Nonlinear reduction of combustion composition space with kernel principal component analysis

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Experimental multi-scalar measurements in laboratory flames have provided important databases for the validation of turbulent combustion closure models. In this work, we present a framework for databased closure in turbulent combustion and establish an a priori validation of this framework. The approach is based on the construction of joint probability density functions (PDFs) and conditional statistics using experimental data based on the parameterization of the composition space using principal component analysis (PCA). The PCA on the data identifies key parameters, principal components (PCs), on which joint scalar PDFs and conditional scalar means can be constructed. To enable a generic implementation for the construction of joint scalar PDFs, we use the multidimensional kernel density estimation (KDE) approach. An a priori validation of the PCA-KDE approach is carried out using the Sandia piloted jet turbulent flames D, E and F. The analysis of the results suggests that a few PCs are adequate to reproduce the statistics, resulting in a low-dimensional representation of the joint scalars PDFs and the scalars' conditional means. A reconstruction of the scalars' means and RMS statistics are in agreement of the corresponding statistics extracted directly from the experimental data. We also propose one strategy to recover missing species and construct conditional means for the reaction rates based on a variation of the pairwise-mixing stirred reactor (PMSR) model. The model is demonstrated using numerical simulations based on the one-dimensional turbulence (ODT) model for the same flames. (T. Echekki). 3 computational cost for complex chemical systems and large computational problems where a large number of notional particles must be retained for an accurate evaluation of the PDFs. Alternative strategies to alleviate the potential cost of a joint PDF transport equation have been proposed, including strategies to parameterize the composition space (e.g. by adopting a flamelet assumption) or via the multi-environment PDF method [10].The two limits of a presumed PDF shape with a limited set of parameters and the solution for a PDF transport equation leave ample room in between for intermediate approaches, which may be based on the construction of PDFs based on simulation [11][12][13][14] or experimental data. For example, Goldin and Menon [11,12], Sankaran et al [13] and Calhoon et al [14] built joint scalar PDFs, which are parameterized by an appropriate set of lower moments using simulations based on the linear-eddy model (LEM) [15].The PDFs are generally trained on simpler canonical flows, such as scalar decay in homogeneous turbulence or co-flowing jet configurations. The LEM is a 1-D model that can accommodate any degree of chemical complexity based on the coupling of reaction and diffusion processes in a deterministic fashion and a stochastic implementation for turbulent stirring. As the model is implemented in physical space, it is capable of generating statistics from which a description of the composition sp...

Section: Parameterization Of the Composition Space With Pcamentioning

confidence: 99%

A framework for data-based turbulent combustion closure: A priori validation

Ranade

Echekki

2019

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“…Although, a similar procedure can be implemented for LES based on multi-scalar line measurement data and the construction of filtered probability density functions. As described earlier, PCs are a representation of the thermochemical scalars in a lower dimensional space [13,[22][23][24][25][26][27][28][29][30]. The vectors of PCs and their chemical source terms are linearly related to the vectors of measured thermo-chemical scalars and their chemical source terms, respectively:…”

Section: Pca Parameterization and Governing Equationsmentioning

confidence: 99%

A framework for data-based turbulent combustion closure: A posteriori validation

Ranade

Echekki

2019

Self Cite

In this work, we demonstrate a framework for developing closure models in turbulent combustion using experimental multi-scalar measurements. The framework is based on the construction of conditional means and joint scalar PDFs from experimental data based on the parameterization of composition space using principal component analysis (PCA). The resulting principal components (PCs) act as both conditioning variables and transport variables. Their chemical source terms are constructed starting from instantaneous temperature and species measurements using a variant of the pairwise mixing stirred reactor (PMSR) approach. A multi-dimensional kernel density estimation (KDE) approach is used to construct the joint PDFs in PC space. Convolutions of these joint PDFs with conditional means are used to determine the unconditional means for the closure terms: the mean PCs chemical source terms and the density. These means are parameterized in terms of the mean PCs using artificial neural networks (ANN). The framework is demonstrated a posteriori using the data from the Sandia piloted turbulent jet flames D, E and F by performing RANS calculations. The radial profiles of mean and RMS of temperature and measured species mass fractions agree well with the experimental means for these flames.

“…is the diffusion flux for the principal component. For a more detailed discussion on the treatment of the PCs diffusive flux, where molecular diffusion is important refer to [27]. According to the proposed formulation, one can theoretically use PCA with its inherent advantages.…”

Section: Theorymentioning

confidence: 99%

“…The work of Biglari and Sutherland showed that the PC parameterization is superior to the standard flamelet parameterization, for the ODT data-set investigated in the study. Mirgolbabaei and Echekki [17] extended the nonlinear mapping concept using artificial neural networks and investigated the potential of kernel PCA [18,19], showing the high compression potential derived by transforming the initial problem into a non-linear featured space where linear PCA is carried out. In addition, several combustion models have been proposed based on the concepts from PCA.…”

Section: Introductionmentioning

confidence: 99%

“…The PSR provides a validation of the approach by comparing the reduced model to the detailed simulation results. To the authors knowledge all published analysis on the PC-transport concept using nonlinear regression has been carried out on various data-sets using a priori analysis [14,17,19,18]. Only recently, a posteriori work has begun in this 3 area.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Advanced regression methods for combustion modelling using principal components

Isaac

Thornock

Sutherland

et al. 2015

Modelling the physics of combustion remains a challenge due to a large range of temporal and physical scales which are important in these systems. Detailed chemical kinetic mechanisms are used to describe the chemistry involved in the combustion process yielding highly coupled partial differential equations for each of the chemical species used in the mechanism. Recently, Principal Components Analysis (PCA) has shown promise in its ability to identify a low-dimensional manifold describing the reacting system. Several PCA-based models have been developed which may be well-suited for combustion problems; however, several challenging aspects of the model must be addressed. In this paper, the parameterization of state-space variables and PC-transport equation source terms are investigated. The ability to achieve highly accurate mapping through various nonlinear regression methods is shown. In addition, the effect of PCA-scaling on the ability to regress the surface is investigated. Finally, the present work demonstrates the capabilities of the model by solving a reduced system represented by several PC-transport equations for a perfectly stirred reactor (PSR) configuration.