Minimal Modeling for Passive Flow Control via a Poro-elastic Coating

Abstract

Minimal models are obtained for vortex-shedding, both from a smooth aerofoil, and from an aerofoil coated with a porous layer of flow-compliant feather-like actuators. The latter is a passive way to achieve flow control. The minimal-order model for a smooth aerofoil is extracted by analyzing the frequencies present in the flow over this aerofoil, and phenomena such as the presence of super-harmonics of these flow frequencies and existence of limit cycle behaviour for this system. Next, the minimal model for the poro-elastically coated aerofoil is realized by linearly coupling the minimal-order model for vortex-shedding from the smooth aerofoil with an equation for the poro-elastic coating, here modeled as a linear damped oscillator. The various coefficients in both of these models, derived using perturbation techniques, not only lead to solutions from the models that match very well with results from expensive and time-consuming computational models, but also aid in our understanding of the physics of this fluid-structure interaction problem. In particular, the minimal model for a coated aerofoil indicates the presence of distinct regimes that are dependent on the flow and coating characteristics and in this process, provide insight into the selection of optimal coating parameters, to enable flow control at low Reynolds numbers.