Static deep stall analysis augmented by numerically constrained turbulent flows

As computational resources have advanced, scale-resolving methods like Large Eddy Simulation (LES) have gained popularity in the aerodynamic design particularly in predicting massively separated flow regions. The limitations of traditional Reynolds-Averaged Navier-Stokes (RANS) are evident in this regime, given the importance of the intrinsic unsteadiness and the strong three dimensionality of the flow. This research focuses on wall-resolved Implicit Large Eddy Simulation (ILES) for airfoil flows in deep stall with a focus on its dynamics. Moreover, it is also of interest to understand how the spanwise extent of the computational domain affects the resolved aerodynamic forces and flow dynamics. The simulations in this study analyzed various spanwise extents ($l_z$ ranging from $0.10c$ to $2c$) under specific conditions: a chord Reynolds number $Re = 10^5$, asymptotic Mach number $M_{\infty} = 0.15$, and angle of attack $\alpha = 20$ degrees. Significant differences were found in aerodynamic coefficients and flow dynamics when the smallest spanwise extent was used. Specifically, spectral proper orthogonal decomposition (SPOD) showed that a small span failed to capture critical low-frequency dynamics necessary for predicting adequate stall behavior. Additionally, the turbulence field in the small span case remained largely \emph{rod-like}, unlike the three-dimensional turbulence seen in larger spans. The current work propose the nondimensional Spanwise Integral Length Scale ($SILS / l_z$) as a metric for determining the sufficiency of spanwise extent, using two point correlations for the streamwise velocity. Findings suggest that a spanwise extent of $l_z = 1c$ is sufficient, with minimal differences observed between $l_z = 1c$ and $l_z = 2c$. The results emphasize the importance of adequate spanwise resolution to accurately capture deep-stall flow structures and their unsteady behaviour.