Subgrid modeling of intrinsic instabilities in premixed flame propagation

Data-driven subfilter modelling of thermo-diffusively unstable hydrogen–air premixed flames

“…In a typical inflow-outflow, spanwise periodic domain in which a nominally planar flame is stabilised, lateral domains of increasing size will therefore be analysed in order to accommodate a sufficient number of unstable wavelengths and eventually achieve domain independence. In [3,7], it was found that thermo-diffusively unstable flames achieve domain independence for domain sizes larger than ∼25 − 30λ c . The DNS datasets analysed in this work feature spanwise domain sizes as large as 76λ c for the one-step chemistry dataset [2] and 300λ c for the multi-step dataset [3].…”

“…The one-step chemistry dataset has been presented in [2] and it has also been used for modelling purposes in [7]. It has been developed using a well-established numerical framework based on a one-step irreversible reaction controlled by the concentration of a deficient reactant [16][17][18][19].…”

“…The computational configuration consists of a downward propagating flame in an inflow/outflow domain with periodic boundary conditions in the crosswise direction x with a lateral domain size L. In the present work, we only select the TD (thermal-diffusive) series from the original dataset, consisting in three thermodynamically identical flames which differ only in the lateral domain size L [7], considered as a reference hydrodynamic length [26][27][28]. The main characteristics of these simulations are reported in Table 1 and are the number of unstable wavelength n c fitting in the domain, defined as the ratio between L and λ c , the reference hydrodynamic length measured in units of D and the average self-wrinkled flame speed S T /S 0 L normalised by the unstretched laminar flame speed.…”

“…It is crucial that such models not only retain the main aspects of such interaction, but, equally important, that they do not lose or overlook any of the main physical characteristics of the laminar flame itself, when, in other words, the effects of turbulence are absent at the subgrid scales. One such characteristic is indeed the intrinsic multi-scale self-wrinkling of thermal-diffusively unstable flames which, at the smallest scale, can be of the order of the flame thickness [3] and can therefore fall at the subgrid level, thus requiring dedicated modelling [7]. Such models, specifically focused on intrinsically unstable flames such as hydrogen flames, are at present missing in the literature and could help increase the fidelity of existing turbulence-chemistry interaction models.…”

“…At this stage, the effect of turbulence is not considered, focusing solely on the modelling of the flame self-wrinkling and non-linear modification of local propagation speed, both due to the intrinsic thermal-diffusive flame instability. A recent study [7] has addressed a similar problem in the context of flame surface density modelling, providing a wrinkling factor model for both Le > Le 0 and Le < Le 0 flames in the absence of background turbulence, which may find application in the context of thickened flame approaches. Such a model was derived on the basis of large-scale DNS data sets, from which the average fuel consumption speed and thus the wrinkling factor was suitably scaled in order to exhibit a universal behaviour representing the model itself.…”