An exact formulation of<i>k</i>-distribution methods in non-uniform gaseous media and its approximate treatment within the Multi-Spectral framework

André, Frédéric; Hou, Longfeng; Solovjov, Vladimir P.

doi:10.1088/1742-6596/676/1/012001

Cited by 8 publications

(13 citation statements)

References 24 publications

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“…Furthermore, comparison of the proposed approach with results obtained by application of a usual C-k model demonstrates that the present model is reliable, both in uniform and nonuniform situations. Its coupling with the Multi-Spectral (MS) approach is natural, as MS describes methods to create spectral interval over which gas spectra can be reasonably treated as scaled [7,8], as assumed here to handle non-uniformities. The use of the CDPC approximation within the Multi-Spectral framework will be studied in future works.…”

Section: Discussionmentioning

confidence: 99%

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On the use of polynomial chaos expansions and generalized moments within the frame of gas radiation in non-uniform media

André

Galtier

2015

Journal of Quantitative Spectroscopy and Radiative Transfer

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In many applications involving gaseous media at high temperature, accurate but computationally efficient models are required for the radiative properties of gases. The aim of the present work is to show how, by combining results from Polynomial Chaos framework and Devyatov's Method of Moments, one can provide simple estimates of the transmission functions of gases both in uniform and non-uniform media. The proposed model only involves polynomials. It is probably one of the simplest in terms of mathematical formulation but also one of the most sophisticated, considering the concepts that it involves. It can be applied in uniform and non-uniform media, where it is shown to be equivalent, in terms of accuracy, to usual C-k models.

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Section: Discussionmentioning

confidence: 99%

“…The C-k model used in the present work was built following the same method as described in Ref. [8].…”

Section: Lbl Data and Model Parametersmentioning

confidence: 99%

On the use of polynomial chaos expansions and generalized moments within the frame of gas radiation in non-uniform media

André

Galtier

2015

Journal of Quantitative Spectroscopy and Radiative Transfer

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“…Over these intervals, the correlation assumption can be considered as exact. It has already been shown that the MSCk model with 25 clusters, defined over a narrow band (25 cm −1 ), is more accurate than the medium resolution (1 cm −1 ) Ck model when compared with LBL benchmark calculations at nearly the same computational cost [2]. Meanwhile, the MSCk model has almost the same accuracy as the CKFG (Correlated-k Fictitious Gas) [13] technique in infrared signature cases, but at lower computational costs [14].…”

Section: Introductionmentioning

confidence: 96%

“…This leads to the breakdown of the assumption of rank correlation of gas spectra in distinct states when large temperature gradients exist in the medium studied [9]. In order to circumvent this problem, we introduced a method based on functional data analysis (FDA) [10] and called the MSCk model [1,2]. The main ideas behind the MSCk approach are not new, as they share similar concepts as used in mapping methods such as described in West and Crisp [11] or in the multiscale method of Zhang [12].…”

Section: Introductionmentioning

confidence: 99%

“…Meanwhile, the MSCk model has almost the same accuracy as the CKFG (Correlated-k Fictitious Gas) [13] technique in infrared signature cases, but at lower computational costs [14]. Another advantage of the MSCk model, compared to CKFG, is that MSCk can be applied in the case of reflecting walls, which is not compatible with the CKFG model which requires a formulation in terms of transmissivities [2].…”

Section: Introductionmentioning

confidence: 99%

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Functional data analysis applied to the multi-spectral correlated–k distribution model

Hou

Galtier

Eymet³

et al. 2018

International Journal of Thermal Sciences

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The Ck (Correlated-k) approach is among the most used method for the approximate modelling of the radiative properties of gases both in uniform and non-uniform media. One of its main defects is that the treatment of nonuniform gas paths is founded on the assumption of correlation-in fact co-monotonicity-of gas absorption coefficients in distinct states which is not rigorously verified for actual spectra. This correlation assumption fails as soon as large temperature gradients are encountered along the radiative path lengths. In order to circumvent this problem, a method based on functional data analysis (FDA)-referred to as the MSCk model in this workwas proposed in Refs. [1,2]. The principle of the method is to group together wavenumbers with respect to the spectral scaling functions-defined as the ratio between spectral absorption coefficients in distinct states-so that the correlation/co-monotonicity assumption can be considered as exact over the corresponding intervals of wavenumbers. Very few details were provided up to now about the application of FDA within the frame of the MSCk model. Indeed, most of our previous works were dedicated to the derivation of the methods itself. Accordingly, in the present paper, we mostly focus our attention on the mathematical definition of clusters of scaling function, quantities which are used to build spectral intervals over which gas spectra in distinct states are assumed to be scaled. The comparison of different clustering methods together with the criterion to select an appropriate number of clusters are described and discussed and the application of this approach for several test cases, including 3D geometries, are presented.

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Comonotonic global spectral models of gas radiation in non-uniform media based on arbitrary probability measures

André

Solovjov

Lemonnier

et al. 2017

Applied Mathematical Modelling

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The aim of the present work is to provide a universal theoretical formulation of global methods for radiative heat transfer in non-uniform gaseous media. Starting from the definition of an arbitrary probability measure on the wavenumber axis, it is shown that no gas reference state is required to develop rigorously a full spectrum model, both in uniform and non-uniform media. This general formulation, which constitutes a novel mathematical modeling of gas radiation, is then applied for: 1/ the theoretical justification of new developments introduced recently in the so-called Rank Correlated SLW method in non-uniform media, 2/ emphasizing the differences and similarities between the SLW and FSK methods, from the point of view of the way these two techniques treat path non-uniformities. The theoretical results provided in the present work can also be used to enlighten the concept of "spectral correlation", widely encountered in gas radiation modeling.

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An exact formulation ofk-distribution methods in non-uniform gaseous media and its approximate treatment within the Multi-Spectral framework

Cited by 8 publications

References 24 publications

On the use of polynomial chaos expansions and generalized moments within the frame of gas radiation in non-uniform media

On the use of polynomial chaos expansions and generalized moments within the frame of gas radiation in non-uniform media

Functional data analysis applied to the multi-spectral correlated–k distribution model

Comonotonic global spectral models of gas radiation in non-uniform media based on arbitrary probability measures

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