Hierarchical model form uncertainty quantification for turbulent combustion modeling

All models invoke assumptions that result in model errors. The objective of model form uncertainty quantification is to translate these assumptions into mathematical statements of uncertainty. If each assumption in a model can be isolated, then the uncertainties associated with each assumption can be independently assessed. In situations where a series of assumptions leads to a hierarchy of models with nested assumptions, physical principles from a higher-fidelity model can be used to directly estimate a physics-based uncertainty in a lower-fidelity model. Turbulent nonpremixed combustion models fall into a natural hierarchy from the full governing equations to Conditional Moment Closure to flamelet-like models to thermodynamic equilibrium, and, at each stage of the hierarchy, a single assumption can be isolated. In this work, estimates are developed for the uncertainties associated with each assumption in the hierarchy. The general method identifies a trigger parameter that can be obtained with information only from the lower-fidelity model that is used to estimate the error in the lower-fidelity model using only physical principles from the higher-fidelity model. Starting from the lowest fidelity model, the trigger parameters identified in this work are the product of a chemical time scale and the scalar dissipation rate for the equilibrium chemistry model, which characterizes the errors associated with neglecting finite-rate chemistry and transport; the reciprocal of the product of a generalized Lagrangian flow time and the scalar dissipation rate for the steady flamelet model, which characterizes the errors associated with neglecting flow history effects; and the relative magnitude of the conditional fluctuations for Conditional Moment Closure. The approach is applied in LES to a turbulent nonpremixed simple jet flame to quantify the errors associated with the equilibrium chemistry model and the steady flamelet model. The results indicate that errors associated with neglecting finite-rate chemistry and transport in the equilibrium chemistry model are dominant upstream while errors associated with neglecting flow history in the steady flamelet model become more important downstream.