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New theory of flight. (English) Zbl 1342.76069
Summary: We present a new mathematical theory explaining the fluid mechanics of subsonic flight, which is fundamentally different from the existing boundary layer-circulation theory by Prandtl-Kutta-Zhukovsky formed 100 year ago. The new theory is based on our new resolution of d’Alembert’s paradox showing that slightly viscous bluff body flow can be viewed as zero-drag/lift potential flow modified by 3d rotational slip separation arising from a specific separation instability of potential flow, into turbulent flow with nonzero drag/lift. For a wing this separation mechanism maintains the large lift of potential flow generated at the leading edge at the price of small drag, resulting in a lift to drag quotient of size 15-20 for a small propeller plane at cruising speed with Reynolds number \({Re\approx 10^{7}}\) and a jumbojet at take-off and landing with \({Re\approx 10^{8}}\) , which allows flight at affordable power. The new mathematical theory is supported by computed turbulent solutions of the Navier-Stokes equations with a slip boundary condition as a model of observed small skin friction of a turbulent boundary layer always arising for \({Re > 10^{6}}\) , in close accordance with experimental observations over the entire range of angle of attacks including stall using a few millions of mesh points for a full wing-body configuration.

MSC:
76G25 General aerodynamics and subsonic flows
76E09 Stability and instability of nonparallel flows in hydrodynamic stability
Software:
Unicorn
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References:
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