 April 2023
Run-up height versus distance from foundation to the focus point. (copy from EOW 2007)
Wave Dir
© Det Norske Veritas AS. All rights reserved Slide 1218 April 2023
Motivation for Re-analyze
The m factor used in De Vos et al. Formula is based on Second Order wave theory, not valid for High waves.
The 2% highest run-up is calculated from 2% highest wave. (The run-up heights should be the extreme as they are used for ULS design of secondary structures)
The run-up heights are highly influenced by possible Wave-Breaking (conclusions made from the DHI model tests and Numerical Simulations )
The crest velocity for breaking waves are equal to the wave celerity
© Det Norske Veritas AS. All rights reserved Slide 1318 April 2023
New Run-Up model
The maximum run-up for breaking waves is here assumed to be described as
Stream function wave inputHmax
Peak Period Tp
Water Depth
)2
(2
max g
cRu crest
C
Breaking Waves: Crest velocity =Phase velocity C
© Det Norske Veritas AS. All rights reserved Slide 1418 April 2023
Theory Vs AUC Measurements
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
0 0.1 0.2 0.3 0.4 0.5Run-Up(m) Measurements
Ru
n-U
p(m
) T
heo
ry
Line of perfect agreementh/D=2h/D=3h/D=4+-20%
© Det Norske Veritas AS. All rights reserved Slide 1518 April 2023
Summary
A conservative estimate for maximum run-up on monopiles for breaking waves is suggested
Stream function waves theory input
Hmax
Peak Period Tp
Water Depth
Current can be included
)2
(*2.12
max g
cRu crest