The document discusses a novel approach for analyzing and designing thermoacoustic stability in combustion systems using Möbius transformations to relate reflection coefficients on the upstream and downstream sides of a flame.
Key points include:
Reflection Coefficients: Stability is analyzed using the upstream (RupR_{\text{up}}Rup) and input reflection coefficients (RinR_{\text{in}}Rin), avoiding direct measurements at the hot side of the flame.
Möbius Transformation: The relation between RinR_{\text{in}}Rin, RdnR_{\text{dn}}Rdn (downstream reflection coefficient), and the flame transfer matrix (TM) is expressed as a Möbius transformation, providing geometric insights into stability conditions.
Passive Stability: The study derives conditions for RdnR_{\text{dn}}Rdn to ensure passive stability (∣Rin∣<1|R_{\text{in}}| < 1∣Rin∣<1) and identifies optimal values of RdnR_{\text{dn}}Rdn for stability across a frequency range.
Experimental Validation: Experimental results validate the theoretical framework, highlighting challenges at specific frequencies (e.g., 300 Hz and 700 Hz) where stability design is critical.
Applications: The findings provide practical design criteria for the acoustic properties of combustion systems, enabling enhanced stability through optimized reflection coefficients.
This method simplifies the stability analysis and provides actionable guidelines for designing combustion appliances with improved thermoacoustic performance.
Kojourimanesh, M., Kornilov, V., de Goey, P., & Lopez Arteaga, I. (2021). Mobius transformation between reflection coefficients at upstream and downstream sides of flame in thermoacoustics systems. Paper presented at 27th International Congress on Sound and Vibration, ICSV 2021, Prague, Virtual, Czech Republic.
