A Space-Time Galerkin Boundary Element Method for Aeroacoustic Scattering

Abstract

Acoustic scattering by vehicle surfaces can have significant effects on overall noise levels. In this paper, we present a space-time Galerkin time-domain boundary element method (TDBEM) that offers several distinct advantages over contemporary scattering methods for prediction of acoustic scattering and shielding of complex aeroacoustic sources such as propellers and rotors. The time-domain approach allows efficient simulation of transient, rotating, and broadband noise sources, while the Galerkin formulation is robust and unconditionally stable without any tuned numerical parameters. The main challenge of the Galerkin approach, namely the numerically difficult double space-time integration, is resolved through an efficient decomposition-based quadrature procedure. We present three cases with analytical solutions to validate the method and study its numerical properties, demonstrating excellent agreement for scattering and shielding by a variety of different geometries. We then apply the TDBEM to a trailing edge-mounted propeller case, comparing the numerical predictions with experimental measurements. The results demonstrate good agreement between predicted and measured scattering and shielding in a practical application case.

Figures (16)

• Figure 1: Flow chart showing the process of computing the scattered acoustic field from the scattering geometry and incident field. The incident field is provided through coupling with another solver (e.g., CFD with integral-based acoustic analogy) or as an analytical expression.
• Figure 2: Geometry for inner spatial integration: (a) definition of local Cartesian ($x'$, $y'$, $z'$) and cylindrical ($r'$, $\theta'$, $z'$) coordinate systems; (b) decomposition of $\Gamma_s$ into three component triangles with a vertex at the origin; (c) decomposition of the domain formed by the intersection of a component triangle and circle into sector and triangle regions.
• Figure 3: Sphere geometry, showing the source (blue dot, $R_{src}$) and observer (red dot, $R_{obs}$) positions.
• Figure 4: Visualizations of the predicted acoustic field of a harmonic point source scattered by a sphere at selected frequencies: (a) $ka=2$; (b) $ka=4$; (c) $ka=8$; (d) $ka=16$. The instantaneous acoustic potential is shown at nondimensional time $t=50$.
• Figure 5: Comparison of predicted and analytical shielding factors for scattering of a harmonic point source by a sphere at selected frequencies: (a) $ka=2$; (b) $ka=4$; (c) $ka=8$; (d) $ka=16$.