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This work aims to extend the techniques used for the optimal control of the NavierStokes systems to control a steady multi-scale FSI system. In particular, we consider a multiscale fluid-structure interaction problem where the structure obeys a membrane model derived from the Koiter shell equations. With this approach, the thickness of the solid wall can be neglected, with a meaningful reduction of the computational cost of the numerical problem. The fluid-structure simulation is then reduced to the fluid equations on a moving mesh together with a Robin boundary condition imposed on the moving solid surface. The inverse problem is formulated to control the velocity on a boundary to obtain a desired displacement of the solid membrane. For this purpose, we use an optimization method that relies on the Lagrange multiplier formalism to obtain the first-order necessary conditions for optimality. The arising optimality system is discretized in a finite element framework and solved with an iterative steepest descent algorithm, used to reduce the computational cost of the numerical simulations.

This work aims to validate a new anisotropic four-parameter turbulence model for low-Prandtl number fluids in forced and mixed convection. Traditional models based on the gradient-diffusion hypothesis and Reynolds analogy are inadequate to simulate the turbulent heat transfer in low-Prandtl number fluids. Additional transport equations for thermal variables are required to predict the characteristic thermal time scale. In a four-parameter turbulence model, two additional transport equations are solved for the temperature variance and its dissipation rate. Thus, it is possible to formulate appropriate characteristic time scales to predict the near-wall and bulk behaviour of mean and turbulent variables. The isotropic version of the four-parameter model has been widely studied and validated in forced and mixed convection. We aim to extend the model validity by proposing explicit algebraic models for the closure of Reynolds stress tensor and turbulent heat flux. For the validation of the anisotropic four-parameter turbulence model, low-Prandtl number fluids are simulated in several flow configurations considering buoyancy effects and numerical results are compared with DNS data.

Computational Fluid Dynamics codes usually adopt velocity-pressure splitting to reduce the computational effort in the solution of the Navier-Stokes equations. In standard projection methods, the finite element approximations show difficulties to find a solution with discrete free-divergence velocity field in all space points. In this work, a new velocity-pressure method for Navier-Stokes equations that projects the velocity field inside the discrete free-divergence velocity space is presented. This algorithm computes the velocity field on the discrete free-divergence space by using Raviart-Thomas finite elements. The projection is obtained by the minimization of the distance, over the discrete free-divergence space, between the auxiliary field and the desired Raviart-Thomas interpolation space. The Raviart-Thomas discretization is based on the quadrilateral and hexahedral finite element space and therefore the divergence mimetic computational approach is used to avoid the well-known degradation of the divergence term convergence. The auxiliary velocity field is obtained by solving the velocity-pressure split system used in the classical Chorin­Temam algorithm. The pressure is recovered by the orthogonal space to the projection on the Raviart-Thomas interpolation space. The method is investigated with an explicit and semi-implicit treatment of the pressure terms. The issues on boundary conditions and the errors in the reproducibility of the tangential components are investigated. Several numerical examples are reported to support this new projection method.

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.

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.

Numerical code coupling is a procedure that allows the solution of multiphysics and multiscale problems. In the present paper we perform a numerical code coupling between the in-house FEM code FEMuS and OpenFOAM. The MED format that come with the SALOME platform is used to exchange data between the two different codes. The test case consists of a squared cavity where the fluid flow is driven by a buoyant force. The momentum and energy equations are solved by both numerical codes. In the coupled case, the temperature field obtained from the FEM solution is used to calculate the buoyancy term of the OpenFOAM momentum balance equation. We investigate the case with low Rayleigh number and report results for both the coupled and uncoupled cases, examining the influences of different domain discretizations.

Engineering applications often require the study of complex systems where multiple physics play a fundamental role in determining the overall dynamics. In order to capture the phenomena of industrial-environmental interest, methods that can capture the influence of the different scales of composite problem must be developed. Due to these necessities multiscale and multiphysics approaches are rapidly becoming a standard in the mathematical-numerical description of engineering systems. This Symposium was organized as an occasion to bring together industrial and environmental researcher and practitioners, in order to discuss techniques that aim to solve this kind of heterogeneous problem in an highly efficient way.