Evolutionary understanding of airfoil lift

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.

Can lift be generated in a steady inviscid flow?

This paper presents a critical evaluation of the physical aspects of lift generation to prove that no lift can be generated in a steady inviscid flow.Hence,the answer to the recurring question in the paper title is negative.In other words,the fluid viscosity is necessary in lift generation.The relevant topics include D’Alembert’s paradox of lift and drag,the Kutta condition,the force expression based on the boundary enstrophy flux(BEF),the vortex lift,and the generation of the vorticity and circulation.The physi-cal meanings of the variational formulations to determine the circulation and lift are discussed.In particular,in the variational formulation based on the continuity equation with the first-order Tikhonov regularization functional,an incompressible flow with the artificial viscosity(the Lagrange multiplier)is simulated,elucidating the role of the artifi-cial viscosity in lift generation.The presented contents are valuable for the pedagogical purposes in aerodynamics and fluid mechanics.

Reconstruction of skin friction topology in complex separated flows

This paper describes a theoretical method for reconstruction of the skin friction topology in complex separated flows,which is developed based on the exact relation between skin friction and surface pressure through the boundary enstrophy flux(BEF).The key of this method is that a skin friction field is reconstructed from a surface pressure field as an inverse problem by applying a variational method.For applications,the approximate method is proposed,where the composite surface pressure field is given by a linear superposition of the base-flow surface pressure field and the surface pressure variation field and the base-flow BEF field is used as the first-order approximation.This approximate method is constructive in a mathematical sense since a complex skin friction field in separated flows can be reconstructed from some elemental skin friction structures(skin friction source/sink,vortex and their combinations)by a linear superposition of some simple surface pressure structures.The distinct topological features,such as critical points,separation lines and attachment lines,naturally occur as a result of such reconstruction.As examples,some elemental skin friction structures in separated flows are reconstructed in simulations,and the skin friction fields in shock-wave/boundary-layer interactions(SWBLIs)are reconstructed from pressure sensitive paint(PSP)images obtained in wind tunnel experiments.