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 can be defined. To cover a meaningful range of possible situations, we consider five different in the range. 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. Reportedly, the observed DR is a non-monotonic function of and, in the present case, is maximum for (flow-rate increase). Upon a detailed analysis of the energy budgets, we are able to show the existence of two different DR mechanisms. For and, 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 <[CDATA[\u3bb, 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 exists, for which DR cannot be observed: for, 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

Heat transfer in drop-laden turbulence

Heat transfer by large deformable drops in a turbulent flow is a complex and rich-in-physics system, in which drop deformation, breakage and coalescence influence the transport of heat. We study this problem by coupling direct numerical simulation (DNS) of turbulence with a phase-field method for the interface description. Simulations are run at fixed-shear Reynolds and Weber numbers. To evaluate the influence of microscopic flow properties, like momentum/thermal diffusivity, on macroscopic flow properties, like mean temperature or heat transfer rates, we consider four different values of the Prandtl number, which is the momentum to thermal diffusivity ratio:, and. The drop volume fraction is for all cases. Drops are initially warmer than the turbulent carrier fluid and release heat at different rates depending on the value of, but also on their size and on their own dynamics (topology, breakage, drop-drop interaction). Computing the time behaviour of the drops and carrier fluid average temperatures, we clearly show that an increase of slows down the heat transfer process. We explain our results by a simplified phenomenological model: we show that the time behaviour of the drop average temperature is self-similar, and a universal behaviour can be found upon rescaling by. Accordingly, the heat transfer coefficient (respectively its dimensionless counterpart, the Nusselt number) scales as (respectively) at the beginning of the simulation, and tends to (respectively) at later times. These different scalings can be explained via the boundary layer theory and are consistent with previous theoretical/numerical predictions

Turbulence and Interface Waves in Stratified Oil–Water Channel Flow at Large Viscosity Ratio

We investigate the dynamics of turbulence and interfacial waves in an oil–water channel flow. We consider a stratified configuration, in which a thin layer of oil flows on top of a thick layer of water. The oil–water interface that separates the two layers mutually interacts with the surrounding flow field, and is characterized by the formation and propagation of interfacial waves. We perform direct numerical simulation of the Navier-Stokes equations coupled with a phase field method to describe the interface dynamics. For a given shear Reynolds number, Reτ= 300 , and Weber number, We= 0.5 , we consider three different types of oils, characterized by different viscosities, and thus different oil-to-water viscosity ratios μr= μo/ μw (being μo and μw oil and water viscosities). Starting from a matched viscosity case, μr= 1 , we increase the oil-to-water viscosity ratio up to μr= 100 . By increasing μr , we observe significant changes both in turbulence and in the dynamics of the oil–water interface. In particular, the large viscosity of oil controls the flow regime in the thin oil layer, as well as the turbulence activity in the thick water layer, with direct consequences on the overall channel flow rate, which decreases when the oil viscosity is increased. Correspondingly, we observe remarkable changes in the dynamics of waves that propagate at the oil–water interface. In particular, increasing the viscosity ratio from μr= 1 to μr= 100 , waves change from a two-dimensional, nearly-isotropic pattern, to an almost monochromatic one

Propagation of capillary waves in two-layer oil-water turbulent flow

We study the dynamics of capillary waves at the interface of a two-layer stratified turbulent channel flow. We use a combined pseudo-spectral/phase field method to solve for the turbulent flow in the two liquid layers and to track the dynamics of the liquid-liquid interface. The two liquid layers have same thickness and same density, but different viscosity. We vary the viscosity of the upper layer (two different values) to mimic a stratified oil-water flow. This allows us to study the interplay between inertial, viscous and surface tension forces in the absence of gravity. In the present set-up, waves are naturally forced by turbulence over a broad range of scales, from the larger scales, whose size is of order of the system scale, down to the smaller dissipative scales. After an initial transient, we observe the emergence of a stationary capillary wave regime, which we study by means of temporal and spatial spectra. The computed frequency and wavenumber power spectra of wave elevation are in line with previous experimental findings and can be explained in the frame of the weak wave turbulence theory. Finally, we show that the dispersion relation, which gives the frequency as a function of the wavenumber , is in good agreement with the well-established theoretical prediction,

Modelling and computation of drops and bubbles in turbulence

Existence of drops and bubbles in turbulence is granted by their interface. Interfaces are a macroscopic perception of molecular properties, are not property of the drop or the carrier fluid and their role is enormously important in a number of environmental and industrial processes: it is across interfaces that momentum, heat and mass transfer fluxes occur. In this talk, We will briefly review the physics modelling and the current computational methodologies used to track interfaces and we will focus on the phase-field approach, in which the phase distribution is a field described by the order parameter φ. We will present several flow instances and phenomena in which surface tension, density and viscosity are varied, and we will also cover the role of surfactants in altering topological changes of drops (breakage and coalescence) in connection with the characteristics of turbulence. Finally, we will examine the heat transfer between a dispersed phase of large deformable drops and a carrier fluid focusing on the flow structure inside the drops

A Phase Field Method for surfactant-laden multiphase flows with different solubilities

In this work we present a new phase field model for multiphase flows with soluble surfactants that accounts for unmatched solubility. The advection-diffusion of the phase field and of the surfactant is described using two Cahn-Hilliard equations together with a two-order-parameter Ginzburg-Landau free energy functional. Here, an asymmetric term is introduced to penalize the presence of surfactant in one of the phases. This modification allows to circumvent existing limitations on phase field method applications to liquid-gas systems. The model has been tested on planar configurations characterized by two phases with different solubility using a pseudo-spectral code. The results demonstrate the ability to accurately reproduce the expected surfactant distribution. The simulation of a single droplet and of a droplet-droplet interaction in shear flow is then examined in order to understand how the difference in surfactant bulk concentration between the phases affects the overall interfacial behavior

Phase-field modeling of complex interface dynamics in drop-laden turbulence

Turbulent flows laden with large, deformable drops are ubiquitous in nature and in a wide range of industrial processes. Prediction of the interactions between drops, which deform under the action of turbulence, exchange momentum via surface tension, and that can also exchange heat or mass, are complicated due to the wide range of scales involved: from the largest scales of the flow, down to the Kolmogorov scales of turbulence, and further down to the molecular scale of the interface. Due to this wide range of scales, the numerical description of these flows is challenging and requires robust and accurate numerical schemes that are able to capture both the turbulence characteristics and the dynamics of ever-moving and deforming interfaces including their topological changes (i.e., coalescence and breakage). In the past decades, various numerical methods have been proposed for simulating two-phase flows, from interface-tracking methods, where the interface is explicitly tracked with the use of marker points to interface-capturing methods, where the interface is identified as the isovalue of a color/marker function. Phase-field methods belong to the category of interface-capturing methods, and have emerged as promising approaches to simulate complex two-phase flows. In phase-field methods, the transport equation to describe the drop motion is obtained from first thermodynamics principles, and phenomena acting at the interface scale can be conveniently modeled. Although in realistic case scenarios, the physical thickness of the interface cannot be directly simulated, this family of methods offers desirable properties that have attracted the interest of researchers in recent years. In this work, we describe the fundamentals of the phase-field modeling associated with the direct numerical simulation of turbulence in the context of drop-laden flows. We discuss the potentials of the phase-field method with reference to breakage and coalescence phenomena, and to the corresponding drop size distribution; we examine how to model surface tension changes due to surfactant distribution, and we outline the framework to model heat and mass transfer fluxes. Finally, we present our perspectives for future developments of phase-field modeling of drop-laden turbulent flows in the context of the current available literature