Algebraic Flame Surface Density Modelling of High Pressure Turbulent Premixed Bunsen Flames

Abstract

Performance of representative algebraic flame surface density (FSD) models have been a-priori assessed based on a direct numerical simulation database consisting of four turbulent premixed Bunsen flames at four different pressure levels. Results indicate that for a given resolution of the flame front, the considered algebraic FSD closures perform in a qualitatively similar manner irrespective of pressure variation. However, for a given computational mesh, the performance deteriorates as flame thickness decreases with increasing pressure. Additionally, the contribution of the subgrid scale surface-filtered density-weighted tangential diffusion component of the displacement speed tends to increase with pressure increment, further complicating the modelling of FSD. Further analysis also indicate that the inner cut-off scale normalized by the thermal flame thickness increases with increasing pressure, possibly due to the presence of Darrieus–Landau instability which is more likely to occur at higher pressure due to a larger ratio of hydrodynamic length scale to thermal flame thickness.

Flame Surface Density based mean reaction rate closure for Reynolds averaged Navier Stokes methodology in turbulent premixed Bunsen flames with non-unity Lewis number

“…It is worth noting that a ratio of Ω/S equal to unity is equivalent to the validity of Damköhler's first hypothesis [24] according to Eq. Ξ has been addressed in the context of Large Eddy Simulation (LES) for the same database in [23,26] and it was found that the algebraic closures might be sufficient for the modelling of FSD in the context of LES.…”

“…1, 2 and 10 reveals that the stretch factor I 0 can be expressed as: I 0 = (ρ S d ) s /ρ 0 S L and therefore I 0 is needed for modelling Ω c = (ρ S d ) s . Although several previous analyses [4,20,21] assumed (ρ S d ) s = ρ 0 S L (or I 0 = 1.0), it has recently been demonstrated [17,22,23] that the assumption of I 0 = 1.0 is often rendered invalid for turbulent premixed combustion.…”

“…Refs. [23,24,40,41] for further information on this database. For the purpose of the evaluation of Reynolds/Favre-averaged values (i.e.…”

Effect of sub-grid wrinkling factor modelling on the large eddy simulation of turbulent stratified combustion

“…It should be noted that the models by Weller et al [18] and by Keppeler et al [21] were indeed proposed in the context of FSD closures and not in the framework of ATF. However, the mathematical definition and physical meaning of the wrinkling factor Ξ are identical for all models, which has also been the basis for several a-priori DNS analyses [16,[32][33][34]. The first algebraic wrinkling factor Ξ W model considered here was proposed by Weller et al [18].…”

Effect of non-ambient pressure conditions and Lewis number variation on direct numerical simulation of turbulent Bunsen flames at low turbulence intensity

“…Here D f , η i and η o are the fractal dimension, the inner cut-off and the outer cut-off, respectively. In [29], it was seen that D f was particularly sensitive to Le variations, whereas it was observed that the inner cut-off normalized by the thermal flame thickness i.e., η i /δ th increased sharply as pressure increased [43]. The relationship between the smallest scale of flame wrinkles and turbulence for high pressure Bunsen flames has also been discussed in detail in [21].…”