Calculation of the steady flow past a sphere at low and moderate Reynolds numbers

TLDR: In this paper, the steady axially symmetric incompressible flow past a sphere is investigated for Reynolds numbers, based on the sphere diameter, in the range 0·1 to 40.

Abstract: The steady axially symmetric incompressible flow past a sphere is investigated for Reynolds numbers, based on the sphere diameter, in the range 0·1 to 40. The formulation is a semi-analytical one whereby the flow variables are expanded as series of Legendre functions, hence reducing the equations of motion to ordinary differential equations. The ordinary differential equations are solved by numerical methods. Only a finite number of these equations can be solved, corresponding to an approximation obtained by truncating the Legendre series at some stage. More terms of the series are required as R increases and the present calculations were terminated at R = 40. The calculated drag coefficient is compared with the results of previous investigations and with experimental data. The Reynolds number at which separation first occurs is estimated as 20·5.