Petrini sapienza-may2015

[email protected]

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GERwww.stronger2012.com

Performance-Based Wind

Engineering (PBWE) procedure

Background

ENVIRONMENT

Wind actions

Structural systems

Non environmental

actions

EXCHANGE ZONE

Site-specific Wind

Aerodynamic and aeroelasticphenomena

Wind site basic parameters

Environmental effects (like

waves)

Structural system as modified

by service loads

STRUCTURAL SYSTEM

Vm

Mean wind velocity profile

Vm+ v(t)

Turbulent wind velocity profileriv

er

Vm

Mean wind velocity profile

Vm+ v(t)

Turbulent wind velocity profileriv

erriv

er

ENVIRONMENT EXCHANGE ZONE

Ciampoli M, Petrini F., Augusti G., (2011). “Performance-Based Wind Engineering: towards a general procedure”, Structural Safety, 33 (6), 367-378. DOI: 10.1016/j.strusafe.2011.07.001.

Schematization of uncertainty in Wind Engineering (I)

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Types of uncertainties

ENVIRONMENT

Wind actions

Structural systems

Non environmental

actions

EXCHANGE ZONE

1. Aleatory

2. Epistemic

3. Model

Interaction

parametersStructural parameters

Site-specific Wind

Aerodynamic and aeroelasticphenomena

Wind site basic parameters

Intensity

measure

1. Aleatory

2. Epistemic

3. Model

1. Aleatory

2. Epistemic

3. Model

Environmental effects (like

waves)

Structural system as modified

by service loads

( )IM ( )IP ( )SP

STRUCTURAL SYSTEM

Ciampoli M, Petrini F., Augusti G., (2011). “Performance-Based Wind Engineering: towards a general procedure”, Structural Safety, 33 (6), 367-378. DOI: 10.1016/j.strusafe.2011.07.001.

Schematization of uncertainty in Wind Engineering (II)

( ) ( ) ( ) ( )SPPIMPSP,IMIPPSP,IP,IMP ⋅⋅=

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O

f(IM|O)

f(IM)f(IP|IM,SP)

f(IP)

f(EDP|IM,IP,SP)

G(EDP)

f(DM|EDP)

G(DM)

f(DV|DM)

G(DV)

Hazard analysis

Interaction

analysisStructural analysis Damage analysis Loss analysis

IM: intensity

measure

IP: interaction

parameters

EDP: engineering

demand param.DM: damage

measure

DV: decision

variable

Select

O, DO: location

D: design

Environme

nt info

Decision-

making

D

f(SP|D)

f(SP)

Structural

characterization

SP: structural

system parameters

Structural

system

info

| | | ||||

Ciampoli M., Petrini F., Augusti G., (2011). “Performance-Based Wind Engineering: towards a general

procedure”, Structural Safety, 33 (6), 367-378

= progress with respect to the

Performance-Based Seismic Design

*

* *

Extension of the Performance-Based

Seismic Design procedure proposed by PEER Research

center

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0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 5 10 15 20 25 30 35

P(Av > av*|Vm(zdeck))

Vm(zdeck) [m/s]

Ciampoli M., Petrini F., Augusti G., (2011). “Performance-Based Wind Engineering: towards a general

procedure”, Structural Safety, 33 (6), 367-378

EDP = Av - DM= max (av) [m/s2]

1.0

0.8

0.6

0.4

0.2

0

G(E

DP

)

0 1 2 3

Vento = f(s,t)

Vento = f(s,t)

Vento = f(s,t)

Vento = f(s,t)

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Preliminary studies:

Offshore Wind Turbines

(parked configuration)

University of Notre Dame , South Bend, IN, USAJune 19, 2012 – EMI/PMC Conference

Francesco Petrini, PhD, PE

x,x’

z’

y’

Waves

Current

P

(t)v P

(t)w P

(t)u P

Turbulent

windP

Mean

wind

Vm(zP)

z

yH

h

vw(z’)

Vcur(z’)

d

Terrain

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( ) ( ) ( ) ( )( )nfexpnSnSnS jkuuuuuu kkjjkj−⋅=

( )( ) 2

t0

0

u

2

u u1.75)log(zarctan1.16(n)dnS ⋅+⋅−== ∫∞

5.0

0

uu2

x

u200

300(x)dxRu

1L

⋅== ∫

∞z

x

z

The mean velocity magnitude varies with the height.

Me

an

con

trib

ution

Sto

ch

astic c

on

trib

utio

n

( )( )[ ]5/3

ju

ju2V

uu/z10,302fL1/2

/zfL6,686S

jj +=

( )j

j

zV2

zf = ( )

( )( ) ( )( )kj

2

kj

2

z

jkzVzV2

zzC

f+

−=

Autospectrum

where:

α

=

hub

hubz

zUzU )(

0.14=α

For normal wind condition

( )( )

−

−−

−

−=

2

5.0exp4

5

4

2

4

5exp

2

P

P

f

ff

Pf

ff

gfS

σγ

π

α

where f=2π/T is the frequency, fP=2π/TP is the peak frequency, α is the equilibrium coefficient, g is gravity acceleration, and γ parameters dependent from HS e TP

−=

−

R

yearHTST

FHSR

11

1

1max,,,

Extreme events analysis (Return period TR).

71

,)(

+⋅=

d

zdUzU refc

x

z

d

water mean level

Wind Current and waves

JONSWAP spectrum

Cross-spectrum

!

"#$

%&$

#'"(

)*+ ,

-.

/

0 1 2 3

0 4 5 6

EDP: )()( hgrhr rrm

p σ⋅+=)T(log2

577.0)T(log2g

winde

winder⋅

+⋅=η

η

1°1°1°1°

rp

1°1°1°1°

rp

7 8 9 : ; 9 <

7 8 9 : ; 9 =

7 8 9 : ; 9 7

7 8 9 : > 9 9

7 8 9 : > 9 77 8 : ; 9 ? 7 8 : ; 9 < 7 8 : ; 9 = 7 8 : ; 9 7 7 8 : > 9 9

@ A B C D E F G

HI

JK

LM

JI

JK

IN

OP

QR

ST

UV

WX

Y Z [ \ ] ^ _ [ ` a

b Z [ \ ] ^ _ [ ` a

Basis of the numerical modelingStructural response (EDP) in frequency domain


Peak along- and across- wind displacementsDavenport’s peak factor

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Previous studies: Numerical applicationUncertainties overview


Importance of SPs

as stochastic

parameters

Effects of the

interactions in the

environment

Effects of dominant

aeroelastic phenomena

1°1°1°1°

rp

1°1°1°1°

rp

EDP = peak

displacement at the rotor

[E

DP

]

EDP [m]

[ED

P]

EDP [m]

Comparison of mean annual frequencies [EDP] of

exceeding any value of the EDP:

Previous studies: Relevance of SP uncertainty Risk Including SP Uncertainty (Monte Carlo 5000 samples)

Barbato M., Ciampoli M., Petrini F. (2010). “Effects of Modelling Parameter Uncertainty on the Structural Response of Offshore Wind Turbines”, Proceedings of the 12th biennial ASCE Aerospace Division International Conference (Earth & Space 2010), Honolulu, USA, 14 – 17 March 2010. ISBN 978-0-7844-1096-7.

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Aerodynamic uncertainty characterization

by the meso-scale modeling

(Rotating Configuration)

Physics (1): Mean wind rotational sampling

Murtagh, P.J., Basu, B., Broderick, B.M., 2005. Along-wind response of a wind turbine tower with blade

coupling subjected to rotationally sampled wind loading. Eng. Struct. 27(8), 1209-1219

( ) ( ) ( )12 ddd zFzFF iii S

X

S

X

S

X −=∆

z1

Ω

z2

Ω

Time t2Time t1

Vm(z1)

Vm(z2)

Tributary

area

S

Ω

dFXS

Angular

rotational

velocity

hub

( ) ( ) ( )tFFtF ii

hub

i S

X

S

X

S

X ⋅⋅∆+= cosd2

1d

Additional peak in the wind force spectra

1.E-15

1.E-11

1.E-07

1.E-03

1.E+01

1.E+05

0.00001 0.001 0.1 10

Frequency [Hz]

Forc

e S

pec

tra

SF

XF

X

1

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Physics (2): Turbulent wind rotational samplingVariation of the turbulent force spectra with the blade position

during its rotational motion

The correlation of the turbulent wind field felt by the BE is a function of its rotational motion

t+

t

Halfpenny A. (1988). Dynamic Analysis of Both On and Offshore Wind Turbines in the Frequency Domain. Ph.D. thesis. University College London..

Connell J.R. (1988). “A PRIMER OF TURBULENCE AT THE WIND TURBINE ROTOR”, Solar Energy, 41 (3), 281-293

Auto-correlation CoherenceOrdinary wind spectra

Separation distance (is function of the motion)

R

ΩΩΩΩ

Vm(r)r

Vm(zhub)

u(r,t)

XY

Z

Aerodynamic actions by the BEM theoryWind velocities and reference systems

- Evaluate the relative angle of attack and the relative speed of the wind with respect to specific blade portions (BEs) at different locations

r(1+a’)

Y

X

DL

φφφφ

VmR(r)=

Vm(r)(1-a)W

Rotor

plane

u(r,t)

v(r,t)

’

FX= ½**Vm2 (cLcos+ cDsin)

aerodynamic force

reference system axis

wind velocity

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ENVIRONMENT

Structure

Non environmental solicitations

STRUCTURE

Structural (non-

environmental)

system

Site-specific

environment

Wind site basic

parameters

Other environmental

agents

Waves site basic

parameters

Wind, wave and current actions

Aerodynamic

and Aeroelastic

phenomena

Hydrodynamic

phenomena

1. Aleatoric

2. Epistemic

3. Model


1. Aleatoric

2. Epistemic

3. Model

1. Aleatoric

2. Epistemic

3. Model

Propagation Propagation

Interaction parameters

Structural parametersIntensity Measure

( )IM ( )IP ( )SP

EXCHANGE ZONE

)10(01.0 1 mzVVcurr hourwind =⋅=

Wind generated currents

)164.00291.0221.0(2

110

2

10 +⋅−⋅= VVH s

Correlation data by Zaaijer, 2006, taking into account the Italy Waves Atlas.

ENVIRONMENT

Structure

Non environmental solicitations

STRUCTURE

Structural (non-

environmental) system

Site-specific

environment

Wind site basic

parameters

Other environmental

agents

Waves site basic

parameters

Wind, wave and current actions

Aerodynamic

and Aeroelastic phenomena

Hydrodynamic phenomena

1. Aleatoric

2. Epistemic

3. Model


1. Aleatoric

2. Epistemic

3. Model

1. Aleatoric

2. Epistemic

3. Model

Propagation Propagation

Interaction parameters

Structural parametersIntensity Measure

( )IM ( )IP ( )SP

EXCHANGE ZONE

Uncertainties in Wind-Blade interactions

Vm

a, a’, cD,cL

r(1+a’)

Y

X

DL

φφφφ

VmR(r)=

Vm(r)(1-a)W

Rotor

plane

u(r,t)

v(r,t)

’

FX= ½**Vm2 (cLcos+ cDsin)

ENVIRONMENT

EXCHANGE

STRUCTURE ,

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32

1

M3

R1

Blade-hub

main reactionsX

Y

r

FSX

VmR(r)

u(r,t)

Numerical applicationMain features of the meso-scale problem

The blade considered in this study has a length of 38 meters and is made of glass fiber (elastic modulus E= 15000106 N/m2).

c

d e f g h i j k l m

n o m k c m m p

q h r c o n s p

t u t t v w x y w z u |

u ~ v w x z u

u v v x w z u t

u t t y x y u | ~

u ~ x w u

u x u

t u t t x w u

u ~ w x u |

u x y y u z z

u t t x w u t

u ~ x v t u |

u v x v t u

z t u t t x v t u |

z u ~ x w t u ~

z u v x v v t u

z u t t x t u

z u ~ w x w t u

z u x t u

t u t t x t u z |

u ~ x w t u z ~

u x y t u z

u t t x v t u z

u ~ w x t u

~ u w x t u

~ u z u t t u

Only the along-wind turbulent component has been considered to generate the drag and lift actions on the blade. The turbulent wind is modeled by an eight-variate Gaussian stochastic process with the wind acting in eight locations along the blade.

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1.E-13

1.E-09

1.E-05

1.E-01

1.E+03

1.E+07

0.0 0.1 1.0 10.0

1P 2P n13P n2 n3

Fo

rce

Sp

ectr

a S

R1

R1

[N

2/H

z]

Frequency [Hz]

1.E-12

1.E-08

1.E-04

1.E+00

1.E+04

1.E+08

0.0 0.1 1.0 10.0 n [Hz]Forc

e S

pec

tra

SR

1R

1 [N

2/H

z]

1P 2Pn1 3P n2 n3

Frequency [Hz]

Evaluation of the blade stress statePSD of the fluctuating component of the reaction R1

produced on the hub by the rotating blade - = 16 rpm

and = 20 rpm

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1012

1416

1820

2224

25

0.00

0.01

0.02

0.03

0.04

0.05

0.3

3

0.4

0.5

a

x [m]

Uncertainties affecting the meso-level problemStandard deviation of the blade tip displacement (x) in function of the rotating speed () and the induction coefficient (a)

( ) ( )( )hubm

hubmRhubm

hV

hVhVa

−=

Vm(hhub): mean wind velocity at the hub

height

VmR(hhub): mean wind velocity at the hub

height and at the rotor plane

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Open Issues for Life-Cycle Performance evaluation

• Identification of additional interaction parameters (IP) determining the uncertainty

in the response (e.g. parameters modeling

aeroelasticity)

• Appropriate probabilistic characterization of

these parameters (e.g. the relevance of the

mean wind field sampling depends on the

daily hours)

• Appropriate and efficient numerical methods to evaluate parameters of multimodal power

spectral densities (e.g. for fatigue

calculations)

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Analyses for investigating other

performances

1- SHIP IMPACT

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1. Tipi di imbarcazione 2. Parametri caratteristici

3. Forma della prua

4. Velocità d’impatto

v 4 - 8 nodi 2 - 4 m/s

SHIP IMPACT

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MODELLAZIONE

• 580 nodi

• 555 elementi Beam188

• 40 elementi Combin14

• 1 elemento

•Mass21Stro N


TERRENO

• Volume di terreno

modellato: cubo di

lato 80m,

discretizzato con

elementi 2x2x2 m

• 5 sottostrati in

materiale elastico

lineare con modulo

di rigidezza variabile

Elementi SOLID

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Terreno modellato

con molle lineari

lungo x e y poste a

metà dei sottostrati

Costante k variabile

con la profondità in

proporzione al

modulo E del terreno

Molle + smorzatori

SCELTA DEI VINCOLI

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Molle + smorzatoriDai parametri relativi al 1° e 2° modo di vibrare ricavo una stima del

coefficiente di smorzamento critico

SCELTA DEI VINCOLI

VERIFICA• impongo uno spostamento in un punto significativo

• rilascio e monitoro l’andamento nel tempo equivalente/reale

eq = 5.30 % eq = 4.08%

2

3

4

1

nodo 144

Dynamic behavior

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nodo 168

Dynamic behavior

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Increase of damage from the reference baseline ULS configuration to the last equilibrium configuration

λλλλ = 1.44λλλλ = 1.00 λλλλ = 1.32λλλλ = 1.10

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2 - Tower Buckling under extreme winds

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Dimopoulos C.A., Koulatsou K., Petrini F., Gantes C.J. (2015). Assessment of Stiffening Type of the Cutout in Tubular Wind Turbine Towers Under Artificial Dynamic Wind Actions. Journal of Computational and Nonlinear Dynamics. 10(4),041004-041004-9.

Stiffening types of the cutout in tubular tower

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FE model

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Static pushover analysis

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Dimopoulos C.A., Koulatsou K., Petrini F., Gantes C.J. (2015). Assessment of Stiffening Type of the Cutout in Tubular Wind Turbine Towers Under Artificial Dynamic Wind Actions. Journal ofComputational and Nonlinear Dynamics. 10(4),041004-041004-9.

Incremental dynamic analysis

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Loss of shape Vs Elephant foot buckling

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Dynamic vs Static

Petrini sapienza-may2015

Engineering

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