The separated flow over an airfoil is characterized by up to three distinct natural frequencies: those of the shear layer, separation bubble, and wake. Previous work has shown that open-loop forcing at sub-and super-harmonics of these frequencies can be especially effective in controlling the extent of the separation bubble. Unfortunately, an understanding of the mechanisms driving this behavior is far from complete. In this work, we investigate the interactions between the shear layer and wake using a combination of direct numerical simulations and spectral analysis. We simulate the forced and unforced flows over a finite-thickness flat plate using an immersed boundary method. Spectral analysis of the resulting dynamics is performed using the Koopman operator, a linear operator applicable even to nonlinear systems, as well as traditional signal processing techniques. Using these two approaches, we identify pertinent flow structures based on their frequency content and posit the nature of their interactions. Nomenclature U ∞ freestream velocity, defined at upstream boundary of domain t thickness of flat plate c chord length of flat plate x/c distance from leading edge, measured in chord lengths v j average velocity of synthetic jet during expulsion phase d j width of synthetic jet slot C μ =v 2 j d j /U 2 ∞ c momentum coefficient for synthetic jet F + = f c/U ∞ nondimensional frequency d w width of wake St = f d w /U ∞ Strouhal number PSD power spectral density
The paper explores a set of simple boundary conditions that can represent the flow emanating from zero-net mass-flux (ZNMF) jets in grazing flow. Results from numerical simulations of ZNMF jets in grazing flows are used to determine the key characteristics of the jet profile, and these are used to construct a series of boundary condition models. These various boundary conditions are then tested for a jet exhausting in an attached boundary layer as well as a boundary layer with an induced separation bubble.
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