Low-order modelling for feedback control of fluid flows around complex geometries

The majority of goods transportation vehicles' power is consumed in overcoming aerodynamic drag which arises due to vortex shedding over the bluff rear end of the vehicle. As such, a reduction in pressure drag via feedback control could have significant economic and environmental effects on CO2 emissions, as well as reducing fatigue acting on the body. The difficulty in designing such controllers lies in obtaining models suited to modern control design methods, which are necessarily of much lesser complexity than typical Computational Fluid Dynamics models, or models derived from immediate spatial discretisation of the equations governing fluid flows. It is with obtaining such low-order models that the work presented in this thesis is concerned. A computationally efficient modelling approach which is suited to obtaining low- order models of complex geometry fluid flows is described, whereby the system's overall input-output frequency response is built up by connecting together the frequency responses of a large number of computational node subsystems in an efficient manner, exploiting the inherent structure of spatially discretised PDAEs. In order to choose a suitable formulation of the governing equations – the Navier- Stokes equations – a rigorous analysis of several of the formulations suggested in the literature is presented, whereby the dynamics of different formulations are compared both at the nodal level, and at the full system level for a 2D channel flow (for which a well studied benchmark model exists). In the penultimate chapter, the work of previous chapters is consolidated by apply- ing the modelling technique to a 2D backward facing step flow. Slot jet actuation on the rear edge is assumed, and two separate output configurations are considered. The resulting models are compared to models obtained in a computational system iden- tification study, which prompts an interesting investigation into the dynamics of the common PISO Computational Fluid Dynamics algorithm.