We consider the second order wave equation in an unbounded domain and propose an advanced perfectly matched layer (PML) technique for its efficient and reliable simulation. In doing so, we concentrate on the time domain case and use the finite-element (FE) method for the space discretization. Our un-split-PML formulation requires four auxiliary variables within the PML region in three space dimensions. For a reduced version (rPML), we present a long time stability proof based on an energy analysis. The numerical case studies and an application example demonstrate the good performance and long time stability of our formulation for treating open domain problems.

The flow-induced sound sources of human voice production are investigated based on a validated voice model. This analysis is performed using a hybrid aeroacoustic workflow based on the perturbed convective wave equation. In the first step, the validated 3D incompressible turbulent flow simulation is computed by the finite volume method using STARCCM+. In a second step, the aeroacoustic sources are evaluated and studied in detail. The formulation of the sound sources is compared to the simplification (neglecting the convective sources) systematically using time-domain and Fourier-space analysis. Additionally, the wave equation is solved with the finite element solver openCFS to obtain the 3D sound field in the acoustic far-field. During the detailed effect analysis, the far-field sound spectra are compared quantitatively, and the flow-induced sound sources are visualized within the larynx. In this contribution, it is shown that the convective part of the sources dominates locally near the vocal folds (VFs) while the local time derivative of the incompressible pressure is distributed in the whole supra-glottal area. Although the maximum amplitude of the time derivative is lower, the integral contribution dominates the sound spectrum. As a by-product of the detailed perturbed convective wave equation source study, we show that the convective source term can be neglected since it only reduces the validation error by 0.6%. Neglecting the convective part reduces the algorithmic complexity of the aeroacoustic source computation of the perturbed convective wave equation and the stored flow data. From the source visualization, we learned how the VF motion transforms into specific characteristics of the aeroacoustic sources. We found that if the VFs are fully closing, the aeroacoustic source terms yield the highest dynamical range. If the VFs are not fully closing, VFs motion does not provide as much source energy to the flow-induced sound sources as in the case of a healthy voice. As a consequence of not fully closing VFs, the cyclic pulsating velocity jet is not cut off entirely and therefore turbulent structures are permanently present inside the supraglottal region. These turbulent structures increase the broadband component of the voice signal, which supports research results of previous studies regarding glottis closure and insufficient voice production.

In an aeroacoustic simulation of human voice production, the effect of the sub-grid scale (SGS) model on the acoustic spectrum was investigated. In the first step, incompressible airflow in a 3D model of larynx with vocal folds undergoing prescribed two-degree-of-freedom oscillation was simulated by laminar and Large-Eddy Simulations (LES), using the One-Equation and Wall-Adaptive Local-Eddy (WALE) SGS models. Second, the aeroacoustic sources and the sound propagation in a domain composed of the larynx and vocal tract were computed by the Perturbed Convective Wave Equation (PCWE) for vowels [u:] and [i:]. The results show that the SGS model has a significant impact not only on the flow field, but also on the spectrum of the sound sampled 1 cm downstream of the lips. With the WALE model, which is known to handle the near-wall and high-shear regions more precisely, the simulations predict significantly higher peak volumetric flow rates of air than those of the One-Equation model, only slightly lower than the laminar simulation. The usage of the WALE SGS model also results in higher sound pressure levels of the higher harmonic frequencies.

The hybrid aeroacoustic approach is an efficient way to address the issue of the disparity of scales in Computational AeroAcoustics (CAA) at low Mach numbers. In the present paper, three wave equations governing propagation of flow-induced sound of low Mach number flows, namely the Perturbed Convective Wave Equation (PCWE), Ribner’s Dilatation (RIB) equation, and Lighthill’s wave equation, are applied using the Finite Element Method (FEM). An airflow through a circular pipe with a half-moon-shaped orifice at three operating flow speeds is considered, where validation data from measurements on a dedicated test rig is available. An extensive analysis of the flow field is provided based on the results of the incompressible flow simulation. The resulting acoustic source terms are investigated, and the relevant source term contributions are determined. The results of the acoustic propagation simulations revealed that the PCWE and RIB are best suited for the present task. The overall deviation of the predicted pressure spectra from the measured mean values amounted to 2.26 and 2.13 times the standard deviation of the measurement compared to 3.55 for Lighthill’s wave equation. Besides reliably predicting the flow-induced sound, the numerical procedure of source term computation is straightforward for PCWE and RIB, where the source term contributions, shown to be relevant, solely consist of time derivatives of the incompressible pressure. In contrast, the Lighthill source term involves spatial derivatives and, thus, is strongly dependent on the spatial resolution and the numerical method actually used for approximating these terms.