Statistical Behaviour and Modelling of Variances of Reaction Progress Variable and Temperature During Flame-Wall Interaction of Premixed Flames Within Turbulent Boundary Layers

Abstract

The statistical behaviour of the transport of reaction progress variable variance, $$\widetilde{{c^{^{\prime\prime}2} }},$$ c ″ 2 ~ , and non-dimensional temperature variance, $$\widetilde{{T^{^{\prime\prime}2} }},$$ T ″ 2 ~ , have been analysed using three-dimensional Direct Numerical Simulation (DNS) data of turbulent premixed flame-wall interaction with isothermal inert walls within turbulent boundary layers for (i) an unsteady head-on quenching of a statistically planar flame propagating across the boundary layer, and (ii) a statistically stationary oblique wall quenching of a V-flame. It has been found that the reaction rate contribution acts as a leading order source term to the transport of both reaction progress variable variance, $$\widetilde{{c^{^{\prime\prime}2} }},$$ c ″ 2 ~ , and non-dimensional temperature variance, $$\widetilde{{T^{^{\prime\prime}2} }},$$ T ″ 2 ~ , whereas the molecular dissipation term remains the leading order sink term for both configurations analysed here. With the progress of flame wall interaction, the magnitude of all the source terms for the transport equations of both reaction progress variable and non-dimensional temperature variances vanish in the near-wall region with the onset of flame quenching. However, the molecular dissipation term continues to act as a sink term. The performances of the existing models for turbulent scalar flux, reaction rate and scalar dissipation rate contributions have been assessed for both flame-wall interaction configurations based on a priori DNS analysis. The existing available models for scalar dissipation rate for temperature and the reaction rate contribution in the variance transport equations even with the previously proposed wall corrections do not adequately predict the behaviour in the near-wall region. Modifications have been suggested to the existing closure models for the scalar dissipation rate and the reaction rate contribution to the scalar variance transport equations to improve the predictions in the near-wall region. Furthermore, the recommended closures for the unclosed terms of both reaction progress variable variance, $$\widetilde{{c^{^{\prime\prime}2} }},$$ c ″ 2 ~ , and non-dimensional temperature variance, $$\widetilde{{T^{^{\prime\prime}2} }},$$ T ″ 2 ~ , are shown to accurately capture the corresponding variations obtained from DNS data for both near to and away from the wall.

Direct Numerical Simulation Analysis of the Closure of Turbulent Scalar Flux during Flame–Wall Interaction of Premixed Flames within Turbulent Boundary Layers

“…The present work will only focus on the statistical behaviour and modelling of ρu ′′ j c ′′ . The closures of ẇ for FWIs in turbulent boundary layers have been discussed elsewhere for FWIs [26] and hence will not be addressed in this paper.…”