Far-field boundary conditions for airfoil simulation at high angle of attack in steady, incompressible, and two-dimensional flow

Abstract Accurate far-field boundary conditions (BCs) are crucial for simulating airfoils at high angles of attack, where lift and drag can be comparable and moments become significant. In this study, we investigate the effects of different BCs on a NACA 0012 airfoil in incompressible and steady flow, using the Spalart-Allmaras turbulence model at an angle of attack of $$45^{\circ }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mn>45</mml:mn> <mml:mo>∘</mml:mo> </mml:msup> </mml:math> and a high Reynolds number. We apply the impulse form of the lift, drag, and moment equations to a control volume coincident with the square computational domain. Our results confirm that satisfying the lift equation requires modeling the airfoil as a point vortex, but they also reveal the importance of including a point source to capture significant drag effects. Omitting the point source creates artificial blockage at the domain sidewalls reminiscent of wind-tunnel blockage. A “Lagally-Filon” correction for cases with laterally-constrained BCs is derived, demonstrating that it substantially improves agreement with the wind tunnel blockage correction. While combining a point vortex and point source is consistent with both lift and drag, additional minor corrections are needed for the moment equation. These corrections may become essential for designs sensitive to aerodynamic moments, such as vertical-axis wind turbines. Overall, this work emphasizes the need for an appropriate point source term in far-field BCs to achieve more accurate airfoil simulations at high angles of attack.