A priori investigation of subgrid correlation of mixture fraction and progress variable in partially premixed flames

Abstract

Subgrid correlation of mixture fraction, Z, and progress variable, c, is investigated using direct numerical dimulation (DNS) data of a hydrogen lifted jet flame. Joint subgrid behaviour of these two scalars are obtained using a Gaussian-type filter for a broad range of filter sizes. A joint probability density function (JPDF) constructed using single-snapshot DNS data is compared qualitatively with that computed using two independent β-PDFs and a copula method. Strong negative correlation observed at different streamwise locations in the flame is captured well by the copula method. The subgrid contribution to the Z-c correlation becomes important if the filter is of the size of the laminar flame thickness or larger. A priori assessment for the filtered reaction rate using the flamelet approach with independent β-PDFs and correlated JPDF is then performed. Comparison with the DNS data shows that both models provide reasonably good results for a range of filter sizes. However, the reaction rate computed using copula JPDF is found to have a better agreement with the DNS data for large filter sizes because the subgrid Z-c correlation effect is included.

Large Eddy Simulation of a dual swirl gas turbine combustor: Flame/flow structures and stabilisation under thermoacoustically stable and unstable conditions

“…This correlation was shown to be important for the Reynolds-Averaged Navier-Stokes (RANS) calculations [56,57] because the fluctuations of Z and c inherently influence each other and this interaction is statistically significant over the sampling period, i.e., time required for the convergence of low-order statistics in RANS. However, a recent DNS study [59] showed that although the Z-c correlation still exists at the SGS level, it is relatively less influential on the time-averaged statistics because the portion of this correlation related to the large-scale fluctuations is resolved in LES. Thus, the subgrid correlation is not considered here for simplicity which allows to model the joint PDF using two statistically independent marginal β-PDFs of Z and c : P(ξ, ζ) ≈ P β ξ; Z, Z 2 × P β ζ; c, c 2 .…”

Analysis of Flame Front Breaks Appearing in LES of Inhomogeneous Jet Flames Using Flamelets

“…where ωfp is the precomputed reaction rate of a laminar, one dimensional freely-propagating planar unstrained flame at a fixed mixture fraction, and P is the joint-PDF of progress variable ( ) and mixture fraction ( ). The joint-PDF is modelled using the Bayesian decomposition P( , ) = P( | ) P( ) , where for simplicity P( | ) = P( ) under the assumption of statistical independence of and , which is a reasonable assumption in well-resolved LES following past studies (Chen et al 2018;Bray et al 2005;Ruan et al 2014). P( ) and P( ) are presumed using beta-functions, which require an expression for the SGS variances of progress variable, 2 c,sgs = c2 − c2 , and mixture fraction, 2 ,sgs = ̃ 2 − ̃ 2 .…”

A posteriori assessment of consumption speed correction for LES with tabulated methods

“…The variable η represents the sample space for a reaction progress variable c, defined to vary monotonically from 0 in the reactants to 1 in the products, and P (η) is the Favre subgrid scale (SGS) presumed PDF, and is often parametrised with first and second order (Favre-filtered) moments of the progress variable (see more details in Section 2.1). Note that in LES context, P (c) is not a probability density function in a strict statistical sense, as it represents an ensemble of realisations in space (at the SGS level) at one time (Chen et al, 2018). This quantity, which is sometimes referred to as filtered density function or FDF, will be referred here as SGS PDF for convenience.…”