Gradient-Free Aeroacoustic Shape Optimization Using Large Eddy Simulation (2312.14167v1)

Abstract: We present an aeroacoustic shape optimization framework that relies on high-order Flux Reconstruction (FR) spatial discretization, the gradient-free Mesh Adaptive Direct Search (MADS) optimization algorithm, and Large Eddy Simulation (LES). Our parallel implementation ensures that the runtime of each optimization iteration remains consistent, irrespective of the number of design parameters involved in the optimization problem, provided sufficient resources are available. This eliminates the dependence of the runtime of gradient-free algorithms on the number of design variables. The objective is to minimize Sound Pressure Level (SPL) at a near-field observer by computing it directly from the flow field. We evaluate this framework across three different problems. First, an open deep cavity is considered at a free-stream Mach number of $M=0.15$ and Reynolds number of $Re=1500$ based on the cavity's depth, reducing the SPL by $12.86dB$. Next, we optimized tandem cylinders at $Re=1000$ and $M=0.2$, achieving over $11dB$ noise reduction by optimizing cylinder spacing and diameter ratio. Lastly, a baseline NACA0012 airfoil is optimized at $Re=23000$ and $M=0.2$. The shape of the airfoil is optimized to generate a new 4-digit NACA airfoil at an appropriate angle of attack to minimize the SPL while ensuring the baseline time-averaged lift coefficient is maintained and prevent any increase in the baseline time-averaged drag coefficient. The SPL is reduced by $5.66dB$ while the mean drag coefficient is reduced by more than $7\%$. These results highlight the feasibility and effectiveness of our aeroacoustic shape optimization framework.

• The paper introduces a novel framework that integrates LES, high-order Flux Reconstruction, and MADS to perform gradient-free aeroacoustic shape optimization.
• It achieves significant noise reduction, demonstrated by a 12.86 dB SPL drop in deep cavity and over 11 dB in tandem cylinders, while enhancing aerodynamic performance.
• The approach overcomes traditional computational limits with parallelized, high-order methods, offering a scalable solution for complex aerospace applications.

Insights into Gradient-Free Aeroacoustic Shape Optimization Using Large Eddy Simulation

The paper "Gradient-Free Aeroacoustic Shape Optimization Using Large Eddy Simulation" by Mohsen Hamedi and Brian C. Vermeire presents a novel framework for optimizing aeroacoustic shapes utilizing gradient-free methods. This framework integrates high-order Flux Reconstruction (FR) with the Mesh Adaptive Direct Search (MADS) optimization algorithm and Large Eddy Simulation (LES). Such an assemblage is noteworthy for its ability to address the traditional computational burdens of gradient-free optimization by parallelizing its implementation, thus making the optimization independent of the number of design parameters.

Methodological Approach

The authors have structured their framework around three pillars:

1. Simulation via Large Eddy Simulation (LES): LES is employed for capturing unsteady and intricate flow physics, which are critical for accurately assessing aeroacoustic performance. This is essential for achieving precise control over acoustic emissions in aerodynamic designs.
2. High-Order Flux Reconstruction (FR): The authors deploy an FR scheme that notably achieves over 55% of the theoretical peak performance on modern hardware, surpassing the 3% typically achieved by conventional Finite Volume (FV) methods. This advancement makes high-fidelity LES more feasible computationally.
3. Gradient-Free Optimization with MADS: MADS is utilized as a gradient-free optimization algorithm, well-suited to overcome challenges in traditional adjoint-based methods, especially for chaotic and non-linear systems such as aeroacoustics. Here, it operates independently of the number of design variables when running on sufficiently capable parallel computing resources.

Numerical Results and Case Applications

The paper applies the framework to three cases—a deep cavity, tandem cylinders, and a baseline NACA0012 airfoil—demonstrating its robustness and efficacy:

• Deep Cavity: The SPL at a near-field observer was reduced by 12.86 dB, showing the capability of the framework in handling complex geometrical changes and modulating flow-induced noise.
• Tandem Cylinders: A noise reduction of over 11 dB was successfully achieved, showcasing the optimization framework’s proficiency in adjusting spatial configurations such as distance between cylinders and diameter ratios to reduce noise.
• NACA0012 Airfoil: The optimization of the airfoil's shape yielded an SPL reduction of 5.66 dB while concurrently maintaining or improving aerodynamic performance metrics like lift and drag.

Theoretical and Practical Implications

This research demonstrates that high-order CFD techniques can be effectively applied to aeroacoustic optimization, which traditionally was dominated by lower-order approaches due to computational constraints. The outcomes present a promising direction for aerospace applications: the methodology not only advances theoretical understanding of aeroacoustic functional forms but also provides pragmatic solutions for designing quieter, more efficient aerodynamic surfaces.

Future Directions

The implications of this paper extend toward future research aimed at scaling the framework to higher Reynolds numbers and more complex 3D shapes, indicative of real-world aerodynamic bodies. The possibility of incorporating far-field acoustic solvers within this framework could further enhance its applicability in industrial contexts, especially where stringent noise control is crucial. Additionally, this research suggests potential developments in personal air transportation systems, urban air mobility solutions, and quieter commercial aircraft designs.

By demonstrating a successful interplay between numerical methods and optimization techniques, Hamedi and Vermeire introduce a paradigm shift in how aeroacoustic shape optimization can be streamlined, potentially leading toward more comprehensive and efficient design processes in aerodynamics and aeroacoustics.