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In this work we apply the residual-based variational multiscale method (RB-VMS) to the volume-of-fluid (VOF) formulation of free-surface flows. Using this technique we are able to solve such problems in a Large Eddy Simulation framework. This is a natural extension of our Navier-Stokes solver, which uses the RB-VMS finite element formulation, edge-based data structures, adaptive time step control, inexact Newton solvers and supports several parallel programming paradigms. The VOF interface capturing variable is advected using the computed coarse and fine scales velocity field. Thus, the RB-VMS technique can be readily applied to the free-surface solver with minor modifications on the implementation. We apply this technique to the solution of two problems where available data indicate complex free-surface behavior. Results are compared with numerical and experimental data and show that the present formulation can achieve good accuracy with minor impacts on computational efficiency.Keywords Variational multiscale method · Edge-based computations · Volume of fluid · Free surface flows

SUMMARYIn this work we extend our edge-based stabilized finite element incompressible flow solver to turbulence modeling with the residual-based variational multiscale (RB-VMS) method. Using the advective-form of the convection term of the Navier-Stokes equations, RB-VMS is implemented as a straightforward extension of standard stabilized methods with a modified advective velocity. This requires minimum modification of the existing highly optimized code. Two test cases were solved to assess accuracy and performance of the present implementation. First, the laminar incompressible flow past a circular cylinder at Re = 100 and second, the fully turbulent incompressible flow in a lid-driven cubic cavity at Re=12 000. Comparisons were made with standard stabilized finite element formulations, highly resolved numerical simulations and experimental data. Results have shown that the present implementation is able to achieve reasonable accuracy without performance degradation in different flow regimes.

The Diffuser Augmented Wind Turbines (DAWTs) have been widely studied, since the diffusers improve the power coefficient of the wind turbine, particularly of small systems. The diffuser is a device which has the function of causing an increase on the flow velocity through the wind rotor plane due to pressure drop downstream, therefore resulting in an increase of the rotor power coefficient. This technology aids the turbine to exceed the Betz limit, which states that the maximum kinetic energy extracted from the flow is 59.26%. Thus, the present study proposes a mathematical model describing the behavior of the internal velocity for three conical diffusers, taking into account the characteristics of flow around them. The proposed model is based on the Biot-Savart's Law, in which the vortex filament induces a velocity field at an arbitrary point on the axis of symmetry of the diffusers. The results are compared with experimental data obtained for the three diffusers, and present good agreement.

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