A Matrix Formalism for Fluid-Borne Sound in Pipe Systems

Abstract

In this paper a general matrix formalism for predicting fluid-borne sound in gas filled pipe systems of arbitrary geometry is presented. Based on the formalism, a code, valid from the low frequency plane wave range up to frequencies where a large number of modes propagate in each pipe, has been developed. The formalism is based on representing the pipe system as an equivalent network of acoustical 2-ports, where each 2-port corresponds to a physical pipe element. Interfaces or branch points between N (≥ 2) pipes in the physical system are represented as node points, which are modelled as multi-ports of order N. For the low frequency range the ports of the equivalent network are defined using travelling pressure wave amplitudes as the state variables. This gives a so-called scattering-matrix formalism that has been described earlier in the literature. For the high frequency multi-mode range it is demonstrated that the same formalism still holds if the state variables are defined via acoustic power. Furthermore, compared to the standard power flow models used today, e.g., the VDI 3733 standard, the suggested matrix formulation can also include the effect of reflections. To enable modelling both of sound generation from fluid machines (fans, compressors,…) and flow generated sound, e.g., from flow separation at constrictions (valves) and bends, both the 2-ports and multi-ports are allowed to be active. In the first version of the code semi-empirical models for flow generated sound from, e.g., valves have been included.