Short-time analysis of large-scale structures in unsteady flows

State-of-the-art investigations of the hydrodynamic stability of flow fields of industrial significance are limited to time-invariant or time-periodic flows. This is due to the lack of a robust and affordable methodology capable of obtaining the stability and sensitivity information of complex aperiodic and chaotic flows. Ground-breaking theoretical and numerical concepts are necessary to provide new insight into the dynamic behaviour of unsteady flow systems and develop models for their physically founded control.This project aims to develop a theoretical/numerical methodology that enables the effective study of the stability and the sensitivity of aperiodic and chaotic flow systems of industrial relevance. A new computational tool will be developed to perform finite-time Lyapunov exponent analysis in three-dimensional compressible unsteady flows, which will allow to characterize the perturbations producing chaos in a given flow system. This tool will be combined with a novel computational methodology based on adjoint shadowing techniques, which will enable the study of the sensitivity of aperiodic and chaotic flows to long-term averaged objectives.The developed tools will be applied to two problems of practical interest in the aerospace industry: the unsteady separated flow in a low-pressure turbine blade and the unsteady flow induced by a real wing undergoing fast variations in the pitching angle. These analyses will allow to extract useful dynamical information about the most relevant coherent structures in the studied flow fields and exploit it to exercise flow control. For the first problem, experimental investigations will also be performed at Purdue Experimental Turbine Aerothermal Laboratory to test flow-control concepts devised during the numerical analyses. For the second problem, the investigations will be performed during a placement at Airbus Defence and Space.