Comprehensive Analysis of Span Size Effects on Scale-Resolving Simulations of Airfoil Stall and Post-Stall Behavior

מושגי ליבה

The choice of appropriate spanwise extent is critical for accurately predicting the stall and post-stall behavior of airfoils using scale-resolving simulations.

תקציר

The study investigates the influence of the spanwise extent on the accuracy of scale-resolving simulations (specifically Implicit Large Eddy Simulations) in predicting the stall and post-stall behavior of the NREL S826 airfoil at a chord Reynolds number of 105.

Key highlights:

• For small angles of attack near stall, the simulations with typical spanwise extents of around 0.1c (where c is the airfoil chord) showed reasonable agreement with experimental data.
• However, for larger angles of attack in the post-stall regime, the computed lift and drag coefficients were found to be highly dependent on the chosen spanwise extent.
• Simulations with smaller spanwise extents (e.g., 0.1395c) exhibited a persistent vortex on the suction side, leading to an overestimation of the lift coefficient compared to the experiments.
• Larger spanwise extents (around 1c) were required to accurately capture the breakdown of this vortex and the associated pressure distribution, resulting in better agreement with the experimental data.
• The analysis of the spanwise autocorrelations of the velocity fluctuations suggested that a spanwise integral length scale of around 0.1 times the spanwise extent can be used as a criterion to determine the sufficiency of the spanwise resolution.

The study highlights the importance of carefully considering the spanwise extent in scale-resolving simulations of airfoil stall and post-stall behavior, as the choice can significantly impact the accuracy of the predicted aerodynamic forces.

סטטיסטיקה

The lift and drag coefficients (CL and CD) for the NREL S826 airfoil at a chord Reynolds number of 105 and Mach number of 0.15 are reported for various angles of attack and spanwise extents.

ציטוטים

"The dramatic influence of the spanwise size even leads to a non stalled airfoil for lz ≤ 0.1395c, only small differences appear for the simulation with lz = 1c and lz = 2c making us confident that, at least for this case, lz = 1c is sufficient to get a converged lift independent of span."
"Empirically, we find that a value of ILS/lz ≈ 0.1 serves as a suitable criterion for defining a sufficient spanwise size, corroborated by the aforementioned analysis."

תובנות מפתח מזוקקות מ:

Effect of span size in Scale Resolving Simulations of airfoil stall and post-stall

by Francesco Ma... ב- arxiv.org 10-03-2024

https://arxiv.org/pdf/2410.01254.pdf

שאלות מעמיקות

How can the insights from this study be extended to other airfoil geometries and flow conditions to develop more general guidelines for the choice of spanwise extent in scale-resolving simulations?

The insights from this study can be extended to other airfoil geometries and flow conditions by establishing a framework that considers the specific characteristics of the airfoil and the flow regime. The key findings regarding the influence of spanwise extent on aerodynamic performance, particularly in stalled and post-stall conditions, suggest that a systematic approach should be adopted.

Geometric Considerations: Different airfoil shapes exhibit varying flow separation characteristics and vortex dynamics. Therefore, the spanwise extent should be tailored to the specific geometry, taking into account the airfoil's camber, thickness, and leading-edge shape. For instance, more complex geometries may require larger spanwise extents to capture the three-dimensional flow structures effectively.

Flow Regime Analysis: The study highlights the importance of the angle of attack and Reynolds number in determining the flow behavior. General guidelines could be developed by categorizing airfoil simulations based on these parameters. For example, airfoils operating at high angles of attack or in low Reynolds number conditions may necessitate larger spanwise extents to accurately resolve the flow features.

Statistical Validity: The criterion based on the spanwise integral length scale (ILS) can serve as a benchmark for other airfoil simulations. By conducting parametric studies across various airfoil geometries and flow conditions, researchers can derive empirical relationships that correlate the required spanwise extent with the ILS, thereby providing a more generalized guideline for future simulations.

Validation with Experimental Data: Extending the findings to other geometries should involve validation against experimental data. This will ensure that the proposed guidelines are robust and applicable across different scenarios, enhancing the reliability of scale-resolving simulations in aerodynamic design.

What are the potential limitations or challenges in applying the proposed criterion based on the spanwise integral length scale to more complex flow scenarios, such as those involving unsteady separation or three-dimensional effects?

While the proposed criterion based on the spanwise integral length scale (ILS) offers a promising approach for determining the necessary spanwise extent in scale-resolving simulations, several limitations and challenges may arise when applied to more complex flow scenarios:

Unsteady Separation: In flows characterized by unsteady separation, such as those found in dynamic stall or rapidly oscillating airfoils, the flow structures can change significantly over time. The ILS, which is based on time-averaged data, may not adequately capture the transient nature of these flows, leading to insufficient resolution of critical flow features.

Three-Dimensional Effects: The criterion primarily addresses two-dimensional representations of flow. In scenarios where three-dimensional effects are pronounced, such as in the presence of significant spanwise vortices or when the airfoil experiences strong crossflow, the ILS may not fully account for the complexities introduced by these three-dimensional interactions. This could result in an underestimation of the required spanwise extent.

Sensitivity to Flow Conditions: The effectiveness of the ILS as a criterion may vary with different flow conditions, such as varying Reynolds numbers or angles of attack. The relationship between the ILS and the necessary spanwise extent may not be linear or consistent across all scenarios, necessitating further empirical validation.

Computational Resources: Implementing the ILS criterion may still require substantial computational resources, particularly for complex flows. The need for high-resolution simulations to accurately capture the flow dynamics can lead to increased computational costs, which may limit the practicality of this approach in certain applications.

Modeling Assumptions: The application of the ILS criterion assumes that the turbulence characteristics are adequately represented in the simulations. In cases where turbulence models or numerical methods introduce significant errors, the reliability of the ILS as a guiding metric may be compromised.

Could the findings from this study be leveraged to develop more efficient computational strategies, such as adaptive mesh refinement or hybrid RANS-LES approaches, to reduce the computational cost while maintaining the accuracy of scale-resolving simulations of airfoil stall and post-stall behavior?

Yes, the findings from this study can indeed be leveraged to develop more efficient computational strategies, such as adaptive mesh refinement (AMR) and hybrid RANS-LES approaches, to optimize computational costs while ensuring the accuracy of scale-resolving simulations of airfoil stall and post-stall behavior:

Adaptive Mesh Refinement (AMR): The insights regarding the influence of spanwise extent on flow characteristics can inform the implementation of AMR techniques. By dynamically adjusting the mesh resolution based on the local flow features, particularly in regions of high turbulence or separation, computational resources can be allocated more efficiently. This approach allows for finer resolution where needed (e.g., near the airfoil surface during stall) while coarsening the mesh in less critical areas, thus reducing overall computational costs.

Hybrid RANS-LES Approaches: The study's findings highlight the importance of accurately capturing turbulent structures in stalled flows. Hybrid RANS-LES methods can be employed to combine the strengths of both turbulence modeling approaches. RANS can be used in regions where the flow is relatively stable and well-predicted, while LES can be applied in areas with complex, unsteady flow dynamics, such as near the airfoil during stall. This strategy can lead to significant computational savings while maintaining the fidelity of the simulation in critical regions.

Guided Simulation Strategies: The established criterion based on the spanwise integral length scale can serve as a guideline for determining the necessary resolution in both AMR and hybrid approaches. By using the ILS to inform mesh refinement strategies, simulations can be tailored to ensure that the spanwise extent is sufficient to capture essential flow features without excessive computational overhead.

Parallel Computing and Resource Allocation: The computational strategies developed from this study can also benefit from advancements in parallel computing. By optimizing the allocation of computational resources based on the flow characteristics identified through the ILS, simulations can be executed more efficiently, allowing for larger and more complex simulations to be performed within reasonable timeframes.

Validation and Iterative Improvement: The findings can be used to iteratively refine computational strategies. By validating the results of AMR and hybrid approaches against experimental data and the established benchmarks from this study, researchers can continuously improve the accuracy and efficiency of their simulations, leading to more reliable predictions of airfoil performance in stall and post-stall conditions.