Compressibility Effects on Leading-Edge Dynamic Stall Criteria at High Reynolds Number

TL;DR

This paper investigates whether the leading-edge stall indicators $LESP$ and $BEF$ can predict stall onset in a high-Re compressible regime. It employs uRANS simulations, with LES data as reference, for a pitching NACA 0012 at $Re = 1 \times 10^6$ and $M_\infty = 0.3$, 0.4, 0.5; it analyzes flow fields, DSV formation timing, and the correlation between stall criteria and onset. The main finding is that at $M_\infty = 0.3$–0.4 the criteria predict stall ahead of DSV, but at $M_\infty = 0.5$ shock–shear interactions cause DSV to precede the criteria, reducing predictive accuracy. The results suggest the stall criteria definitions should be revised to account for compressibility-induced shock effects, and that LES may be necessary for validating stall onset in such regimes.

Abstract

This study examines the applicability of two leading-edge dynamic stall criteria, namely, the maximum magnitudes of the leading-edge suction parameter (LESP) and the boundary enstrophy flux (BEF), in a moderately compressible flow regime. While previously shown to predict stall onset ahead of dynamic stall vortex (DSV) formation in incompressible and mildly compressible regimes, these criteria are assessed here at a Reynolds number of $1 \times 10^6$ and freestream Mach numbers between 0.3 and 0.5. Unsteady RANS simulations indicate that DSV formation occurs in close temporal proximity to the attainment of the stall criteria. However, at the highest Mach number considered, stronger shock interaction effects with the shear layer leads to DSV formation prior to the criteria being reached, reducing their predictive accuracy. These findings suggest that while the criteria remain effective at lower Mach numbers, their definitions require modification in compressible regimes where strong shock interactions significantly influence the stall process.

Figures (11)

• Figure 1: Grid used in the present study for uRANS simulations: full view (left), zoomed-in view (middle) and trailing-edge region (right). Every third point in the radial and circumferential directions are shown for clarity in the left and middle panels.
• Figure 2: Variation in unsteady aerodynamic coefficients, $C_l$, $C_d$ and $C_m$, and maximum magnitude of $C_p$ near the leading edge as the airfoil pitches up, for the uRANS cases.
• Figure 3: Comparison of $C_l$ (a) and $C_m$ (b) variation with $\alpha$ for uRANS and LES (if available), for different $M_{\infty}$ values
• Figure 4: Space-time contours for $M_{\infty} = 0.3$. The ordinate is angle of attack ($\alpha$), which corresponds to time for a constant-rate pitch-up motion.
• Figure 5: (a) Supersonic flow above the shear layer at the leading edge, and (b) subsonic DSV formation. The top panel shows streamlines overlaid with contours of local Mach number and the bottom panel shows the distribution of $-C_p$ over the airfoil suction surface for $M_{\infty}=0.3$.