Fluid Mechanics Webinar Series: Baddoo

Motivated by turbomachinery aeroacoustics, we investigate the flow through a periodic array of disconnected objects, termed a “cascade”. We deploy and develop techniques from complex analysis to elucidate the mathematical structures and physical mechanisms relevant to cascade flows. Our approach considers both aerodynamic and aeroacoustic aspects but we focus efforts toward developing conformal mapping techniques amenable to cascades of complicated geometry and topology. The foundation of practical conformal mapping is the Schwarz–Christoffel (SC) formula; we extend the SC formula to periodic domains which enables analytic constructions of the periodic flow field. By utilising tools from function theory, our solutions are valid for an arbitrary number of obstacles per period window. We also present algorithmic advances that enable rapid and accurate calculations of our mappings. Our theory is applied to classical idealised problems such as steady potential flows, unsteady vortex dynamics, and free-streamline flows. These low-order techniques can be used in turbomachinery design schemes or for real-time flow control with data-driven methods.