A mapping-based projection of detailed kinetics uncertainty onto reduced manifolds

Abstract

Propagating uncertainties introduced by chemical reaction rate parameters to high-fidelity numerical simulations of complex combustion devices is necessary to ascertain impact on computational predictions. However, the high cost of detailed computations combined with the need to conduct multiple simulations to propagate uncertainty makes such an estimation computationally challenging. In order to reduce the computational cost, a two-step framework for quantifying uncertainty introduced by detailed chemical kinetics model parameters using reduced chemistry models is developed here. First, reduced-manifold states are uniquely reconstructed in full-composition space by following trajectories at an unburnt mixing state and integrating forward to a prescribed progress variable constraint. Second, parametric uncertainty is propagated by sampling perturbed rate coefficients from mechanism covariance matrices and integrating each realization to the target state, yielding uncertainty maps for reduced-space quantities. The method is applied in two configurations: a subsonic multi-tube combustor with interacting jet flames and recirculation, and a three-dimensional reacting high-speed flowpath. Uncertainty-instrumented estimated are reported for a trajectory time (time for the reconstructed unreacted mixture to reach the local target state) and for the time to equilibrium, revealing order-of-magnitude spatial variations driven by mixing, stratification, and residence-time effects. The largest relative variability occurs in low-to-intermediate temperature regimes associated with induction and the onset of heat release, where branching-related chemistry amplifies sensitivity, particularly away from stoichiometric conditions. The method provides a scalable route to spatially resolved, physically interpretable chemistry-UQ for practical reacting-flow simulations.

Figures (12)

• Figure 1: Conceptual sketch of the proposed trajectory mapping in composition space. The composition space is spanned by $Z$, $c$, and an unconstrained species $\mu$ (not frozen during reaction evolution). The blue-shaded surface $\mathcal{M}_R^{+}(\xi)$: Reduced-mechanism reaction manifold. Red-shaded plane $\mathcal{M}_c(\xi^S)$: iso-$c$ manifold at state $S$ for $\xi$. Green trajectory $R(\xi, t\rightarrow t_0)$: reconstruction from a given state $S$ of $\xi$. Yellow trajectories $R(\Psi, t_0\rightarrow t^*)$: forward integration of $\Psi$ from $Z_0$ with perturbed reaction rate coefficients $k_i$ towards $\mathcal{M}_c(\Psi^E)$, and reach the target composition $\phi^{\Psi^c}(k_i)$. Dashed black lines: relaxation of different reaction trajectories toward equilibrium ($E$).
• Figure 2: Instantaneous snapshot on the combustor mid-plane showing temperature. Blue arrows indicate the flow direction of the oxidizer stream. Red arrows depict fuel stream issuing perpendicular into the oxidizer stream (inset).
• Figure 3: Ignition delay time (log-scale) comparison for $H_2$ at P = 10 atm and $\phi = 0.5$ as a function of inverse temperature (1000/T), Predictions from the FFCM-2 mechanism ( ) are compared against the H$_2$ mechanism mueller1999flow( ); Bars indicate the FFCM-2 uncertainty band.
• Figure 4: Ensemble of one-cell reaction trajectories in C, $Z$, $\mu$ space, and two different un-constrained coordinate definition. Gray curves span different sample of reaction kinetics; one typical trajectory is emphasized with a thick black dashed line. The blue plane marks $C^{\xi}=0.8$ constraint.
• Figure 5: Instantaneous snapshot on the combustor mid-plane B showing time scale $\widetilde{\tau_{C}}$ in log-scale computed from $\Psi$. Blue arrows indicate the flow direction of the partially premixed stream. Region A represents the flame front, while region B represents the recirculation zone.