Actuator Disc Model

The fundamental principle of the blade element momentum (BEM) theory has been described in numerous references with all its variations (Glauert, 1926a; Hansen, 2015; Sørensen, 2016; Bangga, 2022a). The BEM theory assumes that the blades can be divided into small annular blade elements (annuli) that act independently of the neighbouring elements. In addition, it is assumed that the flow around the aerofoil is two-dimensional, and the aerodynamic load can then be calculated from the local flow conditions, i.e. the undisturbed flow speed, the structural motion, and the rotor speed. These elemental loads are integrated along the span of the blade in order to calculate the total aerodynamic load acting on the blade. The local angle of attack, traditionally denoted as \(\bscalar{\alpha}\), is a function of the direction and magnitude of the local relative flow, which in turn is a function of the incoming undisturbed flow speed at the rotor plane, the rotor speed, the relative structural velocity and the induced velocity. Figure 1 shows a traditional three-bladed turbine with an annular blade element (annulus) at radius \(\bscalar{r}\). In principle, the width \(\bscalar{\delta r}\) of the annulus is assumed to be infinitesimal.

Figure 1: Geometry of rotor including rotor coordinate system and blade coordinate system

Last updated 30-08-2024