Comparison of actuator disc flows representing wind turbines and propellers

Gijs A.M Van Kuik

doi:10.1088/1742-6596/1037/2/022007

Abstract

Actuator disc theory is the basis for rotor design and analysis, valid for discs representing wind turbine rotors as well as propellers. In Froude’s momentum theory swirl is absent, in Joukowsky’s momentum theory this is included. The momentum theory including swirl, developed in WES, 2:307-316,2017, as well as potential flow calculations have been expanded to propeller discs. For the rotational speed Ω → ∞ the classical Froude results are recovered. For low values of Ω the propeller discs show an expanding instead of contracting wake, like wind turbine discs. Both flow regimes show a complete blockage of the flow for a low but non-zero Ωmin. For all wind turbine discs, so irrespective of Ω, the velocity in the meridian plane, is constant at the disc, for all propeller discs this is not.

Highlights

The momentum theory without swirl is valid for high λ rotors, as is shown in figure 1
This representation is well known in helicopter literature like [9], as it is able to show the results for zero wind speed, but for the same reason only rarely used in wind turbine references, see e.g. [5]
The momentum theory plus the potential flow calculations have highlighted some aspects of actuator disc flows representing wind turbines and propellers with a constant circulation Γ:

Summary

Introduction

The momentum theory without swirl is valid for high λ rotors, as is shown in figure 1. The line shows the result of this momentum theory for the wind turbine mode, left, and the propeller mode, right. A numerical confirmation of the momentum theory without swirl for the wind energy regime has been presented in [15], which is expanded to the propeller regime. The momentum theory and the potential flow code have been expanded in [16] to discs generating swirl in the wind energy regime. The flow and pressure patterns are qualitatively similar to c and d and will not be shown

Propeller discs with wake expansion

The velocity at the disc

Conclusions