An Investigation of the Principle of Minimum Pressure Gradient Method on Airfoils through Stall

Airfoil aerodynamics through a range of angles of attack α is crucial for understanding wings, lifting bodies, and the underlying performance is a first-order driver for vehicle efficiency. The aerodynamics are traditionally assessed through lift-to-drag ratio, integral force and moment measures, and/or pressure distributions. In this work, we seek to study how and if the Principle of Minimum Pressure Gradient (PMPG) [1] can offer new aerodynamic insight. PMPG was recently developed an underlying basis for the origin of the Kutta condition [2] and has also been applied in fluid dynamics. We investigate three airfoils (NACA 63-412, NACA 63-412 with flap 15°, and NACA 0018) using computational fluid dynamics (CFD) over a wide range of α to characterize the flow separation, lift, drag, and lift to drag ratio from attached flow through stall. The innovative aspect of this effort aims to exploits data-access provided by a CFD solver to directly assess the flow-field domain and develops an understanding of the PMPG as a new metric to characterize aerodynamic efficiency. Simulated results show that the PMPG develops connections between AOA, Cl, Cd, total separated area, and the PMPG integral. Notably, the lift coefficient rises until stall, then declines with increasing AOA. Furthermore, the volume integral of PMPG shows nonlinear behavior. In summary, our effort aims at understanding these interactions with respect to airfoil design that can potentially develop new tools to enhance aerodynamic efficiency.