Advanced Computational Fluid Dynamics models for liquid metal flows

In this thesis it is shown the development, implementation and numerical solution of several computational fluid dynamics models for the study of liquid metal flows. The work is organized in two main parts in which different modeling techniques are analyzed. These two parts are introduced by a brief chapter on the finite element methods and on the computational platform developed during the Ph.D. studies which have been the basis for the implementation and numerical solution of all the developed mathematical models. In the first part, turbulence modeling based on Reynolds Averaged Navier Stokes equations is considered for the study of turbulent heat transfer in liquid metal flows. A new four parameter turbulence model is introduced and validated in two different k-e and k-w formulations. Several results in four geometries interesting for the fast nuclear reactor field are reported in order to assess and prove the feasibility of this model for the study of turbulent heat transfer in liquid metal flows. In the second part the adjoint optimal control theory is introduced. Some numerical cases are presented by solving the optimality system with state and adjoint variables. The first application is a temperature boundary optimal control in which an improved way of setting boundary conditions in weak form has been developed. The second application is a distributed optimal control problem for the RANS system. Numerical simulations in two and three dimensions have been carried on for this type of applications and are reported in the final chapter.