ABSTRACT
Accurate thermochemical mechanisms that can predict the formation of nitrogen oxides (NO) are important design tools for low-emissions engines. The lack of accurate direct measurements of reaction rates and the associated measurement scatter have resulted in recommended rate parameters for individual chemical reactions that have large uncertainty intervals. In an effort to quantify the impact of these parametric uncertainties on emissions predictions, forward uncertainty propagation is performed with five spectral methods. Sparse grids are identified as the optimal technique to rapidly construct accurate surrogate models. Subsequent polynomial expansions with sparse grids, performed in one-dimensional atmospheric laminar flames for only the 30 uncertain reactions that greatly affect NO formation, produce uncertainty intervals two orders of magnitude larger than nominal predictions. Primary uncertainty sources were identified with reaction pathway analyses to evaluate the contribution of individual formation routes and the uncertainties in prompt NO were found to propagate mostly from the CH chemistry. These results highlight the necessity of a comprehensive approach, using experimental measurements with uncertainty quantification and inference techniques, to reduce uncertainty and develop predictive NO
models.
Nomenclature
Integration operator
Number of terms in the expansion
MC Monte Carlo
Orthogonal polynomial basis of order i
PCE Polynomial chaos expansion
PDF Probability density function
Quadrature operator
Response, quantity of interest
RPA Reaction pathway analysis
SD San Diego mechanism
Reference flame speed
Temperature
Mole fraction of species
Reaction rate uncertainty factor
Concentration of species
Specific reaction rate constant
Level of accuracy of the quadrature rule
Number of variables in the expansion
Order of the polynomial expansion
Weight of the quadrature point
and
Variable studied in the spectral expansion; vector and scalar elements
Coefficients of the polynomial expansion
Nested quadrature operator at level
1
moment, average
Joint probability density function
2
moment, standard deviation
Residence time
Equivalence ratio
One-dimensional polynomial basis
Multivariate polynomial combinations
Subscripts
low Lower uncertainty limit
high Upper uncertainty limit
Superscripts
(1) One-dimensional operator
(2) Two-dimensional operator
(n) N-dimensional operator
Node of the quadrature rule