Lift Build-Up on Circulation Control Airfoils

Circulation control airfoils modify the lift by changing the jet momentum (injected tangent to a blunt trailing edge), whereas conventional sharp trailing-edge airfoils control their lift primarily by changing the angle of attack. For a step input in the angle of attack, the lift develops with a certain indicial time lag, which for sharp trailing-edge airfoils may be represented by Wagner’s function. This paper explores the similarities between Wagner’s lift build-up function and lift build-up over elliptical circulation control airfoils using numerical simulations for a 15% thickness-to-chord ratio elliptic circulation control airfoil. Following a thorough validation, the lift response to a step change in jet momentum is simulated using time-accurate flow simulations. The results highlight an excellent correlation between the time lags of the Wagner function and the circulation control airfoil lift response to the corresponding step input, suggesting that the Wagner function may lend itself for representing circulation control lift dynamics. Additional transient behaviors are also compared, and similarities as well as ranges of applicability are discussed.