(2008) 2, pp. 12-19. (pdf)
T. S. Morton
Aerospace & Biomedical Engineering, University of Tennessee Space Institute, 411 B.H. Goethert Parkway, Tullahoma, TN
Abstract:
A loss in circulation is sometimes cited in connection with bluff-body wakes as a result of comparing the circulation actually observed downstream with a well-known theoretical estimate of the total circulation generated by a cylinder. In an effort to better understand this reported loss in circulation, an alternative estimate of the circulation generated by a cylinder is derived by integrating the velocity on a closed loop containing the attached boundary layer. Predictions of the dimensionless circulation for a cylinder in crossflow are less than the previous theoretical estimate and agree with observed values. This suggests that the total circulation generated by bluff bodies may have been overestimated in the past, and that comparison of observed values with this overestimate is the origin of the perceived “loss” in circulation.
References:
Balligand, H., “Unsteady wake structure behind a solid disk,” Ph.D. Dissertation, Syracuse University (2000).
Bearman, P. W. & Obasaju, E. D., “An experimental study of pressure fluctuations on fixed and oscillating square-section cylinders,” Journal of Fluid Mechanics 119 (1982) pp. 297-321.
Bloor, M. S., “The transition to turbulence in the wake of a circular cylinder,” Journal of Fluid Mechanics 19 (1964) pp. 290-304.
Cantwell, B. J. & Coles, D., “An experimental study of entrainment and transport in the turbulent near wake of a circular cylinder,” Journal of Fluid Mechanics 136 (1983) pp. 321-374.
Davies, M. E., “A comparison of the wake structure of a stationary and oscillating bluff body, using a conditional averaging technique,” Journal of Fluid Mechanics 75 (1976) pp. 209-231.
Fage, A. & Johansen, F. C., “On the Flow of Air behind an Inclined Flat Plate of Infinite Span,” Proceedings of the Royal Society of London A 116 (1927) pp. 170-197.
Fage, A. & Johansen, F. C., “The structure of the vortex street,” Philosophical Magazine 5 (1928) pp. 417-441.
Green, R. B. & Gerrard, J. H., “Vorticity measurements in the near wake of a circular cylinder at low Reynolds numbers,” Journal of Fluid Mechanics 246 (1993) pp. 675-691.
Johari, H. & Stein, K., “Near wake of an impulsively started disk,” Physics of Fluids 14 (2002) pp. 3459-3474.
Kirchhoff, G., “Zur Theorie freier Flüssigkeitsstrahlen,” Journal fuer die reine und angewandte Mathematik (Crelle’s Journal) 70 (1869) pp. 289-298.
Lyn, D. A., Einav, S., Rodi, W., & Park, J.-H., “A laser-Doppler velocimetry study of ensemble-averaged characteristics of the turbulent near wake of a square cylinder,” Journal of Fluid Mechanics 304 (1995) pp. 285-319.
Perrin, R., Braza, M., Cid, E., Cazin, S., Moradei, F., Barthet, A., Sevrain, A., & Hoarau, Y., “Near-Wake Turbulence Properties in the High Reynolds Number Incompressible Flow Around a Circular Cylinder Measured by Two- and Three-Component PIV,” Flow, Turbulence and Combustion 77 (2006) pp. 185-204.
Roshko, A., “On the drag and shedding frequency of bluff cylinders,” NACA-TN-3169 (1954).
Schlichting, H., Boundary-Layer Theory, McGraw-Hill, NY (1979).
Swanson, W. M., “The Magnus Effect: A Summary of Investigations to Date,” ASME Journal of Basic Engineering, D 83 (1961) pp. 461-470.
Tanaka, S. & Murata, S., “An Investigation of the Wake Structure of a Circular Cylinder using a Computer Aided Flow Visualization (1st Report, Generation and Dissipation of the Vorticity),” Bulletin of the JSME 29 (1986) (251) pp. 1446-1454.
Wood, C. J., “Visualizations of an incompressible wake with base bleed,” Journal of Fluid Mechanics 29 (1967) pp. 259-273.
Wu, J., Sheridan, J., Hourigan, K., Welsh, M. C., & Thompson, M., “Longitudinal vortex structures in a cylinder wake,” Physics of Fluids 6 (1994) pp. 2883-2885.
Wu, M.-H., Wen, C.-Y., Yen, R.-H., Weng, M.-C., & Wang, A.-B., “Experimental and numerical study of the separation angle for flow around a circular cylinder at low Reynolds number,” Journal of Fluid Mechanics 515 (2004) pp. 233-260.
Zdravkovich, M., “Comment on the Loss of Vorticity in the Near Wake of Bluff Bodies,” ASME Journal of Fluids Engineering 111 (1989) pp. 104-105.