Modelling of turbulent scalar flux in turbulent premixed flames based on DNS databases

Abstract

A transport equation for scalar flux in turbulent premixed flames was modelled on the basis of DNS databases. Fully developed turbulent premixed flames were obtained for three different density ratios of flames with a single-step irreversible reaction, while the turbulent intensity was comparable to the laminar burning velocity. These DNS databases showed that the countergradient diffusion was dominant in the flame region. Analyses of the Favre-averaged transport equation for turbulent scalar flux proved that the pressure related terms and the velocity-reaction rate correlation term played important roles on the countergradient diffusion, while the mean velocity gradient term, the mean progress variable gradient term and dissipation terms suppressed it. Based on these analyses, modelling of the combustion-related terms was discussed. The mean pressure gradient term and the fluctuating pressure term were modelled by scaling, and these models were in good agreement with DNS databases. The dissipation terms and the velocity-reaction rate correlation term were also modelled, and these models mimicked DNS well. Nomenclature BFrequency factor (1/s·K) c Progress variable C p Specific heat at constant pressure (J/kg·K) D Diffusion coefficient (m 2 /s) e L Laminar flame thickness (m) e t Total energy per volume (J/m 3 ) E Activation energy (J/kg) k Turbulent kinetic energy (m 2 /s 2 )

The impact of dilatation, scrambling, and pressure transport in turbulent premixed flames

“…(29)- (30)) are independent of the form of the reaction rate. Lipatnikov et al [71] analysed the H, M and L flames (see Table 2) in the same DNS database [17,18] and showed that, compared to flame surface density expressions, the mean reaction rate is reduced at the leading edge (c ă 0.2) and increased at the trailing edge (c ă 0.8). The former effect, in particular, is important in the current context and a bridged mean reaction rate expression based on the two scale formulation of Lindstedt and Váos [31] is applied to approximately account for the impact,…”

“…Databases [17,18] used here were generated for fully developed planar premixed flames featuring three different expansion ratios. A single-step irreversible chemical reaction was used to describe the chemistry.…”

DNS Analysis on the Indirect Relationship between the Local Burning Velocity and the Flame Displacement Speed of Turbulent Premixed Flames

“…The conditions described in the database correspond to the boundary between wrinkled flamelets and corrugated flamelets in the turbulent combustion regime diagram [35]. Further details of the calculation method to construct the DNS database can be found in Nishiki et al [29]- [31] and Nishiki [32].…”

Velocity and Reactive Scalar Dissipation Spectra in Turbulent Premixed Flames

“…If the inflow velocity is unmodified, then the flame will gradually travel upstream, due to the increasing turbulent burning velocity resulting from flame wrinkling caused by the turbulent eddies originated from the inlet plane. This strategy to keep the flame stationary in the domain was employed in previous DNS studies (Nishiki et al, 2002(Nishiki et al, , 2006. The computational domain of the SP flame was discretized using a uniform grid of size 20 μm and the time-step used was 10 nano seconds.…”