Discrete conservation principles in large-eddy simulation with application to separation control over an airfoil

An unstructured-grid large-eddy simulation (LES) technique is used to investigate the turbulent flow separation over an airfoil with and without synthetic-jet control. Numerical accuracy and stability on arbitrary shaped mesh elements at high Reynolds numbers are achieved using a finite-volume discretization of the incompressible Navier–Stokes equations based on higher-order conservation principles—i.e., in addition to mass and momentum conservation, kinetic energy conservation in the inviscid limit is used to guide the selection of the discrete operators and solution algorithm. Two different stall configurations, which consist of flow over a NACA 0015 airfoil at 16.6° and 20° angles of attack, are simulated at Reynolds number of 896 000 based on the airfoil chord length and freestream velocity. In the case of 16.6° angle of attack where flow separates around a midchord location, LES results show excellent agreement with the experimental data for both uncontrolled and controlled cases. LES confirms the experimental finding that synthetic jets, which are produced through a slot across the entire span on suction surface at 12% chord location, effectively delay the onset of flow separation and cause a significant increase in the lift coefficient. In the case of 20° angle of attack where flow separates near the leading edge, LES predicts reasonable results comparable to experimental data when grid resolution is sufficient to predict the separated shear layer. In this case, the synthetic-jet actuation at 12% chord location is found marginally effective in controlling leading-edge separation.