| The lattice Boltzmann method (LBM) is based on the kinetic theory of gas. The idea behind this approach is to obtain the macroscopic dynamics of a fluid from the simulated motion of mesoscopic fluid particles. The solution of the Navier-Stokes equations is then recovered from the Boltzmann equation. As the LBM is explicit and only requires simple and local computations, the resulting scheme is highly efficient for parallel computations. Inversely, the change in physical scale behind the LBM leads to several difficulties, such as the imposition of macroscopic boundary conditions. Despite approximations on the phenomena at the boundaries, the LBM has been successfully applied for the simulation of porous media flows and solid-fluid suspensions.;The main objective of this thesis is to develop an efficient lattice Boltzmann method for the simulation of viscous flows in stirred tanks. To do so, the applicability of the different strategies to impose boundary conditions is first compared. Second, the accuracy of the LBM in the case of complex geometry is characterized. Lastly, the applicability of the LBM for highly non-Newtonian fluid is investigated.;Article 1 illustrates that the accuracy of the scheme is largely affected by the selection of the boundary condition strategy. For instance, in the case of close clearance impellers, the immersed boundary method (IBM) seems to be less accurate. Inversely, the simplest approach, the modified bounce-back rule (MBB), and a more elaborate method, the extrapolation method (EM), which uses the distance from the obstacle to extrapolate missing populations, provide a similar accuracy on characteristic mixing numbers. However, only the EM allows investigating variations of the geometry lower than the lattice spacing. For this reason, this boundary condition strategy is used in the other articles.;Article 2 shows that the LBM accurately predicts the power consumption and pumping capacity of a mixing system. In addition, the impact of geometrical parameters, such as bottom clearance, can likewise be effectively investigated. Moreover, in the case of time dependent geometries, the LBM conserves an acceptable accuracy even if perturbations appear near the impeller.;Lastly, article 3 demonstrates that, under constraint on the maximum Reynolds number, the LBM can be used to simulate highly non-Newtonian fluid flows. For instance, a Carreau-Yasuda model with a power index of 0.05 was used without largely affecting the computational cost of the simulation.;In conclusion, this thesis has permitted to verify the degree of efficiency and utilization of the LBM for the simulation of viscous flows in stirred tanks. It has also shown that this approach can be used for the optimisation of process geometry. Moreover, under some limitations of the Reynolds number, it can be extended to the blending of highly non-Newtonian fluids. (Abstract shortened by UMI.). |
