Principal strain rate evolution within turbulent premixed flames for different combustion regimes

Abstract

The statistical behaviours of the principal strain rates and its evolution in turbulent premixed flames have been analysed using a three-dimensional Direct Numerical Simulations dataset of statistically planar turbulent premixed flames with different turbulence intensities spanning from the corrugated flamelets regime to the thin reaction zones regime. It has been found that the scalar gradient predominantly aligns collinearly with the most extensive principal strain rate within the flame for large Damköhler numbers and small values of turbulence intensities and Karlovitz numbers. However, this tendency weakens with increasing turbulence intensity, which for a given integral length scale, amounts to a decrease (an increase) in Damköhler (Karlovitz) number. Moreover, it has been observed that the terms due to molecular diffusion, pressure Hessian and the correlation between pressure and density gradients play key roles in the evolution of principal strain rates for flames with large Damköhler number and small values of Karlovitz number. However, the relative importance of the terms arising from the correlation between pressure and density gradients and the pressure Hessian relative to the strain rate and vorticity contributions of the principal strain rate transport diminishes with increasing Karlovitz number and decreasing Damköhler number. The statistical behaviours of the mean values of the terms of the transport equation of the principal strain rate have been explained based on the relative alignments of principal strain rate eigenvectors with vorticity, pressure gradient and the eigenvectors of the pressure Hessian tensor. The findings of the current analysis suggest that the pressure gradient and pressure Hessian tensor play key roles in the evolution of principal strain rates within premixed turbulent flames, and their influences need to be accounted for high fidelity modelling of the tangential strain rate and scalar-turbulence interaction terms of the Flame Surface Density and Scalar Dissipation Rate transport equations, respectively. This provides possible explanations for the modification in the alignment of the reactive scalar gradient with local principal strain rates in premixed flames in comparison to that in non-reacting turbulent flows.

Inner Flame Front Structures and Burning Velocities of Premixed Turbulent Planar Ammonia/Air and Methane/Air Flames

“…This could be due to severe heat release across the flame brush (Dopazo et al 2015). In their recent work, Kasten et al (2021) reported a similar behavior using simple chemistry under forced turbulence in the reactants. A similar trend was previously reported in Dopazo et al (2015) for a flame under decaying turbulence in the corrugated flamelets regime with an Arrhenius one-step chemistry.…”

“…A similar simplification has been previously performed in the literature, see e.g. Boger et al (1998); Chakraborty (2007); Han and Huh (2008); Dopazo et al (2015); Brearley et al (2020); Kasten et al (2021);Varma et al (2021).…”

“…The flame front orientation statistics have been shown to influence the behavior of normal strain rate (Kasten et al 2021). Since the latter term has a significant effect on flame thinning/broadening, according to Eq.…”

“…5, it is of great importance to study the flame front orientation statistics as well to deepen our perception about the cases examined in this study. According to Kasten et al (2021), 𝜃 i = cos −1 (ê i .n) is the angle between normal to the flame and the corresponding eigenvectors of the strain rate tensor for i = 1 , 2, and 3, where i corresponds to the principle strain rate directions. The mean values of | cos( 1 ) | , | cos( 2 ) | , and | cos( 3 ) | with respect to the progress variable is presented in Fig.…”

“…A similar observation was reported by Nilsson et al (2018) for premixed turbulent planar methane/ air flames under high Karlovitz number test cases. Furthermore, Kasten et al (2021) discussed the flame front orientation statistics and its impact on normal strain rate behavior. Since the latter has an impact on flame thinning/broadening, as mentioned in Dinkelacker et al (1998); Chakraborty (2007); Sankaran et al (2007); Wang et al (2017); Nilsson et al (2018), investigating the flame front orientation statistics can deepen our understanding on flame front topologies.…”