Physics:Drag crisis
In fluid dynamics, drag crisis (also known as the Eiffel paradox[1]) 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.
History
The drag crisis was observed in 1905[citation needed] 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.[2]
Later the paradox was independently discovered in experiments by Gustave Eiffel[3] and Charles Maurain.[4] Upon Eiffel's retirement, he built the first wind tunnel in a lab located at the base of the Eiffel Tower, 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.[5]
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) [11]. 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
- ↑ Birkhoff, Garrett (2015). Hydrodynamics: A study in logic, fact, and similitude. Princeton University Press. p. 41. ISBN 9781400877775. https://books.google.com/books?id=Vj7WCgAAQBAJ.
- ↑ Zhukovsky, N.Ye. (1938). Collected works of N.Ye.Zukovskii. p. 72. http://books.e-heritage.ru/book/10075061.
- ↑ Eiffel G. Sur la résistance des sphères dans l'air en mouvement, 1912
- ↑ Toussaint, A. (1923). Lecture on Aerodynamics. NACA Technical Memorandum No. 227. p. 20. https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19930084658.pdf.
- ↑ Prandtl, Ludwig (1914). "Der Luftwiderstand von Kugeln". Nachrichten der Gesellschaft der Wissenschaften zu Göttingen: 177–190. Reprinted in Tollmien, Walter; Schlichting, Hermann; Görtler, Henry; Riegels, F. W. (1961). Ludwig Prandtl Gesammelte Abhandlungen zur angewandten Mechanik, Hydro- und Aerodynamik. Springer Berlin Heidelberg. doi:10.1007/978-3-662-11836-8_45. ISBN 978-3-662-11836-8.
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
- "Simulating Drag Crisis for a Sphere Using Skin Friction Boundary Conditions". http://www.nada.kth.se/~jhoffman/archive/papers/eccomas06.pdf. Retrieved 2008-10-24.
- "Flow past a cylinder: Shear layer instability and drag crisis". http://home.iitk.ac.in/~smittal/publi_&_present/sm_journals/drag_crisis.pdf. Retrieved 2008-10-24.
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