Abstract
In this work we study the turbulence modulation in a viscosity-stratified two-phase flow using Direct Numerical Simulation (DNS) of turbulence and the Phase Field Method (PFM) to simulate the interfacial phenomena. Specifically we consider the case of two immiscible fluid layers driven in a closed rectangular channel by an imposed mean pressure gradient. The present problem, which may mimic the behaviour of an oil flowing under a thin layer of different oil, thickness ratio h2/h1 = 9, is described by three main flow parameters: the shear Reynolds number Reτ (which quantifies the importance of inertia compared to viscous effects), the Weber number We (which quantifies surface tension effects) and the viscosity ratio λ = ν1/ν2 between the two fluids. For this first study, the density ratio of the two fluid layers is the same (ρ2 = ρ1), we keep Reτ and We constant, but we consider three different values for the viscosity ratio: λ = 1, λ = 0.875 and λ = 0.75. Compared to a single phase flow at the same shear Reynolds number (Reτ = 100), in the two phase flow case we observe a decrease of the wall-shear stress and a strong turbulence modulation in particular in the proximity of the interface. Interestingly, we observe that the modulation of turbulence by the liquid-liquid interface extends up to the top wall (i.e. the closest to the interface) and produces local shear stress inversions and flow recirculation regions. The observed results depend primarily on the interface deformability and on the viscosity ratio between the two fluids (λ).
Highlights
Fluid transportation inside pipelines and channels requires the application of an external pumping power to win the friction losses at the walls
Regardless of the value of the viscosity ratio λ, the presence of the liquid-liquid interface influences the mean flow velocity
The simulations were run at a reference shear Reynolds number Reτ = 100 and different values of the viscosity ratio, λ = ν1/ν2, were considered (λ = 1.000 − 0.875 − 0.750)
Summary
Fluid transportation inside pipelines and channels requires the application of an external pumping power to win the friction losses at the walls. One possible strategy to limit the corresponding cost for fluid transportation is obtained by the injection of a low-viscosity fluid, which in most cases is water [1] The effectiveness of this technique is due to the natural tendency of water to migrate towards the wall, in the high-shear region, so to lubricate the flow [2]. Due to its importance in the petroleum industry and in the process and chemical engineering, the present flow configuration has been extensively studied and analyzed in the past [3, 3,4,5,6] Literature in this field is vaste and old, dating back to the seminal industrial patents of [7] and [8]. An exhaustive literature review on the various aspects of the problem, together with an in-depth analysis of patents and solutions already existing is given for instance by [9] and [1]
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