Turbulent boundary layers along straight and curved long thin circular cylinders at low angles-of-incidence

Abstract

Long thin circular cylinders commonly serve as towed sonar tracking devices, where the radius-of-curvature along the longitudinal axis is quite low [ρr = O(10−4)]. Because no understanding presently exists about the direct impact of longitudinal curvature on the turbulent statistics, the long cylinder is simply viewed as a chain of straight segments at various (increasing then decreasing) small inclinations to the freestream direction. Realistically, even our statistical evidence along straight thin cylinders at low incidence angles is inadequate to build solid evidence towards forming reliable empirical models. In the present study, we address these shortcomings by executing Large-Eddy Simulations (LESs) of straight and longitudinally curved thin cylinders at low to moderate turbulent radius-based Reynolds numbers (500 ≤ Rea ≤ 3500) and small angles-of-incidence (α = 0° → 9°). Coupled with the previous experimental measurements and numerical results, the new expanded database (311 ≤ Rea ≤ 56 500) delivered sufficient means to propose power-law expressions for the longitudinal evolution of the skin friction, normal drag, and turbulent boundary layer (TBL) length scales. Surprisingly, the LES computations of the curved cylinders at analogous geometric and kinematic conditions as the straight cylinder showed similar character in terms of the longitudinal skin friction. Beyond incidence 1°-3° (upper end corresponds to the highest simulated Rea), the skin friction was directly proportional to the yaw angle and monotonically shifted downward with higher Rea. Conversely, the flow structure, normal drag, TBL length scales, Reynolds stresses, and the separation state of the transverse shear layers towards regular vortex shedding for the curved cylinder were highly dissimilar than the straight one at equivalent incidence angles.