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In fluid dynamics, drag crisis (also Eiffel paradox or Lukyanov–Eiffel paradox) is a phenomenon in which drag coefficient drops off suddenly as Reynolds number increases. This has been well studied for round bodies like spheres and cylinders. The drag coefficient of a sphere will change rapidly from about 0.5 to 0.2 at a Reynolds number in the range of 300000. This corresponds to the point where the flow pattern changes, leaving a narrower turbulent wake. The behavior is highly dependent on small differences in the condition of the surface of the sphere.
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The drag crisis was first identified in 1905 by a Russian student G.I.Lukyanov in experiments on wind tunnel of Moscow University. The superviser of the experiments, Zhukovsky correctly guessed that this paradox can be explained by ``detachment of streamlines at different points of the sphere at different velocities``.
Later the paradox was independently discovered in experiments by G.Eiffel and Maurain. Gustave Eiffel is known as a man who designed and built the Eiffel Tower, and the Statue of Liberty. Upon his retirement, he built the first wind tunnel in a lab located at the basis of the Eiffel Tower, to investigate wind loads on structures and early aircraft. In a series of test he found that the force loading experienced an abrupt decline at a critical Reynolds number.
This transition is associated with a transition from laminar to turbulent boundary layer flow adjacent to the object in question. In the case of cylindrical structures this transition is associated with a transition from well organized vortex shedding to randomized shedding behavior for super-critical Reynolds numbers, eventually returning to well organized shedding at the post-critical Reynolds number with a return to elevated drag force coefficients.
The super-critical behavior can be described semi-empirically using statistical means or by sophisticated computational fluid dynamics software (CFD) that takes into account the fluid-structure interaction for the given fluid conditions.
The critical Reynolds number is a function of turbulence intensity, upstream velocity profile, and wall-effects (velocity gradients). The semi-empirical descriptions of the drag crisis are often described in terms of a Strouhal bandwidth and the vortex shedding is described by broad-band spectral content.
- Birkhoff, Garrett (2015). Hydrodynamics: A study in logic, fact, and similitude. Princeton University Press. p. 41.
- Drag crisis. Lukyanov–Eiffel paradox
- A table with drag coefficient data for Lukyanov's experiments can be found on page 73 in Zhukovsky, N.Ye. (1938). Collected works of N.Ye.Zukovskii.
- Op.cit, p. 72.
- Eiffel G. Sur la résistance des sphères dans l'air en mouvement, 1912
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- Prandtl L. Der Luftwiderstand von Kugeln (1914)
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- "Simulating Drag Crisis for a Sphere Using Skin Friction Boundary Conditions" (PDF). Retrieved 2008-10-24.
- "Flow past a cylinder: Shear layer instability and drag crisis" (PDF). Retrieved 2008-10-24.
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