Turbulent drag reduction in channel flow with viscosity stratified fluids

Abstract

In this work, the turbulent flow of two immiscible fluids in a closed channel has been investigated. A thin layer of lubricating fluid (viscosity _1 ) flows on top of a thick layer of transported fluid (viscosity _2 ). The system has been analysed performing Direct Numerical Simulation (DNS) of the Navier-Stokes equations coupled with a Phase- Field Method (PFM) to describe the interfacial dynamics. The aim is to investigate the influence of the viscosity ratio = _1 /_2 (ratio between the viscosities of the two fluids) and of the Weber number W e = u_ h/ (ratio between inertial and surface tension forces) on the system behaviour. The setup consists of a thin lubricating layer (thickness t_1 = 0.15h) which flows on top of a thick layer (thickness t_2 = 1.85h) in a channel of total height 2h. Different combinations of the parameters have been considered, three viscosity ratios: = 1.00 (matched viscosity), = 0.50 and = 0.25 and three Weber numbers: We = 0.25 (higher surface tension), We = 0.50 and We = 1.00 (lower surface tension). The simulations are performed at a fixed shear Reynolds number Re_ = 300 and driving the flow along the streamwise direction with a constant mean pressure gradient. The simulation outcomes show that drag reduction (flow-rate increase) is obtained for all the six different cases considered. In particular, even when the matched viscosity case is considered a strong increase of the main layer flow-rate is observed. The analysis performed highlight two distinct drag reduction mechanisms: For the matched viscosity cases ( = 1), the drag reduction is directly linked to the laminarization of the thin lubricating layer, by opposite for the low viscosity cases ( < 1), turbulence can be sustained in the lubricating layer and drag reduction is achieved thanks to the low viscosity of the lubricating layer.