Network Models, Helmholtz Solvers and Adjoint Analysis for Thermoacoustics

by Joachim Ottinger and Wolfgang Polifke

This project aims to advance the understanding of thermoacoustic modes and improve predictive tools used in industry and research. The work involves enhancing low-order numerical methods such as network models and Helmholtz solvers so that they are able to capture a broader range of physical effects and deliver more accurate stability predictions.

A modular framework for a Helmholtz solver and accompanying closure models, formulated in a linear state-space representation, is developed. This combination enables flexible model construction, efficient analysis, and investigation from a control theory perspective. The solver is designed to handle non-trivial acoustic boundary conditions, including nonlinearities in the form of frequency-dependent acoustic impedances, which are present in realistic systems. Since unphysical „spurious" modes can arise when using such a modelling approach, it is important to identify and, if possible, eliminate them. In addition, the framework is designed to enable adjoint analysis, which is key to understanding a system's structure and parameter sensitivities.

By bridging the gap between high-fidelity simulations and reduced-order models, this research supports the development of gas turbines that are stable, efficient, and environmentally responsible. The new tools are also meant to support the ongoing quest for physical insights into the interactions of the different components of a thermoacoustic system.