The underlying thread of the research work presented in this thesis is the development of a robust, accurate and computationally efficient general-purpose Reynolds-Averaged Navier-Stokes code for the analysis of complex turbulent flow unsteady aerodynamics, ranging from low-speed applications such as hydrokinetic and wind turbine flows to high-speed applications such as vibrating transonic wings. The main novel algorithmic contribution of this work is the successful development of a fully-coupled multigrid solution method of the Reynolds-Averaged Navier-Stokes equations and the two-equation shear stress transport turbulence model of Menter. The new approach, which also includes the implementation of a high-order restriction operator and an effective limiter of the prolonged corrections, is implemented and successfully demonstrated in the existing steady, time-domain and harmonic balance solvers of a compressible Navier-Stokes research code. The harmonic balance solution of the Navier-Stokes equations is a fairly new technology which can substantially reduce the run-time required to compute nonlinear periodic flow fields with respect to the conventional time-domain approach. The thesis also features the investigation of one modelling and one numerical aspect often overlooked or not comprehensively analysed in turbulent computational fluid dynamics simulations of the type discussed in the thesis. The modelling aspect is the sensitivity of the turbulent flow solution to the, to a certain extent, arbitrary value of the scaling factor appearing in the solid wall boundary condition of the second turbulent variable of the Shear Stress Transport turbulence model. The results reported herein highlight that the solution variability associated with the typical choices of such a scaling factor can be similar or higher than the solution variability caused by the choices of different turbulence models. The numerical aspect is the sensitivity of the turbulent flow solution to the order of the discretisation of the turbulence model equations. The results reported herein highlight that the existence of significant solution differences between first and second order space-discretisation of the turbulence equations vary with the flow regime (e.g. fully subsonic or transonic), operating conditions that may or may not result in flow separation (e.g. angle of attack), and also the grid refinement. The newly developed turbulent flow capabilities are validated by considering a wide range of test cases with flow regime varying from low-speed subsonic to transonic. The solutions of the research code are compared with experimental data, theoretical solutions and also numerical solutions obtained with a state-of-the-art time-domain commercial code. The main computational results of this research regard a low-speed renewable energy application and an aeronautical engineering application. The former application is a thorough comparative analysis of a hydrokinetic turbine working in a low-speed laminar and a high-Reynolds number turbulent regime. The time-domain results obtained with the newly developed turbulent code are used to analyse and discusses in great detail the unsteady aerodynamic phenomena occurring in both regimes. The main motivation for analysing this problem is both to highlight the predictive capabilities and the numerical robustness of the developed turbulent time-domain flow solver for complex realistic problems, and to shed more light on the complex physics of this emerging renewable energy device. The latter application is the time-domain and harmonic balance turbulent flow analysis of a transonic wing section animated by pitching motion. The main motivation of these analyses is to assess the computational benefits achievable by using the harmonic balance solution of the Reynolds-Averaged Navier-Stokes and Shear Stress Transport equations rather than the conventional time-domain solution, and also to further demonstrate the predictive capabilities of the developed Computational Fluid Dynamics system. To this aim, the numerical solutions of this research code are compared to both available experimental data, and the time-domain results computed by a state-of-the-art commercial package regularly used by the industry and the Academia worldwide.

This research work developed an innovative computational approach to the preliminary design of low-thrust trajectories optimising multiple mission criteria. Low-Thrust (LT) propulsion has become the propulsion system of choice for a number of near Earth and interplanetary missions. Consequently, in the last two decades a good wealth of research has been devoted to the development of computational method to design low-thrust trajectories. Most of the techniques, however, minimise or maximise a single figure of merit under a set of design constraints. Less effort has been devoted to the development of efficient methods for the minimisation (or maximisation) of two or more figures of merit. On the other hand, in the preliminary mission design phase, the decision maker is interested in analysing as many design solutions as possible against different trade-off criteria. Therefore, in this PhD work, an innovative Multi-Objective (MO), memetic optimisation algorithm, called Multi-Agent Collaborative Search (MACS2), has been implemented to tackle low-thrust trajectory design problems with multiple figures of merit. Tests on both academic and real-world problems showed that the proposed MACS2 paradigm performs better than or as well as other state-of-the-art Multi-Objective optimisation algorithms. Concurrently, a set of novel approximated, first-order, analytical formulae has been developed, to obtain a fast but reliable estimation of the main trade-off criteria. These formulae allow for a fast propagation of the orbital motion under a constant perturbing acceleration. These formulae have been shown to allow for the fast and relatively accurate propagation of long LT trajectories under the typical acceleration level delivered by current engine technology. Various applications are presented to demonstrate the validity of the combination of the analytical formulae with MACS2. Among them, the preliminary design of the JAXA low-cost DESTINY mission to L2, a novel approach to the optimisation under uncertainty of deflection actions for Near Earth Objects (NEO), and the de-orbiting of space debris with low-thrust and with a combination of low-thrust and solar radiation pressure.

Increasing interest in renewable energy sources for electricity production complying with stricter environmental policies has greatly contributed to further optimisation of existing devices and the development of novel renewable energy generation systems. The research and development of these advanced systems is tightly bound to the use of reliable design methods, which enable accurate and efficient design. Reynolds-averaged Navier-Stokes Computational Fluid Dynamics is one of the design methods that may be used to accurately analyse complex flows past current and forthcoming renewable energy fluid machinery such as wind turbines and oscillating wings for marine power generation. The use of this simulation technology offers a deeper insight into the complex flow physics of renewable energy machines than the lower-fidelity methods widely used in industry. The complex flows past these devices, which are characterised by highly unsteady and, often, predominantly periodic behaviour, can significantly affect power production and structural loads. Therefore, such flows need to be accurately predicted. The research work presented in this thesis deals with the development of a novel, accurate, scalable, massively parallel CFD research code COSA for general fluid-based renewable energy applications. The research work also demonstrates the capabilities of newly developed solvers of COSA by investigating complex three-dimensional unsteady periodic flows past oscillating wings and horizontal-axis wind turbines. Oscillating wings for the extraction of energy from an oncoming water or air stream, feature highly unsteady hydrodynamics. The flow past oscillating wings may feature dynamic stall and leading edge vortex shedding, and is significantly three-dimensional due to finite-wing effects. Detailed understanding of these phenomena is essential for maximising the power generation efficiency. Most of the knowledge on oscillating wing hydrodynamics is based on two-dimensional low-Reynolds number computational fluid dynamics studies and experimental testing. However, real installations are expected to feature Reynolds numbers of the order of 1 million and strong finite-wing-induced losses. This research investigates the impact of finite wing effects on the hydrodynamics of a realistic aspect ratio 10 oscillating wing device in a stream with Reynolds number of 1.5 million, for two high-energy extraction operating regimes. The benefits of using endplates in order to reduce finite-wing-induced losses are also analyzed. Three-dimensional time-accurate Reynolds-averaged Navier-Stokes simulations using Menter's shear stress transport turbulence model and a 30-million-cell grid are performed. Detailed comparative hydrodynamic analyses of the finite and infinite wings highlight that the power generation efficiency of the finite wing with sharp tips for the considered high energy-extraction regimes decreases by up to 20 %, whereas the maximum power drop is 15 % at most when using the endplates. Horizontal-axis wind turbines may experience strong unsteady periodic flow regimes, such as those associated with the yawed wind condition. Reynolds-averaged Navier-Stokes CFD has been demonstrated to predict horizontal-axis wind turbine unsteady flows with accuracy suitable for reliable turbine design. The major drawback of conventional Reynolds-averaged Navier-Stokes CFD is its high computational cost. A time-step-independent time-domain simulation of horizontal-axis wind turbine periodic flows requires long runtimes, as several rotor revolutions have to be simulated before the periodic state is achieved. Runtimes can be significantly reduced by using the frequency-domain harmonic balance method for solving the unsteady Reynolds-averaged Navier-Stokes equations. This research has demonstrated that this promising technology can be efficiently used for the analyses of complex three-dimensional horizontal-axis wind turbine periodic flows, and has a vast potential for rapid wind turbine design. The three-dimensional simulations of the periodic flow past the blade of the NREL 5-MW baseline horizontal-axis wind turbine in yawed wind have been selected for the demonstration of the effectiveness of the developed technology. The comparative assessment is based on thorough parametric time-domain and harmonic balance analyses. Presented results highlight that horizontal-axis wind turbine periodic flows can be computed by the harmonic balance solver about fifty times more rapidly than by the conventional time-domain analysis, with accuracy comparable to that of the time-domain solver.