On the Large-eddy Simulation ofCoupled Flows in Air-Water Systems

The objective of this work is to develop an efficient domain decomposition method for the simulation of multiple fluid flows, of interest in geophysical and environmental fluid mechanics, using non-overlapping grids. An explicit sub-structuring domain decomposition method that enforces the compatibility conditions present between non-miscible fluid flows is shown. The current methodology is used for the study of coupled canonical co-current, and counter-current, flows for low Reynolds Numbers. Additionally, the study around immersed obstacles in coupled Poiseuille-Couette flows is made. An incremental-pressure correction method for the numerical integration of the semidiscrete projection dual of the Navier-Stokes equations is implemented, replacing the one implemented originally in the present code [52], LES-COAST. The inclusion of the pressure gradient in the predictor step of the solution method guarantees a higher-order of convergence in the L2 space, while dispensing of the deferred-correction needed at the boundaries for the fluxes in the pressure Poisson equation. For LES modelling, the method explicitly guarantees that inertia should balance with the gradient of pressure in the momentum equation, for sufficiently small time steps, hence the increase in convergence rate. A large-eddy simulation of a counter-current gas-liquid flow is performed. At the flat interface where the different fluids meet, continuity of momentum and momentum fluxes are enforced following the proposed coupling strategy. The increase in vertical vorticity fluctuations near the interface increases mixing, reducing the thickness of the inner region of the boundary layer. Such increase reduces shear while allowing for more frequent backflow motions in the inner region, being this phenomenon stronger on water. Due to the higher inertia of water these backflow motions are ultimately responsible for the streaky structure of shear stresses seen along the interface. By extracting the motions that are relevant for fluid Reynolds stress coupling [29], such motions reveal a bimodal behavior of streamwise velocities that are only weakly related to its vertical counterparts. The present study shows that such bimodality in the streamwise velocities is also seen in the angle distribution of vorticity relative to the interface, where such angles are linked to the presence of interfaceconnected and quasi-streamwise vortex cores. Finally, it is shown that backflow events on i the interface shear stresses correlate with coupled ‘strong’ ejections in the near interface region despite the disparagingly different near-interface streamwise velocity distributions on the near interface boundary layers. The problem of a low-Reynolds number wind-driven Couette flow on water is computed by solving the spatially filtered Navier-Stokes equations, where the flow of the wind is also solved numerically and coupled to the lower shallow whater channel. The unresolved, subgrid scales are modelled via a Dynamic Smagorinsky model. The present work emphasize on the results obtained for the water phase of the system, while for the air phase some first-order statistics are shown. Results of the simulation indicate that the flow in the shallow channel shares some similarities with classical Couette flows, nevertheless the new boundary condition allows for the increase in intermittency of the flow variables and of horizontal turbulent mixing which render a thinner boundary layer near the interface. The now thinner interface boundary layer is more dependent on outer region motions, where inclined vortex structures impinge the near-interface sub-layer. Unlike Couette flows the peak of Reynolds stress is no more at the centreline of the channel, instead the maximum is located on the buffer region of the interface boundary layer breaking the skew-symmetry present in classical Couette flows. Finally, the influence of a row of circular cylinders immersed in the turbulent boundary layers formed across the interface between two highly stratified, non-miscible fluids is investigated numerically using LES. A co-current Poiseuille-Couette flow is generated on the binary fluid system, and is used as inflow for the current flow study. The interaction between the flows is enforced via the implemented coupling strategy, where each subdomain passes to the other either the kinematic or the dynamic interface conditions. It is found that for low-Re the structure acts partly a modulator of the incoming turbulent structures in the lighter fluid side, while at the heavier fluid side the maxima of TKE are found on the interface. Also, it is shown that the coupling induces an inclination on the near-interface coherent structures generated on the heavier fluid flow.