Impact of Gusts on Performance of NACA-0012 Airfoil at Low-Re

The focus of this study is to experimentally quantify the impact of gusts on the performance of a NACA-0012 airfoil and provide a load estimation strategy from modal decomposition coefficients. Experiments are performed in a water tunnel facility at chord-based Reynolds number $Re\approx4\times10^4$ for a range of angles of attack $-6^\circ\le\alpha\le12^\circ$. The gust generator functioned as a bluff body with a controlled shedding phase, producing a von K\'{a}rm\'{a}n vortex street. The generator was tested at two different locations; in the first configuration, the gust generator was positioned inline 1.5 chords upstream of the airfoil leading edge (referred to as the centered-gust case), and, in the second configuration, the gust generator was positioned upstream of the airfoil with a 0.5 chord transverse offset (referred to as the offset-gust case). Aerodynamic load experiments were performed for both configurations, $\alpha$ from $-6^\circ$ to $12^\circ$ with an increment of $1^\circ$. Synchronized load-cell and time-resolved PIV measurements were performed for selected $\alpha$ (i.e., $0^\circ$, $6^\circ$, and $12^\circ$) for both configurations. Proper Orthogonal Decomposition (POD) of the velocity field was used to extract coherent structures and identify dominant modes across different scenarios. Cross-correlation between the time-varying POD coefficients of the dominant modes and $c_l$, together with magnitude-squared coherence, was used to quantify the impact of the flow field on $c_l$. The centered-gust preserved a near-linear $c_l(\alpha)$ but reduced lift-curve slope and significantly increased variance; the offset-gust induced earlier deviation from a linear slope and higher drag values. Time-resolved PIV showed the rise/fall of $c_l$ associated with leading-edge upwash/downwash due to vortical structures convecting over the airfoil. The gust footprint is shown to be captured by a pair of POD modes; coherence between lift-curve and time-varying coefficient approached peak value at the gust frequency ($\sim$2.1~Hz) and the dominant mode led $c_l$ by $t^*\sim$0.12 and 0.18, with correlation peaks of 0.92 and 0.83, for centered and offset-gust configurations, respectively, at $\alpha = 12^\circ$. These findings showed a phase-accurate linkage between a coherent gust and lift response. This enabled the use of multi-time-delay Linear-Stochastic-Estimation to predict $c_l$ from the time-varying POD coefficient. The estimated $c_l$ values using this approach had a Root Mean Square Error (RMSE) of 0.135. The resulting low-order model description enables estimation of $c_l$ from select dominant modes.