Analysis of the Principle of Minimum Pressure Gradient Method on Airfoil Behavior through Stall

Understanding overall airfoil aerodynamic performance is critical to design wings and lifting bodies as it is a first-order driver of vehicle efficiency. Traditionally, aerodynamics is assessed by examining the lift-to-drag ratio, integral forces, moment measurements, and/or pressure distribution patterns. In this research, we aim to explore the Principle of Minimum Pressure Gradient (PMPG) [1] and if it can provide new aerodynamic insight. PMPG is a newly introduced concept that proposes Navier Stokes solutions are minimizations of the pressure gradient norm in various fluid flows. PMPG offers a potentially transformative approach to fluid mechanics as it proposes a new minimization scalar that is not directly the traditional Navier-Stokes equations. In this work, we investigate PMPG on three airfoils (NACA 63-412, NACA 63-412 with flap 15 degree, and Eppler 25) using computational fluid dynamics (CFD) over a wide range of angles of attack (α) to characterize the flow separation, lift, drag, pitch moment, and lift-to-drag ratio from attached flow through stall. The innovative aspect of this effort aims to exploit data-access provided by a CFD solver to directly assess the flow-field domain and develop an understanding of the PMPG as a new metric to characterize aerodynamic efficiency. Some preliminary results of the analysis suggest that the PMPG develops connections between , Cl, Cd, flow-separation point, Cl/Cd, and the PMPG integral. The PMPG integral indicates a nonlinear behavior and a loss of the PMPG integral as stall is approached. This character will be evaluated quantitatively and qualitatively to better understand the metric as an aerodynamic tool to drive aerodynamic design.

Keywords: Principle of Minimum Pressure Gradient (PMPG), Kutta Condition, Angle of Attack, Flow Separation, Lift-to-drag ratio, Aerodynamic behaviors.