Predicting airfoil stalling dynamics using upwind numerical solutions to non-viscous equations

Abstract

Over the last few decades, researchers have been focusing on determining the critical attack angle at which dynamic stall occurs. This angle is usually determined by solving the Navier-Stokes equations, which include viscosity, pressure, gravity, and acceleration terms. However, Navier-Stokes equations are quite complex to solve and consequently difficult to simulate, thus the simulation is not accurate enough. Therefore, this article predicts the critical attack angle for the first time using Euler equations devoid of viscous terms. One of the key advantages of Euler equations is their ability to capture the vortices and predict stall dynamics. The Euler equations are thus integrated and the resulting equations are discretized using the finite volume method. A first-order upwind-based method is used to calculate the convective fluxes at the cell boundaries in the finite volume approach. A NACA 0012 airfoil is chosen for this study at various attack angles with a Mach number of 0.3. Based on the justification of Crocco's theorem, the Euler equations successfully act as Navier-Stokes equations. The vortex patterns are found to behave independently of the artificial dissipation. All the vortices are successfully predicted using the inviscid governing equations. The numerical results obtained are validated by other published experimental and numerical data.