Evaluating the accuracy of the actuator line model against blade element momentum theory in uniform inflow

TL;DR

This study assesses the accuracy of the actuator line model (ALM) for wind turbine simulations by comparing it with blade element momentum (BEM) theory across different grid resolutions, showing convergence with increased resolution and insights for simulation efficiency.

Contribution

It demonstrates that ALM results converge towards BEM theory with finer grid resolution and provides guidelines for the number of actuator points needed for accurate simulations.

Findings

ALM and BEM agree within 1% for power and thrust coefficients at grid spacing ≤ 5.25 m.

Increasing numerical resolution reduces differences between ALM and BEM, approaching convergence.

The number of actuator points influences results minimally when spaced about three times the grid spacing.

Abstract

We evaluate the accuracy of the actuator line model (ALM) approach by performing simulations for the NREL~5~MW wind turbine in uniform inflow using three large eddy simulation codes. The power and thrust coefficients obtained using the three codes agrees within $1\%$ when the grid spacing $\Delta_{\rm grid} \le 5.25$~m, and are cross-validated against blade element momentum (BEM) theory. We find that the results of ALM converge towards BEM theory without the need for tip correction when the numerical resolution is increased. For $\Delta_{\rm grid}=0.98$~m the difference between the power and thrust coefficient obtained using ALM and BEM is $4.5\%$ and $2.1\%$, respectively, although we note that no absolute convergence between ALM and BEM can be obtained as both models use different assumptions, such as the use of a force projection method in the ALM. The difference in the local axial and tangential forces along the blades obtained from ALM simulations using $\Delta_{\rm grid} = 1.97$~m and $\Delta_{\rm grid} = 0.98$~m can be as large as $10\%$. The effect of the number of actuator points on the obtained turbine power and thrust coefficients is limited as the results converge when the spacing between the actuator points is about three times the grid spacing. This insight on the required number of blade points can be used to improve the efficiency of actuator line simulations.