Far-Field Aeroacoustic Shape Optimization Using Large Eddy Simulation

TL;DR

The paper addresses reducing far-field aeroacoustic emissions while maintaining aerodynamic performance by integrating a high-order FR-ILES flow solver with a time-domain FW-H acoustic solver and a gradient-free OrthoMADS optimization framework. A two-layer parallelization strategy decouples design evaluations from optimization iterations, enabling scalable exploration of design spaces without dependency on the number of parameters. Demonstrated on NACA 4-digit airfoils at $Re=23{,}000$, the approach achieved a $5.9$ dB OASPL reduction and a $14\%$ drag decrease with lift nearly unchanged, validating the method’s potential for practical quiet-airfoil design. The study also highlights the necessity of data-surface duplication for accurate FW-H predictions in spanwise-periodic problems and provides a rigorous validation and grid-independence assessment, underscoring the framework’s reliability and applicability to more complex, industry-relevant problems.

Abstract

This study presents a shape optimization framework that combines a Flux Reconstruction (FR) spatial discretization, Large Eddy Simulation (LES), the Ffowcs-Williams and Hawkings (FW-H) formulation, and the gradient-free Mesh Adaptive Direct Search (MADS) optimization algorithm. We emphasize the necessity of duplicating the data surface to achieve accurate far-field noise prediction in spanwise periodic problems using the FW-H formulation. The proposed parallel implementation of the optimization framework ensures consistent runtime per optimization iteration, regardless of the number of design parameters, thereby addressing a common limitation of many gradient-free algorithms. The framework is demonstrated through far-field aeroacoustic shape optimization of NACA 4-digit airfoils at a Reynolds number of $23,000$. The objective function minimizes the Overall Sound Pressure Level (OASPL) at a far-field observer positioned $10$ unit chords below the trailing edge, while preserving the mean lift coefficient and reducing the mean drag coefficient. The optimized airfoil achieves an OASPL reduction of $5.9~dB$ and over $14\%$ decrease in mean drag, while maintaining the mean lift coefficient. These results underscore the feasibility and effectiveness of the proposed approach for practical shape optimization applications.

Figures (28)

• Figure 1: Visualization of the proposed far-field aeroacoustic shape optimization framework. The two-layer parallel part of the framework is highlighted in yellow, in which, each red rectangle is run on multiple GPUs while all the red rectangles are also performed concurrently.
• Figure 2: The computational grid for NACA0012 airfoil at $\alpha = 6^\circ$.
• Figure 3: Different solution polynomial distributions for grid independence study of NACA0012 airfoil at $\alpha = 6^\circ$.
• Figure 4: Schematic diagram of the data surface with $L_z = 0.2c$.
• Figure 5: The time-averaged pressure coefficient for both $\mathcal{P}3$ and $\mathcal{P}4$ simulations.