Modelling and linear feedback control of bluff body flows

Abstract

The unsteady separated wakes that develop downstream of vehicles, buildings, and other bluff objects are the source of many environmental, safety, and performance concerns. Feedback flow control has the ability to deeply modify the dynamics of these flows in ways that often surpass other approaches. In this thesis, we focus on two complementary feedback control strategies and show that they can be readily applied to a wide range of bluff body flows in order to reduce their drag and wake fluctuations. The goal of the first approach is to stabilise an unstable steady state of the flow. It relies on models that are generated either with balanced proper orthogonal decomposition or the eigensystem realisation algorithm. Although these two modelling techniques were designed exclusively for stable systems, we show from a theoretical perspective that they can be applied directly to unstable systems such as bluff body flows and yield accurate models. Using the flow over a D-shaped body at low Reynolds numbers as a test case, we then demonstrate that only a standard nonlinear flow solver is required to design robust stabilising controllers using H-infinity loop-shaping. In the second approach, we do not assume that full flow stabilisation is possible. Instead, we reduce the losses associated with unsteady flow structures in the near wake by attenuating the fluctuations measured with a body-mounted sensor. To this end, large eddy simulations are used to simulate the three-dimensional flow over a backward-facing step with side walls. A linear input-output model is then obtained in the frequency domain using harmonic forcing, and this model is used to design controllers that target specific frequency ranges. We show that all controllers are able to suppress fluctuations as predicted by linear theory and that this leads to an increase in the time-averaged base pressure. Encouraging results were thus obtained computationally with these two approaches. The next steps will now be to apply these model-based linear feedback control techniques experimentally and to more complex and higher Reynolds number flows.