Supplementary data for: An extended method for analysing the hydroacoustic transfer functions of fluid-carrying test objects

Abstract of related publication This article investigates the acoustic transmission behaviour of fluid-carrying systems under static and flow conditions. For the experimental analysis, sound field decomposition is used to determine the forward- and backward-travelling plane waves, the effective speed of sound, the flow velocity and the damping. Three extended decomposition variants are presented.

The multiple sound-state decomposition (MSD) improves robustness by evaluating several sound-states simultaneously. The multiple frequency decomposition (MFD) yields consistent frequency-independent parameters and allows frequency-dependent damping models. The multiple sound-state multiple frequency decomposition (MSMFD) combines both in an overdetermined formulation and enables robust identification of the effective speed of sound in air, water and dilute water-air mixtures.

The mean flow velocity can also be included in the inverse formulation, but is determined with considerably larger uncertainty in the investigated low-Mach-number liquid configurations. The Acoustic Transmission Line (ATL) method based on four-pole theory is used to model the transmission behaviour. It is extended by funnel-shaped elements and by the directional complex propagation constants γ+ and γ-, which account for damping and mean flow.

Structural compliance is included through section-wise effective speeds of sound. The model is validated against acoustic FEM simulations with and without fluid-structure interaction (FSI), one-dimensional method-of-characteristics (MOC) simulations and measurements from an experimental test rig. The results show good agreement for the dominant transmission behaviour within the investigated frequency range.

The developed methods provide a physically interpretable basis for future investigations of cavitating flows and their acoustic properties. Acknowledgement Some results were obtained as part of IGF project 22709 / N, which is funded by DLR / BMWE. The FEM calculations were performed with Ansys Mechanical 2023 on the Linux HPC cluster at TU Dortmund University, which is funded by the DFG.

(Project no. 271512359).