TY - JOUR
T1 - Hierarchical model form uncertainty quantification for turbulent combustion modeling
AU - Klemmer, Kerry S.
AU - Mueller, Michael E.
N1 - Funding Information:
The authors gratefully acknowledge funding from the Princeton University School of Engineering and Applied Sciences Project X Fund. The simulations presented in this article were performed on computational resources managed supported by the Princeton Institute for Computational Science and Engineering (PICSciE) and the Princeton University Office of Information Technology's Research Computing department.
Funding Information:
The authors gratefully acknowledge funding from the Princeton University School of Engineering and Applied Sciences Project X Fund. The simulations presented in this article were performed on computational resources managed supported by the Princeton Institute for Computational Science and Engineering (PICSciE) and the Princeton University Office of Information Technology’s Research Computing department.
Publisher Copyright:
© 2020
Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.
PY - 2020/11
Y1 - 2020/11
N2 - 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.
AB - 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.
KW - Large Eddy Simulation
KW - Model form error
KW - Turbulent combustion modeling
KW - Uncertainty quantification
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U2 - 10.1016/j.combustflame.2020.08.002
DO - 10.1016/j.combustflame.2020.08.002
M3 - Article
AN - SCOPUS:85089484280
SN - 0010-2180
VL - 221
SP - 288
EP - 295
JO - Combustion and Flame
JF - Combustion and Flame
ER -