Abstract
We study the flow past a rough sphere considering the rugosity as a parameter and its effect on the drag coefficient. The numerical implementation is carried out via a novel approach using Galerkin’s method combined with an asymptotic expansion for the stream function. The amplitude of the spatial fluctuation is used as the perturbation parameter. The numerical results for the size of the vortex ring and streamlines in the smooth case are compared with experimental data found in the literature. In addition, when the surface is rough, we compare the numerical results with the smooth case and the implications of the rugosity in the separation point and other features of the flow are discussed.
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Acheson, D.J.: Elementary fluid dynamics. J. Acoust. Soc. Am. 89(6), 3020 (1991). https://doi.org/10.1121/1.400751
Babout, L., Grudzien, K., Maire, E., Withers, P.J.: Influence of wall roughness and packing density on stagnant zone formation during funnel flow discharge from a silo: an x-ray imaging study. Chem. Eng. Sci. 97, 210–224 (2013). https://doi.org/10.1016/j.ces.2013.04.026
Bhingare, N.H., Dhamale, S.K.: Effect of vehicle geometry on drag coefficient. Res. J. Eng. Technol. 10(2), 71 (2019). https://doi.org/10.5958/2321-581x.2019.00013.8
Biringen, S., Chow, C.Y.: An Introduction to Computational Fluid Mechanics by Example. Wiley, New York (2011). https://doi.org/10.1002/9780470549162
Bonnivard, M., Bucur, D.: Microshape control, riblets, and drag minimization. SIAM J. Appl. Math. 73(2), 723–740 (2013). https://doi.org/10.1137/100814846
Bons, J.P.: A review of surface roughness effects in gas turbines. J. Turbomach. 132(2) 021004 (2010). https://doi.org/10.1115/1.3066315
Busse, A., Thakkar, M., Sandham, N.D.: Reynolds-number dependence of the near-wall flow over irregular rough surfaces. J. Fluid Mech. 810, 196–224 (2017). https://doi.org/10.1017/jfm.2016.680
Domel, A.G., Domel, G., Weaver, J.C., Saadat, M., Bertoldi, K., Lauder, G.V.: Hydrodynamic properties of biomimetic shark skin: effect of denticle size and swimming speed. Bioinspir. Biomimet. 13(5), 056014 (2018). https://doi.org/10.1088/1748-3190/aad418
Evans, L.: Marine algae and fouling: a review, with particular reference to ship-fouling. Botan. Marina 24(4), 167–172 (1981). https://doi.org/10.1515/botm.1981.24.4.167
Fung, Y.C.: Flying and swimming. In: Biomechanics, pp. 106–154. Springer, New York (1990). https://doi.org/10.1007/978-1-4419-6856-2_4
Goluskin, D., Doering, C.R.: Bounds for convection between rough boundaries. J. Fluid Mech. 804, 370–386 (2016). https://doi.org/10.1017/jfm.2016.528
Hoerner, D.F.: Fluid-dynamic drag, illustrated. J. R. Aeronaut. Soc. 62(571), 400 (1958). https://doi.org/10.1017/S0368393100069200
Currie, I.G.: Fundamental mechanics of fluids, 3rd edn. In: Taylor & Francis e-Library Mechanical Engineering, vol. 154. Marcel Dekker, New York (2002)
Bottom Ii, R.G., Borazjani, I., Blevins, E.L., Lauder, G.V.: Hydrodynamics of swimming in stingrays: numerical simulations and the role of the leading-edge vortex. J. Fluid Mech. 788, 407–443 (2016). https://doi.org/10.1017/jfm.2015.702
Jimenez, J.: Turbulent flows over rough walls. Ann. Rev. Fluid Mech. 36(1), 173–196 (2004). https://doi.org/10.1146/annurev.fluid.36.050802.122103
Kawaguti, M.: The critical Reynolds number for the flow past a sphere. J. Phys. Soc. Jpn. 10(8), 694–699 (1955). https://doi.org/10.1143/jpsj.10.694
Lauder, G.V., Wainwright, D.K., Domel, A.G., Weaver, J.C., Wen, L., Bertoldi, K.: Structure, biomimetics, and fluid dynamics of fish skin surfaces. Phys. Rev. Fluids 1(6), 1–18 (2016). https://doi.org/10.1103/physrevfluids.1.060502
Martínez Hernández, J.E.: Modelado y simulación de parques eólicos integrados a los sistemas eléctricos de potencia. Master’s thesis, Facultad de Ingeniería, Universidad Nacional Autónoma de México (2017)
Nevard, J., Keller, J.B.: Homogenization of rough boundaries and interfaces. SIAM J. Appl. Math. 57(6), 1660–1686 (1997). https://doi.org/10.1137/S0036139995291088
Nikuradse, J.: Laws of flow in rough pipes (Strömungsgesetze in rauhen Rohren, 1933). Natl. Advisory Comm. Aeronaut. Wash. Tech. Memo. 1292, 1–62 (1950)
Shockling, M.A., Allen, J.J., Smits, A.J.: Roughness effects in turbulent pipe flow. J. Fluid Mech. 564, 267 (2006). https://doi.org/10.1017/s0022112006001467
Taneda, S.: Experimental investigation of the wake behind a sphere at low Reynolds numbers. J. Phys. Soc. Jpn. 11(10), 1104–1108 (1956). https://doi.org/10.1143/jpsj.11.1104
Tuck, E., Kouzoubov, A.: A laminar roughness boundary condition. J. Fluid Mech. 300, 59–70 (1995). https://doi.org/10.1017/S0022112095003600
Wen, L., Weaver, J.C., Thornycroft, P.J.M., Lauder, G.V.: Hydrodynamic function of biomimetic shark skin: effect of denticle pattern and spacing. Bioinspir. Biomimet. 10(6), 066010 (2015). https://doi.org/10.1088/1748-3190/10/6/066010
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The financial resources were provided by CONACYT. Authors would like to thank to the Instituto de Ingenieria, PREI-DGAPA and MyM-IIMAS, UNAM.
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Báez, Á., Ramírez-Trocherie, MA., Lobato, A. et al. Modelling flow past a rough sphere via stream functions and solution through Galerkin’s method. Arch Appl Mech 91, 1897–1905 (2021). https://doi.org/10.1007/s00419-020-01860-7
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DOI: https://doi.org/10.1007/s00419-020-01860-7