Simulation of a Wing with Wingtip Devices Using the Actuator Line Method

The actuator line method (ALM) was developed to represent blades or wings as lifting lines in numerical simulations of the Navier-Stokes equations. In order to accurately calculate the forces, imposed as body forces along the line, a tip correction is usually applied. Recent advances on the understanding of the vorticity created by the smeared actuator line led to corrections based on complementing the velocity with the difference between the velocity induced by a Lamb-Oseen and a singular vortex. Since these corrections are more physically meaningful, they offer the possibility of simulating wingtip devices. In the present work, we simulate a straight wing with winglets using the code Nek5000 with ALM. It is shown that these corrections miss a relevant effect for this case, even when including the correction due to the bound vortex: when imposing the corrected lift coefficient in the numerical domain, the local generated circulation is inaccurate, due to the difference between the velocity measured in the numerical domain and the corrected velocity. We propose a correction that takes this difference into account. The results of both methods are compared to the lifting line method and the presently proposed correction shows better agreement.