A super-grid approach for LES combustion closure using the Linear Eddy Model

LES–LEM is a simulation approach for turbulent combustion in which the stochastic Linear Eddy Model (LEM) is used for sub-grid mixing and combustion closure in Large-Eddy Simulation (LES). LEM resolves, along a one-dimensional line, all spatial and temporal scales, provides on-the-fly local turbulent flame statistics, captures finite rate chemistry effects and directly incorporates turbulence-chemistry interaction. However, the approach is computationally expensive as it requires advancing an LEM-line in each LES cell. This paper introduces a novel turbulent combustion closure model for LES using LEM to address this issue. It involves coarse-graining the LES mesh to generate a coarse- level ‘super-grid’ comprised of cell-clusters. Each cell-cluster, instead of each LES cell, then contains a single LEM domain. This domain advances the combined advection–reaction–diffusion solution and also provides suitably conditioned statistics for thermochemical scalars such as species mass fractions. Local LES-filtered thermochemical states are then obtained by probability-density-function (PDF) weighted integration of binned conditionally averaged scalars, akin to standard presumed PDF approaches for reactive LES but with physics-based determination of the full thermochemical state for particular values of the conditioning variables. The proposed method is termed ‘super-grid LEM’ or ‘SG-LEM’. The paper describes LEM reaction–diffusion advancement, the LEM representation of turbulent advection, a novel splicing algorithm (a key feature of LES–LEM) formulated for the super-grid approach, a wall treatment, and a thermochemical LES closure procedure. To validate the proposed model, a pressure-based solver was developed using the OpenFOAM library and tested on a premixed ethylene flame stabilised over a backward facing step, a setup for which some DNS data is available. SG-LEM provides high resolution flame structures, temperature and mass fractions suitable for LES thermochemical closure. Additionally, it provides reaction-rate data at the coarse level, a unique feature compared to other mapping-type closure methods. Quantitative comparisons are made between the proposed model and time-averaged DNS data, focussing on velocity, temperature and species mass fraction. Results show good agreement downstream of the step. Furthermore, comparison with an equivalent Partially-Stirred Reactor (PaSR) simulation demonstrates the superior predictive capability of SG-LEM. Additionally, the paper briefly examines the sensitivity of the model to coarse-graining parameters and finally, explores computational efficiency highlighting the substantial speedup achieved when compared to the standard LES–LEM approach with potentially significant speedup relative to PaSR closure for the intensely turbulent regimes of principal interest.