Calculation of the eigenfunctions of the two-group neutron diffusion equation and application to modal decomposition of BWR instabilities

In this thesis, numerical methods aiming at determining the eigenfunctions, their adjoint and the corresponding eigenvalues of the two-group neutron diffusion equations representing any heterogeneous system are investigated. First, the classical power iteration method is modified so that the calculation of modes higher than the fundamental mode is possible. Thereafter, the Explicitly-Restarted Arnoldi method, belonging to the class of Krylov subspace methods, is touched upon. Although the modified power iteration method is a computationally-expensive algorithm, its main advantage is its robustness, i.e. the method always converges to the desired eigenfunctions without any need from the user to set up any parameter in the algorithm. On the other hand, the Arnoldi method, which requires some parameters to be defined by the user, is a very efficient method for calculating eigenfunctions of large sparse system of equations with a minimum computational effort. These methods are thereafter used for off-line analysis of the stability of Boiling Water Reactors. Since several oscillation modes are usually excited (global and regional oscillations) when unstable conditions are encountered, the characterization of the stability of the reactor using for instance the Decay Ratio as a stability indicator might be difficult if the contribution from each of the modes are not separated from each other. Such a modal decomposition is applied to a stability test performed at the Swedish Ringhals-1 unit in September 2002, after the use of the Arnoldi method for pre-calculating the different eigenmodes of the neutron flux throughout the reactor. The modal decomposition clearly demonstrates the excitation of both the global and regional oscillations. Furthermore, such oscillations are found to be intermittent with a time-varying phase shift between the first and second azimuthal modes.

Turbulence models in the atmospheric boundary layer under convective conditions

In this work a modelization of the turbulence in the atmospheric boundary layer, under convective condition, is made. For this aim, the equations that describe the atmospheric motion are expressed through Reynolds averages and, then, they need closures. This work consists in modifying the TKE-l closure used in the BOLAM (Bologna Limited Area Model) forecast model. In particular, the single column model extracted from BOLAM is used, which is modified to obtain other three different closure schemes: a non-local term is added to the flux- gradient relations used to close the second order moments present in the evolution equation of the turbulent kinetic energy, so that the flux-gradient relations become more suitable for simulating an unstable boundary layer. Furthermore, a comparison among the results obtained from the single column model, the ones obtained from the three new schemes and the observations provided by the known case in literature ”GABLS2” is made.

Efficiency limits for silicon/perovskite tandem solar cells: a theoretical model

The primary goal of this work is related to the extension of an analytic electro-optical model. It will be used to describe single-junction crystalline silicon solar cells and a silicon/perovskite tandem solar cell in the presence of light-trapping in order to calculate efficiency limits for such a device. In particular, our tandem system is composed by crystalline silicon and a perovskite structure material: metilammoniumleadtriiodide (MALI). Perovskite are among the most convenient materials for photovoltaics thanks to their reduced cost and increasing efficiencies. Solar cell efficiencies of devices using these materials increased from 3.8% in 2009 to a certified 20.1% in 2014 making this the fastest-advancing solar technology to date. Moreover, texturization increases the amount of light which can be absorbed through an active layer. Using Green’s formalism it is possible to calculate the photogeneration rate of a single-layer structure with Lambertian light trapping analytically. In this work we go further: we study the optical coupling between the two cells in our tandem system in order to calculate the photogeneration rate of the whole structure. We also model the electronic part of such a device by considering the perovskite top cell as an ideal diode and solving the drift-diffusion equation with appropriate boundary conditions for the silicon bottom cell. We have a four terminal structure, so our tandem system is totally unconstrained. Then we calculate the efficiency limits of our tandem including several recombination mechanisms such as Auger, SRH and surface recombination. We focus also on the dependence of the results on the band gap of the perovskite and we calculare an optimal band gap to optimize the tandem efficiency. The whole work has been continuously supported by a numerical validation of out analytic model against Silvaco ATLAS which solves drift-diffusion equations using a finite elements method. Our goal is to develop a simpler and cheaper, but accurate model to study such devices.

Boundary condition identification of a bridge pier using experimental data and FEM modal updating

Over the past twenty years, new technologies have required an increasing use of mathematical models in order to understand better the structural behavior: finite element method is the one mostly used. However, the reliability of this method applied to different situations has to be tried each time. Since it is not possible to completely model the reality, different hypothesis must be done: these are the main problems of FE modeling. The following work deals with this problem and tries to figure out a way to identify some of the unknown main parameters of a structure. This main research focuses on a particular path of study and development, but the same concepts can be applied to other objects of research. The main purpose of this work is the identification of unknown boundary conditions of a bridge pier using the data acquired experimentally with field tests and a FEM modal updating process. This work doesn’t want to be new, neither innovative. A lot of work has been done during the past years on this main problem and many solutions have been shown and published. This thesis just want to rework some of the main aspects of the structural optimization process, using a real structure as fitting model.