Turbomachinery design optimization using adjoint method and accurate equations of state

This research work presents a shape optimization approach for turbomachinery applications based on the adjoint method and accurate equations of state for the thermo-physical description of the fluids. The nature of the research is numerical, hence most of the work expense has been dedicated to the development of the tools embedded in the optimization framework. The algorithm proposed is based on a discrete inviscid adjoint method able to treat real-gas flows, state-of-the-art parametrization techniques (NURBS) and a preconditioned steepest descent optimizer to reach the optimal point. Built-in equations of state and look-up tables (LuT) are introduced within the optimization algorithm to handle real-gas effects. In particular, a novel consistent LuT method is devised. The potential of the optimization approach is investigated on different 2D design problems encountering in aerodynamics and turbomachinery The design methodology is initially applied to the re-design of a wind tunnel nozzle operating under both ideal and real gas flows. Two different turbomachinery design examples are reported. The former focuses on the maximization of the performances of a transonic cascade and represents the earliest test case performed in this research. The latter aims at optimizing an existing converging-diverging turbine cascade operating under supersonic conditions, with the objective of achieving a more uniform flow at the blade outlet section. Real-gas equations of state are herein considered, properly introduced at both flow and adjoint level through the LuT approach. An original extension of the algorithm for treating off-design conditions is also envisaged in the present work. The method devised combines a standard multi-point optimization technique with an uncertainty quantification algorithm to assess the design points and the weights of the multi-point problem. The capability of the novel approach in providing robust designs is finally investigated by maximizing the performances of the mentioned supersonic blade configuration, now working under a relatively wide range of operating conditions. In all test cases remarkable outcomes are achieved in terms of improvement of performances of the initial configuration and computational efficiency. Most of the applications of adjoint method are still restricted to shape optimization, however new perspectives have been recently risen on the use of adjoint. In this regard, the last part of the thesis is devoted to illustrate the potential of adjoint-based methods for uncertainty quantification and robust optimization. The study is carried out by taking a quasi-1D transonic problem as reference test case.

Questo lavoro di ricerca presenta un approccio per l'ottimizzazione di forma basato sul metodo aggiunto e su equazioni di stato accurate per la descrizione termo-fisica dei fluidi. Il lavoro è interamente numerico e propone un algoritmo di ottimizzazione basato su un metodo aggiunto discreto non viscoso per gas reali, tecniche di parametrizzazione di tipo NURBS e un metodo a gradiente di tipo steepest descent. Le potenzialità del metodo vengono testate attraverso diversi problemi fluidodinamici bidimensionali non viscosi tipici del settore turbomacchine e aerodinamico.