The steady flow of a viscous fluid past a circular cylinder at Reynolds numbers 40 and 44

Abstract

This paper describes the numerical solution of the complete Navier-Stokes equations for the steady flow of an incompressible viscous fluid of unlimited extent past a circular cylinder at Reynolds number 40. A new device developed for the numerical solution is described. The results of the investigation are: (a) A steady-state solution does exist at Reynolds number 40 and is in good agreement with experimental results. (b) It seems that steady-state solutions are possible for somewhat higher Reynolds numbers even though they may not exist in nature. A solution has been obtained at Reynolds number 44 but it has not been carried to the same accuracy as the solution at Reynolds number 40. (c) The length of the stationary vortex pair attached to the downstream portion of the cylinder continues to increase with Reynolds number in such steady-state solutions up to a Reynolds number 44 and no indication has been found that this process will not continue as the Reynolds number is increased beyond 44.