Model form uncertainty quantification in turbulent combustion simulations: Peer models

摘要

Turbulent combustion simulations invoke a number of component models for chemical kinetics, turbulence, flame structure, etc., each of which has an error associated with its structural form and contributes to overall uncertainties in simulation results. These model form errors arise from the necessity of making assumptions in deriving a model. Conventional approaches to estimating model form errors rely on an ad hoc additive error that is then calibrated against experimental or computational data. These approaches inherently neglect any a priori knowledge of physics in developing the model error estimate. Instead, in this work, an inherently physics-based approach to estimating model form error is developed based on the notion of "peer" models. In the generic approach, the error in a candidate model is determined by taking the difference between it and an equally plausible alternative "peer" model with a different set of assumptions. The generic approach is applied in this work to the modeling of the subfilter mixture fraction dissipation rate, which is typically modeled as the ratio of the subfilter mixture fraction variance and a time scale. The typical time scale approximation invokes a turbulent time scale, and a "peer" model is proposed in which a chemical time scale is invoked to estimate the model form error. Using stochastic collocation, the subfilter mixture fraction dissipation rate model form error as well as the uncertainty in a model parameter are propagated through LES calculations of the Sandia D Flame utilizing the steady flamelet model. The results indicate that the mixture fraction, temperature, and carbon monoxide uncertainties increase with downstream distance due to an increase in the relative subfilter mixture fraction variance and increased sensitivity to the time scale approximations, which diverge in magnitude with downstream distance. Uncertainties in these quantities arising from the model form error are shown to be more significant than uncertainties arising from the model constant uncertainty. For the temperature, uncertainties due to chemical kinetic rate uncertainty are shown to be slightly smaller than uncertainties due to the subfilter mixture fraction dissipation rate model error; for the carbon monoxide mass fraction, uncertainties due to chemical kinetic rate uncertainty are twice as large as uncertainties due to the sub filter mixture fraction dissipation rate error since carbon monoxide is more kinetically-controlled than the temperature. (C) 2017 The Combustion Institute. Published by Elsevier Inc. All rights reserved.