fluid dynamics In physics, physical chemistry and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids – liquids and gases. It has several subdisciplines, including (the study of air and other gases in motion ...

, the drag crisis (also known as the Eiffel paradox) is a phenomenon in which drag coefficient drops off suddenly as

Reynolds number In fluid dynamics, the Reynolds number () is a dimensionless quantity that helps predict fluid flow patterns in different situations by measuring the ratio between Inertia, inertial and viscous forces. At low Reynolds numbers, flows tend to ...

increases. This has been well studied for round bodies like

sphere A sphere (from Ancient Greek, Greek , ) is a surface (mathematics), surface analogous to the circle, a curve. In solid geometry, a sphere is the Locus (mathematics), set of points that are all at the same distance from a given point in three ...

s and

cylinders A cylinder () has traditionally been a three-dimensional solid, one of the most basic of curvilinear geometric shapes. In elementary geometry, it is considered a prism with a circle as its base. A cylinder may also be defined as an infinite ...

. 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 In fluid dynamics, turbulence or turbulent flow is fluid motion characterized by chaotic changes in pressure and flow velocity. It is in contrast to laminar flow, which occurs when a fluid flows in parallel layers with no disruption between ...

wake. The behavior is highly dependent on small differences in the condition of the surface of the sphere.

History

The drag crisis was observed in 1905 by Nikolay Zhukovsky, who guessed that this paradox can be explained by the detachment of streamlines at different points of the sphere at different velocities. Later the paradox was independently discovered in experiments by

Gustave Eiffel Alexandre Gustave Eiffel ( , ; Bonickhausen dit Eiffel; 15 December 1832 – 27 December 1923) was a French civil engineer. A graduate of École Centrale des Arts et Manufactures, he made his name with various bridges for the French railway net ...

and Charles Maurain. Upon Eiffel's retirement, he built the first wind tunnel in a lab located at the base of the

Eiffel Tower The Eiffel Tower ( ; ) is a wrought-iron lattice tower on the Champ de Mars in Paris, France. It is named after the engineer Gustave Eiffel, whose company designed and built the tower from 1887 to 1889. Locally nicknamed "''La dame de fe ...

, to investigate wind loads on structures and early aircraft. In a series of tests he found that the force loading experienced an abrupt decline at a critical Reynolds number. The paradox was explained from boundary-layer theory by German fluid dynamicist

Ludwig Prandtl Ludwig Prandtl (4 February 1875 – 15 August 1953) was a German Fluid mechanics, fluid dynamicist, physicist and aerospace scientist. He was a pioneer in the development of rigorous systematic mathematical analyses which he used for underlyin ...

. Reprinted in

Explanation

The drag crisis is associated with a transition from laminar to turbulent boundary layer flow adjacent to the object. For 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 a higher 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 using Large Eddy Simulation (LES) that includes the dynamic displacements of the structure (DLES) 1 These calculations also demonstrate the importance of the blockage ratio present for intrusive fittings in pipe flow and wind-tunnel tests. 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.

References

Additional reading

# Fung, Y.C. (1960). "Fluctuating Lift and Drag Acting on a Cylinder in a Flow at Supercritical Reynolds Numbers," J. Aerospace Sci., 27 (11), pp. 801–814. # Roshko, A. (1961). "Experiments on the flow past a circular cylinder at very high Reynolds number," J. Fluid Mech., 10, pp. 345–356. # Jones, G.W. (1968). "Aerodynamic Forces on Stationary and Oscillating Circular Cylinder at High Reynolds Numbers," ASME Symposium on Unsteady Flow, Fluids Engineering Div. , pp. 1–30. # Jones, G.W., Cincotta, J.J., Walker, R.W. (1969). "Aerodynamic Forces on Stationary and Oscillating Circular Cylinder at High Reynolds Numbers," NASA Report TAR-300, pp. 1–66. # Achenbach, E. Heinecke, E. (1981). "On vortex shedding from smooth and rough cylinders in the range of Reynolds numbers 6x103 to 5x106," J. Fluid Mech. 109, pp. 239–251. # Schewe, G. (1983). "On the force fluctuations acting on a circular cylinder in crossflow from subcritical up to transcritical Raynolds numbers," J. Fluid Mech., 133, pp. 265–285. # Kawamura, T., Nakao, T., Takahashi, M., Hayashi, T., Murayama, K., Gotoh, N., (2003). "Synchronized Vibrations of a Circular Cylinder in Cross Flow at Supercritical Reynolds Numbers", ASME J. Press. Vessel Tech., 125, pp. 97–108, DOI:10.1115/1.1526855. # Zdravkovich, M.M. (1997). Flow Around Circular Cylinders, Vol.I, Oxford Univ. Press. Reprint 2007, p. 188. # Zdravkovich, M.M. (2003). Flow Around Circular Cylinders, Vol. II, Oxford Univ. Press. Reprint 2009, p. 761. # Bartran, D. (2015). "Support Flexibility and Natural Frequencies of Pipe Mounted Thermowells," ASME J. Press. Vess. Tech., 137, pp. 1–6, DOI:10.1115/1.4028863 # Botterill, N. ( 2010). "Fluid structure interaction modelling of cables used in civil engineering structures," PhD dissertation (http://etheses.nottingham.ac.uk/11657/), University of Nottingham. # Bartran, D. (2018). "The Drag Crisis and Thermowell Design", J. Press. Ves. Tech. 140(4), 044501, Paper No: PVT-18-1002. DOI: 10.1115/1.4039882.

External links

* * {{DEFAULTSORT:Drag Crisis Drag (physics) Fluid dynamics