Evolutionary understanding of airfoil lift

Abstract

This review attempts to elucidate the physical origin of aerodynamic lift of an airfoil using simple formulations and notations, particularly focusing on the critical effect of the fluid viscosity. The evolutionary development of the lift problem of a flat-plate airfoil is reviewed as a canonical case from the classical inviscid circulation theory to the viscous-flow model. In particular, the physical aspects of the analytical expressions for the lift coefficient of the plate-plate airfoil are discussed, including Newton’s sine-squared law, Rayleigh’s lift formula, thin-airfoil theory and viscous-flow lift formula. The vortex-force theory is described to provide a solid foundation for consistent treatment of lift, form drag, Kutta condition, and downwash. The formation of the circulation and generation of lift are discussed based on numerical simulations of a viscous starting flow over an airfoil, and the evolution of the flow topology near the trailing edge is well correlated with the realization of the Kutta condition. The presented contents are valuable for the pedagogical purposes in aerodynamics and fluid mechanics.