Incorporating swirl effects into the coefficient of momentum for separation control

Addition of swirl in flow control has been known to enhance suppression of separation over airfoils at high angles of attack. Utilizing large eddy simulations, the present open-loop control study examines the influence of wall-normal and angular momentum injections in mitigating separation over a NACA0012 airfoil at $\alpha = 9^\circ$ and $Re = 23,000$. We introduce these swirling jets near the separation point with wall-normal momentum and swirl independently prescribed through velocity boundary conditions. The changes to the flow from control are examined and the corresponding lift enhancement and drag reduction are assessed as a function of the two velocity components. Since the standard coefficient of momentum does not consider swirling effects, we extend its definition to incorporate both the wall-normal momentum and swirl to quantify the overall flow control effectiveness. We are able to observe a trend in lift force enhancement over this single modified coefficient of momentum (that is dependent on the non-dimensional jet velocity ratio and swirl number). Moreover, we are able to identify a critical value for the modified momentum coefficient and categorize controlled flows into separated, transitional, and attached flows.