Computation of high Reynolds number flow around a circular cylinder with surface roughness

Incompressible high-Reynolds-number flow around a circular cylinder is analyzed by direct integration of the Navier-Stokes equations using the finite-difference method. A generalized coordinate system is used, so that enough grid points are distributed in the boundary layer and the wake. A new numerical scheme which suppresses nonlinear instability for calculations of high-Reynolds-number flow is developed. The computation of the impulsively started flow at Re = 1200 is compared with corresponding experimental observations and excellent agreement is obtained. A series of computations are carried out on the flow around a circular cylinder with surface roughness. The height of the roughness in these computations is 0.5 percent of the diameter. The range of Reynolds number is from 1,000 to 100,000; no turbulent model is employed. A sharp reduction of the drag coefficient is observed near Re = 20,000, which indicates that the critical Reynolds number is captured in the present computation.