Effect of airfoil thickness on onset of dynamic stall is investigated using large eddy simulations at chord-based Reynolds number of 200 000. Four symmetric NACA airfoils of thickness-to-chord ratios of 9 %, 12 %, 15 % and 18 % are studied. The three-dimensional Navier–Stokes solver, FDL3DI is used with a sixth-order compact finite difference scheme for spatial discretization, second-order implicit time integration and discriminating filters to remove unresolved wavenumbers. A constant-rate pitch-up manoeuver is studied with the pitching axis located at the airfoil quarter chord. Simulations are performed in two steps. In the first step, the airfoil is kept static at a prescribed angle of attack ( $=4^{\circ }$ ). In the second step, a ramp function is used to smoothly increase the pitch rate from zero to the selected value and then the pitch rate is held constant until the angle of attack goes past the lift-stall point. The solver is verified against experiments for flow over a static NACA 0012 airfoil. Static simulation results of all airfoil geometries are also compared against XFOIL predictions with a generally favourable agreement. FDL3DI predicts two-stage transition for thin airfoils (9 % and 12 %), which is not observed in the XFOIL results. The dynamic simulations show that the onset of dynamic stall is marked by the bursting of the laminar separation bubble (LSB) in all the cases. However, for the thickest airfoil tested, the reverse flow region spreads over most of the airfoil and reaches the LSB location immediately before the LSB bursts and dynamic stall begins, suggesting that the stall could be triggered by the separated turbulent boundary layer. The results suggest that the boundary between different classifications of dynamic stall, particularly leading edge stall versus trailing edge stall, is blurred. The dynamic-stall onset mechanism changes gradually from one to the other with a gradual change in some parameters, in this case, airfoil thickness.
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A vorticity-based criterion to characterise leading edge dynamic stall onset
We propose a more conservative, physically-intuitive criterion, namely, the boundary enstrophy flux ( $BEF$ ), to characterise leading-edge-type dynamic stall onset in incompressible flows. Our results are based on wall-resolved large-eddy simulations of pitching aerofoils, with fine spatial and temporal resolution around stall onset. We observe that $|BEF|$ reaches a maximum within the stall onset regime identified. By decomposing the contribution to $BEF$ from the flow field, we find that the dominant contribution arises from the laminar leading edge region, due to the combined effect of large clockwise vorticity and favourable pressure gradient. A relatively small contribution originates from the transitional/turbulent laminar separation bubble (LSB) region, due to LSB-induced counter-clockwise vorticity and adverse pressure gradient. This results in $BEF$ being nearly independent of the integration length as long as the region very close to the leading edge is included. This characteristic of $BEF$ yields a major advantage in that the effect of partial or complete inclusion of the noisy LSB region can be filtered out, without changing the $BEF$ peak location in time significantly. Next, we analytically relate $BEF$ to the net wall shear and show that its critical value ( $=\max (|BEF|)$ ) corresponds to the instant of maximum net shear prevailing at the wall. Finally, we have also compared $BEF$ with the leading edge suction parameter ( $LESP$ ) (Ramesh et al. , J. Fluid Mech. , vol. 751, 2014, pp. 500–538) and find that the former reaches its maximum value between $0.3^{\circ }$ and $0.8^{\circ }$ of rotation earlier.
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- NSF-PAR ID:
- 10358136
- Date Published:
- Journal Name:
- Journal of Fluid Mechanics
- Volume:
- 935
- ISSN:
- 0022-1120
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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We evaluate different approaches to characterize the onset of leading-edge type dynamic stall in pitching airfoils for incompressible flows. The first approach is by calculating the time variation of two flow parameters, namely, the Leading Edge Suction Parameter (LESP) and the Boundary Enstrophy Flux (BEF), both of which reach a critical value in the vicinity of stall onset. The alternate approaches include the use of Dynamic Mode Decomposition (DMD) and Wavelet Transform (WT) to identify the occurrence of critical flow states. Using wall-resolved LES results, we found that both LESP and BEF were effective in indicating stall onset, with the critical value of the BEF preceding that of the LESP. However, we were not able to identify any distinguishing behavior from DMD or WT that clearly indicates stall onset. DMD yielded unstable eigenvalues both within and outside of the stall onset regime. WT indicated the presence of energetic small scale structures, whose time of incidence varied relative to the stall onset regime for different cases with no observable trend. The novel element in the current work is the use of CFD data with fine spatial and temporal resolution within the stall onset regime, to provide a composite picture of the stall onset process using different types of analyses.more » « less
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We evaluate two leading-edge-based dynamic stall-onset criteria (namely, the maximum magnitudes of the leading-edge suction parameter and the boundary enstrophy flux) for mixed and trailing-edge stall. These criteria have been shown to successfully predict the onset of leading-edge stall at Reynolds numbers of O(10^5), where the leading-edge suction drops abruptly. However, for mixed/trailing-edge stall, leading-edge suction tends to persist even when there is significant trailing-edge reversed flow and stall is underway, necessitating further investigation into the effectiveness of these criteria. Using wall-resolved large-eddy simulations and the unsteady Reynolds-averaged Navier–Stokes method, we simulate one leading-edge stall and three mixed/trailing-edge stall cases at Reynolds numbers of 200,000 and 300,000. We contrast the progression of flow features such as trailing-edge separation and vortex formation across different stall types and evaluate the stall-onset criteria relative to critical points in the flow. We find that the criteria nearly coincide with the instance of leading-edge suction collapse and are reached in advance of dynamic stall vortex formation and lift stall for all four cases. We conclude that the two criteria effectively signal dynamic stall onset in cases where the dynamic stall vortex plays a prominent role.more » « less
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We evaluate two leading-edge-based dynamic stall onset criteria, namely, the maximum magnitudes of the Leading Edge Suction Parameter and the Boundary Enstrophy Flux, for mixed and trailing-edge stall. These criteria have been shown to successfully predict the onset of leading-edge stall at Reynolds numbers >= O(10^5), where the leading-edge suction drops abruptly. However, for mixed/trailing-edge stall, leading-edge suction tends to persist even when there is significant trailing-edge reversed flow and stall is underway, necessitating further investigation of the effectiveness of these criteria. Using wall-resolved, large-eddy simulations and unsteady Reynolds-Averaged Navier-Stokes method, we simulate one leading-edge stall and three mixed/trailing-edge stall cases at Reynolds numbers 2x10^5 and 3x10^6. We contrast the progression of flow features such as trailing-edge separation and vortex formation across different stall types and evaluate the stall onset criteria relative to critical points in the flow. We find that the criteria nearly coincide with the instance of leading-edge suction collapse and are reached in advance of dynamic stall vortex formation and lift stall for all four cases. We conclude that the two criteria effectively signal dynamic stall onset in cases where the dynamic stall vortex plays a prominent role.more » « less
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The current work evaluates the effectiveness of two leading-edge dynamic stall criteria in mild to moderately compressible regimes using numerical simulations. The two criteria under consideration, namely, the maximum magnitudes of the leading edge suction parameter (max(𝐿𝐸 𝑆𝑃)) and boundary enstrophy flux (max(|𝐵𝐸𝐹|)), have previously been found to be effective at signaling dynamic stall in the incompressible regime. Based on unsteady Reynolds-averaged Navier-Stokes simulations at a Reynolds number of 2 × 105 and freestream Mach numbers between 0.1 - 0.5, we observe that these criteria are directly applicable in the mild to moderately compressible regimes, since they are reached shortly after suction collapse at the leading edge and well in advance of dynamic stall vortex formation for all the cases. This is attributed to compressibility effects promoting adverse-pressure-gradient(APG)-induced stall for the flow conditions considered. For the highest Mach number of 0.5, shock wave interactions with the separated shear layer are observed. It is noted that although compressibility leads to separation at a lower APG, the maximum APG scaled by the local flow density remains in the same range for all the cases.more » « less
- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1017/jfm.2021.1149
