A tangent linear approximation is developed to estimate the sensitivity of the ignition delay time with respect to individual rate parameters in a detailed chemical mechanism. Attention is focused on a gas mixture reacting under adiabatic, constant-volume conditions. The uncertainty in the rates of elementary reactions is described in terms of uncertainty factors, and are parametrized using independent canonical random variables. The approach is based on integrating the linearized system of equations governing the evolution of the partial derivatives of the state vector with respect to individual random variables, and a linearized approximation is developed to relate the ignition delay sensitivity to the scaled partial derivatives of temperature. The efficiency of the approach is demonstrated through applications to chemical mechanisms of different sizes. In particular, the computations indicate that for detailed reaction mechanisms the TLA leads to robust local sensitivity predictions at a computational cost that is order-of-magnitude smaller than that incurred by finite-difference approaches based on one-at-a-time rate perturbations.

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, H 2 , 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 H 2 mechanism, TLA is about ten times faster than finite differences, and this enhancement becomes even more substantial when more complex mechanisms are considered.

This work focuses on constructing functional representations of quantities of interest (QoIs) of an uncertain system in high dimension. Attention is focused on the ignition delay time of an iso-octane air mixture, using a detailed chemical mechanism with 3,811 elementary reactions. Uncertainty in all reaction rates is directly accounted for using associated uncertainty factors, assuming independent log-uniform priors. A Latin hypercube sample (LHS) of the ignition delay times was first generated, and the resulting database was then exploited to assess the possibility of constructing polynomial chaos (PC) representations in terms of the canonical random variables parametrizing the uncertain rates. We explored two avenues, namely sparse regression (SR) using LASSO, and a coordinate transform (CT) approach. Preconditioned variants of both approaches were also considered, namely using the logarithm of the ignition delay time as QoI.Both approaches resulted in representations of the ignition delay with similar representation errors. However, the CT approach was able to reproduce better the empirical distribution of the underlying LHS ensemble, and also preserved the positivity of the ignition delay time. When preconditioned representations were considered, however, similar performances were obtained using CT and SR representations. The results also revealed that both the CT and SR representations yield consistent global sensitivity estimates. The results were finally used to test a reduced dimension representation, and to outline potential extensions of the work.