Simulation of Tubes

Introduction

Modelling sound radiation from open tubes is an important topic in acoustics, e.g., when simulating music instruments like tube bells or bag pipes or the human vocal tract. Simple models for tubes assume that the sound wave inside the tube can be modelled by two plane waves travelling from one end to the other. Using this assumption in combination with a correction for the sound radiation it is easy to determine resonance frequencies of the tube. However, this approach is restricted with respect to frequency and shape of the tube.

Aims

In order to allow for a more general setup than a (segmented) straight tube with constant cross section, we want to combine the tube model with the boundary element method (BEM) where special (infinitely) thin elements are used.

Left: Resonances of a tube with two holes at the top - Right: Sound pressure at 835 Hz

Research Problems

To model the thin walls of the tube, we use a special type of boundary elements that is formulated for infinitely thin elements and that should help in avoiding almost singular integrals in the boundary integral equation. Using the BEM with these thin elements offers the additional advantage, that no special boundary conditions need to be used at the tube ends. Nevertheless, there are some stability issues that need to be investigated and understood. Numerical experiments, for example, have shown, that the common rule of 8 to 10 boundary elements per wavelength cannot be used in the case of these open tubes.