Description du sujet de thèse

Background
The potential uses of high-temperature molten salts for energy applications such as nuclear and solar energy, energy storage, and liquid batteries have attracted significant interest in recent years. For nuclear reactor applications, molten salts have been proposed both as fuel carriers and as reactor coolants, with the potential to improve safety and fuel recycling performance in next-generation reactors, and possibly surpassing the current standards. In addition, many of these new reactor designs rely on passive systems to ensure three fundamental safety functions of a nuclear reactor which are: reactivity control, fuel cooling, and confinement of radioactive materials during accidents. Passive safety systems are by definition designed to provide these functions without operator intervention or external power supply.

Among the various physical mechanisms commonly employed in passive systems, natural circulation of the coolant is a key phenomenon used in nuclear reactors to remove decay heat, which is the residual heat generated after the fission chain reaction has been halted, during normal and accidental scenarios. Natural circulation enables heat transport from a hot source to a cold sink by exploiting density differences in the coolant caused by temperature gradients along the circuit. The use of such a simple heat removal mechanism enhances the reliability of passive systems compared to active safety systems, which typically rely on pumps, motors, mechanical components, and external power supplies. The implementation of passive safety systems in nuclear reactors has become a major recommendation following the lessons learned from the Fukushima accident.

Molten salts are well suited for developing reactor heat removal systems based on natural circulation due to their high operating temperatures, low pressures, excellent stability under irradiation, very good fission product retention, and high thermal energy storage capacity. Natural circulation heat removal systems are particularly important in Generation IV reactors, such as Molten Salt Reactors (MSRs), as these designs are intended to meet very high safety standards. Therefore, a fundamental understanding of natural circulation systems, both in steady-state and transient conditions, is essential for reactor design and safety assessment of these new designs. One of the key aspects of a natural circulation flow is its stability with respect to an external or internal perturbation or change. A methodology for stability analysis that enables the characterization of natural circulation systems in Generation IV reactors using molten salts is thus necessary. The development of such methodology has been carried-out through previous PhD projects [1][2][3][4][5] and is currently being continue through a collaboration between Politecnico di Milano and CNRS in the framework of the European project ENDURANCE (2024–2028). Within this project, Work Package 3 (WP3) focuses on various experiments aimed at studying phenomena relevant to MSR safety. Task 3.3 of WP3 specifically addresses the extension of the stability analysis methodology and the related experimental work. The proposed PhD thesis will make a major contribution to this task. The PhD candidate will join the teams at Politecnico di Milano and LPSC-Grenoble working on this subject.

PhD project objectives
The main goal of this PhD project is to conduct new experimental studies to extend an existing numerical stability analysis methodology by incorporating phenomena that were either previously unaccounted for or insufficiently addressed. These enhancements aim to enable the application of the stability analysis method to more complex engineering systems, particularly those resembling the Passive Decay Heat Removal systems found in Molten Salt Reactors (MSRs). The additional phenomena to be considered include, but are not limited to: variations in fluid viscosity and density due to large temperature gradients (i.e., low-Mach-number compressibility effects), Prandtl number influences, heat exchange with the surroundings, three-dimensional flow effects, and turbulence effects. The PhD work is also expected to contribute to improving the computational efficiency of the methodology by building upon prior efforts involving the use of Reduced Order Methods (ROM) for numerical implementation. Further improvements to the numerical tool may include implementing an exhaustive search for the system's equilibrium states and characterizing the system's response using Power Spectral Density and coherence analyses of the flow velocity field, as obtained from both experiments and numerical simulations. Regarding the experimental aspect, the current project aims to enhance the results from the existing Flat Cavity experiment (2D flow) developed at the LPSC [4] by modifying the experimental setup and performing new experiments, and to develop a new 3D cavity experiment at Politecnico di Milano (Polimi) to study 3D and turbulence flows. Finally, another potential area of exploration in this project is the use of alternative approaches, such as entropy balance methods, to characterize the stability of the experimentally measured flow field.

Work organization
The PhD work will be organized according to the following four phases. Phases 1 and 2 will last a total of 18 months and the work will be developed at the LPSC-Grenoble. Phases 3 and 4 will be developed in the following 18 months at the department of energy of the Politecnico di Milano (Polimi).

Phase 1 (~9 months): Experimental Setup Enhancement
During this phase, the existing Flat Cavity experiment at LPSC [4] will be modified to improve the quality of flow measurements (such as temperature measurements using more accurate thermocouples), the control of boundary conditions (by reducing heat exchange with the surroundings through the use of an insulated experiment box), and the initialization conditions and the search of the system states (by developing a new experimental startup procedure). The experimental setup will also be refined to better control operating parameters, including the choice of coolant, cavity dimensions or geometry, and setup conditions (heat flux, temperature variation, etc.). Additionally, lateral heaters will be used to simulate a volumetric heat source. In the first months of this phase, several configurations will be tested to identify the most performant ones. The most performant configurations will be those in which the natural circulation system exhibits the greatest number of possible flow states, bifurcation points, and eventually hysteresis behavior. Based on these preliminary experimental studies (that will last approximately 6 months), a focused experimental campaign will be conducted during the remaining 3 months. Measurements will include thermocouple data and Particle Image Velocimetry (PIV) readings. Data analysis will involve reconstructing flow velocity fields and applying frequency and phase analysis tools (e.g., Power Spectral Density and coherence analyses) to study oscillatory flow behaviors and enable comparison with numerical simulations. The possibility of performing experimental stability analysis will also be investigated.

Phase 2 (~9 months): Numerical Modeling and Stability Analysis
During this phase, the existing CFD model of the Flat Cavity will be adapted to match the conditions observed in the new experiments. Most configurations will involve laminar flow regimes. The simulated flow fields will be compared with experimental measurements to assess model accuracy. Then for tor selected configurations, detailed stability analyses will be performed using the numerical tool and compared against the experimental data. Results from both these experimental and numerical investigations will be documented in an internal progress report that will be used later in the PhD manuscript.

Phase 3 (~12months): Design of a 3D Experimental Facility and experimental campaign
In this phase, the PhD candidate will contribute to the design of a new 3D experimental setup to be constructed at Politecnico di Milano (Polimi). Since most test case studies for natural circulation stability relies on a two-dimensional setup, a set of experiments will be performed at PoliMi to avoid neglecting three-dimensional effects related to recirculation regions and local turbulence. This is meant to prove the capability of the stability analysis methodology also for three-dimensional geometry. Indeed, some of the current MSR designs are characterized by a lack of internal structures thus requiring experimental and numerical studies of natural circulation in full 3D systems. This setup will be based on an existing metallic container filled with molten salt (nitride salt) and equipped with internal electric heaters to simulate internal heat generation. The heat sink will be represented by an aptly chosen heat exchanger. The new facility will allow for the characterization of the 3D natural circulation regime within a cylindrical cavity.. A critical aspect of the design will be the implementation of temperature measurement systems to enable flow pattern identification and comparison against numerical results. The facility will also serve as a platform for studying the effects of turbulence in natural circulation systems, in particular concerning the stability and to validate the stability analysis methodology

Phase 4 (~6 months): 3D Modeling and Dissertation Writing
During this phase, a CFD model for the 3D natural circulation experiment will be developed. This will serve both as pre-test tool in order to guide the design of the experiment (e.g., positioning of the thermocouple and the heat exchanger) and for post-test analysis. Simulation results will be compared against experimental data, and, if appropriate, the model will be used to conduct a stability analysis. In the final part of this phase, the PhD manuscript will be finalized for the dissertation defense.

References:
[1] A. Pini, A. Cammi, M. Cauzzi, F. Fanale, L. Luzzi, “An experimental facility to investigate the natural circulation dynamics in presence of distributed heat sources”, Energy Procedia 101 (2016) 10–17.
[2] A. Pini, A. Cammi, S. Lorenzi, M.T. Cauzzi, L. Luzzi, “A CFD-based simulation tool for the stability analysis of natural circulation systems”, Progress in Nuclear Energy 117 (2019) 103093.
[3] J. Narvaez, A. Cammi, S. Lorenzi, P. Rubiolo, “Numerical methodology for design and evaluation of natural circulation systems for MSR applications”, International Topical Meeting on Advances in Thermal Hydraulics 2022 (ATH'22), Anaheim, USA, June 2022.
[4] J. Narvaez, P. Rubiolo, A. Cammi, S. Lorenzi, “Design of a Natural Circulation Experiment to Investigate Flow Stability”, 20th International Topical Meeting on Nuclear Reactor Thermal Hydraulics (NURETH-20), Washington, USA, August 2023.
[5] J. Narvaez, “Numerical and experimental study of the dynamic behavior of natural circulation systems using molten salts for heat removal”, PhD Thesis, Université Grenoble Alpes, I-MEP2 (November 2024).


Recommended technical background and skills for candidates:
(i) Fluid mechanics and heat transfer; (ii) Basic knowledge of Computational Fluid Dynamics (CFD), particularly in thermal-hydraulics; (iii) Basic understanding of experimental fluid techniques, such as Particle Image Velocimetry (PIV), and familiarity with measurement instruments like thermocouples; (iv) Programming skills in Python and C++; (v) Basic knowledge of nuclear reactor design and safety. Experience with the OpenFOAM software is a plus. During the project, the student is expected to present their work at least once at an international conference in the field. The candidate is also expected to publish at least one paper in a peer-reviewed international journal.

Language proficiency:
• English proficiency: Advanced level (C1)
• French proficiency (optional): Beginner level (A1)

Contexte de travail

The Laboratoire de Physique Subatomique et de Cosmologie (LPSC) in Grenoble (http://lpsc.in2p3.fr) is a joint research unit affiliated with CNRS-IN2P3, Université Grenoble Alpes (UGA), and Grenoble INP. The laboratory hosts an average of approximately 230 staff members. The PhD candidate will be assigned to the Reactor Physics group at LPSC, which is composed of 10 staff members. The candidate will work within at the FEST (Fluids Experiments and Simulations in Temperature) experimental Platform and will report directly to the head of the group. His thesis co-directors (supervisors) will be Pablo RUBIOLO (40%) and Stefano LORENZI (50%), with Nicolas CAPELLAN (10%) as the co-advisor.
Modalities of PhD supervision, training monitoring, and research progress tracking
The proposed PhD work will be carried out as part of an ongoing research collaboration between the Laboratoire de Physique Subatomique et de Cosmologie in Grenoble (LPSC-CNRS/IN2P3) and Politecnico di Milano (POLIMI). The PhD will be supervised by P. Rubiolo from LPSC (Co-Director, 40%), S. Lorenzi from POLIMI (Co-Director, 50%), and co-supervised by N. Capellan from LPSC (10%). The PhD student will spend the first 18 months at LPSC (Grenoble) and the remaining 18 months at the Department of Energy at POLIMI (Milan). During the project, the student will participate in biweekly project meetings, held in person at the host institution and remotely with the partner laboratory. During these meetings, the student will report on progress and engage with team members to discuss challenges and potential solutions. These meetings will also help improve the student's scientific communication skills. The student is expected to participate in the international meetings of the ENDURANCE project, which are held twice a year. At LPSC, the student will also benefit from the support of an independent ad-hoc committee dedicated to PhD follow-up. In addition to the courses offered by the doctoral schools at each host institution, the student is expected to attend the summer school organized by ENDURANCE project, as well as any workshop that would be pertinent to the PhD suject.

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