Asymmetric turbulent boundary layers along long thin circular cylinders at low-Re

Abstract

Notable deviations of the asymmetric turbulent boundary layer (TBL) statistics from their axisymmetric counterpart along long thin circular cylinders are vitally important to the naval and oceanographic jurisdictions. Although the available experimental evidence backs their concern, the realm of parametric variability (both geometric and kinematic) is extremely limited to draw solid conclusions. We know that only small misalignments which quantify less than one degree of incidence between the freestream and the straight cylinder axis can substantially alter the boundary layer thicknesses, mean axial velocity, and Reynolds stresses. But the statistical database is plainly inadequate to justify modifying the design tools that were founded solely for axisymmetric flow conditions. Herein, we begin rectifying this drawback by numerical means. The investigation centers on low turbulent Reynolds numbers (500 ≤ Rea ≤ 2500) and small angles-of-incidence (0° < α < 9°) to validate and complement the lions-share of the present database (Rea = aUo/ν, where a, Uo, and ν are the cylinder radius, freestream velocity, and kinematic viscosity, respectively). In particular, we numerically resolved the statistical responses of the TBL, mean axial velocity, Reynolds stresses, and skin friction under angles-of-incidence up to the earliest signs of Strouhal-type shedding. Clearly, the first prominent response was the thinning and thickening of the TBL along the respective windward and leeward sides to only a minor misalignment. Tilting the straight cylinder to slightly higher yaw angles transformed the TBL to a transitional boundary layer along the windward side for all simulated Reynolds numbers. For yaw angles α > 2°, all turbulent statistics of the asymmetric boundary layer were measurably dissimilar to those of the axisymmetric state.