Simulating the dynamics of wind turbine blades: part I, model development and verification

Abstract

In the state of the art of modeling and simulation of wind turbines, verification and validation (V&V) is a somewhat underdeveloped field. The purpose of this paper is to spotlight the process of a completely integrated V&V procedure, as it is applied to a wind turbine blade. The novelty, besides illustrating the application of V&V to blade modeling, is to challenge the conventional separation between verification and validation activities. First, simple closed‐form solutions for bending stress, torsional stress and mode shapes of a hollow cylinder are derived analytically to verify the ANSYS finite element software. Shell‐281 elements are used to approximate these closed‐form solutions and demonstrate that the software runs properly. The grid convergence index is used to quantify the degree of numerical uncertainty that results. Next, model development and verification activities are applied to the CX‐100 blade designed at the Sandia National Laboratories. A three‐dimensional model is developed based on the actual geometry of the CX‐100 blade. For simplicity, the model assumes smeared cross sections with uniform, isotropic material properties. Solution verification is performed to quantify the numerical uncertainty due to mesh discretization of the finite element model. The mesh refinement study provides evidence that the model leads to numerical solutions located in the regime of asymptotic convergence. We depart from the conventional V&V paradigm by proposing that the level of mesh discretization should be based on an assessment of experimental variability. Instead of choosing the mesh size ‘in a vacuum’, it is selected such that the overall numerical uncertainty caused by truncation effects is similar to, or smaller than, the test‐to‐test variability. This rationale guarantees that predictions are sufficiently accurate relative to the level of uncertainty with which physical tests can be replicated. Part II of this work highlights the V&V steps implemented to quantify sensitivities of the model and further quantify the prediction uncertainty caused by our imperfect knowledge of the idealized material description. Copyright © 2012 John Wiley & Sons, Ltd.

Evaluating the fidelity and robustness of calibrated numerical model predictions

“…The numerical uncertainties in this 3D model were evaluated through an in depth verification study in Mollineaux et al (2012). The 3D model was then calibrated against natural frequencies measured during the tests conducted at Los Alamos National Laboratory (Farinholt et al, 2012), and validated against mode shapes using modal assurance criterion .…”

A Resource Allocation Framework for Experiment-Based Validation of Numerical Models

“…The optimal values for the coefficients computed from Eq. (12) and shown in Tables 3 and 4 for the two models, are treated as starting values during model calibration (discussed in the next section). The aforementioned analysis yields 5 calibration parameters for the G model and 10 for the C&G model as listed in Tables 3 and 4, along with the ranges, within which these parameters are allowed to vary to encompass available experimental data.…”

“…These imprecise model parameters are typically the main contributors to the uncertainty in predictions. Numerical uncertainties, the third factor, can be treated by code and solution verification activities that ensure the mathematical equations are solved correctly [11][12][13]. Verification is a prerequisite to experiment-based validation [14] and, thus, the third factor, which involves numerical uncertainties, is excluded from the scope of the present article.…”

Development of Simplified Models for Wind Turbine Blades with Application to NREL 5 MW Offshore Research Wind Turbine

“…Mollineaux et al [2] developed a simplified three dimensional FE model based on an accurate description of the geometry for the CX-100 blade designed at Sandia National Laboratory. As the main simplification, the cross sectional areas of the blade are modeled using isotropic material properties instead of complex multilayer composite materials.…”