An Inviscid Theory of Lift

Cody Gonzalez, Haithem E. Taha

Published 2021-04-28Version 1

We exploit a special, less-common, variational principle in analytical mechanics (the Hertz' principle of least curvature) to develop a variational analogue of Euler's equations for the dynamics of an ideal fluid. We apply this variational formulation to the classical problem of the flow over an airfoil. The developed variational principle reduces to the Kutta-Zhukovsky condition in the special case of a sharp-edged airfoil, which challenges the accepted wisdom that lift generation is a viscous phenomenon wherein the Kutta condition is a manifestation of viscous effects. Rather, it is found that lift arises from enforcing a necessary condition of momentum preservation of the inviscid flow field. Moreover, the developed variational principle provides a closure condition for smooth shapes without sharp edges where the Kutta condition is not applicable. The presented theory is validated against Reynolds-Averaged Navier-Stokes simulations. Finally, in the light of the developed theory, we provide a simple explanation for lift generation.