An Analytical Solution of Steady Viscous Flow past a Circular Cylinder in the Region of Intermediate Reynolds Number

Abstract In this study, a solution of a steady viscous flow past a circular cylinder in a uniform flow in the region of intermediate Reynolds numbers is studied using an analytical approach. The governing equations of this flow are Navier-Stokes equation (N-S equation) and continuity equation. It is well known that a mathematical difficulty called the Stokes' paradox occurs when the perturbation method is applied to this problem. To avoid this paradox, many analytical methods, such as the Oseen approximation or matching technique, have been developed. However, because the solutions obtained by these analytical methods are only valid under the condition of a small Reynolds number, these solutions cannot express the flow separation behind a circular cylinder observed in the experiments in the region of intermediate Reynolds number. In this study, we construct an analytical solution of N-S equation asymptotically by developing the homotopy analysis method, which is an analysis method for nonlinear differential equations, without the assumption that the Reynolds number is small. In contrast to the existing theoretical solution, the present solution can express the flow separation agrees with the experiments behind a circular cylinder in the region of R d <20 ( R d is the Reynolds number based on the diameter of the circular cylinder) although the existing analytical solutions could not express the separation. It also gives the drag coefficient in agreement with the experimental and numerical results in the region of R d <30. For example, in comparison with numerical or experimental values, the difference is 4.4% at R d =15.0 for the vortex length. Also, for the drag coefficient ( C D ), the differences are 0.4% at R d =10 and 0.5% at R d =20 (The present C D =2.77 at R d =10, also C D =2.00 at R d =20).