Understanding the fundamental roles of momentum and vorticity injections in flow control

The objective of this study is to numerically investigate the fundamental roles that momentum and vorticity injections play in suppressing flow separation over a canonical airfoil. Open-loop control of separated, incompressible flow over a NACA 0012 airfoil at Re = 23, 000 is examined through large-eddy simulations. In particular two conditions are considered: (1) α = 6◦ – shallow stall and (2) α = 9◦ – deep stall for applications of flow control. This study does not attempt to replicate a specific actuator but aims to independently introduce wall-normal momentum and vorticity flux into the flow through model boundary conditions. We find that the modification to the flow field can be captured by quantifying both the effects of wall-normal momentum (coefficient of momentum) and wall-normal vorticity (derived coefficient of circulation), by considering a newly defined total input parameter (total coefficient). The influence of spanwise spacing is also examined and is shown that the total coefficient accounts for spacing, as long as the actuators are spaced sufficiently far enough to avoid destructive interference. The result from this study is hoped to lead to a general approach for quantifying the control input for a family of actuators. Moreover, the study has developed advanced analysis techniques. First, the capability to perform bi-global stability analysis has been developed and validated, which can serve as a basis for physics-based active flow control guided by the knowledge of hydrodynamic instabilities. Second, as part of modeling complex unsteady flows in general, efforts in this study have led to the initial development of a novel network-theoretic approach in quantifying nonlinear interactions present in vortical flows. Dense fluid flow graphs, with vortices as nodes and induced velocity as edge weights are distilled to the key structures using spectral sparsification, while preserving nonlinear dynamics and invariants. We have also been able to quantify two-dimensional turbulence as a weighted scale-free network and evaluate its resilience to perturbations. The network-based approach to analyze interactions in fluid flows should provide a refreshing perspective to examine a wide range of unsteady flow phenomena. DISTRIBUTION A: Distribution approved for public release. Resulting Publications 1. P. M. Munday & K. Taira, “Separation control on NACA 0012 airfoil using momentum and wall-normal vorticity injection,” AIAA 2014-2685, 2014. 2. P. M. Munday & K. Taira, “Surface vorticity flux analysis in separation control on NACA 0012 airfoil,” AIAA 2015-2632, 2015. 3. A. G. Nair & K. Taira, “Network-theoretic approach to sparsified discrete vortex dynamics,” J. Fluid Mech. 768, 549-571, 2015 4. K. Taira, A. G. Nair, & S. L. Brunton, “Network structure of two-dimensional decaying isotropic turbulence,” J. Fluid Mech. 795, R2, 2016