Analysis of optimal control problems for the incompressible MHD equations and implementation in a finite element multiphysics code

This thesis deals with the study of optimal control problems for the incompressible Magnetohydrodynamics (MHD) equations. Particular attention to these problems arises from several applications in science and engineering, such as fission nuclear reactors with liquid metal coolant and aluminum casting in metallurgy. In such applications it is of great interest to achieve the control on the fluid state variables through the action of the magnetic Lorentz force. In this thesis we investigate a class of boundary optimal control problems, in which the flow is controlled through the boundary conditions of the magnetic field. Due to their complexity, these problems present various challenges in the definition of an adequate solution approach, both from a theoretical and from a computational point of view. In this thesis we propose a new boundary control approach, based on lifting functions of the boundary conditions, which yields both theoretical and numerical advantages. With the introduction of lifting functions, boundary control problems can be formulated as extended distributed problems. We consider a systematic mathematical formulation of these problems in terms of the minimization of a cost functional constrained by the MHD equations. The existence of a solution to the flow equations and to the optimal control problem are shown. The Lagrange multiplier technique is used to derive an optimality system from which candidate solutions for the control problem can be obtained. In order to achieve the numerical solution of this system, a finite element approximation is considered for the discretization together with an appropriate gradient-type algorithm. A finite element object-oriented library has been developed to obtain a parallel and multigrid computational implementation of the optimality system based on a multiphysics approach. Numerical results of two- and three-dimensional computations show that a possible minimum for the control problem can be computed in a robust and accurate manner.

Radiative neutron capture cross section on 238U at the n_TOF CERN facility: a high precision measurement

The aim of this work is to provide a precise and accurate measurement of the 238U(n,gamma) reaction cross-section. This reaction is of fundamental importance for the design calculations of nuclear reactors, governing the behaviour of the reactor core. In particular, fast neutron reactors, which are experiencing a growing interest for their ability to burn radioactive waste, operate in the high energy region of the neutron spectrum. In this energy region inconsistencies between the existing measurements are present up to 15%, and the most recent evaluations disagree each other. In addition, the assessment of nuclear data uncertainty performed for innovative reactor systems shows that the uncertainty in the radiative capture cross-section of 238U should be further reduced to 1-3% in the energy region from 20 eV to 25 keV. To this purpose, addressed by the Nuclear Energy Agency as a priority nuclear data need, complementary experiments, one at the GELINA and two at the n_TOF facility, were scheduled within the ANDES project within the 7th Framework Project of the European Commission. The results of one of the 238U(n,gamma) measurement performed at the n_TOF CERN facility are presented in this work, carried out with a detection system constituted of two liquid scintillators. The very accurate cross section from this work is compared with the results obtained from the other measurement performed at the n_TOF facility, which exploit a different and complementary detection technique. The excellent agreement between the two data-sets points out that they can contribute to the reduction of the cross section uncertainty down to the required 1-3%.

Safety, Security And safeguards In GEN IV sodium fast reactors

This work presents first a study of the national and international laws in the fields of safety, security and safeguards. The international treaties and the recommendations issued by the IAEA as well as the national regulations in force in France, the United States and Italy are analyzed. As a result of this, a comparison among them is presented. Given the interest of the Japan Atomic Energy Agency for the aspects of criminal penalties and monetary, also the Japanese case is analyzed. The main part of this work was held at the JAEA in the field of proliferation resistance (PR) and physical protection (PP) of a GEN IV sodium fast reactor. For this purpose the design of the system is completed and the PR & PP methodology is applied to obtain data usable by designers for the improvement of the system itself. Due to the presence of sensitive data, not all the details can be disclosed. The reactor site of a hypothetical and commercial sodium-cooled fast neutron nuclear reactor system (SFR) is used as the target NES for the application of the methodology. The methodology is applied to all the PR and PP scenarios: diversion, misuse and breakout; theft and sabotage. The methodology is applied to the SFR to check if this system meets the target of PR and PP as described in the GIF goal; secondly, a comparison between the SFR and a LWR is performed to evaluate if and how it would be possible to improve the PR&PP of the SFR. The comparison is implemented according to the example development target: achieving PR&PP similar or superior to domestic and international ALWR. Three main actions were performed: implement the evaluation methodology; characterize the PR&PP for the nuclear energy system; identify recommendations for system designers through the comparison.

Catalytic liquid- and gas-phase oxidations for the synthesis of intermediates and specialty chemicals: some examples of industrial relevance

Nowadays, it is clear that the target of creating a sustainable future for the next generations requires to re-think the industrial application of chemistry. It is also evident that more sustainable chemical processes may be economically convenient, in comparison with the conventional ones, because fewer by-products means lower costs for raw materials, for separation and for disposal treatments; but also it implies an increase of productivity and, as a consequence, smaller reactors can be used. In addition, an indirect gain could derive from the better public image of the company, marketing sustainable products or processes. In this context, oxidation reactions play a major role, being the tool for the production of huge quantities of chemical intermediates and specialties. Potentially, the impact of these productions on the environment could have been much worse than it is, if a continuous efforts hadn’t been spent to improve the technologies employed. Substantial technological innovations have driven the development of new catalytic systems, the improvement of reactions and process technologies, contributing to move the chemical industry in the direction of a more sustainable and ecological approach. The roadmap for the application of these concepts includes new synthetic strategies, alternative reactants, catalysts heterogenisation and innovative reactor configurations and process design. Actually, in order to implement all these ideas into real projects, the development of more efficient reactions is one primary target. Yield, selectivity and space-time yield are the right metrics for evaluating the reaction efficiency. In the case of catalytic selective oxidation, the control of selectivity has always been the principal issue, because the formation of total oxidation products (carbon oxides) is thermodynamically more favoured than the formation of the desired, partially oxidized compound. As a matter of fact, only in few oxidation reactions a total, or close to total, conversion is achieved, and usually the selectivity is limited by the formation of by-products or co-products, that often implies unfavourable process economics; moreover, sometimes the cost of the oxidant further penalizes the process. During my PhD work, I have investigated four reactions that are emblematic of the new approaches used in the chemical industry. In the Part A of my thesis, a new process aimed at a more sustainable production of menadione (vitamin K3) is described. The “greener” approach includes the use of hydrogen peroxide in place of chromate (from a stoichiometric oxidation to a catalytic oxidation), also avoiding the production of dangerous waste. Moreover, I have studied the possibility of using an heterogeneous catalytic system, able to efficiently activate hydrogen peroxide. Indeed, the overall process would be carried out in two different steps: the first is the methylation of 1-naphthol with methanol to yield 2-methyl-1-naphthol, the second one is the oxidation of the latter compound to menadione. The catalyst for this latter step, the reaction object of my investigation, consists of Nb2O5-SiO2 prepared with the sol-gel technique. The catalytic tests were first carried out under conditions that simulate the in-situ generation of hydrogen peroxide, that means using a low concentration of the oxidant. Then, experiments were carried out using higher hydrogen peroxide concentration. The study of the reaction mechanism was fundamental to get indications about the best operative conditions, and improve the selectivity to menadione. In the Part B, I explored the direct oxidation of benzene to phenol with hydrogen peroxide. The industrial process for phenol is the oxidation of cumene with oxygen, that also co-produces acetone. This can be considered a case of how economics could drive the sustainability issue; in fact, the new process allowing to obtain directly phenol, besides avoiding the co-production of acetone (a burden for phenol, because the market requirements for the two products are quite different), might be economically convenient with respect to the conventional process, if a high selectivity to phenol were obtained. Titanium silicalite-1 (TS-1) is the catalyst chosen for this reaction. Comparing the reactivity results obtained with some TS-1 samples having different chemical-physical properties, and analyzing in detail the effect of the more important reaction parameters, we could formulate some hypothesis concerning the reaction network and mechanism. Part C of my thesis deals with the hydroxylation of phenol to hydroquinone and catechol. This reaction is already industrially applied but, for economical reason, an improvement of the selectivity to the para di-hydroxilated compound and a decrease of the selectivity to the ortho isomer would be desirable. Also in this case, the catalyst used was the TS-1. The aim of my research was to find out a method to control the selectivity ratio between the two isomers, and finally to make the industrial process more flexible, in order to adapt the process performance in function of fluctuations of the market requirements. The reaction was carried out in both a batch stirred reactor and in a re-circulating fixed-bed reactor. In the first system, the effect of various reaction parameters on catalytic behaviour was investigated: type of solvent or co-solvent, and particle size. With the second reactor type, I investigated the possibility to use a continuous system, and the catalyst shaped in extrudates (instead of powder), in order to avoid the catalyst filtration step. Finally, part D deals with the study of a new process for the valorisation of glycerol, by means of transformation into valuable chemicals. This molecule is nowadays produced in big amount, being a co-product in biodiesel synthesis; therefore, it is considered a raw material from renewable resources (a bio-platform molecule). Initially, we tested the oxidation of glycerol in the liquid-phase, with hydrogen peroxide and TS-1. However, results achieved were not satisfactory. Then we investigated the gas-phase transformation of glycerol into acrylic acid, with the intermediate formation of acrolein; the latter can be obtained by dehydration of glycerol, and then can be oxidized into acrylic acid. Actually, the oxidation step from acrolein to acrylic acid is already optimized at an industrial level; therefore, we decided to investigate in depth the first step of the process. I studied the reactivity of heterogeneous acid catalysts based on sulphated zirconia. Tests were carried out both in aerobic and anaerobic conditions, in order to investigate the effect of oxygen on the catalyst deactivation rate (one main problem usually met in glycerol dehydration). Finally, I studied the reactivity of bifunctional systems, made of Keggin-type polyoxometalates, either alone or supported over sulphated zirconia, in this way combining the acid functionality (necessary for the dehydrative step) with the redox one (necessary for the oxidative step). In conclusion, during my PhD work I investigated reactions that apply the “green chemistry” rules and strategies; in particular, I studied new greener approaches for the synthesis of chemicals (Part A and Part B), the optimisation of reaction parameters to make the oxidation process more flexible (Part C), and the use of a bioplatform molecule for the synthesis of a chemical intermediate (Part D).

Neutronics analyses for fast spectrum nuclear systems and scenario studies for advanced nuclear fuel cycles

The present PhD thesis summarizes the three-years study about the neutronic investigation of a new concept nuclear reactor aiming at the optimization and the sustainable management of nuclear fuel in a possible European scenario. A new generation nuclear reactor for the nuclear reinassance is indeed desired by the actual industrialized world, both for the solution of the energetic question arising from the continuously growing energy demand together with the corresponding reduction of oil availability, and the environment question for a sustainable energy source free from Long Lived Radioisotopes and therefore geological repositories. Among the Generation IV candidate typologies, the Lead Fast Reactor concept has been pursued, being the one top rated in sustainability. The European Lead-cooled SYstem (ELSY) has been at first investigated. The neutronic analysis of the ELSY core has been performed via deterministic analysis by means of the ERANOS code, in order to retrieve a stable configuration for the overall design of the reactor. Further analyses have been carried out by means of the Monte Carlo general purpose transport code MCNP, in order to check the former one and to define an exact model of the system. An innovative system of absorbers has been conceptualized and designed for both the reactivity compensation and regulation of the core due to cycle swing, as well as for safety in order to guarantee the cold shutdown of the system in case of accident. Aiming at the sustainability of nuclear energy, the steady-state nuclear equilibrium has been investigated and generalized into the definition of the ``extended'' equilibrium state. According to this, the Adiabatic Reactor Theory has been developed, together with a New Paradigm for Nuclear Power: in order to design a reactor that does not exchange with the environment anything valuable (thus the term ``adiabatic''), in the sense of both Plutonium and Minor Actinides, it is required indeed to revert the logical design scheme of nuclear cores, starting from the definition of the equilibrium composition of the fuel and submitting to the latter the whole core design. The New Paradigm has been applied then to the core design of an Adiabatic Lead Fast Reactor complying with the ELSY overall system layout. A complete core characterization has been done in order to asses criticality and power flattening; a preliminary evaluation of the main safety parameters has been also done to verify the viability of the system. Burn up calculations have been then performed in order to investigate the operating cycle for the Adiabatic Lead Fast Reactor; the fuel performances have been therefore extracted and inserted in a more general analysis for an European scenario. The present nuclear reactors fleet has been modeled and its evolution simulated by means of the COSI code in order to investigate the materials fluxes to be managed in the European region. Different plausible scenarios have been identified to forecast the evolution of the European nuclear energy production, including the one involving the introduction of Adiabatic Lead Fast Reactors, and compared to better analyze the advantages introduced by the adoption of new concept reactors. At last, since both ELSY and the ALFR represent new concept systems based upon innovative solutions, the neutronic design of a demonstrator reactor has been carried out: such a system is intended to prove the viability of technology to be implemented in the First-of-a-Kind industrial power plant, with the aim at attesting the general strategy to use, to the largest extent. It was chosen then to base the DEMO design upon a compromise between demonstration of developed technology and testing of emerging technology in order to significantly subserve the purpose of reducing uncertainties about construction and licensing, both validating ELSY/ALFR main features and performances, and to qualify numerical codes and tools.