Evidence of sublaminar drag naturally occurring in a curved pipe

Abstract

Steady and unsteady flows in a mildly curved pipe for a wide range of Reynolds numbers are examined with direct numerical simulation. It is shown that in a range of Reynolds numbers in the vicinity of Reb ≈ 3400, based on bulk velocity and pipe diameter, a marginally turbulent flow is established in which the friction drag naturally reduces below the laminar solution at the same Reynolds number. The obtained values for friction drag for the laminar and turbulent (sublaminar) flows turn out to be in excellent agreement with experimental measurements in the literature. Our results are also in agreement with Fukagata et al. [“On the lower bound of net driving power in controlled duct flows,” Phys. D 238, 1082 (2009)], as the lower bound of net power required to drive the flow, i.e., the pressure drop of the Stokes solution, is still lower than our marginally turbulent flow. A large-scale traveling structure that is thought to be responsible for that behaviour is identified in the instantaneous field. This mode could also be extracted using proper orthogonal decomposition. The effect of this mode is to redistribute the mean flow in the circular cross section which leads to lower gradients at the wall compared to the laminar flow.