Conference Agenda

Thermal convection is a phenomenon seen in almost all facets of life, ranging from planetary convection to ocean currents and convection inside the earth. The physics of thermal convection complicates when a porous wall layer is present. Flow over urban canopies, forest canopies or flow in underground aquifers are classic examples of such scenarios where thermal buoyancy-driven convection occurs in the presence of turbulent flow over a porous wall layer. The present research work focuses on simulating pressure-driven turbulent flow over a simplified, ordered porous medium consisting of a regular array of cubes. The work further couples it with natural convection arising due to unstable stratification, to provide insight into the momentum and heat transfer characteristics of such a flow scenario.

Direct numerical simulations (DNS) have been performed with a finite-difference solver to validate the model for buoyancy-driven convection and the classical Rayleigh-B´enard convection. Further, we extended the solver with an Immersed Boundary Method (IBM) to model the ordered porous medium, which was validated against reference data. The focal point of the present research, analyzing mixed convection over a porous wall layer, brings into the picture a large number of dimensionless control parameters. The bulk Reynolds in the overlying free channel region is fixed at 5500, the Prandtl number at 0.71. We impose an adiabatic boundary condition on the surface of the cubes. We varied the flux Richardson number to cover different flow scenarios between pure shear and purely buoyancy-driven flows. The porous and free regions are expected to show different convective patterns and different critical flux Richardson numbers for the transition to natural convection cells. Further, the interface regime dynamics should provide insight into the heat transfer characteristics, since the heat transfer timescales vary drastically between the porous region and the turbulent flow region.

We use direct numerical simulation (DNS) to study the problem of drag reduction in a lubricated channel, a flow instance in which two thin layers of a lubricating fluid (e.g. water) are injected in the near-wall region of a plane channel, so to favor the transportation of a primary fluid (e.g. oil). All DNS are run within the constant power input (CPI) approach, which prescribes that the flow-rate is adjusted according to actual pressure gradient so to keep constant the power injected into the flow. A phase-field method (PFM) is used to describe the dynamics of the liquid-liquid interface and when prescribed, also the presence of surfactants/contaminants. As this technique is tailored toward the transport of very viscous fluids like oils, we study the drag reduction performance of the system by keeping fixed the lubricating fluid properties (water) and by considering two different types of oil characterized by different viscosities, 10 and 100 times larger than that of water, respectively. As these systems are also characterized by the presence of contaminants and surfactants – which act by locally reducing the local value of the surface tension – for each type of transported oil, we consider a clean and a surfactant-laden interface. For all the four tested configurations, we unambiguously show that a significant drag reduction (DR) can be achieved. Upon a detailed analysis of the turbulence activity in the two lubricating layers, the interfacial wave dynamics and their interplay, we are able to characterize the effects of surface tension forces, surfactant concentration and viscosity contrast on the drag reduction performance.

We use pseudo-spectral Direct Numerical Simulation (DNS), coupled with a Phase Field Method (PFM), to investigate the turbulent Poiseuille flow of two immiscible liquid layers inside a channel. The two liquid layers, which have the same thickness (h1 = h2 = h), are characterised by the same density (ρ1 = ρ2 = ρ) but different viscosities (η1≠ η2), so mimicking a stratified oil-water flow. This setting allows for the interplay between inertial, viscous and surface tension forces to be studied in the absence of gravity. We focus on the role of turbulence in initially deforming the interface and on the subsequent growth of capillary waves. Capillary wave propagation and interaction is studied by means of a spatiotemporal spectral analysis and compared with previous theoretical and experimental results. Wave propagation is found in agreement with the theoretical dispersion relation. At wave scales larger than the turbulent forcing range the observed scaling of the one-dimensional wavenumber spectrum suggests an energy equipartition regime, which is predicted by theory and recently has been observed in experiments with capillary wave turbulence in microgravity. At wave scales directly forced by hydrodynamic turbulence an initially mild slope of the wavenumber spectrum is succeeded by a sharp decay of wave energy at larger wavenumbers, with the transition taking place near the Kolmogorov-Hinze critical scale, where surface tension forces and turbulent inertial forces are balanced.