Thermo-acoustic instability identification techniques have received increasing attentions in modern propulsion systems, and one of the most popular approaches is the flame transfer function. Despite the prominent role it plays in instability analysis, the formulation and data-driven estimation for transfer function identification are still primitive. In this study, we present a novel transfer function methodology which incorporates prior physical knowledge into a data-driven statistical model. The contributions in terms of methodology are two-fold. First, an improvement on the standard Wiener-Hopf approach is proposed by the introduction of an L_1 regularization term, which addresses the estimation deficiencies for the standard method. Second, the authors employ a physics-based criterion which incorporates prior information on dominant frequencies to tune the regularization penalty. This two-stage transfer function approach is then applied to study the combustion dynamics of a liquid-oxygen/kerosene bi-swirl injector at supercritical conditions. The high-fidelity dataset is generated on the basis of a unified theoretical and numerical framework using large eddy simulation, in accordance with fully compressible conservative equations and real-fluid properties. Dominant frequencies of 5.6 kHz and 8.2 kHz are identified and explained. For this combustion system, the two-stage approach provides an improved transfer function which better reflects the underlying physics of the system. The current study will provide a benchmark for the future applications of this new flame transfer function.
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