Low-order network model of a duct with non-uniform cross-section and varying mean temperature in the presence of mean flow

Stability analysis of thermoacoustic systems is often carried out with low-order network models. This paper introduces a method to include a duct element with varying cross-sectional area and an arbitrary mean temperature profile in a thermoacoustic network model. Based on the quasi one-dimensional form of the linearized Euler equations (LEEs) for a perfect, inviscid gas, the system equations are formulated in a state space framework in terms of the Riemann invariants f and g. This approach is predicated on one additional assumption, i.e. that the direct impact of entropy fluctuations on the acoustic waves inside the duct is small. A comparison of model results with analytical analysis shows excellent agreement. Eigenvalues are predicted with good accuracy, even for coarse grids. Furthermore, the mode shapes and frequency responses match those found in the literature, demonstrating the validity of the approach.