ewec2011 samtech offshore paper

Article submitted to EWEC 2011:

Numerical simulation of offshore wind turbines by a coupled aerodynamic, hydrodynamic and structural dynamic approach A. Heege, P. Bonnet, L. Bastard, S. G. Horcas,J.L. Sanchez, P. Cucchini, A. Gaull

Numerical simulation of offshore wind turbines

by a coupled aerodynamic, hydrodynamic and structural dynamic approach

A. Heege, P. Bonnet, L. Bastard, S. G. Horcas,J.L. Sanchez, P. Cucchini, A. Gaull

SAMTECH Iberica E-08007 Barcelona

[email protected]

Abstract Central point of the present publication is an implicitly coupled aero-elastic, hydrodynamic and structural approach which is dedicated to the simulation of offshore wind turbines. The applied mathematical approach relies on an implicit non-linear dynamic Finite Element Method which is extended by Multi-Body-System functionalities, aerodynamics based on the Blade Element Momentum theory, controller functionalities, hydrodynamic wave loads through the implementation of the Morison equation and finally buoyancy loads which account for variable wave height. In order to account for the hydro-dynamic and structural coupling effects, the Morison equation is implemented in its extended form which accounts for the dynamic response of the loaded offshore structure.

First, the impact of hydrodynamic and structural dynamic coupling effects is analyzed for a jacket based offshore wind turbine. As second example, the aerodynamic and hydrodynamic coupling effects are put in evidence by a transient dynamic analysis of a floating offshore wind turbine which is anchored by structural cables to the seabed.

1 Introduction The operation deflection modes and associated dynamic loads of offshore wind turbines originate, on the one hand, from aero-elasticity and hydrodynamic loading of the submerged offshore structure, and, on the other hand, from the proper dynamics of the entire wind turbine system, including all control mechanisms.

Especially in the case of the numerical simulation of floating offshore wind turbines, a decoupling of the dynamic offshore wind turbine system into sub-systems bears risks to miss coupling effects which might prevail during many operation modes. In

particular in the case of floating offshore wind turbines, a decoupled aero-elastic and hydrodynamic formulation does not permit to reproduce properly the global dynamic response of the wind turbine. This is because the speed variations which are induced in the rotor plane by dynamic operation deflections of the offshore wind turbine and/or by a floating wind turbine, affect directly the aerodynamic loads and associated controller actions on the blade pitch position and/or on the generator torque. A major drawback of decoupled simplified approaches is that a proper tuning of controller parameters of floating offshore wind turbines is not possible and as a consequence the dynamic behavior might be wrongly evaluated.

In order to remedy these deficiencies, the proposed mathematical approach is specifically formulated in order to capture dynamic coupling effects which might be induced simultaneous by aero-elastic and hydrodynamic loading of the offshore structure. Accordingly, the relative velocity and acceleration fields which are induced by a floating and/or vibrating offshore wind turbine are accounted in the coupled aerodynamic and hydrodynamic formulation.

The implementation of aerodynamic loads is based on the Blade Element Theory where wind turbine specific corrections for tip and hub losses, wake effects and the impact of the tower shadow are accounted.

Hydrodynamic loads are composed of drag loads and of inertia loads which account for the relative velocity and acceleration fields in between the fluid and the moving and/or vibrating offshore structure.

Two different applications of dynamic analysis of offshore wind turbines will be presented. The applied wind turbine models are discretized by more than 3000 DOF and account for all mentioned coupling effects.



2 Coupled aero-elastic, hydro-dynamic, structural dynamic FEM and MBS analysis The applied mathematical approach is based on a non-linear Finite Element formalism, which accounts simultaneously for flexible Multi-Body-System functionalities [1][2][3], control devices, aerodynamics in terms of the Blade Element Momentum Theory [3][4][5][6], buoyancy and hydrodynamic loads in terms of the Morsion equation [7] [8][9][10][11]

The applied aero-elastic wind turbine models include flexible component models through dynamic Finite Element models, or respectively in its condensed form as Super Elements. Further on, the most relevant mechanisms like pitch and yaw drives or detailed power train models are included in the same aero-elastic analysis model [3].

2.1 Mathematical background In the context of an “Augmented Lagrangian Approach” and the “one-step time integration method of Newmark” [1][2], the incremental form of the equations of motions in the presence of constraints is stated in terms of equations (1,2,3).

According to the definition of the residual vector of equation (2a,b), the vector gr assembles the sum of

elasto-visco-plastic internal forces Int.gr ,

complementary inertia forces where centrifugal and gyroscopic effects are included, external forces

Ext.gr , the aero-dynamic forces AeroF

r and finally the

hydro-dynamic and hydrostatic loads HydroFr . The

Vector φr introduces additional equations of the

generalized solution [ ]λrr,q , which are used to include general Multi-Body-System functionalities for the modelling of the power train, pitch and yaw drives and finally further Degrees of Freedom/DOF which are related to controller state variables for blade pitches, yaw orientation and generator modelling.

Further details on time integration procedure, error estimators and solution strategies for equation solvers, can be found in the SAMCEF-Mecano user manual [1].

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The discretisation of aerodynamic loads corresponds to the structural discretisation in terms of retained Super Element nodes or, respectively, beam nodes and the aero-elastic coupling is performed generally at the ¼ chord length positions of 15 equally spaced blade sections.

The a-priori unknown induced velocities are defined in equations (6a,b,c) in terms of the induction normal to the rotor plane, i.e. the axial induction a, and the induction tangential to the rotor plane a’ [4][5][6]. It is noted that the inductions in the normal and the tangential rotor plane directions are computed iteratively by solving a system of non-linear equations which is resulting from expressions (1), (4), (5) and (6a,b,c). The elemental aerodynamic forces at each blade section are assembled to the global aerodynamic force vector

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overestimation of hydrodynamic drag and/or inertia loads, because hydrodynamic inductions and/or wave dispersion are not accounted in that formulation.

As it is shown in Figure 1, the direction of drag is determined in the aerodynamic and in the hydrodynamic implementation by the relative fluid-structural velocity vector which is projected onto a plane which is perpendicular to the span wise direction.

The vector of the fluid drag formulated in equation (9) and the vector of fluid inertia loads formulated in equation (10) are contained in the same plane which is perpendicular to the span wise direction, but show generally different vector directions, i.e. the “angle of attack of the drag forces” and the “angle of attack of the inertia forces” are frequently not coincident.

A coupled formulation of Morison’s approach is exposed in several references [8][9] in a form analogous to equation (10) and might be interpreted as an extension of an empirical one-dimensional formulation which was dedicated initially to the modelling of uncoupled fluid loads [7] to a coupled three-dimensional formulation. It is stipulated that the coupled Morison formulation might require further adaptations in order to improve the precision of that empirical method. Important hydrodynamic and structural dynamic coupling effects might be induced by floating offshore structures, but the coupled formulation exposed in references [8][9] include an “uncoupled inertia term” which does not depend on the relative dynamics of the fluid and the structure. It is conjectured that the inclusion of an “uncoupled inertia term” might not be indicated for a formulation which is prone to the simulation of coupled hydrodynamic and structural dynamic phenomena.

The direction of the Morison inertia load is determined by 2 distinct contributions with a-priori 2 different vector orientations:

a) The first term of equation (10) tu∂∂r

r t),q(effV ρ ,

presents a vector component which direction corresponds to the unperturbed fluid

acceleration tu∂

∂r

which is projected into the

plane which is perpendicular to the span wise direction of the structural component.

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)( t),q(effV tv

tu

aC

∂∂

−∂∂

rrr

ρ , presents a vector

component which direction corresponds to the

relative fluid-structure acceleration )(tv

tu

∂

∂−

∂

∂rr

which is projected onto the plane which is perpendicular to the span wise direction of the structural component.

Both mentioned inertia load components are contained in the same plane which is perpendicular to the span wise direction, but the respective vector orientations are not necessarily aligned if the structure is vibrating and/or floating. It is conjectured that the coupled Morison formulation might require further adaptations, because the first term of equation (10) includes an uncoupled term

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∂r

r t),q(effV ρ which does not depend on the

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In the case of nodes of structural FEM components which are subjected to large displacements & rotations and/or a variable wave height, the relative nodal position & rotation vector (t)qr and the instantaneous Free Water Level/FWL vector t),q(W

rr

define the effective depth ) ,q(effE tr of a node and the associated effective submerged component

span t),q(effL r .

lue)(scalar va node toassociatedlength span :)SpanLMod(L

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L

node structural toassociatedctor length vespan :t),q(SpanL

height) wave(variable vector Level/FWL Water Free :t),q(W

:with

(14) )2D)4/(( t),q(effLt),q(effV

: volumesubmerged Effective

(13d) .0t),q(effL

fluid ofout span entire 0effE SpanProj

L :for

(13c) )SpanProj

L/effE-(1 Lt),q(effL

submerged partially span 0effE SpanProj

L :for

(13b) Lt),q(effL

submergedfully span 0effE SpanProj

L :for

(13a) )SpanProj

L/eff(E Lt),q(effL

submerged partially span 0effE SpanProj

L :for

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FWL) below node.0eff(E

(12) t)),q(W-(t)q ( )g/Tg() ,q(effE

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The adopted time dependent span t),q(effL r which enters in the computation of drag forces and the

resulting effective submerged volume t),q(effVr for

the computation of buoyancy and Morison inertia loads, are outlined in equations (13,14). For each structural node which is subjected to hydrostatic or hydrodynamic loads, a time dependent direction of the span wise component

length is defined in terms of the vector t),q(SpanL rr. It

is noted that the span wise length vector t),q(SpanL rr

is moving and rotating with the associated structural node. In case of a component which is partially submerged below the free water level, the proportion of the submerged span is approximated through the projection of the span length vector

t),q(SpanL rronto the gravity vector gr yielding the

“projected span wise length” t),q(SpanProj

Lr . Finally, the

effectively submerged span wise length t),q(effL r is computed through equations (13a,b,c,d) and the

effectively submerged volume t),q(effV r is

resulting from equation (14).

2.3.3 Added Mass & Eigen-Modes

The inertia term InertiaFr

of the Morison equation (11) modifies the total mass associated to the submerged offshore structure and as consequence the resulting Eigen-Modes of the offshore wind turbine.

As depicted in Figures 2 & 3 and as outlined in section 2.3.2, the implemented algorithm accounts for the large transformations induced by a floating offshore wind turbine and the relative wave height. The total mass which is accounted in the Eigen-mode computation of the offshore structure is complemented through the derivative of the inertia term of the Morison equation (11) with respect to the relative accelerations in between the fluid and the vibrating and/or floating offshore structure. Equations (15,16) define the added mass term in terms of the derivative of the Morison inertia force with respect to the structural accelerations of the respective node of the FEM model. As stated in equation (16), the “added fluid mass” which is added to the global mass & inertia matrix of the FEM equations stated in equation (1) is obtained through the derivative of the Morison inertia term and can be presented in terms of two contributions.

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Hydrodynami49

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ent work, Min its extendeferences innamic and was outlinedm of the composed in twcoupled inertacceleration

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“uncoupled inertia term” in a formulation which is prone to the simulation of coupled hydrodynamic and structural dynamic phenomena. Further fundamental research might be indicated in order to remedy that deficiency.

It is concluded that the presented coupled aero-elastic, structural and hydrodynamic approach can be applied with some minor adaptations in an efficient manner to the analysis of floating offshore wind turbines. In order to speed up the model preparation phase, procedures for an automatized generation of Hydrodynamic Load Elements are presently under development. Future enhancements will include the improvement of mechanical mooring line models. In order to reduce the observed rotor plane speed variations which are induced in by the floating wind turbine, a specific controller tuning for blade pitch and generator torque will be required. Finally, further research will be performed in order to implement more advanced hydrodynamic wave models.

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14.1., http://www.samtech.com [2]. Geradin, M. and Cardona, A., Flexible

Multibody Dynamics: A Finite Element Approach. John Wiley and Sons Ltd, 2001

[3]. Heege A., Betran J., Radovcic Y., “Fatigue Load Computation of Wind Turbine Gearboxes by Coupled Finite Element, Multi-Body-System and Aerodynamic Analysis”, Wind Energy, vol. 10:395-413, 2007.

[4]. Bossanyi, E. A., GH-Bladed User Manual, Issue 14, Garrad Hassan and Partners Limited, Bristol, UK, 2004

[5]. AeroDyn Theory Manual, December 2005• NREL/EL-500-36881, Patrick J. Moriarty, National Renewable Energy Laboratory Golden, Colorado A. Craig Hansen Windward Engineering, Salt Lake City, Utah

[6]. Buhl, M.L., Jr. 2004. A New Empirical Relationship between Thrust Coefficient and Induction Factor for the Turbulent Windmill State. NREL/TP-500-36834. Golden, CO: National Renewable Energy Laboratory, September.

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[8]. Germanischer Lloyd Wind Energie GmbH, Guideline for the Certification of Offshore Wind Turbines. 1st June 2005

[9]. American Petroleum Institute. Recommended Practice for Flexible Pipe, API Recommended Practice 17B. Third Edition, March 2002

[10]. K.Mittendorf,B.Nguyen and M.Blümel. WaveLoads, A computer program to calculate wave loading on vertical and inclined tubes.User manual. Gigawind, Universität Hannover. Version 1.01, August 2005

[11]. Robert G.Dean, Robert A. Dalrymple. Advanced Series on Ocean Engineering, Volume 2: Water wave mechanics for engineers and scientists. World Scientific Publishing Co. Singapore, 1991

[12]. F. Vorpahl, W. Popko, D. Kaufer. Description of a basic model of the "Upwind reference jacket" for code comparison in the OC4 project under IEA Wind Annex XXX; Fraunhofer Institute for Wind Energy and Energy System Technology (IWES), 4 February 2011

[13]. J. Jonkman, Definition of the Floating System for Phase IV of OC3,Technical Report, NREL/TP-500-47535, National Renewable Energy Laboratory Golden Colorado/USA, May 2010.

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