Modelagem matemática e simulação numérica de correntes de gravidade em uma configuração canal-bacia

Abstract

Gravity currents are flows generated by the pressure gradient due density differences between two fluids which are in contact. In this work are presented a set of three-dimensional highly resolved direct numerical simulations of particle-laden gravity currents, solved in an original configuration called channel-basin. The focus is on low concentrations gravity currents, where the density differences are small enough for the Boussinesq approximation may be valid. The mathematical model is based on an Eulerian description of the concentration field by using a transport equation, combined with the incompressible Navier-Stokes equations. The equations are solved by the open-source code Incompact3d, which is based on high-order compact schemes for the concentration and velocity fields discretization, and a spectral method for the pressure field. The adopted mathematical modeling allows the particle sedimentation, however there is no possibility of re-suspension of the particles already deposited, nor the bottom deformation due the growth of the sediment layer thikness. The main goal of this reserach is to know how the initial parameters, such as Reynolds number, settling velocity and channel geometry, affect the dynamics of the current spreading. The results have shown that the spreading form is highly dependent of the settling velocity. For the front velocity of the current, the channel geometry and settling velocity are more important when the Reynolds is lower than when it is higher. The sedimentation rate is highly affected by the settling velocity. The increasing of the Reynolds number mainly affects the size of the turbulent structures such as vortex and lobes. The energy budget is strongly dependent of the settling velocity and slightly dependent of the channel geometry and Reynolds number.