A general numerical unsteady non-linear lifting line model for engineering aerodynamics studies

Abstract

The lifting-line theory is widely used for obtaining aerodynamic performance results in various engineering fields, from aircraft conceptual design to wind-power generation. Many different models were proposed, each tailored for a specific purpose, thus having a rather narrow applicability range. This paper presents a general lifting-line model capable of accurately analysing a wide range of engineering problems involving lifting surfaces, both steady-state and unsteady cases. It can be used for lifting surface with sweep, dihedral, twisting and winglets and includes features such as non-linear viscous corrections, unsteady and quasi-steady force calculation, stable wake relaxation through fictitious time marching and wake stretching and dissipation. Possible applications include wing design for low-speed aircraft and unmanned aerial vehicles, the study of high-frequency avian flapping flight or wind-turbine blade design and analysis. Several validation studies are performed, both steady-state and unsteady, the method showing good agreement with experimental data or numerical results obtained with more computationally expensive methods.

Usefulness of Inviscid Linear Unsteady Lifting-Line Theory for Viscous Large-Amplitude Problems

“…Further work [48,49] extended the frequency range before Guermond and Sellier [50] produced a method suitable for swept wings at any oscillation frequency. Research in the time domain has been less extensive, and asymptotically limited by the assumptions made in modeling the wake [51][52][53][54][55][56]. A more detailed review can be found in Bird and Ramesh [57].…”

Unsteady lifting-line theory and the influence of wake vorticity on aerodynamic loads

“…Bird et al [5] apply this method to a geometrically nonlinear inner solution. Sugar-Gabor et al [59] suggested a method where the unsteady wake was only accounted for in the outer 3D problem, allowing for roll and yaw kinematics. Lifting-line theory has also been used to model wings in large-scale simulations where resolving the chord-scale would be prohibitively expensive, for example, in Caprace et al [11].…”

Fast and accurate quasi-3D aerodynamic methods for aircraft conceptual design studies

“…[9,10] was extended to unsteady flows in ref. [40]. In the context of unsteady flows, the continuous distribution of bound vorticity over the lifting surface and of trailing vorticity in the wake are approximated using a finite number N of ring vortices bound to the geometry, and at each time step, a new row of N vortex rings are shed into the wake, as illustrated in Fig.…”

“…The various terms appearing in the above equation are lengthy and will not be presented here but can be found in full in ref. [40].…”