Numerical Exploration of Flow Control for Delay of Dynamic Stall on a Pitching Airfoil

摘要

A flow control strategy for the delay of the onset of unsteady separation and dynamic stall on a constant-rate pitching airfoil is explored by means of high-fidelity large-eddy simulations. The flow fields are computed employing a previously developed and extensively validated high-fidelity implicit large-eddy simulation (ILES) approach based on 6th-order compact schemes and 8th-order low-pass spatial filters which provide an effective alternative to standard sub-grid-stress model closures. A NACA 0012 airfoil is pitched about its quarter-chord axis from a small angle of attack (α_o = 4°) to an incidence beyond the onset of dynamic stall. The flow and kinematic parameters are: non-dimensional pitch rate Ω_o~+ = 0.05, freestream Mach number M_∞ =0.1 and chord Reynolds numbers Re_c = 2 × 10~5 and 5 × 10~5. For the baseline case, dynamic stall is analyzed and found to be initiated with the bursting of a contracted laminar separation bubble (LSB) present in the leading-edge region. This observation motivated a flow control of the LSB employing high-frequency pulsed actuation imparted through a zero-net mass flow blowing/suction slot located on the airfoil lower surface just downstream of the leading edge. Both 2D and spanwise-nonuniform forcing are considered at a very high non-dimensional frequency St_f = fU/c = 50.0 which corresponds to a sub-harmonic of the dominant natural LSB fluctuations for the baseline static case. This approach is first tested for a static angle of attack α = 8° and found to significantly reduce the LSB size. Application to the pitching airfoil demonstrates that a significant delay in the onset of dynamic stall is achievable. This delay results in a stronger suction peak near the leading edge and in an increase in maximum lift. High-frequency forcing energizes the LSB allowing the flow to remain attached in the leading-edge region. Instead of the abrupt LSB bursting and dynamic stall vortex formation found for the baseline situation, the control cases exhibit the upstream propagation of a trailing-edge separation region which eventually precipitates stall but at a much higher incidence. Both spanwise uniform and non-uniform modes of actuation were found to be effective suggesting that control effectiveness relies primarily on the very high actuation frequency to which the LSB is receptive.