Friction drag model for axial turbulent flow along the surface of a circular cylinder based on the universal characteristics of wall turbulence

Abstract

The friction drag of the axial flow along the outer surface of a cylinder varies with the cylinder radius and flow conditions. This study included direct numerical simulations of the axial turbulent flow along a circular cylinder under different conditions for obtaining the turbulence statistics and wall friction coefficient. Then the characteristics of velocity streaks were observed from a geometrical perspective of turbulence structures around the circular cylinder, and compared with the characteristics of the turbulence structures in a boundary layer on a flat plate. The results showed that the velocity streak spacing and the distance between the velocity streak and the cylinder surface in the viscous length scale do not vary substantively with the radius of the cylinder, and are the same as those of the turbulent flow along a flat plate. Therefore, they can be considered geometrical characteristics of the turbulence structure independent of the cylinder radius. Moreover, the friction coefficient per pair of high- and low-speed velocity streaks is the same as that of flat-plate turbulent flow, independent of the cylinder radius, and can be regarded as a dynamical characteristic for a pair of velocity streaks. Two equations were derived based on the characteristics of wall turbulence. The characteristics of the turbulence predicted by the two formulae were consistent with the simulation results. Consequently, we showed that the wall friction coefficient and number of the velocity streak pairs, which are statistical and structural characteristics of wall turbulence, can be predicted appropriately by specifying the radius Reynolds number.