Aero-servo-elastic analyses are required to determine the wind turbine loading for a wide range of load cases as specified in certification standards. The floating reference frame (FRF) formulation can be used to model the structural response of long and flexible wind turbine blades. Increasing the number of bodies in the FRF formulation of the blade increases both the fidelity of the structural model and the size of the problem. However, the turbine load analysis is a coupled aero-servo-elastic analysis, and computation cost not only depends on the size of the structural model, but also depends on the aerodynamic solver and the number of iterations between the solvers. This study presents an investigation of the performance of the different fidelity levels as measured by the computational cost and the turbine response (e.g., blade loads, tip clearance, tower-top accelerations). The analysis is based on aeroelastic simulations for normal operation in turbulent inflow load cases as defined in a design standard. Two 10 MW reference turbines are used. The results show that the turbine response quickly approaches the results of the highest-fidelity model as the number of bodies increases. The increase in computational costs to account for more bodies can almost entirely be compensated for by changing the type of the matrix solver from dense to sparse.

Modern wind turbine blades are large, slender and flexible composite structures with a complex pre-bent and twisted geometry. Over their operational life blades undergo large deflections and rotations due to external loads (e.g., aerodynamic, inertial and control actuator loads). An aero-servo-elastic code or framework is used to accurately calculate the complex dynamical response of wind turbines with large and flexible blades. This has led to the implementation of geometrically nonlinear structural solvers in wind-turbine-specific aero-servo-elastic codes. For example, the structural solver BeamDyn

The effect of large blade deflections on the turbine response has been studied since the early 2000s in megawatt-sized turbines.

Literature shows that large blade deflections are important to consider for a turbine response analysis, especially for long and flexible blades. The focus of the existing studies is generally limited to the blade response only, and considering a small selection of load cases. However, what is lacking is a full overview of the turbine response and a broad selection of load cases when comparing linear and nonlinear blade models without mentioning the additional computational time needed by nonlinear models. The aim of this study is to investigate the performance differences between various nonlinear blade modeling “fidelities” (in terms of number of bodies in a floating reference frame) using HAWC2. The performance of a model here is defined by its computational time and how close the loads are compared to a reference case. This is defined as the case with the highest blade model fidelity. The design load cases for power production under normal turbulence according to the International Electrotechnical Commission (IEC) 61400 standard

In this study the turbine responses of DTU10MW

Evaluating the aero-servo-elastic response of large and flexible wind turbines using time domain simulations under turbulent inflow conditions requires rigorous analysis. Both the aero-servo-elastic solver and the considered model and load cases are therefore carefully outlined in the following two sections. The applied analysis method presented here is based on a numerical experiment of blades with varying structural model fidelity levels.

The turbine analyses for the presented work were performed with HAWC2 version 12.6, which is a strongly coupled aero-servo-elastic wind turbine simulation tool. The aerodynamic solver of HAWC2 uses the blade element momentum formulation

A general wind turbine structure can be built out of

Structural modeling of a cantilever beam in floating reference system with multiple bodies, in deflected and undeflected states.

HAWC2 constructs a system of differential equations representing the equations of motion of the system with constraints (see Eq.

As the reference–rigid body (

The main driving factors in computation time of the multibody solver are the simulation time, the size of the problem (matrices) and the number of iterations. The vector

In HAWC2 the time integration is performed using the Newmark algorithm

The approach in the study is based on numerical experiments of two turbines: the DTU10MW

The properties of the blade models are shown in Table

General properties of the reference wind turbines: DTU10MW and IEA10MW.

It is practical to call the bodies used for a continuous structure or a component the main body, and the bodies defined in a main body are called sub-bodies. A main body can be attached to other bodies or boundaries by constraints in any direction, whereas the constraints between the sub-bodies are always in 6 dof to satisfy the continuity of the structure. In the analyses the number of sub-bodies of the blade varied from 1 (linear response) to 30 (one body for each element, equivalent to a corotational approach). The rest of the turbine model was kept the same for a coherent comparison. The HAWC2 models of the considered turbines for this publication are composed of nine main bodies: tower, tower top, nacelle, three hubs and three blades. Table

HAWC2 turbine models' main bodies and number of elements and sub-bodies used in each main body.

The number of bodies in the model alters the problem size since it changes the number of generalized coordinates and constraints in the equations. The number of generalized coordinates and constraint equations can be determined by Eqs. (

Number of generalized coordinates

The turbine analyses were carried out for steady, deterministic wind load cases, power production load cases according to DLC 1.2 and stability load cases in overspeed conditions. Steady-load cases include a full turbine model including controller under a constant wind speed with wind shear and without any yaw error. There are

Qualitative breakdown of the fatigue load contributions of various design load cases for the IEA10MW (based on the loads reported in

Design load cases (DLC) 1.2 power production on normal turbulence load case simulation setup.

The stability analysis includes a turbine model which is free to speed up without generator torque and has a fixed blade pitch angle at 0

The simulation results of the blade models with different numbers of sub-bodies are compared to the blade with the

The activity of the pitch bearing is evaluated by integrating the pitch angle signal over time for all load cases; see Eq. (

Figure

The total number of iterations is normalized by the result of the

The maximum dense solver computation time is observed for the

Since the sparsity of the matrices in Eq. (

Turbine power, blade pitch, blade effective radius change and blade tip torsion results are given for steady, deterministic wind speed conditions. Figure

Linear and nonlinear blade model power, blade pitch (left axis in the figures) and effective blade radius change (right axis in the figures) results with respect to wind speeds for steady-wind-load cases. Panel

Figure

Linear and nonlinear blade model torsion deformations at

Turbine blade deflection, damage equivalent load, maximum load and cross-section load results are given for the DLC 1.2 load cases. Figure

Normalized blade tip minimum tower clearance, maximum effective blade radius and blade edgewise deflection results. Values are normalized with respect to the results of the

Figure

Flapwise, edgewise and torsion moment DEL ratios between linear (one sub-body) and nonlinear (

Normalized flapwise, edgewise and torsion moment DEL ratio variations with respect to the number of blade model sub-bodies at blade stations where the maximum deviations between linear and nonlinear cases occur.

Figure

Figure

Linear and nonlinear blade absolute maximum moment load result ratio variation in DTU10MW and IEA10MW turbines with respect to blade span location.

Alternatively, the ultimate cross-sectional loads can be visualized by considering the load envelopes. The load envelopes are the convex boundaries of the flap- and edgewise bending moment time traces considering all load cases. In doing so, the absolute magnitude and corresponding angle of the extreme loads are visualized. Figure

Cross-section flapwise and edgewise load envelopes at 43.6 m blade radius of the DTU turbine and 51.1 m blade radius of the IEA turbine for

Turbine tower damage equivalent load, maximum and cross-section load results are given for the DLC 1.2 load cases. The turbine performance results are also mentioned here. Figure

Normalized tower-top maximum torsion moments, side–side and fore–aft accelerations. Values are normalized with respect to the results of the

Figure

Normalized tower-top torsion, side–side and fore–aft DEL moment with respect to number of sub-bodies in blade model.

Tower bottom fore–aft and side–side load envelopes of the DTU and the IEA turbines for

Figure

Normalized blade pitch actuator (blade root torsion moment) DEL, total pitch angle change for all load cases and maximum power at pitch actuator with respect to number of blade sub-bodies.

The difference in annual energy production (AEP) between the different blade models is well below

The stability of DTU and IEA turbines is evaluated by considering the linear (one body) and nonlinear (

DTU10MW

The effects of blade structural model fidelity on the turbine response, loads, stability and computation time are investigated in this study. The blades are modeled by different numbers of sub-bodies in the multibody formulation of HAWC2. The blade model geometric nonlinearity is changed from linear to the highest available fidelity level, which is equivalent to a corotational formulation. The effects of blade geometric nonlinearities are compared by exploring the results of two different blade designs with otherwise identical tower and shaft configuration. The normal power production load cases are selected according to the IEC 61400-1 standard (DLC1.2) but considering 12 instead of six turbulent seeds. In addition, the computational speed of the dense and sparse matrix solvers as used by HAWC2 is compared for different blade model fidelities.

CPU time can decrease by increasing the number of bodies, since the total number of aero-elastic iterations decreases as the number of bodies increases. After the total number of aero-elastic iterations becomes independent of the number of bodies, the CPU time increases by the number of bodies explicitly. The linear models have larger deflections compared to the nonlinear models and these large deflections cause larger changes in the aerodynamic forces. Consequently, the cycle between the structural response and aerodynamic forces requires more iterations for linear models. Since the sparsity of the matrices increases by the number of bodies, the sparse solver becomes more effective than the dense solver in terms of required CPU time for nonlinear problems. The geometric nonlinear effects are the most apparent in the blade responses. The effective blade length, computed by linear and nonlinear blade models, is different by up to

Although there are significant differences between the linear and the nonlinear blade models (with

The work outlined here confirms earlier studies that the nonlinear geometrical effects are significant for wind turbine blades, even more so for new turbine designs (DTU10MW vs. IEA10MW). The geometrically nonlinear effects are model dependent and are related to the size, prebend shape and flexibility of the considered blade model. The authors conclude that users are recommended to model blades with as many sub-bodies as there are structural elements, while also using a sparse matrix solver for models that have symmetric effective stiffness matrices in HAWC2. In doing so within the context of HAWC2, no increase in CPU time is noted while at the same time having the blade model with the highest structural fidelity.

The corresponding HAWC2 input files used for this study can be found in

OG conducted the study as part of his PhD research. The idea was developed by OG and DRV. OG ran the analyses and performed the post-processing including results and figures with tools developed by DRV. The manuscript was written jointly by OG and DRV.

DTU Wind Energy develops, supports and distributes HAWC2 on commercial terms.

The authors are grateful to Sergio González Horcas and Anders Melchior Hansen for their contribution to the HAWC2 solver. Furthermore, the authors would like to acknowledge their colleagues, Sergio González Horcas, Mathias Stolpe, Suguang Dou, Riccardo Riva and Georg Pirrung for their comments on the manuscript.

This study was funded by DTU Wind Energy.

This paper was edited by Lars Pilgaard Mikkelsen and reviewed by two anonymous referees.