Introduction
Aeroacoustic shape optimization plays a critical role in minimizing noise pollution and enhancing the aerodynamic performance of structures, especially in industries like aviation and wind energy. This optimization involves computational frameworks that integrate a flow solver, an acoustic solver, and an optimization algorithm. In this blog, we delve into an innovative framework applied in our study, demonstrating how these components come together to tackle complex aeroacoustic problems.
Methodology
There are three main components to our proposed shape optimization framework: a flow solver, an acoustic solver, and an optimization algorithm, each of which are briefly described in the following.
1. Flow Solver
The backbone of our framework is the High-Order Unstructured Solver (HORUS). This solver is based on the Flux Reconstruction (FR) approach for spatial discretization. FR is a high-order numerical scheme for solving conservation laws. It bridges the gap between Discontinuous Galerkin (DG) and Spectral Difference (SD) methods by using a single grid for solution and flux points, ensuring simplicity and computational efficiency. The key strength of FR lies in its ability to achieve high-order accuracy by reconstructing continuous flux polynomials across cell boundaries, maintaining conservation and stability. It is highly versatile, offering adaptability to various mesh types and efficient handling of complex physics with lower computational costs compared to traditional high-order methods. Furthermore, Large Eddy Simulation (LES) is employed over the Reynolds-Averaged Navier Stokes (RANS) approach as it is superior for acoustics due to its ability to resolve large-scale turbulent structures and provide time-dependent solutions, which are critical for capturing sound generation and broadband noise. Unlike RANS, which averages turbulence and loses unsteady flow information, LES accurately represents flow-acoustic interactions, particularly in complex, separated, or recirculating flows. This makes LES more suitable for predicting noise sources and far-field acoustics.
2. Acoustic Solver
In near-field aeroacoustic problems, the direct approach is used, where the acoustic field is resolved within the flow solver. However, for the far-field aeroacoustic problems, the hybrid approach is used, and the Ffowcs Williams and Hawkings (FW-H) formulation is implemented in Python, developing the PyFWH acoustic solver. The PyFWH solver requires the density, velocity, and pressure fields as inputs to the solver, and then, PyFWH computes the sound pressure level at any observer point at a significantly low computational cost. In the FW-H formulation, the positioning of the data surface requires careful attention to ensure it captures all relevant turbulence-induced noise sources while avoiding spurious acoustic artifacts, which can compromise prediction accuracy.
3. Optimization Algorithm
Aeroacoustic optimization involves highly nonlinear and chaotic flow behaviors, where conventional gradient-based optimization methods often fail due to divergence or an inability to handle non-smooth objective functions. The Mesh Adaptive Direct Search (MADS) algorithm provides a robust gradient-free alternative, capable of efficiently navigating complex design spaces by iteratively refining its search on a discretized mesh. Its ability to handle black-box functions, such as those from CFD solvers, makes it particularly suited for aeroacoustic optimization, where the objective function depends on turbulent and unsteady flow characteristics.
Multi-Layer Parallelism
Gradient-free optimization algorithms suffer from scalability as their runtime increases linearly by increasing the number of design parameters. To be more clear, if there are n number of design parameters in an optimization problem, 2n simulations must be run within each optimization iteration. In our proposed framework, each simulation is run in parallel on multiple GPUs, leveraging high-performance computing resources; and all the simulations within each optimization iteration is also run concurrently on multiple nodes. This approach, reduces the runtime of each optimization iteration to that of a single simulation, regardless of the number of design parameters, provided adequate resources are available. The proposed two-layer parallel shape optimization framework, reduces the runtime of gradient-free shape optimization problems significantly.
Some Results of the Aeroacoustic Shape Optimization
Flow Over Open Deep Cavity. In here we have the animation of the flow over open deep cavity for both the baseline and optimum designs. The iso-surfaces of Q-criterion is colored by velocity magnitude and the acoustic field is shown in grey scale.
Flow Over Tandem Cylinders. In here we have the animation of the flow over two tandem cylinders for both the baseline and optimum designs. The iso-surfaces of Q-criterion is colored by velocity magnitude and the acoustic field is shown in grey scale.
The NACA 4-Digit Airfoil. In here we have the animation of the flow over two tandem cylinders for both the baseline and optimum designs. The iso-surfaces of Q-criterion is colored by velocity magnitude and the acoustic field is shown in grey scale.
Published Articles
1. Mohsen Hamedi, Brian Vermeire. Near-Field Aeroacoustic Shape Optimization at Low Reynolds Numbers. AIAA Journal (2024): 1-15. [AIAA Journal, arXiv Pre-Print]
2. Mohsen Hamedi, Brian Vermeire. Gradient-Free Aeroacoustic Shape Optimization Using Large Eddy Simulation. Accepted in the AIAA Journal (2025). [AIAA Journal, arXiv Pre-Print]
3. Mohsen Hamedi, Brian Vermeire. Far-Field Aeroacoustic Shape Optimization Using Large Eddy Simulation. In Review in the Journal of Sound and Vibration. [arXiv Pre-Print]