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This dissertation focuses on the well-known issue of mass conservation in the context of the finite element technique for computational fluid dynamic simulations. Specifically, non-conventional finite element families for solving Navier-Stokes equations are investigated to address the mathematical constraint of incompressible flows. Raviart-Thomas finite elements are employed for the achievement of a discrete free-divergence velocity. Quadrilateral and hexahedral finite element spaces are considered to investigate the error convergence of different variables. In particular, the proposed algorithm projects the velocity field into the discrete free-divergence space by using the lowest-order Raviart-Thomas element. This decomposition is applied in the context of the projection method, a numerical algorithm employed for solving Navier-Stokes equations. Numerical examples validate the approach’s effectiveness, considering different types of computational grids. Additionally, the dissertation considers an interface advection problem using marker approximation, in the context of multiphase flow simulations. A C++ library is presented, where the implemented algorithm is able to initialize, advect, and reconstruct a marker cloud performing a best-fit quadratic interpolation. Several numerical tests, equipped with an analytical velocity field for the surface advection, are presented to demonstrate the robustness of the algorithm. Lastly, a comparison with an interpolated velocity by using Raviart-Thomas basis functions is shown, with the aim of maintaining zero divergence, mitigating the classical issue of finite element mass loss.

In the framework of a global transition to a low-carbon energy mix, the interest in advanced nuclear Small Modular Reactors (SMRs) has been growing at the international level. Due to the high level of maturity reached by Severe Accident Codes for currently operating rectors, their applicability to advanced SMRs is starting to be studied. Within the present work of thesis and in the framework of a collaboration between ENEA, UNIBO and IRSN, an ASTEC code model of a generic IRIS reactor has been developed. The simulation of a DBA sequence involving the operation of all the passive safety systems of the generic IRIS has been carried out to investigate the code model capability in the prediction of the thermal-hydraulics characterizing an integral SMR adopting a passive mitigation strategy. The following simulation of 4 BDBAs sequences explores the applicability of Severe Accident Codes to advance SMRs in beyond-design and core-degradation conditions. The uncertainty affecting a code simulation can be estimated by using the method of Input Uncertainty Propagation, whose application has been realized through the RAVEN-ASTEC coupling and implementation on an HPC platform. This probabilistic methodology has been employed in a study of the uncertainty affecting the passive safety system operation in the DBA simulation of ASTEC, providing a further characterization of the thermal-hydraulics of this sequence. The application of the Uncertainty Quantification method to early core-melt phenomena has been investigated in the framework of a BEPU analysis of the ASTEC simulation of the QUENCH test-6 experiment. A possible solution to the encountered challenges has been proposed through the application of a Limit Surface search algorithm.

The main purpose of this work is to develop a numerical platform for the turbulence modeling and optimal control of liquid metal flows. Thanks to their interesting thermal properties, liquid metals are widely studied as coolants for heat transfer applications in the nuclear context. However, due to their low Prandtl numbers, the standard turbulence models commonly used for coolants as air or water are inadequate. Advanced turbulence models able to capture the anisotropy in the flow and heat transfer are then necessary. In this thesis, a new anisotropic four-parameter turbulence model is presented and validated. The proposed model is based on explicit algebraic models and solves four additional transport equations for dynamical and thermal turbulent variables. For the validation of the model, several flow configurations are considered for different Reynolds and Prandtl numbers, namely fully developed flows in a plane channel and cylindrical pipe, and forced and mixed convection in a backward-facing step geometry. Since buoyancy effects cannot be neglected in liquid metals-cooled fast reactors, the second aim of this work is to provide mathematical and numerical tools for the simulation and optimization of liquid metals in mixed and natural convection. Optimal control problems for turbulent buoyant flows are studied and analyzed with the Lagrange multipliers method. Numerical algorithms for optimal control problems are integrated into the numerical platform and several simulations are performed to show the robustness, consistency, and feasibility of the method.

The main purpose of this work is to develop mathematical and numerical methods for the optimal control of fluid-structure interaction simulations. In particular, we focus on the Koiter shell fluid-structure model and on the adjoint formalism for the control problem. Using the Koiter approach, the dimensionality of the solid is reduced to reduce the computational cost of the fluid-structure simulations. In order to couple the fluid and the structure domains, the Koiter shell equations are embedded into the fluid equations as a Robin boundary condition. The coupling fluid-structure conditions are automatically treated in an implicit way, so the stability of the numerical scheme is preserved. This model has many applications in cases where a fluid interacts with a thin membrane that deforms mainly in the normal direction. Then, an adjoint-based optimal control theory of the presented Koiter fluid-structure model in the steady case is studied. In fact, a boundary optimal control theory is applied to the fluid-structure Koiter model, including the existence of the solution of the fluid-structure problem, the existence of the optimal solution and regularity and differentiability properties. Moreover, the fractional operators are introduced to be applied to the framework described above, in order to model properly the regularization term in the boundary optimal control problems. All the numerical simulations presented in this work, with the exception of the fractional simulations, have been simulated with the in-house multigrid finite element based code FEMuS.

Fluid-structure interaction (FSI) systems consist of one or more solid structures that deform by interacting with a surrounding fluid flow and are commonly studied in many engineering and biomedical fields. Usually those kind of problems are solved in a direct approach, however it is also interesting to study the inverse problem, where the goal is to find the optimal value of some control parameters, such that the FSI problem solution is close to a desired one. In this work the optimal control problem is formulated with the Lagrange multipliers and adjoint variables formalism. In order to recover the symmetry of the state-adjoint system an auxiliary displacement field is introduced and used to extend the velocity field to the structure domain. As a consequence, the adjoint interface forces are balanced automatically. The optimality system is derived from the first order necessary condition by taking the Fréchet derivatives of the augmented Lagrangian with respect to all the variables involved. The optimal solution is obtained through a gradient-based algorithm applied to the optimality system. In order to support the proposed approach numerical test with distributed control, boundary control and parameter estimation are performed.

Mathematical modeling of physical phenomena is at the basis of many scientific field researches. Complex systems show multiscale and multiphysics aspects that cannot be always taken into account in detail. In the past many numerical codes have been developed and specialized to solve different aspects of turbulence and, in general, fluid motion for a very wide range of engineering applications. Nowadays, numerical code coupling and computational platforms are gaining a lot of interest for the simulation of very complex phenomena. This PhD study focuses on modeling physical systems with coupled simulations, in particular turbulent heat transfer for liquid metals. This type of fluids, known as low Prandtl number fluids, requires more sophisticated turbulent heat transfer models since those used to simulate fluids such as air or water lead to a sensible heat transfer overestimation. Seeking an increased numerical stability, a four logarithmic parameter turbulence model is proposed, starting from a model that has already been validated with simulations of Lead-Bismuth-Eutectic (LBE) fully developed turbulent flows. The turbulence model has been implemented in the finite element code FEMuS to perform an extensive validation by comparing obtained results with Direct Numerical Simulations and experimental data. Many simulations are performed, for fully developed turbulent flows in plane channels, cylindrical pipes and 19 pin nuclear reactor bundles and for turbulent forced and mixed convection over a backward facing step. When conservation equations of mass, momentum and energy need be coupled with dynamic two-equation or thermal turbulence four-equation models the use of numerical coupling becomes important. In order to dispose of a greater choice of dynamical turbulence models, a computational platform containing OpenFOAM and FEMuS codes has been developed.

LORELEI (Light Water One-Rod Equipment for LOCA Experimental Investigation) test device is currently under design in the framework of the planned experimental facilities of the Jules Horowitz Reactor. The main objective of this device is to analyze the thermal-mechanical behavior of the fuel rod and its consequences during a Loss of Coolant Accident (LOCA). The objective of this Thesis is to produce a comprehensive thermal analysis of the LORELEI apparatus by means of CATHARE2 code in order to verify the behavior of the device and to determine the best thermal-hydraulic conditions for the experimental performing. The preliminary part of this thesis aims to illustrate the system and mathematical architecture of the code with a general explanation of the thermal mechanical laws implemented for the FUEL module. An overview of the experimental apparatus, devised so far, is briefly presented to show the characteristics of LORELEI apparatus that can be considered the State of the Art of the LOCA-type facilities. According to the last updated LORELEI geometry, an exhaustive description of apparatus is finalized for a better understanding the CATHARE modeling proposed. This work is aimed to simulate the experimental phase called Re-irradiation phase. This is not a part of the LOCA accidental sequence but it is modeled to provide a study concerning the nominal conditions and to find out the device thermal-hydraulic limits. In this first phase, needed to create a realistic fission product inventory, the device is filled with water and the fuel rod is cooled by using convection flow. The work of this Thesis starts with the simulation of the first part of a LOCA accidental scenario. The fuel cladding temperature is increased and a small amount of water is set in the bottom of the device to produce steam needed for exothermic reactions of the fuel cladding.

In recent years numerical simulations are becoming fundamental for the design of many engineering components. For this reason many multiphysical and multiscale problems are investigated by coupling different existent software created specifically for solving each single problem. However, because of the intrinsic differences among these codes, such coupling is very challenging. In this thesis we develop a computational platform that can be used to integrate different computing tools into the common framework of the SALOME platform. Inside this platform various codes are coupled through numerical libraries with the purpose of exchanging data and melting intrinsic differences. After a description of the generic code integration procedure into the numerical platform, we introduce three classes of problems where different codes have been coupled and complex computational problems are studied. In the irst problem class, the computational platform is used to study a nuclear reactor system. We study the dynamics of a multiscale primary loop of a liquid metal reactor by coupling a mono-dimensional system code with the high resolution three-dimensional full scale core components models. Also we investigate a thermal-hydraulic-neutron multiphysics problem. The heat energy production in the reactor core, obtained by solving the neutron code DRAGON-DONJON, is coupled with the solution of the thermal-hydraulics conservative equations implemented in a in-house code. In the second problem class, we consider multiscale multiphysics Fluid Structure Interaction problems implemented in different modules of the FEMUs code. The mechanics of a three-dimensional particular component of the cardiovascular system is coupled with a mono-dimensional model that takes into account the remaining parts of a simplified circulatory system. Finally, in the last class of problems, Multiphase Fluid tructure Interaction problems are investigated by coupling the solution of a multiphase fluid interface a

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.