Effects of the Approximations Embodied in the Momentum Theory as Applied to the NREL PHASE VI Wind Turbine

Rodolfo Bontempo,Marcello Manna

doi:10.3390/ijtpp2020009

Abstract

This paper investigates the impact of the standard approximations embodied in the well-known Momentum Theory on its performance prediction capabilities. To this aim, the results of the momentum theory, which is still widely used in all Blade Element/Momentum codes for the analysis and/or design of wind turbines, are compared with those obtained with an actuator disk model based on Computational Fluid Dynamics techniques. In this method, the axisymmetric and steady Euler equations are solved with a classical finite volume approach, while the turbine effects are modelled through a set of axial and tangential body forces distributed over a disk shaped region representing the rotor swept surface. Since this method does not rely on the momentum theory simplifying assumptions, it can be suitably employed to verify the momentum theory validity. The analysis is carried out using the well documented experimental data of the National Renewable Energy Laboratory Phase VI wind turbine.

Highlights

Nowadays, the performance analysis and design of wind turbines are frequently carried out by coupling a through-flow with a blade-to-blade method
For a prescribed value of the wind speed vz,∞ and of the angular velocity Ω, the axial and tangential induction factors are computed both with the Computational Fluid Dynamics (CFD)-actuator disk (AD)
The impact of the errors embodied in the momentum theory has been evaluated for the well-documented National Renewable Energy Laboratory (NREL) Phase VI wind turbine for which a large highly accurate experimental database is available

Summary

Introduction

The performance analysis and design of wind turbines are frequently carried out by coupling a through-flow with a blade-to-blade method. Due to the large diffusion of the BEM methods, the evaluation of the MT errors is of the utmost importance; a few works dealing with this issue have recently appeared [24,36,37,38,39,40,41] These studies present the comparison between the MT and AD methods based on flow equations not polluted by the typical MT approximations, e.g., CFD-AD and SA-AD. The NREL Phase VI data have been successfully exploited to validate and develop the analysis of several wind turbines and design approaches which often rely on simplified inflow characteristics These data have been employed to validate BEM tools (see for instance [43,44,45,46]). The results of the MT and of the CFD-AD method are compared with each other to quantify the errors embodied in the MT for different values of the tip speed ratio

The Momentum Theory

The CFD Actuator Disk Method

Validation of the CFD-AD Method

Evaluation of the Momentum Theory Errors

Conclusions