A direct numerical simulation investigation of the synthetic jet frequency effects on separation control of low-Re flow past an airfoil

We present results of direct numerical simulations of a synthetic jet (SJ) based separation control of flow past a NACA-0018 (National Advisory Committee for Aeronautics) airfoil, at 10° angle of attack and Reynolds number 10⁴ based on the airfoil chord length C and uniform inflow velocity U₀. The actuator of the SJ is modeled as a spanwise slot on the airfoil leeward surface and is placed just upstream of the leading edge separation position of the uncontrolled flow. The momentum coefficient of the SJ is chosen at a small value 2.13 × 10⁻⁴ normalized by that of the inflow. Three forcing frequencies are chosen for the present investigation: the low frequency (LF) F⁺ = f_eC/U₀ = 0.5, the medium frequency (MF) F⁺ = 1.0, and the high frequency (HF) F⁺ = 4.0. We quantify the effects of forcing frequency for each case on the separation control and related vortex dynamics patterns. The simulations are performed using an energy conservative fourth-order parallel code. Numerical results reveal that the geometric variation introduced by the actuator has negligible effects on the mean flow field and the leading edge separation pattern; thus, the separation control effects are attributed to the SJ. The aerodynamic performances of the airfoil, characterized by lift and lift-to-drag ratio, are improved for all controlled cases, with the F⁺ = 1.0 case being the optimal one. The flow in the shear layer close to the actuator is locked to the jet, while in the wake this lock-in is maintained for the MF case but suppressed by the increasing turbulent fluctuations in the LF and HF cases. The vortex evolution downstream of the actuator presents two modes depending on the frequency: the vortex fragmentation and merging mode in the LF case where the vortex formed due to the SJ breaks up into several vortices and the latter merge as convecting downstream; the discrete vortices mode in the HF case where discrete vortices form and convect downstream without any fragmentation and merging. In the MF case, the vortex dynamics is at a transition state between the two modes. The low frequency actuation has the highest momentum rate during the blowing phase and substantially affects the flow upstream of the actuator and triggers early transition to turbulence. In the LF case, the transverse velocity has a 1%U₀ pulsation at the position 18%C upstream of the actuator.