Effects of Body Forces on the Statistics of Flame Surface Density and Its Evolution in Statistically Planar Turbulent Premixed Flames

Abstract

Body forces such as buoyancy and externally imposed pressure gradients are expected to have a strong influence on turbulent premixed combustion due to the considerable changes in density between the unburned and fully burned gases. The present work utilises Direct Numerical Simulation data of three-dimensional statistically planar turbulent premixed flames to study the influence of body forces on the statistical behaviour of the flame surface density (FSD) and its evolution within the flame brush. The analysis has been carried out for different turbulence intensities and normalised body force values (i.e., Froude numbers). A positive value of the body force signifies an unstable density stratification (i.e., body force is directed from the heavier unburned gas to the lighter burned gas) and vice versa. It is found that for a given set of turbulence parameters, flame wrinkling increases with an increase in body force magnitude in the unstable configuration. Furthermore, higher magnitudes of body force in the unstable density stratification configuration promote a gradient type transport of turbulent scalar and FSD fluxes, and this tendency weakens in the stable density stratification configuration where a counter-gradient type transport is promoted. The statistical behaviours of the different terms in the FSD transport equation and their closures in the context of Reynolds Averaged Navier–Stokes simulations have been analysed in detail. It has been demonstrated that the effects of body force on the FSD and the terms of its transport equation weakens with increasing turbulence intensity as a result of the diminishing relative strength of body force in comparison to the inertial force. The predictions of the existing models have been assessed with respect to the corresponding terms extracted from the explicitly averaged DNS data, and based on this evaluation, suitable modifications have been made to the existing models to incorporate the effects of body force (or Froude number).

Effects of Body Forces on Turbulent Kinetic Energy Transport in Premixed Flames

“…3). This non-monotonic trend between g * = −3.12 and 1.56 is also observed in the variation of turbulent scalar flux u ′′ 1 c ′′ for Set-A [reported elsewhere (Varma et al 2021)]. However, this behaviour is not observed for higher values of turbulence intensity as the inertial effects tend to dominate over buoyancy effects where k∕ k0 shows a monotonic trend with the variations of g * .…”

“…( 25) and ( 28) depend also on the closures of Σ and ε , which are also unclosed terms. In the context of k − model (Jones and Launder 1973) a separate modelled transport equation is solved for ε (Jones and Launder 1973;Durbin and Reif 2010;Wilcox 2002), whereas the effects of buoyancy on the modelling of Σ for this database have been addressed elsewhere (Varma et al 2021) by the present authors.…”

“…However, both Σ and ẇ need closure in the context of RANS simulations and it is possible to model the mean reaction rate ẇ in terms of Σ . The effects of g * on the closure of the FSD Σ and the FSD based mean reaction rate ẇ have been addressed elsewhere(Varma et al 2021) by thepresent authors and the interested readers are referred toVarma et al (2021) forfurtherinformation in thisregard.…”

Effects of body force on the statistical behaviour and modelling of scalar variance in turbulent premixed flames

“…As density changes significantly and the flame normal acceleration due to thermal expansion induces a selfinduced pressure gradient within the flame, the presence of external pressure gradient and buoyancy are known to affect the evolution of turbulence and turbulent scalar flux within the flame brush [1][2][3]. The unstable stratification, caused by a body force which is directed from the heavier reactants to lighter products, tends to promote a gradient-type transport, whereas a counter-gradient transport is promoted for the stable configuration when the body force is directed from the lighter products to heavier reactants [1][2][3][4]. Recently, it has been demonstrated that the alteration of turbulence level within the flame brush under the action of external pressure gradient/body force can also affect the statistics of the reactive scalar gradient, which has implications on the statistical behaviours of the Flame Surface Density (FSD) and on the unclosed terms of its transport equation [4].The effects of external pressure gradient/body forces on premixed turbulent combustion can be characterised in terms of Froude number F r (i.e., ratio of inertial forces to body forces).…”

“…The unstable stratification, caused by a body force which is directed from the heavier reactants to lighter products, tends to promote a gradient-type transport, whereas a counter-gradient transport is promoted for the stable configuration when the body force is directed from the lighter products to heavier reactants [1][2][3][4]. Recently, it has been demonstrated that the alteration of turbulence level within the flame brush under the action of external pressure gradient/body force can also affect the statistics of the reactive scalar gradient, which has implications on the statistical behaviours of the Flame Surface Density (FSD) and on the unclosed terms of its transport equation [4].The effects of external pressure gradient/body forces on premixed turbulent combustion can be characterised in terms of Froude number F r (i.e., ratio of inertial forces to body forces). It has been found that an increase in the magnitude of Froude number F r increases the flame wrinkling in the unstable configuration, whereas an increase in F r magnitude in the stable configuration leads to reduced flame wrinkling and tends to laminarise the flame [2][3][4].…”