Computational considerations for the prediction of airfoil Stall Flutter

TL;DR

This work tackles the prediction of stall flutter for a NACA0012 airfoil by deploying a 2D URANS-based aeroelastic framework (MaPFlow) capable of simulating SAO and LAO across transitional and moderate Reynolds number regimes. It combines a $\gamma$-$Re_\theta$ transition model for SAO and a $k$-$\omega$ SST turbulence model for LAO, with a rigorous grid- and time-step sensitivity analysis to establish robust numerical requirements. The study demonstrates qualitative agreement with experimental observations of dynamic stall mechanics and bifurcations, while systematically overpredicting onset velocity and underpredicting LCO amplitudes due to reduced aerodynamic excitation peaks. The findings provide practical guidelines for grid and time-step choices in aeroelastic simulations and identify key limitations and future directions for improving quantitative accuracy in stall flutter predictions, with implications for aeroelastic design and monitoring in engineering applications.

Abstract

This paper presents a comprehensive numerical investigation of a NACA0012 undergoing Stall Flutter Limit Cycle Oscillations (LCO) across distinct fluid dynamics regimes. It accurately models Small Amplitude Oscillations (SAO) in the transitional Reynolds regime and Large Amplitude Oscillations (LAO) in the moderate regime, observed in different experimental campaigns. The SAO analysis servs as a verification of the computational framework against established numerical benchmarks. Crucially, the LAO simulations represent the first documented prediction across the full experimental velocity range correlated against available measured data, addressing a significant literature gap. The predictions fidelity relies on rigorous computational criteria defined through a detailed sensitivity analysis. This demonstrated numerical requirements significantly more demanding than those typically employed for computing static polars or simulating dynamic pitching motion of rigid airfoils, underscoring the severity of the aeroelastic problem. Overall, the results show strong qualitative agreement with experimental observations, successfully reproducing key dynamic stall mechanics and bifurcation phenomena. Quantitatively, however, the simulation systematically over--predicts the critical onset velocity and under--predicts the LCO amplitudes, a discrepancy attributed to reduced aerodynamic excitation peaks.

Figures (20)

• Figure 1: Schematic diagram of different flutter types.
• Figure 2: Schematic of the experimental set--up used to study Small Amplitude Stall Flutter Oscillations. Image adapted from poirel2008self.
• Figure 3: Image of the experimental set--up used to study Large Amplitude Stall Flutter Oscillations. Image copied from li2007experimental.
• Figure 4: Schematic of the computational set--up used to study the Small Amplitude Stall Flutter Oscillations measured in poirel2008self and the Large Amplitude Stall Flutter Oscillations measured in dimitriadis2009bifurcation. The aerodynamic analysis is performed through a 2D URANS CFD framework, whereas for the prediction of the system dynamics response, only the pitch DOF is considered.
• Figure 5: Flow chart of the fluid--structure coupling. Within every physical time step, internal iterations between the aerodynamics and rigid body dynamics solver are made to ensure a strong coupling and high--fidelity FSI computations.