Assessment of SGS closure for isochoric combustion of hydrogen-air mixture

Direct numerical simulations (DNS) of low and high Karlovitz number (Ka) flames are analysed to investigate the behaviour of the reactive scalar sub-grid scale (SGS) variance in premixed combustion under a wide range of combustion conditions (regimes). An order of magnitude analysis is performed to assess the importance of various terms in the variance evolution equation and the analysis is validated using the DNS results. This analysis sheds light on the relative behaviour among turbulent transport and production, scalar dissipation and chemical processes involved in the evolution of the SGS variance at different Ka. The common expectation is that the variance equation shifts from a reaction-dissipation balance at low Ka to a production-dissipation balance at high Ka with diminishing reaction contribution. However, in large eddy simulation (LES), a high Ka alone does not make the reaction term negligible, as the relative importance of the reaction term has a concurrent increase with filter size. The filter size can be relatively large compared with the Kolmogorov length scale in practical LES of high Ka flames, and as a consequence a reaction-production-dissipation balance may prevail in the variance equation even in a high Ka configuration, and this possibility is quantified using the DNS analysis in this work. This has implications from modelling perspectives, and therefore two commonly used closures in LES for the SGS scalar dissipation rate are investigated a priori to estimate the importance of the above balance in LES modelling. The results are explained to highlight the interplay among turbulence, chemistry and dissipation processes as a function of Ka.

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“…This trend of β c is consistent with the physical definition of this parameter. Indeed, β c can be defined as [2,47]:…”

Section: Modelling Of the Dissipation Termmentioning

confidence: 99%

A priori analysis of sub-grid variance of a reactive scalar using DNS data of high Ka flames

Nilsson

Langella

Doan

et al. 2019

Combustion Theory and Modelling

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“…Now, it is becoming clear that the full scaling of scalar spectrum in turbulent premixed combustion involves both turbulence and chemical scales as contemplated by Kolla et al 33 The above scaling on Ka is based on the analysis of turbulent premixed flames of hydrocarbon-and hydrogen-air mixtures in past studies which considered statistically 1D propagating flame in spatially decaying turbulence, 8,16,17,52,55 oblique flames, [56][57][58][59] spherically expanding flames, 60,61 , slot-jet flames, 62 and swirling flames. 63,64 These studies used both single and multi-step chemical kinetics, and also unity and non-unity Lewis numbers. Hence, the above scaling may be considered to be quite robust.…”

Section: Discussionmentioning

confidence: 99%

Scalar fluctuation and its dissipation in turbulent reacting flows

Swaminathan

Chakraborty

2021

Physics of Fluids

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The dissipation rate of a scalar variance is related to mean heat release rate in turbulent combustion. Mixture fraction is the scalar of interest for non-premixed combustion and a reaction progress variable is relevant for premixed combustion. A great deal of work is conducted in past studies to understand the spectra of passive scalar transport in turbulent flows. A very brief summary of these studies to bring out salient characteristics of passive scalar spectrum is given first. Then, the classical analysis of reactive scalar spectrum is revisited in the lights of recent understanding gained through analyzing the scalar spectrum deduced from direct numerical simulation data of both non-premixed and premixed combustion. The analysis shows that the reactive scalar spectral density in premixed combustion has a dependence on Karlovitz and Damköhler numbers, which comes through the mean scalar dissipation rate appearing in the spectral expression. In premixed combustion, the relevant scale for the scalar dissipation rate is shown to be of the order of the chemical length scale and the dissipation rate is not influenced by the scales in the inertial-convective range unlike for the passive scalar dissipation rate. The scalar fluctuations produced near the chemical scales cascade exponentially to larger scales. These observations imply that the passive scalar models cannot be extended to premixed combustion.

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“…The algebraic model developed in [41] and tested in a number of studies [31,36,40] is used for χ c,sgs . This revised flamelet formulation for partially premixed combustion was referred to as FlaRe (Flamelets Revised for consistencies) in earlier studies [42,43].…”

Section: Numerical Approachmentioning

confidence: 99%