# Experimental/Numerical Acoustic Assessment of Aircraft Beat Headsets Based on Electrospupn Mats
## 3 Numerical Simulations  
Numerical simulations were performed with the aim to compare the related results with the experimental data measured in the semi-anechoic chamber. The commercial code VA One [26] was selected as numerical tool for such calculations. In particular, the BEM module was selected to simplify the modelling strategy thanks to the inherent advantages of BEM when simulating a free field radiation. The adoption of BEM (instead of FEM) allowed us to not model the surrounding walls (being perfectly absorbent in the considered frequency range), nor the fluid itself, eventually resulting in a closer similarity with the acoustic conditions reached in the semi-anechoic chamber. A BEM formulation based on a Galerkin method [13; 26] is used in this present work. This allows the generation of the modal radiation impedance matrix, the modal blocked force vectors due to internal acoustic sources and the nodes for computation of pressures and velocities due to internal acoustic sources and elastic modes of the BEM fluid subsystems. A direct BEM approach is adopted in this work because faces are wetted on one side only (BEM faces with single sides must fully enclose the fluid). The aforementioned BEM procedure is intended for mid-sized scattering, radiation and coupled problems, and the matrices used to describe the nodal impedance of a BEM fluid are complex and full. The memory and runtime needed to store and invert the matrices imposed constraints on the size of the model. For an exterior problem as in the present case, the Burton-Miller formulation [27] is used to prevent spurious frequencies. An iterative flexible Generalized Minimal Residual method (fGMRES) [26] is used to compute the solution and a preconditioner to increase the convergence rate of the fGMRES iterative solver. The headrest was modelled by CAD in the folded and unfolded configurations, see Figure 8. Particular attention was devoted to the separation of the two circular areas from the remaining part of the headrest in order to accommodate the two nanofiber insertions. Figure 7: (a) Calibrated monopolar volume velocity source (Simcenter Qsource) and (b) binaural head (HEAD Acoustics HMS) adopted for the tests. Three different load locations, two headrest shapes and two types of circular insertions were considered for the simulations, for a total number of 12 different configurations (Figure 9a). Nominally, all of the configurations in Table 1, having the source position at 75 cm from the head, were reproduced numerically. The final close up of one of the models is shown in Figure 9b, where the different entities are highlighted. The models are comprised of the BEM surface meshes for the headrest (with the circular insertions) and the dummy head, the monopole source representing the acoustic source, the BEM fluid definition and the two data recovery surfaces on which the acoustic measurements were displayed. The considered frequency range was 200-1600 Hz, with 20 Hz constant resolution. Figure 8: CAD models for the head and the folded and unfolded configurations. Figure 9: _Cont_. The mesh presented an average element size of nearly 15 mm that guaranteed about 15 nodes per wavelength at a frequency of 1600 Hz. It is a common practice to guarantee at least 4 to 8 nodes per wavelength to consider a mesh as sufficiently fine and, therefore, no convergence study was considered as required here. Simulations were performed up to 1600 Hz due to the availability of material data only up to that frequency (Figure 10). The monopole source was set up in such a way to emit the same power spectrum as in the experiments (Figure 6). The BEM fluid was air, with a sound speed equal to 343 m/s and mass density equal to 1.21 kg/m\({}^{3}\). A null damping loss factor was assumed in air. The two circular insertions were modelled either having an area impedance corresponding to a traditional reference material or, alternatively, having the nanofiber textile impedance.