Energy and Nuclear Engineering

ALESSANDRO TASSONE

After successfully undertaking the course, the student will acquire the following competences:

1. Understanding the specific thermal-hydraulic phenomena associated with liquid metals that are relevant for industrial applications

2. Performing back-of-the-envelope engineering calculations (pressure drop, heat transfer coefficient, etc.) for liquid metal flows in various prototypical problems

3. Characterizing and critically assessing the thermal performance of a liquid metal component in an energy engineering system

4. Performing computational fluid-dynamic simulations to support the design of a liquid metal component

Prior knowledge of electromagnetism, fluid mechanics, and heat transfer at Bachelor level is required. Supplementary learning material may be provided at the discretion of the teachers. Previous familiarity with computational fluid dynamics tools, in general, and OpenFOAM, in particular, is beneficial, but it is not assumed at the onset of the course. Basic familiarity with the command terminal in Unix-based operative systems (Ubuntu, RedHat, CentOS, etc.) is a plus, but you will have time to get acquainted during the course.

Please note that the course programme listed below should be taken as a roadmap, rather than a strict schedule. Given the ”hands-on” nature of the laboratory, we will strive to minimize the frontal presentation of the learning material in favor of activities intended to operate with these concepts. The goal is to develop and refine the tools to be applied during the capstone project. Moreover, depending on the project selected for each project iteration, not all material may be covered.

1. Fundamentals of liquid metal thermal-hydraulics: industrial applications of liquid metals, thermophysical properties. Continuity equation, incompressible flow. Navier-Stokes equations, Newtonian fluid. Energy equation.
2. Introduction to Computational Fluid Dynamics (CFD) and discretization in the Finite Volume Method (FVM): how CFD works and CFD in a nutshell, discretization global view, the FVM, how to apply the FVM: the case of a heat spreader.
3. Fluid mechanics in ordinary (OHD) and magnetohydrodynamic (MHD) conditions: OHD governing paramenters, laminar boundary layer, pressure loss in OHD conditions, from OHD to MHD, MHD governing parameters, the MHD boundary layer, laminar MHD flows in rectangular and circular channels, pressure loss estimate in MHD conditions
4. The pressure-velocity coupling for incompressible flows: the SIMPLE, PISO and PIMPLE algorithms, segregated and monolithic solvers.
5. A deeper look to two OpenFOAM solvers: introduction to OpenFOAM, pimpleFoam: a walkthrough in a transient turbulent solver, phimpleFoam: multiphysics solver for MHD applications.
6. Your first OpenFOAM simulations: laminar OHD and MHD flows in prototypical configurations. Capstone project presentation.
7. An introduction to turbulence and turbulence modeling in OpenFOAM: instability and transition, vortex stretching and energy cascade, Reynolds decomposition and mean-flow equations, turbulent viscosity models, other modeling approaches. Simulation of turbulent flows in prototypical configuration.
8. Heat transfer in liquid metals: laminar heat transfer in OHD and MHD conditions. Limitations of Reynolds analogy for turbulent heat transfer in fluids at low Prandtl number, turbulent Prandtl number, prediction of turbulent heat flux beyond the Reynolds analogy. Effect of magnetic field on turbulence and transition. MHD turbulent heat transfer.
9. Revising your first OpenFOAM simulation... now with heat transfer!
10. Capstone project no.1: definition of the physical problem and sketch of the mathematical model. Identification of design quantities and preliminary back-of-the-envelope calculations.
11. Capstone project no.2: definition of the boundary and initial conditions for the numerical model. Implementation of the numerical model. Test matrix for mesh independence and convergence analysis.
12. Capstone project no.3: open discussion of the preliminary detailed numerical results.

No comprehensive textbook exists to cover the learning material discussed in this course. The following are suggestions intended to expand and integrate what is present in the lecture notes distributed by the teachers through the course website, which can be found at this link: https://elearning.uniroma1.it/course/view.php?id=13385. Fundamental elements of liquid metal thermal-hydraulics are covered in Chapter 10 of the NEA handbook on lead and lead alloys. This resource can be freely downloaded on the following web page: https://inis.iaea.org/ records/m5n7f-ehr11.This resource covers most of the material discussed in the course section Theory and phenomenology and, as such, it is the most important reference.
For the interested reader, a more in-depth discussion with a particular focus on liquid metal applications in nuclear fission reactors can be found on: Roelofs, Ferry, ed. Thermal Hydraulics Aspects of Liquid Metal Cooled
Nuclear Reactors. Woodhead Publishing, 2018, https://doi.org/10.1016/C2016-0-01216-0. Table of Contents.
Regarding theoretical aspects of liquid metal magneto-thermal-hydraulics, which are relevant for applications in magnetic confinement fusion reactors and liquid metal batteries, one may refer to the following textbook: Müller, Ulrich, and Bühler, Leo. Magnetofluiddynamics in Channels and Containers. Springer Berlin, Heidelberg, 2001. Table of Contents.
Concerning the Numerical modelling section of the course, the following reference is recommended: Moukalled, Fadl and Mangani, Luca and Darwish, Marwan. The Finite Volume Method in Computational Fluid Dynamics: An Advanced Introduction with OpenFOAM® and Matlab, Springer Cham, 2016. Table of Contents.

No comprehensive textbook exists to cover the learning material discussed in this course. The following are suggestions intended to expand and integrate what is present in the lecture notes distributed by the teachers through the course website, which can be found at this link: https://elearning.uniroma1.it/course/view.php?id=13385. Fundamental elements of liquid metal thermal-hydraulics are covered in Chapter 10 of the NEA handbook on lead and lead alloys. This resource can be freely downloaded on the following web page: https://inis.iaea.org/ records/m5n7f-ehr11.This resource covers most of the material discussed in the course section Theory and phenomenology and, as such, it is the most important reference.
For the interested reader, a more in-depth discussion with a particular focus on liquid metal applications in nuclear fission reactors can be found on: Roelofs, Ferry, ed. Thermal Hydraulics Aspects of Liquid Metal Cooled
Nuclear Reactors. Woodhead Publishing, 2018, https://doi.org/10.1016/C2016-0-01216-0. Table of Contents.
Regarding theoretical aspects of liquid metal magneto-thermal-hydraulics, which are relevant for applications in magnetic confinement fusion reactors and liquid metal batteries, one may refer to the following textbook: Müller, Ulrich, and Bühler, Leo. Magnetofluiddynamics in Channels and Containers. Springer Berlin, Heidelberg, 2001. Table of Contents.
Concerning the Numerical modelling section of the course, the following reference is recommended: Moukalled, Fadl and Mangani, Luca and Darwish, Marwan. The Finite Volume Method in Computational Fluid Dynamics: An Advanced Introduction with OpenFOAM® and Matlab, Springer Cham, 2016. Table of Contents.

Lectures are delivered in Italian or English according to the audience. Study material is provided only in English. One office hour per week, communicated at the onset of the course, is reserved for private meetings with students. After successfully undertaking the course, the student will acquire the following competences:
• Understanding the specific thermal-hydraulic phenomena associated to liquid metals that are relevant for industrial applications
• Performing back-of-the-envelope engineering calculations (pressure drop, heat transfer coefficient, etc.) for liquid metal flows in various prototypical problems
• To be able to characterize and critically assess the thermal performance of a liquid metal component in an energy engineering system
• To be able to perform computational fluid-dynamic simulations to support the design of a liquid metal component
The course is taught over 15 hours of frontal lectures and 15 hours of laboratory sessions, for a total of 30 hours of lectures and, thus, upon completion, it awards 3 ETCS/CFU.

The course is delivered in presence according to the official timetable released by the University. Lectures are typically recorded (depending on the state of the in-class equipment) and are then distributed through the course website. Transcripts may be produced upon request. A minimum attendance to 75% of the delivered lectures is required in order to be eligible for a passing grade.

Passing grade (idoneità) is awarded after the presentation of the capstone student project. Please note that, since this is an AAF, the grade is not expressed in numbers but only as a ”GO/No-GO”. The student project is dedicated to the design of an industrial component operating with liquid metals among those discussed in the course material. The workload estimated for the project completion is about one week. The project evaluation is individual but cooperation across the student cohort is encouraged.
A brief presentation (≈10 minutes) should be prepared summarizing the project methodology and results. The exam will consist on the delivery and discussion of this presentation (≈10 minutes of Q&A about the project and course material). It should be shared with the teacher no later than a week before the scheduled date for the examination. The date can be scheduled by email within any of the allowable exam sessions and at least one week prior of the desired date.

The following are some examples of possible capstone projects. Actual course projects may differ depending on external circumstances:
1. Once-through Helical Steam Generator for Fission and Fusion reactors: lead-bismuth eutectic external crossflow over rod bundles.
2. Receiver Tube for Concentrated Solar Power: molten sodium internal flow in circular pipes.
3. First Wall Cooling System for Magnetic Fusion Reactors: liquid lithium internal MHD flow in square conduits.
4. Liquid Metal Compact Heat Exchanger: gallium alloy laminar heat transfer in internal flows.
5. Lead-cooled Fast Reactor Pool Thermal-hydraulics: external natural convection triggered by internal heated square obstacle.

The following are some examples of possible capstone projects. Actual course projects may differ depending on external circumstances:
1. Once-through Helical Steam Generator for Fission and Fusion reactors: lead-bismuth eutectic external crossflow over rod bundles.
2. Receiver Tube for Concentrated Solar Power: molten sodium internal flow in circular pipes.
3. First Wall Cooling System for Magnetic Fusion Reactors: liquid lithium internal MHD flow in square conduits.
4. Liquid Metal Compact Heat Exchanger: gallium alloy laminar heat transfer in internal flows.
5. Lead-cooled Fast Reactor Pool Thermal-hydraulics: external natural convection triggered by internal heated square obstacle.

• Fundamentals of liquid metal thermal-hydraulics


• Introduction to Computational Fluid Dynamics (CFD) and discretization in the Finite Volume Method (FVM)


• Fluid mechanics in ordinary (OHD) and magnetohydrodynamic (MHD) conditions


• The pressure-velocity coupling for incompressible flows


• A deeper look to two OpenFOAM solvers


• Your first OpenFOAM simulations


• An introduction to turbulence and turbulence modeling in OpenFOAM


• Heat transfer in liquid metals


• Revising your first OpenFOAM simulation... now with heat transfer!


• Capstone project