A tangent linear approximation of the ignition delay time. II: Sensitivity to thermochemical parameters

The tangent linear approximation (TLA) developed in Almohammadi et al. (Combust. Flame 230, 111426) is extended to estimate the sensitivity of the ignition delay time with respect to species enthalpies and entropies. The proposed method relies on integrating the linearized system of equations governing the evolution of the state vector's partial derivatives with respect to variations in thermodynamic parameters. The sensitivity of the ignition delay time is estimated through a linearized approximation of a temperature functional. The TLA approach is applied to three gas mixtures, H₂, n-butanol, and iso-octane, reacting in air under adiabatic, constant-volume conditions. The numerical experiments indicate that the linearized approximation of the ignition delay time's sensitivity is in excellent agreement with the finite-difference estimates. This is also the case for sensitivity estimates obtained using the TLA approach. Further, significant computational speed-ups are achieved with the TLA approach, and the method scales well with the number of perturbed parameters. In the case of the H₂ mechanism, TLA is about ten times faster than finite differences, and this enhancement becomes even more substantial when more complex mechanisms are considered.