Assessment of Reynolds Averaged Navier–Stokes Modeling of Scalar Dissipation Rate Transport in Turbulent Oblique Premixed Flames

Abstract

The statistical behavior of scalar dissipation rate (SDR) transport of reaction progress variable and its modeling in the context of Reynolds averaged Navier–Stokes (RANS) simulations has been analyzed based on a-priori analysis of direct numerical simulation (DNS) data for a turbulent premixed V-flame configuration. It has been found that the terms in the scalar dissipation rate transport equation originating from density variation due to heat release, chemical reaction rate gradient, molecular dissipation, and diffusivity gradient are the major contributors to the scalar dissipation rate transport for different downstream axial locations from the flame holder. By contrast, the contribution of turbulent transport of scalar dissipation rate assumes negligible values in comparison to the unclosed terms due to density variation, chemical reaction rate gradient, molecular dissipation, and diffusivity gradient. The statistical behaviors of the unclosed terms arising from density variation, chemical reaction rate gradient, and molecular dissipation for V-flame have been found to be qualitatively consistent with previous results for statistically planar flames. The models for the unclosed turbulent transport, density variation, chemical reaction rate gradient, and molecular dissipation terms of the scalar dissipation rate transport equation, which were proposed based on previous a-priori analysis of statistically planar flames, have been found to predict the corresponding terms satisfactorily at different downstream axial locations in the V-flame configuration considered here. The present analysis shows that the unclosed term in the scalar dissipation rate transport equation originating from diffusivity gradient can assume magnitudes comparable to the density variation contribution to the SDR transport equation, and a model has been proposed for the combined contribution of the chemical reaction rate gradient, molecular dissipation, and diffusivity gradient terms, which has been found to satisfactorily predict the corresponding quantity extracted from DNS data at different axial locations.

Keywords:

• Direct numerical simulation
• Reynolds averaged Navier–Stokes simulation
• Scalar dissipation rate
• Turbulent premixed V-flame

Additional information

Funding

The authors are grateful to EPSRC, UK for the financial assistance (Grant number EP/IO28013/1).