One of the key components of a thermonuclear fusion reactor is the breeding blanket, which fulfills the essential functions of power extraction, tritium breeding, and shielding for radiation-sensitive components and personnel. Liquid metals, like the eutectic alloy lithium lead (PbLi), are considered attractive blanket working fluids due to their combination of excellent thermal properties, high boiling temperature, and tritium breeding capabilities. However, they are characterized also by less desirable features, one of which being the elevate electrical conductivity that results in the reactor intense magnetic field influencing the fluid motion in multiple and subtle ways. In such conditions, the liquid metal behavior can only by described by the governing equations of magnetohydrodynamics (MHD). The transition to the MHD regime is accompanied by several effects including, but not limited to, increased pressure losses due to resistive Lorentz forces, turbulence suppression, modified mass and heat transport mechanisms, etc. A complete understanding of these phenomena is of paramount importance to accurately assess the blanket performances and to realize a design able to fulfill the reactor requirements. The Water Cooled Lithium Lead (WCLL) breeding blanket is one of the two concepts actually being studied for implementation in the DEMOnstration Fusion Power Plant (DEMO) reactor within the framework of the R\&D activities coordinated by the EUROfusion consortium. This concept relies on the separate-cooled architecture, where the liquid metal is utilized exclusively as tritium breeder and neutron multiplier, whereas the role of coolant is fulfilled by pressurized water that, being a non-electrically conductive fluid, is not influenced by the MHD effects. Even if the liquid metal velocity can be minimized to a value determined only by the tritium management requirements, thus reducing the electromagnetic pressure losses compared with blanket where the liquid metal fulfills also the role of coolant, MHD phenomena are still going to drive the blanket design. Despite the importance of a full understanding of these aspects, in the past years only few research activities have been focused on the MHD phenomena occurring in WCLL concept and this was identified as a significant drawback for the blanket design hindering the achievement of a satisfying design maturity. The research activity described in this PhD dissertation has the objective to characterize the basic MHD phenomena for the WCLL blanket with regard to pressure losses and heat transfer with the coolant. The dissertation is divided in two main parts. The first part, described in \Cref{part:companalysis}, concerns a comparative analysis of several alternative configuration for the PbLi in-vessel flow path. The analysis is conducted to identify the solution with most potential for further optimization in the blanket development cycle. The main criteria adopted are MHD pressure losses minimization, flow path simplicity, ease of integration with the other reactor systems, and compliance with the remote maintenance requirements. Successively, in \Cref{part:numericalmodeling}, the effect of the magnetic field on the heat transfer is studied through numerical modeling of prototypical cases derived from the blanket configurations studied during the comparative analysis. The Computational Fluid Dynamics (CFD) code ANSYS CFX is used for this purpose and its thorough validation for several MHD benchmarks is a core part of the modeling section. Four PbLi in-vessel flow path configurations (T01.A, T01.B, T02, and T03) are studied in the comparative analysis, investigating the effect of different preferential flow orientation, distribution and feeding scheme, cooling system layout, and structural elements arrangement on the MHD pressure losses. A detailed analysis of the PbLi path for each configuration is carried out, identifying possible critical elements and investigating alternative strategies to minimize the pressure drop for the liquid metal evolution. The study is divided according to the four main hydraulic regions of the flow path: feeding pipe, manifold, breeding zone, and draining pipe. Pressure drop correlations available in the literature are used for the estimate of both the two-dimensional and three-dimensional pressure drop term, whereas inertial and viscous effects are neglected. A detailed overview of the methodology adopted is available in \Cref{sec:companalysismeth}. In \Cref{sec:feeddrain}, the analysis results have highlighted how the bulk of the pressure drop is localized within the connection pipes with the PbLi ex-vessel loop, where the highest flow rate in the blanket is concentrated and velocity up to several cm/s is encountered. The routing scheme adopted for the feeding and draining pipe is found to significantly impact the pressure drop due to the different pipe size allowed by the remote maintenance constraints set upon the lower and upper vacuum vessel port. Although a routing through the former would be preferable due to the easier integration with the PbLi path in the blanket, the impossibility to accommodate a feeding pipe larger than 80 mm makes this approach unfeasible without recurring to electrically insulating flow channel insert (FCI) or coatings to minimize the pressure losses in the component. Moreover, the current PbLi ex-vessel loop design adopts a reference pressure of just 4.6 MPa, well below the maximum assumed value reached during the in-box LOCA transient (18 MPa). Since the wall thickness effect on the pressure losses is of paramount importance, the feasibility of feeding and draining pipes without electrical insulation for the WCLL is questionable and their layout is in need of urgent revision. In \Cref{sec:pblimani,sec:breedzone}, the flow in the manifold and the breeding zone is less important on the overall blanket pressure loss, but it is characterized by electromagnetic coupling and complex geometrical elements; phenomena that need to be thoroughly characterized to assess the flow distribution and avoid the formation of regions with stagnant fluid that can increase the tritium inventory above the safety limits in both the breeder and, through enhanced permeation, in the coolant. In particular, critical geometrical elements that have been identified for numerical modeling are orifices, contracting/expanding bends, and flow around obstacles. The relative slow velocity of the liquid metal in the breeding zone requires also to consider the influence of buoyancy effects on the fluid dynamics and heat transfer. Moreover, the prediction of the electromagnetic coupling effect on flow distribution is deemed to be another important aspect warranting in-depth numerical modeling. Despite configuration T02 being the one with the lowest pressure losses, it is configuration T01.A that is found to be the one with the most potential for further optimization due to superior mechanical stability, flow path flexibility allowing alternative feeding scheme, and acceptable pressure losses in both the manifold and the breeding zone. The main uncertainties highlighted by the analysis, and that will require further study, are the complex flow distribution scheme, which relies on a complex system composed by three manifolds (one of which constituted by two parallel arrays of channel arranged along the whole blanket spinal length), and the effect of the buoyancy forces on the breeding zone with regard to the flow around the cooling pipes and the heat transfer. To study the influence of the magnetic field on the heat transfer, two numerical models have been created and investigated, representing the prototypical flow in the two best configurations emerged from the comparative study: T01.A and T02. The CFD code ANSYS CFX is used for this purpose. In \Cref{sec:cfx}, five benchmarks are carried out to validate the code performances for forced convection, natural convection (magneto-convection), and free surface flows. Theoretical solutions and experimental data are the means of comparison selected to evaluate the code capability. For the forced convection flow, the laminar two-dimensional and three-dimensional MHD problems proposed by Smolentsev et al. \cite{smolentsev2015approach} are carried out. For the former, the fully developed flow in a rectangular duct with insulating walls (Shercliff case) and with conducting Hartmann walls and insulating side walls (Hunt-II case) is simulated up to $Ha=10^4$ with a 2\% maximum error on the dimensionless flow rate. The flow in a circular pipe for a non-uniform applied magnetic field (fringing) is considered for the three-dimensional problem, being modeled over the experimental campaign described in \cite{reed1987alex,picologlou1989experimental}. The code is found to have a reasonable agreement with the experimental data employed for the validation, with an error margin consistent with the results reported in the literature by other CFD codes. For the magneto-convection case, the fully developed flow in a differentially and internally heated rectangular duct are simulated and compared with the analytical solutions provided by B\"{u}hler \cite{buhler1998laminar}, showing an excellent agreement. Finally, the thin-film flow in a rectangular chute with insulating walls is considered for the free surface benchmark. A good agreement is found with the analytical solution by Shishko \cite{shishko1993theoretical}, but the code is not able to simulate $Ha > 10^3$. In \Cref{chap:forcpipe}, the forced convection around a single transverse pipe is studied in a configuration very similar to the one encountered in T01.A breeding zone. Both skewed magnetic field and duct walls of non-uniform thickness are preserved to model realistic electric boundary conditions. The case is analyzed in the parameter range $Re=20\div80, \ Ha = 0\div100, \ \alpha = 0\div32^{\circ}, \ \mathrm{and} \ c_o = 0\div \infty$, where $\alpha$ is the magnetic field inclination on the obstacle axis and $c_o$ is the obstacle wall conductance ratio. The heat transfer is found to increase with $Ha$ due to the promotion of the flow rate in the sub-channel below the pipe, caused by leakage currents coming from the upper sub-channel through the duct electro-conductive wall. The flow pattern around the obstacle is dampened with increasing $Ha$ and reverts to a creeping regime for $Ha\rightarrow \infty$. Pipe wall conductivity and magnetic field inclination are found to have negligible influence on both the heat transfer and three-dimensional obstacle pressure drop term, despite influencing significantly the problem flow pattern. The three-dimensional pressure drop term is estimated and found to be a weaker function of the magnetic field intensity compared with the two-dimensional pressure drop and its weight on the overall loss decreases with $Ha$. A correlation is proposed to estimate this quantity at higher $Ha$, derived from the numerical data gathered in this study and from basic physics considerations. Further studies considering mixed convection with non-uniform volumetric heating and a more complex geometry with multiple pipes are deemed necessary to completely characterize this case. In \Cref{sec:mixedConvectionChapter}, mixed convection flow in the upward direction in presence of transverse curved obstacles is investigated to gain some insights about the heat transfer for the elementary cell of configuration T02. The case is analyzed for a single cooling element of the FW channel (two nested double walled Eurofer U-pipes) in both hydrodynamic ($Ha = 0$) and MHD conditions ($Ha = 8.5 \cdot 10^3$). The non-uniform volumetric heating in the FW channel is accurately modeled with an exponentially decreasing function with average volumetric power density $Q = 7 \ \mathrm{MW/m^3}$ corresponding to $Gr = 5.76 \cdot 10^{10}$, and the conservative boundary condition of perfectly conducting duct and pipe walls is assumed. The breeding zone cooling system is found to perform well in hydrodynamic conditions due to the flow being dominated by the buoyancy forces, which cause the onset of an intense turbulent regime. However, the transition to the MHD regime is accompanied by severely dampened velocity oscillations and heat transfer with the temperature in the cell exceeding 1000 K, which is not acceptable with the Eurofer temperature limit ($T_{\mathrm{max}}\leq 823 \ \mathrm{K}$). To reduce the maximum PbLi temperature, a reduction in the vertical pitch separating two successive cooling elements (i.e. increasing their density) from $60 \ \mathrm{mm}$ to $40 \ \mathrm{mm}$ and moderate passive refrigeration from the first wall cooling system ($100 \ \mathrm{kW/m^2}$) are adopted, bringing the maximum temperature in the cell at $T\approx 820 \ \mathrm{K}$. Altering the pipe layout could conceivably result in enhanced performances, but it is unlikely to be feasible due to manufacturing issues in the fabrication of the curved Eurofer pipes. Overall, the proper refrigeration of the elementary cell seems to be quite challenging even considering less conservative boundary conditions for the solid surfaces. A possible strategy could involve a radical rearrangement of the breeding zone to allow the placement of pipes complying with the manufacturing requirements and more able to provide an effective cooling of the region close to the FW.

Il breeding blanket \`{e} uno dei componenti chiave per il funzionamento di un reattore a fusione termonucleare, in quanto responsabile dell'estrazione della potenza termica generata dalle reazioni nucleari, della surgenerazione del trizio, e della schermatura per i componenti sensibili alle radiazioni e il personale. I metalli liquidi, come la lega eutettica di piombo e litio (PbLi), sono considerati come attraenti fluidi tecnici da impiegare in questo componente a causa della loro combinazione di eccellenti propriet\`{a} termiche, alta temperatura di ebollizione e capacit\`{a} di generare trizio. Tuttavia, questi sono caratterizzati anche da caratteristiche meno desiderabili, una tra tante l'elevata conduttivit\`{a} elettrica che, interagendo con l'intenso campo magnetico del reattore, causa cambiamenti multiformi e significativi nel comportamento fluidodinamico. In tali condizioni, il moto del metallo liquido non pu\`{o} essere pi\`{u} descritto con le usuali equazioni della fluidodinamica, ma bisogna ricorrere alla teoria magnetoidrodinamica (MHD). La transizione al regime MHD \`{e} accompagnata da diversi effetti tra cui, a titolo esemplificativo, si possono ricordare maggiori perdite di carico dovute ad attrito elettromagnetico, soppressione della turbolenza, modifiche nelle caratterische di scambio termico e fenomeni di trasporto della massa, ecc. Una comprensione completa di questi fenomeni \`{e} di fondamentale importanza per valutare con precisione le prestazioni generali del componente e realizzare un progetto in grado di soddisfare i requisiti del reattore. Uno dei due concept di breeding blanket attualmente studiati per l'implementazione nel reattore DEMO nell'ambito delle attivit\`{a} di ricerca e sviluppo coordinate dal consorzio EUROfusion \`{e} il Water Cooled Lithium Lead (WCLL). Questo blanket si basa sull'architettura a raffreddamento separato, dove il metallo liquido \`{e} utilizzato esclusivamente come breeder triziogeno e moltiplicatore di neutroni, mentre il refrigerante \`{e} acqua pressurizzata che, essendo un fluido non elettricamente conduttivo, non \`{e} influenzata dagli effetti MHD. In questo modello di blanket, la velocit\`{a} del metallo liquido pu\`{o} essere minimizzata a un valore sufficiente a garantire l'estrazione del trizio ma, anche se le perdite di carico MHD sono ridotte rispetto a un blanket dove il fluido svolge anche la fuzione di refrigerante, i fenomeni MHD continuano a guidare il design globale. Nonostante l'importanza di una piena comprensione dei fenomeni MHD per progettare efficacemente una blanket a metallo liquido, negli anni passati non \`{e} stata condotta alcuna attivit\`{a} di ricerca dedicata sul WCLL e questa importante mancanza \`{e} stata identificata come pregiudizievole al raggiungimento di una soddisfacente maturit\`{a} del progetto. L'attivit\`{a} di ricerca descritta in questa tesi di dottorato ha come obiettivo la caratterizzazione dei principali fenomeni MHD nel WCLL blanket, in particolare riguardo alla stima della perdita di carico e dello scambio termico con il refrigerante. La tesi \`{e} divisa in due parti principali. La prima parte, discussa nella Parte \ref{part:companalysis}, copre l'analisi comparata di diverse configurazioni alternative per il percorso del PbLi all'interno del Vaacum Vessel (VV). L'obiettivo principale di questa analisi \`{e} l'identificazione della configurazione con il maggior potenziale, la quale verr\`{a} poi ulteriormente sviluppata nelle successive fasi del progetto del blanket. I criteri considerati sono stati l'entit\`{a} della perdita di carico MHD, la semplicit\`{a} del percorso idraulico, la facilit\`{a} di integrazione con gli altri sistemi di DEMO e la capacit\`{a} di soddisfare i requisiti del Remote Maintenance. Nella seconda parte, descritta nella Parte \ref{part:numericalmodeling}, l'effetto del campo magnetico sullo scambio termico \`{e} studiato con l'ausilio di codici numerici per alcuni casi prototipici sviluppati a partire da due delle configurazioni analizzate nella prima parte della tesi. Il codice di Fluidodinamica Computazione (CFD) ANSYS CFX \`{e} utilizzato per questo scopo e, all'interno della tesi, \`{e} sottoposto a un approfondito processo di validazione articolato in numerosi benchmark per i pi\`{u} comuni flussi MHD. Quattro diverse configurazioni del WCLL (identificate dalle sigle T01.A, T01.B, T02 e T03) sono analizzate nel contesto dell'analisi comparata per evidenziare l'effetto sulla perdita di carico MHD di differenti direzioni preferenziali per il flusso, schemi di distribuzione e raccolta del metallo liquido, geometria del sistema di refrigerazione e disposizione degli elementi strutturali. Un'analisi dettagliata del percorso del PbLi \`{e} eseguita per evidenziare elementi geometrici critici e strategie alternative per la minimizzazione della perdita di carico. Lo studio \`{e} suddiviso secondo le principali regioni idrauliche identificate nel percorso del PbLi: il feeding pipe, il manifold, la breeding zone e il draining pipe. La stima della perdita di carico \`{e} effettuata attraverso correlazioni disponibili in letteratura per la valutazione dei termini bidimensionali e tridimensionali. L'effetto dell'attrito viscoso e delle forze inerziali \`{e} invece trascurato, seguendo la trattazione pi\`{u} comune per flussi MHD ad elevata intensit\`{a} del campo magnetico. Una completa descrizione della metodologia adottata nello studio \`{e} presentata nel Capitolo \ref{sec:companalysismeth}. Nel Capitolo \ref{sec:feeddrain}, il feeding e il draining pipe sono il focus dell'analisi. I risultati dell'analisi hanno dimostrato come il massimo della perdita di carico sia localizzato nel feeding e draining pipe, ossia gli elementi di connessione tra il percorso del PbLi all'interno del VV e il loop principale dislocato al di fuori di questo, dove \`{e} concentrata tutta la portata in ingresso (o uscita) dal segmento di blanket e il metallo liquido raggiunge velocit\`{a} di diversi cm/s. Lo schema di carico e scarico adottato dal blanket ha un effetto significativo sulla perdita di carico, giacch\'{e} i vincoli imposti dal Remote Maintenance sulla dimensione del condotto sono pi\`{u} permissivi per la VV upper port rispetto alla lower port. Malgrado uno schema di carico attraverso quest'ultima sia preferibile per semplificare il percorso idraulico all'interno del blanket, la necessit\`{a} di utilizzare un condotto con diametro massimo di 80 mm rende questo approccio impossibile da adottare a meno di revisioni consistenti nel progetto della lower port o tramite il disaccoppiamento elettrico del flusso di metallo liquido dal feedign pipe utilizzando appositi Flow Channel Inserts (FCIs). In aggiunta, l'attuale loop del PbLi adotta una pressione di progetto uguale a 4.6 MPa, insufficiente per sopportare il massimo valore (18 MPa) previsto per il transitorio accidentale dell'in-box LOCA, uno dei design basis accidents del blanket, e una revisione di questo parametro comporterebbe un sensibile incremento nello spessore della parete del condotto. Data la grande sensibilit\`{a} della perdita di carico su questo parametro, l'utilizzo di feeding e draining pipe privi di un isolamento elettrico, come attualmente previsto nel WCLL, potrebbe non essere fattibile in condizioni pi\`{u} realistiche di quelle attualmente considerate nell'ambito del design del blanket. Nel Capitolo \ref{sec:pblimani,sec:breedzone}, il manifold e la breeding zone sono il focus dell'analisi. Il flusso nel manifold e nella breeding zone \`{e} meno importante in termini di perdita di carico, ma \`{e} in ogni caso caratterizzato da importanti fenomeni che impattano direttamente la distribuzione del metallo liquido e che devono essere investigati; in particolare, l'accoppiamento elettromagnetico tra canali in contatto elettrico e la presenza di elementi geometrici complessi. Caratterizzare questi fenomeni \`{e} necessario per localizzare dove il fluido potrebbe accumularsi e stagnare: questo comporterebbe rilevanti problemi di sicurezza dovuti all'accumulo del trizio e alla sua permeazione nel refrigerante. Elementi geometrici che sono relativamente poco caratterizzati e che rivestono un ruolo fondamentale nel percorso idraulico del WCLL sono gli orifizi, curve con variazione di area di passaggio e flusso attorno ad ostacoli. Giacch\'{e} il fluido si muove a basse velocit\`{a}, l'influenza delle forze di galleggiamento sulla fluidodinamica e lo scambio termico vanno attentamente considerati. Malgrado la configurazione con le minori perdite di carico sia la T02, la configurazione ad avere il miglior potenziale per il successivo sviluppo del blanket \`{e} la T01.A grazie alla sua maggiore stabilit\`{a} meccanica, flessibilit\`{a} nel variare il collegamento con il loop del PbLi e relativamente basse perdite di carico nel manifold e nella breeding zone. Tuttavia, alcune incertezze sono emerse nel corso dell'analisi, le quali meriteranno ulteriore studio nei prossimi anni: il complesso schema di distribuzione, che utilizza un complesso sistema composto di tre manifold (uno dei quali costituito da due insiemi di stretti canali rettangolari che corrono per tutta l'altezza del blanket), e l'effetto delle forze di galleggiamento sul flusso e lo scambio termico nella breeding zone, specialmente nel contesto del flusso intorno ai tubi di refrigerazione. Per studiare l'effetto del campo magnetico sullo scambio termico, due modelli numerici sono stati creati per investigare il flusso in due configurazioni prototipiche rappresentative rispettivamente della breeding zone di T01.A e T02. Il codice CFD ANSYS CFX \`{e} stato utilizzato a questo scopo. Nel Capitolo \ref{sec:cfx}, cinque benchmark sono impiegati per validare il codice per casi di magneto-idraulica (convezione forzata MHD), magneto-convezione (convezione naturale MHD) e flussi MHD a superficie libera. Soluzioni analitiche e dati sperimentali sono utilizzati per dimostrare la fisicit\`{a} dei risultati ottenuti dal codice. Due casi di magneto-idraulica sono utilizzati per validare il codice, un problema bidimensionale e uno tridimensionale, entrambi proposti da Smolentsev et al. \cite{smolentsev2015approach}. Per il problema bidimensionale, il flusso completamente sviluppato in un canale rettangolare con pareti perfettamente isolate (flusso di Shercliff) e nello stesso canale con pareti di Hartmann perfettamente conduttive (flusso di Hunt-II) \`{e} simulato per un'intensit\`{a} del campo magnetico fino a $Ha=10^4$ con un errore massimo del 2\% sulla portata adimensionale. Per il problema tridimensionale, il flusso in un condotto circolare sottoposto a un campo magnetico non uniforme \`{e} considerato, prendendo a modello l'esperimento descritto nelle Refs. \cite{reed1987alex,picologlou1989experimental}. Il codice riproduce con buona qualit\`{a} i dati sperimentali, mostrando un margine d'errore consistente con quanto riportato in letteratura da altri codici simili. Due casi di magneto-convezione sono trattati per il flusso completamente sviluppato in un canale rettangolare verticale e infinitamente alto sottoposto a riscaldamento differenziale e interno. I risultati del codice sono confrontati con la soluzione analitica proposta da B\"{u}hler \cite{buhler1998laminar}, dimostrando un'eccellente accuratezza. Come ultimo benchmark, un flusso completamente sviluppato a superficie libera per un condotto inclinato con substrato isolato \`{e} simulato fino ad $Ha = 10^3$ dimostrando una buona accuratezza con la soluzione analitica sviluppata da Shishko \cite{shishko1993theoretical}. Nel Capitolo \ref{chap:forcpipe}, il flusso in convezione forzata intorno a un cilindro transversale \`{e} studiato come rappresentativo della breeding zone della configurazione T01.A. Realistiche condizioni al contorno elettromagnetiche, quali il campo magnetico inclinato e pareti del condotto con spessore non uniforme, sono impiegate per aumentare l'accuratezza del modello. Il caso \`{e} analizzato nello spazio dei parametri $Re=20\div80, \ Ha = 0\div100, \ \alpha = 0\div32^{\circ}, \ \mathrm{and} \ c_o = 0\div \infty$, dove $\alpha$ \`{e} l'inclinazione del campo magnetico sull'asse dell'ostacolo e $c_o$ \`{e} il rapporto di conducibilit\`{a} caratteristico dell'ostacolo. Lo scambio termico aumenta con l'aumentare di $Ha$ a causa della promozione del flusso nel sotto-canale inferiore, dove correnti indotte nel sotto-canale nella parte superiore dell'ostacolo penetrano e tendono a generare forze di Lorentz non resistive, con conseguente incremento localizzato della velocit\`{a} media rispetto al caso puramente idrodinamico. Tuttavia, il regime di efflusso attorno all'ostacolo \`{e} gradualmente soppresso all'aumentare di $Ha$ e assume le caratteristiche di un creeping flow per $Ha \rightarrow \infty$. La conducibilit\`{a} dell'ostacolo e l'inclinazione del campo magnetico hanno un'influenza secondaria sullo scambio termico e la perdita di carico, malgrado alterino in maniera sensibile la fluidodinamica del problema. Il valore della perdita di carico tridimensionale \`{e} stimato e si osserva che la sua dipendenza da $Ha$ sembra essere pi\`{u} debole rispetto alla componente bidimensionale, la quale tende a dominare la perdita di carico totale all'aumentare di $Ha$. Una correlazione per predire il valore della perdita di carico tridimensionale ad $Ha$ pi\`{u} elevati di quelli considerati in questo studio \`{e} proposta a partire dai dati numerici raccolti. Un'estensione dell'analisi al flusso in convezione mista e per geometrie pi\`{u} complesse, per esempio cilindri multipli ravvicinati, \`{e} consigliabile per caratterizzare completamente questo problema. Nel Capitolo \ref{sec:mixedConvectionChapter}, la convezione mista per un flusso ascendente in presenza di ostacoli curvi trasversali \`{e} analizzato nel contesto dello scambio termico tra il PbLi e il sistema di refrigerazione della breeding zone per la configurazione T02. L'analisi \`{e} focalizzata su un singolo elemento refrigerante (due tubi a U annidati) per il canale vicino alla FW, cio\'{e} la zona maggiormente sollecitata dal punto di vista termico, in condizioni puramente idrodinamiche ($Ha=0$) e magnetoidrodinamiche ($Ha = 8.5 \cdot 10^3$). Il riscaldamento non-uniforme nel canale \`{e} modellato con una funzione esponenziale decrescente con valore medio $Q = 6.7 \ \mathrm{MW/m^3}$, il quale corrisponde a $Gr = 5.76 \cdot 10^{10}$, e le superifici confinanti il metallo liquido sono ipotizzate avere conducibilit\`{a} infinita. Il sistema di refrigerazione funziona in maniera accettabile in condizioni idrodinamiche grazie all'efficiente scambio termico promosso dal regime turbolento innescato dalle forze di galleggiamento. La transizione al regime MHD comporta la soppressione della turbolenza e il degrado dello scambio termico; la temperatura massima del PbLi nel canale supera i 1000 K, chiaramente incompatibile con i requisiti per il funzionamento dei materiali strutturali ($T_{\mathrm{max}}\leq 823 \ \mathrm{K}$). Per ridurre la temperatura nel PbLi, il pitch verticale tra elementi di refrigerazione viene ridotto da 60 a 40 mm e un moderato flusso termico ($100 \ \mathrm{kW/m^2}$) dovuto alla refrigerazione passiva della BZ da parte del sistema di raffreddamento della FW \`{e} introdotto, portando la temperatura massima nella cella a $T\approx 820 \ \mathrm{K}$. Modifiche al layout dei tubi potrebbero portare a un ulteriore incremento nelle performance del sistema di refrigerazione. In ogni caso, garantire la refrigerazione del condotto sembra essere particolarmente complicato, anche considerando condizioni al contorno elettromagnetiche meno conservative di quelle ipotizzate in questo studio, a causa dei limiti imposti nella struttura degli elementi di rinforzo del blanket e dei tubi da parte delle tecniche di manufacturing.

Study on liquid metal magnetohydrodynamic flows and numerical application to a water-cooled blanket for fusion reactors / Tassone, Alessandro. - (2019 Feb 11).

Study on liquid metal magnetohydrodynamic flows and numerical application to a water-cooled blanket for fusion reactors

TASSONE, ALESSANDRO
11/02/2019

Abstract

One of the key components of a thermonuclear fusion reactor is the breeding blanket, which fulfills the essential functions of power extraction, tritium breeding, and shielding for radiation-sensitive components and personnel. Liquid metals, like the eutectic alloy lithium lead (PbLi), are considered attractive blanket working fluids due to their combination of excellent thermal properties, high boiling temperature, and tritium breeding capabilities. However, they are characterized also by less desirable features, one of which being the elevate electrical conductivity that results in the reactor intense magnetic field influencing the fluid motion in multiple and subtle ways. In such conditions, the liquid metal behavior can only by described by the governing equations of magnetohydrodynamics (MHD). The transition to the MHD regime is accompanied by several effects including, but not limited to, increased pressure losses due to resistive Lorentz forces, turbulence suppression, modified mass and heat transport mechanisms, etc. A complete understanding of these phenomena is of paramount importance to accurately assess the blanket performances and to realize a design able to fulfill the reactor requirements. The Water Cooled Lithium Lead (WCLL) breeding blanket is one of the two concepts actually being studied for implementation in the DEMOnstration Fusion Power Plant (DEMO) reactor within the framework of the R\&D activities coordinated by the EUROfusion consortium. This concept relies on the separate-cooled architecture, where the liquid metal is utilized exclusively as tritium breeder and neutron multiplier, whereas the role of coolant is fulfilled by pressurized water that, being a non-electrically conductive fluid, is not influenced by the MHD effects. Even if the liquid metal velocity can be minimized to a value determined only by the tritium management requirements, thus reducing the electromagnetic pressure losses compared with blanket where the liquid metal fulfills also the role of coolant, MHD phenomena are still going to drive the blanket design. Despite the importance of a full understanding of these aspects, in the past years only few research activities have been focused on the MHD phenomena occurring in WCLL concept and this was identified as a significant drawback for the blanket design hindering the achievement of a satisfying design maturity. The research activity described in this PhD dissertation has the objective to characterize the basic MHD phenomena for the WCLL blanket with regard to pressure losses and heat transfer with the coolant. The dissertation is divided in two main parts. The first part, described in \Cref{part:companalysis}, concerns a comparative analysis of several alternative configuration for the PbLi in-vessel flow path. The analysis is conducted to identify the solution with most potential for further optimization in the blanket development cycle. The main criteria adopted are MHD pressure losses minimization, flow path simplicity, ease of integration with the other reactor systems, and compliance with the remote maintenance requirements. Successively, in \Cref{part:numericalmodeling}, the effect of the magnetic field on the heat transfer is studied through numerical modeling of prototypical cases derived from the blanket configurations studied during the comparative analysis. The Computational Fluid Dynamics (CFD) code ANSYS CFX is used for this purpose and its thorough validation for several MHD benchmarks is a core part of the modeling section. Four PbLi in-vessel flow path configurations (T01.A, T01.B, T02, and T03) are studied in the comparative analysis, investigating the effect of different preferential flow orientation, distribution and feeding scheme, cooling system layout, and structural elements arrangement on the MHD pressure losses. A detailed analysis of the PbLi path for each configuration is carried out, identifying possible critical elements and investigating alternative strategies to minimize the pressure drop for the liquid metal evolution. The study is divided according to the four main hydraulic regions of the flow path: feeding pipe, manifold, breeding zone, and draining pipe. Pressure drop correlations available in the literature are used for the estimate of both the two-dimensional and three-dimensional pressure drop term, whereas inertial and viscous effects are neglected. A detailed overview of the methodology adopted is available in \Cref{sec:companalysismeth}. In \Cref{sec:feeddrain}, the analysis results have highlighted how the bulk of the pressure drop is localized within the connection pipes with the PbLi ex-vessel loop, where the highest flow rate in the blanket is concentrated and velocity up to several cm/s is encountered. The routing scheme adopted for the feeding and draining pipe is found to significantly impact the pressure drop due to the different pipe size allowed by the remote maintenance constraints set upon the lower and upper vacuum vessel port. Although a routing through the former would be preferable due to the easier integration with the PbLi path in the blanket, the impossibility to accommodate a feeding pipe larger than 80 mm makes this approach unfeasible without recurring to electrically insulating flow channel insert (FCI) or coatings to minimize the pressure losses in the component. Moreover, the current PbLi ex-vessel loop design adopts a reference pressure of just 4.6 MPa, well below the maximum assumed value reached during the in-box LOCA transient (18 MPa). Since the wall thickness effect on the pressure losses is of paramount importance, the feasibility of feeding and draining pipes without electrical insulation for the WCLL is questionable and their layout is in need of urgent revision. In \Cref{sec:pblimani,sec:breedzone}, the flow in the manifold and the breeding zone is less important on the overall blanket pressure loss, but it is characterized by electromagnetic coupling and complex geometrical elements; phenomena that need to be thoroughly characterized to assess the flow distribution and avoid the formation of regions with stagnant fluid that can increase the tritium inventory above the safety limits in both the breeder and, through enhanced permeation, in the coolant. In particular, critical geometrical elements that have been identified for numerical modeling are orifices, contracting/expanding bends, and flow around obstacles. The relative slow velocity of the liquid metal in the breeding zone requires also to consider the influence of buoyancy effects on the fluid dynamics and heat transfer. Moreover, the prediction of the electromagnetic coupling effect on flow distribution is deemed to be another important aspect warranting in-depth numerical modeling. Despite configuration T02 being the one with the lowest pressure losses, it is configuration T01.A that is found to be the one with the most potential for further optimization due to superior mechanical stability, flow path flexibility allowing alternative feeding scheme, and acceptable pressure losses in both the manifold and the breeding zone. The main uncertainties highlighted by the analysis, and that will require further study, are the complex flow distribution scheme, which relies on a complex system composed by three manifolds (one of which constituted by two parallel arrays of channel arranged along the whole blanket spinal length), and the effect of the buoyancy forces on the breeding zone with regard to the flow around the cooling pipes and the heat transfer. To study the influence of the magnetic field on the heat transfer, two numerical models have been created and investigated, representing the prototypical flow in the two best configurations emerged from the comparative study: T01.A and T02. The CFD code ANSYS CFX is used for this purpose. In \Cref{sec:cfx}, five benchmarks are carried out to validate the code performances for forced convection, natural convection (magneto-convection), and free surface flows. Theoretical solutions and experimental data are the means of comparison selected to evaluate the code capability. For the forced convection flow, the laminar two-dimensional and three-dimensional MHD problems proposed by Smolentsev et al. \cite{smolentsev2015approach} are carried out. For the former, the fully developed flow in a rectangular duct with insulating walls (Shercliff case) and with conducting Hartmann walls and insulating side walls (Hunt-II case) is simulated up to $Ha=10^4$ with a 2\% maximum error on the dimensionless flow rate. The flow in a circular pipe for a non-uniform applied magnetic field (fringing) is considered for the three-dimensional problem, being modeled over the experimental campaign described in \cite{reed1987alex,picologlou1989experimental}. The code is found to have a reasonable agreement with the experimental data employed for the validation, with an error margin consistent with the results reported in the literature by other CFD codes. For the magneto-convection case, the fully developed flow in a differentially and internally heated rectangular duct are simulated and compared with the analytical solutions provided by B\"{u}hler \cite{buhler1998laminar}, showing an excellent agreement. Finally, the thin-film flow in a rectangular chute with insulating walls is considered for the free surface benchmark. A good agreement is found with the analytical solution by Shishko \cite{shishko1993theoretical}, but the code is not able to simulate $Ha > 10^3$. In \Cref{chap:forcpipe}, the forced convection around a single transverse pipe is studied in a configuration very similar to the one encountered in T01.A breeding zone. Both skewed magnetic field and duct walls of non-uniform thickness are preserved to model realistic electric boundary conditions. The case is analyzed in the parameter range $Re=20\div80, \ Ha = 0\div100, \ \alpha = 0\div32^{\circ}, \ \mathrm{and} \ c_o = 0\div \infty$, where $\alpha$ is the magnetic field inclination on the obstacle axis and $c_o$ is the obstacle wall conductance ratio. The heat transfer is found to increase with $Ha$ due to the promotion of the flow rate in the sub-channel below the pipe, caused by leakage currents coming from the upper sub-channel through the duct electro-conductive wall. The flow pattern around the obstacle is dampened with increasing $Ha$ and reverts to a creeping regime for $Ha\rightarrow \infty$. Pipe wall conductivity and magnetic field inclination are found to have negligible influence on both the heat transfer and three-dimensional obstacle pressure drop term, despite influencing significantly the problem flow pattern. The three-dimensional pressure drop term is estimated and found to be a weaker function of the magnetic field intensity compared with the two-dimensional pressure drop and its weight on the overall loss decreases with $Ha$. A correlation is proposed to estimate this quantity at higher $Ha$, derived from the numerical data gathered in this study and from basic physics considerations. Further studies considering mixed convection with non-uniform volumetric heating and a more complex geometry with multiple pipes are deemed necessary to completely characterize this case. In \Cref{sec:mixedConvectionChapter}, mixed convection flow in the upward direction in presence of transverse curved obstacles is investigated to gain some insights about the heat transfer for the elementary cell of configuration T02. The case is analyzed for a single cooling element of the FW channel (two nested double walled Eurofer U-pipes) in both hydrodynamic ($Ha = 0$) and MHD conditions ($Ha = 8.5 \cdot 10^3$). The non-uniform volumetric heating in the FW channel is accurately modeled with an exponentially decreasing function with average volumetric power density $Q = 7 \ \mathrm{MW/m^3}$ corresponding to $Gr = 5.76 \cdot 10^{10}$, and the conservative boundary condition of perfectly conducting duct and pipe walls is assumed. The breeding zone cooling system is found to perform well in hydrodynamic conditions due to the flow being dominated by the buoyancy forces, which cause the onset of an intense turbulent regime. However, the transition to the MHD regime is accompanied by severely dampened velocity oscillations and heat transfer with the temperature in the cell exceeding 1000 K, which is not acceptable with the Eurofer temperature limit ($T_{\mathrm{max}}\leq 823 \ \mathrm{K}$). To reduce the maximum PbLi temperature, a reduction in the vertical pitch separating two successive cooling elements (i.e. increasing their density) from $60 \ \mathrm{mm}$ to $40 \ \mathrm{mm}$ and moderate passive refrigeration from the first wall cooling system ($100 \ \mathrm{kW/m^2}$) are adopted, bringing the maximum temperature in the cell at $T\approx 820 \ \mathrm{K}$. Altering the pipe layout could conceivably result in enhanced performances, but it is unlikely to be feasible due to manufacturing issues in the fabrication of the curved Eurofer pipes. Overall, the proper refrigeration of the elementary cell seems to be quite challenging even considering less conservative boundary conditions for the solid surfaces. A possible strategy could involve a radical rearrangement of the breeding zone to allow the placement of pipes complying with the manufacturing requirements and more able to provide an effective cooling of the region close to the FW.
11-feb-2019
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1243658
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