On the Dynamics of the Flow and the Sound Field of an Organ Pipes's Mouth Region

TL;DR

This study uses numerical simulations to analyze the flow and sound field dynamics near an organ pipe's mouth, revealing nonlinear interactions and comparing results with real measurements.

Contribution

It introduces a detailed numerical approach using OpenFOAM to separate flow and sound components in organ pipes, validated against experimental data.

Findings

Velocity field dynamics can be separated into jet flow and sound-induced components.

Numerical SPL spectra agree with real organ pipe measurements.

Nonlinearities are present in the mouth region, affecting sound production.

Abstract

The dynamics of an organ pipe's mouth region has been studied by numerical simulations. The investigations presented here were carried out by solving the compressible Navier-Stokes equations under suitable initial and boundary conditions using parts of the open source C++ toolbox OpenFOAM. The focus of the study is on the examination of the velocity field close to the jet. The components of the velocity field sampled at a cross-section spanning the mouth were analyzed by using methods of coarse-graining. It is shown that the dynamics of the sampled velocity field can be separated into two fractions, a velocity component mainly comprising the jet's flow velocity and a component that essentially carries particle velocity caused by back-propagating sound waves inside the resonator. The SPL-spectra calculated of the data sets of the numerical simulations are compared with the measurements on real organ pipes. The phase-space representations of sound pressure and particle velocity indicate the presence of nonlinearities in the organ pipes's mouth region. The numerical results are consistent with measurements on real organ pipes.