Numerical solution for laminar unsteady flow about fixed and oscillating cylinders

Abstract

This paper presents a finite-difference solution of the two-dimensional, time dependent incompressible Navier-Stokes equations for laminar flow about fixed and oscillating cylinders placed in an otherwise uniform flow. Using boundary fitted coordinates, the equations are transformed to a non-inertial reference frame fixed to the cylinder. The primitive variable formulation is used for the solution of the problem. A special transformation provides a fine grid scale near the cylinder walls and a coarse grid in the far field. Forward difference is used in time, fourth order central difference in space except for convective terms for which a modified third-order upwind scheme is used. Velocity values are obtained explicitly, and the successive over-relaxation (SOR) method yields the pressure distribution. Computed drag coefficients and dimensionless vortex shedding values were compared with experimental results for rigid cylinders and a very good agreement has been obtained. Amplitude bounds of locked-in vortex shedding due to forced crossflow oscillation of a circular cylinder are also determined for Re= 180.