Laminar Cylinder at Re = 40 (Drag Coefficient)

Overview

Steady laminar flow past a circular cylinder is a documented benchmark in incompressible fluid dynamics. At a diameter Reynolds number $Re=40$ the flow is steady and two-dimensional, with a symmetric pair of standing vortices in the near wake. The drag coefficient has been computed and measured in independent studies. The case is solved on a family of progressively refined grids, and the drag coefficient is compared with accepted literature values.

Problem Setup

The cylinder has unit diameter and is immersed in a uniform free stream at a diameter-based Reynolds number $Re=40$, with constant density and viscosity. The cylinder surface is a no-slip adiabatic wall, and the outer boundary is a circle placed 50 diameters from the surface that applies free-stream conditions.

The verification is a grid-convergence study over four curvilinear O-grids, from 64 × 49 to 512 × 71 cells. Each grid places equally spaced nodes around the cylinder and extrudes them outward along the radial direction, with the first cell sized to the surface node spacing and a geometric growth ratio of 1.1 out to the far field. The low-dissipation discretization is used, and every grid is converged to its residual floor.

Quantities of Interest

The quantity of interest is the total drag coefficient $C_D$, the sum of the pressure and friction contributions integrated over the cylinder surface and normalized by the free-stream dynamic pressure and the diameter. It is plotted against the grid spacing $h=(1/N{)}^{1/2}$ and tabulated on the finest grid beside the accepted values of Park et al. ($C_D=1.51$) and Sen et al. ($C_D=1.509$). On the finest grid (512 × 71) Luminary computes $C_D=1.5096$, within 0.04% of Sen et al. and within 0.03% of Park et al.