Analytical Solution for the Sensitivity Coefficients of Ignition Delay Times

In this study, a theoretical analysis of the sensitivity coefficients of ignition delay times is performed by using eigenvalue analysis. Using H₂/O₂ and CH₄/H₂/O₂ kinetic systems as examples, it is demonstrated that the analytical solutions achieve accurate predictions of the sensitivity coefficients of the ignition delay time as compared with the computational solutions. Furthermore, the temperature dependence of the sensitivity coefficients can also be predicted by the theory. For the H₂/O₂ system, the sensitivity coefficients of the key elementary reactions can be predicted with high accuracy at wide ranges of temperature, pressure, and equivalence ratio. For the CH₄/H₂/O₂ system, due to the complexity of the kinetic interactions, while the sensitivity of some reactions with relatively low values can be less accurate, the key reactions with high sensitivity can all be accurately predicted. The comparison of theory with various sizes shows that high-dimensional analysis can achieve closer prediction with the same computational cost. The potential to calculate sensitivity coefficients based on the eigenvalue is noteworthy and encouraging.