A high-order compact finite-difference scheme for large-eddy simulation of active flow control

The purpose of this article is to summarize a computational approach, which developed and matured over an extended period of time, and has been shown to be useful for performing large-eddy simulation (LES) of flows with active control. Because of the nature of active flow control, simulation of this class of problems typically cannot be carried out accurately by methods less sophisticated than LES. Active control flowfields are highly unsteady, and can be characterized by small-scale fluid structures which are produced by the control process, but may also be inherent in the original uncontrolled situation. The numerical scheme is predicated upon an implicit time-marching algorithm, and utilizes a high-order compact finite-difference approximation to represent spatial derivatives. Robustness of the scheme is maintained by employing a low-pass Pade-type nondispersive spatial filter, which also accounts for the fine-scale turbulent dissipation that otherwise is traditionally provided by an explicitly added subgrid-scale (SGS) stress model. Geometrically complex applications are accommodated by an overset grid technique, where spatial accuracy is preserved through use of high-order interpolation. Utility of the method is illustrated by specific computational examples, including suppression of acoustic resonance in supersonic cavity flow, leading-edge vortex control of a delta wing, efficiency enhancement of a transitional highly loaded low-pressure turbine blade, and separation control of a wall-mounted hump model. Control techniques represented in these examples are comprised of both steady and pulsed mass injection or removal, as well as plasma-based actuation. For each case, features of the flowfield are elucidated and the solutions are compared to the baseline situation where no control was enforced. Where available, comparisons are also made with experimental data.