Time-Domain Acoustic Scattering

Most UAM designs to date employ tightly integrated rotor-airframe configurations which rise to strong acoustic installation effects due to scattering and shielding by vehicle surfaces. These effects are not captured in widely-used integral-based aeroacoustic analogy methods typically used for noise propagation. It has been shown that neglecting the acoustic scattering effect of installed propellers leads to significant errors in noise prediction and consequently the wrong design decision.

The Galerkin Retarded potential boundary integral Acoustic Space-Time Scattering (GRASS) developed in our group is a time-domain boundary element method (TDBEM) solver which employs the full space-time Galerkin discretization of the energetic weak form for the boundary integral equation. Compared to contemporary TDBEM approaches, the full space-time Galerkin formulation is particularly robust and efficient, benefiting from unconditional stability and a quasi-best approximation property that provides accurate solutions on relatively coarse surface meshes.

A key strength of GRASS lies in its ability to accept arbitrary pressure gradient time histories specified on the scattering surfaces, as well as arbitrarily moving source surfaces or distributions. This capability is especially critical for UAM applications where the main noise sources are rotational in nature (associated with rotor blades) and the acoustic scattering of the vehicle in transitional maneuver where noise sources undergo configurational changes is of interest to low-noise operations. GRASS can also be readily applied to predict the noise footprint of UAM vehicles in urban environments where there is significant reflection, shielding and reverberation due to buildings. By applying the appropriate absorbing/impedance boundary conditions, GRASS can be used to model acoustic liners and metamaterials.

With a dedicated GPU card, GRASS is capable of completing full-vehicle acoustic scattering computations in near real time, making it well suited for many-query tasks such as design optimization and parametric configuration studies, as well as active noise control.

Finally, the GRASS solver has been algorithmically differentiated, culminating in a discrete adjoint solver capable of evaluating acoustic design sensitivities at a cost independent of the number of design variables. The adjoint capability opens the door to acoustic optimization and control while accounting for the full vehicle acoustic scattering/shielding effects.

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