A Geometrically Non-Linear Time-Domain Unsteady Lifting-Line Theory

Abstract

An unsteady lifting-line theory for time-domain problems with arbitrary kinematics is presented. This is formulated by matching a vortex particle based 2D inner model with a 3D vortex lattice wake. This and a small-amplitude frequency-domain unsteady lifting-line theory are then verified against experiment and computational fluid dynamics for the case of a flat rectangular plate oscillating in heave at aspect ratios 3 and 6. Both lifting-line theories were found to generally be in good agreement with experimental and CFD results, providing reasonable solutions even in cases dominated by LEV shedding. For larger amplitude problems, the new non-linear geometry lifting-line theory predicted larger amplitudes and higher average lift coefficient than the small-amplitude lifting-line theory.

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

“…The pressure implicit with splitting of operators (PISO) algorithm implements pressure-velocity coupling. This in-house setup has previously been used with the incompressible Navier-Stokes governing equations to study leadingedge vortex shedding on finite wings [5,6], and with the incompressible Euler equations to verify unsteady potential flow solutions for an airfoil [51].…”

“…Devinant [19] presents a method by which the pseudosteady assumption can be numerically removed for wake wavelengths of the wing span scale or larger. 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.…”

On the leading-edge suction and stagnation-point location in unsteady flows past thin aerofoils

“…2018), and leading-edge vortex shedding on finite wings of different aspect ratios (Bird & Ramesh 2018; Bird et al. 2019). In this research, the incompressible Euler equations are implemented in order to best match the conditions under which the theory (potential flow) is derived.…”

“…The pressure implicit with splitting of operators (PISO) algorithm is employed to achieve pressure-velocity coupling. This set-up has been previously used to implement the incompressible Navier-Stokes equations and study limit-cycle oscillation of a two-degree-of-freedom aerofoil (Wang et al 2018), and leading-edge vortex shedding on finite wings of different aspect ratios (Bird & Ramesh 2018;Bird et al 2019). In this research, the incompressible Euler equations are implemented in order to best match the conditions under which the theory (potential flow) is derived.…”

Effect of Three-Dimensional Geometry on Harmonic Gust–Airfoil Interaction

“…In later developments, the field of unsteady lifting line theory accounted for 3D effects by using 2D models, such as the Theodorsen function, with the angle of attack corrected to account for the downwash from the streamwise wake vorticity [3][30]. However, unsteady lifting line theory retains the assumption that the spanwise wake vorticity extends infinitely in the spanwise direction, which does not apply for low aspect ratios or in the proximity of the wing tips [31].…”