Combustion modeling using principal component analysis

The thermochemical state of a single-phase reacting system containing ns species is ns + 1 dimensional. However, it is widely recognized that low-dimensional manifolds exist in this space. The question then arises as to the best way to approximate these manifolds. Common chemistry reduction approaches for combustion simulation (such as laminar flamelet, equilibrium, and flame-sheet (Burke–Schuman) chemistry) specify a priori the manifold dimensionality and the parameters that form the basis for representing the thermochemical state, which is then prescribed as a unique function of these parameters. If high-fidelity data are available from experiment or direct numerical simulation (DNS), manifolds may be determined via a principal component analysis (PCA), with the principal components (PCs) forming a new basis for describing the thermochemical state. By considering a truncated set of PCs, one may approximate the thermochemical state with rigorous error bounds, extract a parameterized representation of the thermochemical state, and derive transport equations for the principal components. This paper outlines a methodology for constructing a reduced model for the thermochemical state from high-fidelity data with particular focus on the ability to parameterize source terms appearing in the transport equations for the principal components. The modeling approach allows quantitative a priori control of the error in the state-space parameterization, and can be applied to both laminar and turbulent simulations in all combustion regimes. 2009 The Combustion Institute. Published by Elsevier Inc. All rights reserved.