Fractional Order Modeling and Control of a Flexible Satellite

Researchers have engrossed fractional-order modeling because of its ability to capture phenomena that are nearly impossible to describe owing to its long-term memory and inherited properties. Motivated by the research in fractional modeling, a fractional-order prototype for a flexible satellite whose dynamics are governed by fractional differential equations is proposed for the first time. These relations are derived using fractional attitude dynamic description of rigid body simultaneously coupled with the fractional Lagrange equation that governs the vibration of the appendages. Two attitude controls are designed in the presence of the faults and uncertainties of the system. The first is the fractional-order feedback linearization controller, in which the stability of the internal dynamics of the system is proved. The second is the fractional-order sliding mode control, whose asymptotic stability is demonstrated using the quadratic Lyapunov function. Several nonlinear simulations are implemented to analyze the performance of the proposed controllers.

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.

Impact of convective motions on pollutant dispersion in urban canyons: an analysis through RANS simulations

Since the majority of the population of the world lives in cities and that this number is expected to increase in the next years, one of the biggest challenges of the research is the determination of the risk deriving from high temperatures experienced in urban areas, together with improving responses to climate-related disasters, for example by introducing in the urban context vegetation or built infrastructures that can improve the air quality. In this work, we will investigate how different setups of the boundary and initial conditions set on an urban canyon generate different patterns of the dispersion of a pollutant. To do so we will exploit the low computational cost of Reynolds-Averaged Navier-Stokes (RANS) simulations to reproduce the dynamics of an infinite array of two-dimensional square urban canyons. A pollutant is released at the street level to mimic the presence of traffic. RANS simulations are run using the k-ɛ closure model and vertical profiles of significant variables of the urban canyon, namely the velocity, the turbulent kinetic energy, and the concentration, are represented. This is done using the open-source software OpenFOAM and modifying the standard solver simpleFoam to include the concentration equation and the temperature by introducing a buoyancy term in the governing equations. The results of the simulation are validated with experimental results and products of Large-Eddy Simulations (LES) from previous works showing that the simulation is able to reproduce all the quantities under examination with satisfactory accuracy. Moreover, this comparison shows that despite LES are known to be more accurate albeit more expensive, RANS simulations represent a reliable tool if a smaller computational cost is needed. Overall, this work exploits the low computational cost of RANS simulations to produce multiple scenarios useful to evaluate how the dispersion of a pollutant changes by a modification of key variables, such as the temperature.

Testing of subgrid scale (SGS) models for large-eddy simulation (LES) of turbulent channel flow

Sub-grid scale (SGS) models are required in order to model the influence of the unresolved small scales on the resolved scales in large-eddy simulations (LES), the flow at the smallest scales of turbulence. In the following work two SGS models are presented and deeply analyzed in terms of accuracy through several LESs with different spatial resolutions, i.e. grid spacings. The first part of this thesis focuses on the basic theory of turbulence, the governing equations of fluid dynamics and their adaptation to LES. Furthermore, two important SGS models are presented: one is the Dynamic eddy-viscosity model (DEVM), developed by \cite{germano1991dynamic}, while the other is the Explicit Algebraic SGS model (EASSM), by \cite{marstorp2009explicit}. In addition, some details about the implementation of the EASSM in a Pseudo-Spectral Navier-Stokes code \cite{chevalier2007simson} are presented. The performance of the two aforementioned models will be investigated in the following chapters, by means of LES of a channel flow, with friction Reynolds numbers $Re_\tau=590$ up to $Re_\tau=5200$, with relatively coarse resolutions. Data from each simulation will be compared to baseline DNS data. Results have shown that, in contrast to the DEVM, the EASSM has promising potentials for flow predictions at high friction Reynolds numbers: the higher the friction Reynolds number is the better the EASSM will behave and the worse the performances of the DEVM will be. The better performance of the EASSM is contributed to the ability to capture flow anisotropy at the small scales through a correct formulation for the SGS stresses. Moreover, a considerable reduction in the required computational resources can be achieved using the EASSM compared to DEVM. Therefore, the EASSM combines accuracy and computational efficiency, implying that it has a clear potential for industrial CFD usage.

Fluid dynamic analysis of trees influence in dispersion of pollutant in urban street canyon

degli elementi vegetali nella dinamica e nella dispersione degli inquinanti nello street canyon urbano. In particolare, è stato analizzata la risposta fluidodinamica di cespugli con altezze diverse e di alberi con porosità e altezza del tronco varianti. Il modello analizzato consiste in due edifici di altezza e larghezza pari ad H e lunghezza di 10H, tra i quali corre una strada in cui sono stati modellizati una sorgente rappresentativa del traffico veicolare e, ai lati, due linee di componenti vegetali. Le simulazioni sono state fatte con ANSYS Fluent, un software di "Computational Fluid Dynamics"(CFD) che ha permesso di modellizare la dinamica dei flussi e di simulare le concentrazioni emesse dalla sorgente di CO posta lungo la strada. Per la simulazione è stato impiegato un modello RANS a chiusura k-epsilon, che permette di parametrizzare i momenti secondi nell'equazione di Navier Stokes per permettere una loro più facile risoluzione. I risultati sono stati espressi in termini di profili di velocità e concentrazione molare di CO, unitamente al calcolo della exchange velocity per quantificare gli scambi tra lo street canyon e l'esterno. Per quanto riguarda l'influenza dell'altezza dei tronchi è stata riscontrata una tendenza non lineare tra di essi e la exchange velocity. Analizzando invece la altezza dei cespugli è stato visto che all'aumentare della loro altezza esiste una relazione univoca con l'abbassamento della exchange velocity. Infine, andando a variare la permeabilità delle chiome degli alberi è stata trovatta una variazione non monotonica che correla la exchange velocity con il parametro C_2, che è stata interpretata attraverso i diversi andamenti dei profili sopravento e sottovento. In conclusione, allo stadio attuale della ricerca presentata in questa tesi, non è ancora possibile correlare direttamente la exchange velocity con alcun parametro analizzato.

Hidden Schrödinger symmetry in FLRW and Bianchi I minisuperspace models of cosmology and black holes Schwarzschild dynamics

A broad sector of literature focuses on the relationship between fluid dynamics and gravitational systems. This thesis presents results that suggest the existence of a new kind of fluid/gravity duality not based on the holographic principle. The goal is to provide tools that allow us to systematically unearth hidden symmetries for reduced models of cosmology. The focus is on the field space of these models, i.e. the superspace. In fact, conformal isometries of the supermetric leave geodesics in the field space unaltered; this leads to symmetries of the models. An innovative aspect is the use of the Eisenhart-Duval’s lift. Using this method, systems constrained by a potential can be treated as free ones. Moreover, charges explicitly dependent on time, i.e. dynamical, can be found. A detailed analysis is carried out on three basic models of homogenous cosmology: i) flat Friedmann-Lemaître-Robertson-Walker’s isotropic universe filled with a massless scalar field; ii) Schwarzschild’s black hole mechanics and its extension to vacuum (A)dS gravity; iii) Bianchi’s anisotropic type I universe with a massless scalar field. The results show the presence of a hidden Schrödinger’s symmetry which, being intrinsic to both Navier-Stokes’ and Schrödinger’s equations, indicates a correspondence between cosmology and hydrodynamics. Furthermore, the central extension of this algebra explicitly relates two concepts. The first is the number of particles coming from the fluid picture; while the second is the ratio between the IR and UV cutoffs that weighs how much a theory has of “classical” over “quantum”. This suggests a spacetime that emerges from an underlying world which is described by quantum building blocks. These quanta statistically conspire to appear as gravitational phenomena from a macroscopic point of view.