Energy balance in lubricated drag-reduced turbulent channel flow

We use direct numerical simulation (DNS) to study drag reduction in a lubricated channel, a flow instance in which a thin layer of lubricating fluid is injected in the near-wall region so as to favour the transportation of a primary fluid. In the present configuration, the two fluids have equal density but different viscosity, so that a viscosity ratio. =.1/.2 can be defined. To cover a meaningful range of possible situations, we consider five different lambda in the range 0.25 <= lambda <= 4. All DNS are run using the constant power input (CPI) approach, which prescribes that the flow rate is adjusted according to the actual pressure gradient so as to keep constant the power injected into the flow. The CPI approach has been purposely extended here for the first time to the case of multiphase flows. A phase-field method is used to describe the dynamics of the liquid-liquid interface. We unambiguously show that a significant drag reduction (DR) can be achieved for lambda <= 2.00. Reportedly, the observed DR is a non-monotonic function of. and, in the present case, is maximum for lambda = 1.00 (similar or equal to 13% flow-rate increase). Upon a detailed analysis of the energy budgets, we are able to show the existence of two different DR mechanisms. For lambda = 1.00 and lambda = 2.00, DR is purely due to the effect of the surface tension - a localized elasticity element that separates the two fluids - which, decoupling the wall-normal momentum transfer mechanisms between the primary and the lubricating layer, suppresses turbulence in the lubricating layer (laminarization) and reduces the overall drag. For lambda < 1.00, turbulence can be sustained in the lubricating layer, because of the increased local Reynolds number. In this case, DR is simply due to the smaller viscosity of the lubricating layer that acts to decrease directly the corresponding wall friction. Finally, we show evidence that an upper bound for lambda exists, for which DR cannot be observed: for lambda = 4.00, we report a slight drag enhancement, thereby indicating that the turbulence suppression observed in the lubricating layer cannot completely balance the increased friction due to the larger viscosity.

Automated summary

This study investigates drag reduction in a lubricated channel using direct numerical simulation, revealing a significant reduction in drag under certain conditions dependent on the viscosity ratio of the two fluids. Through detailed energy budget analysis, two distinct drag reduction mechanisms are identified.