Application of control methods to fluid mechanics problems: flow past a cylinder - Μαστρόκαλος, Μάριος (Σχολή Ναυπηγών Μηχανολόγων Μηχανικών, 2016)
The optimal suppression of the Kármán vortex street in flow past a circular cylinder, by use of either, passive, active open-loop or active feedback control schemes is investigated by coupling a CFD solver with an optimization tool. The control action consists of either application of slip conditions or mass transpiration on the cylinder surface. The results are interepreted by means of local and global instability calculations utilizing an Orr-Sommerfeld solver and signal processing based on the Stuart-Landau model, respectively. The study is limited to two-dimensional flow at low Reynolds numbers, Re<180, where the non-manipulated flow is either steady or characterized by vortex shedding. Firstly, steady slip conditions are applied on a part or on the entire cylinder surface utilizing a passive control scheme. For slip conditions applied on the entire cylinder surface, the present results demonstrate the stabilizing effect of increasing the non-dimensional slip length, b*=b/D, b being the slip length and D the cylinder diameter, in agreement with recent studies. In particular, the Kármán vortex street is supressed at a critical value of b*, which is an increasing function of Re. Further, it is shown that, for the same levels of b*, the wake can be stabilized by implementing slip conditions only on a part of the cylinder surface. Guided by this observation, the problem of fully or partially suppressing the Kármán vortex street by means of a partially hydrophobic cylinder is addressed by formulating a multi-objective optimization problem, in which the product of slip length and hydrophobic area quantifies the control effort; a second objective function, characterizing flow unsteadiness, is thereby introduced. The optimization results demonstrate that, both for full and partial suppression of the Kármán vortex street, a proper use of partial hydrophobicity can lead to a significant reduction in passive control effort, in comparison to the case of the fully hydrophobic cylinder. Computed optimal solutions of the Pareto front are characterized by means of local stability calculations based on an Orr-Sommerfeld solver. It is shown that flow stabilization is attained when a global intensity of absolute instability, involving local absolute growth rates and the streamwise extent of absolute instability, is sufficiently reduced. Further characterization of the flow stability is performed by means of transient lift coefficient signal analysis in the frame of the Stuart-Landau equation. Secondly, steady mass transpiration is introduced on the cylinder surface. Three regimes on the cylinder surface are considered: (a) the front stagnation point region, (b) the rear stagnation point region, and (c) the region in-between. First, parametric studies are performed, by introducing suction or blowing on each of the three regimes, and assessing the effects on the global stability of the flow. Guided by these results, a multi-objective optimization problem is formulated, aiming at the partial or full suppression of the Kármán vortex street, at a minimal control effort. In this setup, blowing is applied on the rear stagnation point regime, while suction velocities of different magnitude are considered for the front stagnation point and the sideway regimes. A zero net transpiration flow rate is imposed. The absolute value of suction/blowing flow rate quantifies the control effort, while a second objective function, characterizing flow unsteadiness, is also introduced. The goal of optimization is to find proper combinations of the extent of the three regimes, as well as the corresponding suction/blowing velocities, which minimize simultaneously the two objective functions. The calculation of the optimal flow fields demonstrates that flow stabilization can be attained with a control effort substantially lower in comparison to previous literature studies. Optimal solutions are characterized by means of local stability analysis, as well as analysis of transient lift signals. Finally, in order to attain partial or complete vortex street cancellation, by even lower levels of control effort, two proportional feedback control schemes are developed, utilizing both control actions introduced above. In the first feedback control scheme, actuation consists in time-dependent mass transpiration, while, in the second one, in time-dependent slip conditions. In both cases, the feedback signal is generated based on a velocity measurement in the near wake. Further, for both feedback control schemes, optimization problems are developed, aiming at the partial or full cancelation of the vortex street at a minimal control effort. In comparison to passive flow control, a reduction in control effort by two orders of magnitude is attained with the present optimized feedback control schemes.