On the viscous steady flow around a circular cylinder

F. M, ujano. , R. Peralta-Fabi

Abstract


A series truncation method is proposed to obtain approximate solutions to the flow past a circular cylinder. This procedure is based on a change in the radial coordinate ($x$), such that this new coordinate is defined in a finite interval. Solutions are truncated power series in $x$, so that the full Navier-Stokes equations are transformed into three recurrence relations with two independent coefficients. The boundary conditions on the cylinder's surface are satisfied in trivially way, and the conditions at infinity lead to a system of two non linear ordinary differential equations. These are solved using Fourier series in the angular variable and, for the sake of argument, in a power series in $R_{e}$. Results on the convergence of the series, with varying order of truncation, and comparison with earlier results are discussed.

Keywords


low Reynolds number; stationary Navier-Stokes eqn's; slow viscous flow; series truncation; flow past a cylinder; drag coefficient

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REVISTA MEXICANA DE FÍSICA, year 67, issue 2, March-April 2021. Bimonthly Journal published by Sociedad Mexicana de Física, A. C. Departamento de Física, 2º Piso, Facultad de Ciencias, Universidad Nacional Autónoma de México, Ciudad Universitaria, Alcaldía Coyacán, C.P. 04510 , Ciudad de México. Apartado Postal 70-348. Tel. (+52)55-5622-4946, https://rmf.smf.mx/ojs/rmf, e-mail: rmf@ciencias.unam.mx. Chief Editor: José Alejandro Ayala Mercado. INDAUTOR Certificate of Reserve: 04-2019-080216404400-203, ISSN: 2683-2224 (on line), 0035-001X (print), both granted by Instituto Nacional del Derecho de Autor. Responsible for the last update of this issue, Technical Staff of Sociedad Mexicana de Física, A. C., Fís. Efraín Garrido Román, 2º. Piso, Facultad de Ciencias, Universidad Nacional Autónoma de México, Ciudad Universitaria, Alcaldía Coyacán, C.P. 04510 , Ciudad de México. Date of last modification, March 1st., 2021.

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