Analysis of the drag reduction in turbulent viscosity stratified flows

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 (fluid 2) flowing under a thin layer of different oil (fluid 1), thickness ratio $h_2/h_1=9$, is described by three main flow parameters: the shear Reynolds number $Re_\tau$ (which quantifies the importance of inertia compared to viscous effects), the Weber number $We$ (which quantifies surface tension effects) and the viscosity ratio $\lambda=\nu_1/\nu_2$ between the two fluids. For this first study, the density ratio of the two fluid layers is the same ($\rho_2=\rho_1$), we keep $Re_\tau$ and $We$ constant, but we consider three different values of the viscosity ratio: $\lambda=1$, $\lambda=0.875$ and $\lambda=0.75$. Compared to a single phase flow at the same shear Reynolds number ($Re_\tau = 100$), in the two phase flow case we observe a decrease of the wall-shear stress associated with a substantial increase of the volume-flowrate 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 ($\lambda$).\\ The investigations in this thesis are also for the the case of capillary wave turbulence to describe Weak Turbulence Theory (WTT) from both theoretical and computational considerations.