The Flow Over a Flat Plate: Did Kutta Get It Right?

Taha, Haitham E.; Gonzalez, Cody

doi:10.2514/6.2022-1665

Cited by 2 publications

(1 citation statement)

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“…over the modified flat plate: a flat plate with a naturally rounded nose) is lifting; the minimization principle (5.3), which is equivalent to the Kutta condition in this case of a sharp trailing edge, results in a circulation Γ that is close to Kutta's. For a more detailed presentation on this topic, the reader is referred to the recent effort by Taha & Gonzalez (2022a).…”

Section: Discussionmentioning

confidence: 99%

A variational theory of lift

Gonzalez

Taha

2022

J. Fluid Mech.

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In this paper we revive a special, less-common, variational principle in analytical mechanics (Hertz’ principle of least curvature) to develop a novel variational analogue of Euler's equations for the dynamics of an ideal fluid. The new variational formulation is fundamentally different from those formulations based on Hamilton's principle of least action. Using this new variational formulation, we generalize the century-old problem of the flow over a two-dimensional body; we developed a variational closure condition that is, unlike the Kutta condition, derived from first principles. The developed variational principle reduces to the classical Kutta–Zhukovsky condition in the special case of a sharp-edged airfoil, which challenges the accepted wisdom about the Kutta condition being a manifestation of viscous effects. Rather, we found that it represents conservation of momentum. Moreover, the developed variational principle provides, for the first time, a theoretical model for lift over smooth shapes without sharp edges where the Kutta condition is not applicable. We discuss how this fundamental divergence from current theory can explain discrepancies in computational studies and experiments with superfluids.

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Section: Discussionmentioning

confidence: 99%