Computational aeroacoustics to identify sound sources in the generation of sibilant /s/

Abstract

A sibilant fricative /s/ is generated when the turbulent jet in the narrow channel between the tongue blade and the hard palate is deflected downwards through the space between the upper and lower incisors and then impinges the space between the lower incisors and the lower lip. The flow eddies in that region become a source of direct aerodynamic sound, which is also diffracted by the speech articulators and radiated outwards. The numerical simulation of these phenomena is complex. The spectrum of an /s/ typically peaks between 4 and 10 kHz, which implies that very fine computational meshes are needed to capture the eddies producing such high frequencies. In this work, a large-scale computation of the aeroacoustics of /s/ has been performed for a realistic vocal tract geometry, resorting to two different acoustic analogies. A stabilized finite element method that acts as a large eddy simulation model has been adopted to solve the flow dynamics. Also, a numerical strategy has been implemented that allows the determination, in a single computational run, of the separate contribution of the sound diffracted by the upper incisors from the overall radiated sound. Results are presented for points located close to the lip opening showing the relative influence of the upper teeth depending on frequency.

Finite element generation of sibilants /s/ and /z/ using random distributions of Kirchhoff vortices

“…As regards the sizes of the vortices, a n , they deserve some closer inspection. In Pont et al, the CFD simulations revealed that for frequencies below approximately 2.3 kHz, the pressure energy spectrum was apparently constant in average. Beyond that frequency, the energy smoothly decreased until 12 kHz, where the Kolmogorov turbulent cascade started.…”

“…Given that we need to capture frequencies up to 12 kHz for the correct reproduction of a sibilant sound like /s/, and that we have Mach numbers (though locally values of 0.2 can be reached), very fine computational meshes are required to solve the problem. To get a better idea of the computational demands, we notice that generating 10.8 ms of an /s/ took 30 hours in a cluster of 256 processors with a mesh of 45 million tetrahedral elements in Pont et al The 10.8 ms suffice for spectral analysis but not if one wants to generate an audio file from the computed acoustic pressure, or if one wished to produce a more complex sound like syllable /sa/. Therefore, our goal is to try to find an approximation to Lighthill tensor (3), which essentially results in a similar acoustic output (ie, the sibilant sound) to one obtained from CFD.…”

“…One could think of assigning uniform probability density functions to them, but several considerations have been made regarding the sampling space of the parameters in . The considerations are based on heuristic reasoning taking into account the outputs from the large‐scale simulations in Pont et al To begin with and for simplicity, the eccentricity ɛ n has been directly set constant for all vortices because it only plays a scaling role for their strength. Therefore, ɛ n is not considered as a random variable for .…”

“…Beyond that frequency, the energy smoothly decreased until 12 kHz, where the Kolmogorov turbulent cascade started. Since our interest to tailor the Kirchhoff vortex distribution is on the kinetic energy spectrum of the incompressible flow, we have recomputed the CFD in Pont et al to know how behaves with a coarser mesh of approximately 15 million linear elements. The results are shown in Figure for three different points located at the source region.…”

“…Finally, the various realizations of the tensor are assigned to approximately 6% of the elements in the source region, which comprises the space between the teeth occlusion and the lower lip, according to the CFD calculation in Pont et al This relatively low density of quadrupoles is necessary to prevent shadowing of the small, high energy eddies, by the largest ones; otherwise the acoustic output would not be representative of the prescribed source. It must be stated that the system is strongly sensitive to the size of the filter.…”