A skin friction model for axisymmetric turbulent boundary layers along long thin circular cylinders

Abstract

Only a few engineering design models are presently available that adequately depict the axisymmetric skin friction (Cf) maturity along long thin turbulent cylinders. This deficit rests essentially on the experimental and numerical difficulties of measuring (or computing) the spatial evolution of the thin cylinder turbulence. Consequently, the present axisymmetric Cf models have questionable accuracy. Herein, we attempt to formulate a more robust Cf model that owns acceptable error. The formulation is founded on triple integration of the governing equation system that represents a thin cylinder turbulent boundary layer (TBL) at statistical steady-state in appropriate dimensionless units. The final model requires only the radius-based Reynolds number (Rea) and transverse curvature (δ/a) as input parameters. We tuned the accompanying coefficients empirically via an expanded statistical database (over 60 data points) that house new Cf values from large-eddy simulations (LES). The LES computations employed a turbulence inflow generation procedure that permits spatial resolution of the TBL at low-high Reynolds numbers and transverse curvatures. Compared to the new skin friction database, the Cf model revealed averaged predictive errors under 5% with a 3.5% standard deviation. Apart from owning higher values than the flat plate TBL, the most distinguishing characteristic of the axisymmetric skin friction is its rising levels when the boundary layer thickness exceeds the cylinder radius. All Cf levels diminish with increasing Reynolds number. These unique features differentiate the axisymmetric TBL along thin cylinders as a separate canonical flow when compared to the turbulent wall shear-layers of channels, pipes, and planar-type geometries.