Combustion modeling using principal component analysis

Sutherland, James C.; Parente, Alessandro

doi:10.1016/j.proci.2008.06.147

Cited by 142 publications

(65 citation statements)

References 21 publications

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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

Combustion and Flame

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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.

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Section: Pca Parameterization and Governing Equationsmentioning

confidence: 99%

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

Ranade

Echekki

2019

Combustion and Flame

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“…Then, we attempt to demonstrate a key component of this framework by efficiently constructing joint PDFs and conditional statistics based on the experimental data and a dimensionality reduction of the thermochemical space. This dimensionality reduction is carried out using principal component analysis (PCA) [18]. PCA generates a map from the thermo-chemical scalars' vector to a smaller vector of principal component (PCs).…”

Section: Introductionmentioning

confidence: 99%

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

Ranade

Echekki

2019

Combustion and Flame

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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...

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“…[34][35][36][37] These ELDM's are not limited by any physical assumptions (since they are only based on regression techniques) and the resulting M parameters from these dimension reduction techniques make up a strong attracting M -dimensional reduced manifold. It should also be noted that these PCA and MARS generated manifolds have been shown to be stronger attracting than other common LDM's used in turbulent reacting flows, including flamelet-based manifolds.…”

Section: Turbulent Scalar Manifold Reduction Assumptionsmentioning

confidence: 99%

Survey of Turbulent Combustion Models for Large-Eddy Simulations of Propulsive Flowfields

Foster

Miller

2015

53rd AIAA Aerospace Sciences Meeting

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A general review of turbulent combustion modeling closures applicable to large eddy simulations (LES) is provided. The focus is on "regime-independent" models able to provide turbulent combustion closures ranging from purely premixed to purely non-premixed and all regimes between these two limits. Special emphasis is placed on primary propulsion applications, including liquid rocket engines, diesel engines, gas turbines, and scramjets. These applications span a large range of physical phenomena including both ideal-and real-gas behavior, single-phase and multi-phase combustion, relatively low Mach number to supersonic and hypersonic combustion, and relatively simple geometries to highly complex geometries. Three classes of models are identified as possibly providing such broad based modeling closures: flamelet-library/presumed probability density function (PDF) models, linear eddy based models (LEM), and transported PDF or filtered density function (FDF) based models. This review focuses both on fundamental physical assumptions that apply across all of the models and assumptions that apply to each of the models individually. Namely, assumptions regarding the presumed size of the large dimensional turbulent scalar manifold apply to all of the models; however, flamelet models almost always presume only a few dimensions are necessary to yield adequate representation of the larger, turbulent manifold. In contrast, LEM and FDF models are not, in theory, bound by any manifold size assumptions (i.e. direct calculation of the turbulent scalar manifold is possible); however, due to current computational limitations, these models often employ manifold reduction techniques which are usually not as restrictive as those used by flamelet models. Individual assumptions associated with the specific formulation of each model are also analyzed. From these discussions, additional novel results testing some of the fundamental physical assumptions associated with each model are provided from a unique database of DNS of high pressure turbulent reacting temporally developing shear flames. The DNS database includes simulations of H2/O2, H2/Air, and Kerosene/Air flames with both detailed and reduced chemistry. The DNS include real property models, a real-gas equation of state, and generalized heat and mass diffusion derived from non-equilibrium thermodynamics. The simulations span a large range of Reynolds numbers and pressures (up to 125 atm), with resolutions approaching 1 billion grid points. Finally, some general comments towards the future challenges related to LES combustion modeling are offered. NomenclatureA m , B m = mixture parameters for the equation of state C Ω = modeling constant dW = differential increment of the Wiener process D = molecular diffusivitytotal energy (internal plus kinetic) E = modeling term F L = filtered mass density function F stir = triplet mapping advection model G = filter kernel H ,α = partial molar enthalpy of species α J i,α = mass flux vector of species α k sgs = subgrid turbulence kinetic energy M...

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Combustion modeling using principal component analysis

Cited by 142 publications

References 21 publications

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

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

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

Survey of Turbulent Combustion Models for Large-Eddy Simulations of Propulsive Flowfields

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