Advancements in automated design methods for NICFD turbomachinery

The transition towards a more affordable, reliable, and sustainable energy provision paradigm is one of the main 21st century challenges that humanity must overcome to protect the planet from the harmful effect caused by climate change. The concentration of CO2 in the atmosphere has been dramatically increasing since the pre-industrial era. If the increase of green-house gasses emissions continues unabated, this will bring dramatic consequences for planet Earth, compromising eventually the existence of many species, including the human race. To avoid a climate change catastrophe, the share of primary energy coming from renewable energy resources must increase from around 15% in 2015 to 65% in 2050. This energy transition can not rely solely on few successful technologies (i.e., solar photovoltaic, and wind energy), but it must count on a larger variety of technical solutions that are suitable for a wider range of renewable sources and diversity of circumstances. For instance, renewable thermal energy sources for power generation (i.e., geothermal reservoir, biomass fuel, and concentrated solar radiation), can provide a large portion of the world electricity demand in the future. However, the exploitation of a good portion of these sources strongly depends on the market success of technologies such as the Organic Rankine Cycle (ORC) power system. One of the key aspects to make ORC systems economically competitive, especially at the smaller sizes (⇡ 1 − 50 kW), is the realization of highly efficient turbomachinery components. The fluid-dynamic design of ORC turbomachinery significantly differs from the design of traditional machines (i.e., steam and gas turbines), and this is mainly due to the different thermo-physical properties and gas dynamic behavior of the organic working fluids. This means that design methods devised for standard steam and gas turbomachinery can not be used for turbomachinery operating in the Non-ideal compressible fluid dynamics (NICFD) region. Furthermore, no experimental campaigns have ever been carried out to create a body of empirical knowledge to support the design highly efficient ORC turbomachinery. As a consequence, the entire design process of ORC turbomachinery relies only on the use of advanced CFD software. The current trend is to couple CFD tools with numerical optimization techniques in order to automatically obtain optimal flow passage geometries. In particular, adjoint-based methods have clearly demonstrated to be the only optimization technique capable of tackling the multi-stage turbomachinery design problem, in which thousands of design variable must be concurrently optimized. Therefore, the research documented in this PhD dissertation aimed at extending the adjoint method in order to perform the fully-turbulent fluid-dynamic shape optimization of 3D multi-stage ORC turbomachinery. This document contains an extensive introduction, three main chapters, each documenting a building block towards the accomplishment of the main goal of this PhD project, and a final concluding chapter that summarizes all the research outcomes of this work and proposes future steps for research in this field. The first part of the thesis describes the extension of the RANS equations, the convective numerical schemes, and the viscous numerical schemes to the use of complex thermo-physical laws, so to simulate turbulent flows of components working in the NICFD thermodynamic region. The second part documents the derivation of the adjoint solver in order to resolve shape-optimization design problems for 2D single row of ORC turbomachinery. Finally, the last part reports the extension of the adjoint method to 3D multi-stage turbomachinery design.Flight Performance and Propulsio