Assessing Transfer Matrix Models and Measurements Using Acoustic Energy Conservation Principles

Abstract

Acoustic transfer matrices are widely used in the analysis of combustion dynamics of gas turbines. The reliability of the analysis thus depends on the quality of the determination of the transfer matrices of the individual acoustic elements composing the system's acoustic network. These matrices are, in some simple cases, deduced analytically using one-dimensional acoustic modeling. For more complex elements, such as swirlers, perforated plates, or injection units, the transfer matrix has to be obtained experimentally using an impedance tube setup. There are, however, uncertainties in the experimental determination of the transfer matrix coefficients and in the modeling of key elements like injection units. It is thus worth examining experimental data and assessing models using acoustic energy conservation principles. The general idea is to consider the acoustic power flow in the element represented by the transfer matrix T and compare the power input to the power output. This is best accomplished by obtaining a representation in terms of a scattering matrix S, which may be deduced from the transfer matrix T. It is first shown that standard models like those corresponding to a constant area duct or an area change comply with acoustic energy conservation. This analysis is then employed to assess the L−ζ model, widely used to describe injection unit dynamics. Acoustic conservation principles are then used to assess transfer matrices of a family of injectors determined experimentally and check that the data complies with these principles.