Super-grid Linear Eddy Model (SG-LEM): Efficient mode- and regime-independent combustion closure for Large Eddy Simulation (LES)

Licentiate thesis, 2022

Next-generation combustion technology such as ‘lean burn’ and HCCI (Homogeneous Charge Compression Ignition) present new challenges for  combustion modelling. The presence of locally varying combustion modes (premixed vs. non-premixed) and regimes (fast/non-fast chemistry vs.  turbulent time scales) belie a need for combustion models that make few assumptions of the underlying combustion process and can also incorporate  turbulent stirring. Lean burn for gas-turbines introduce complex ignition sequences and phenomena like blowout which requires both a finite-rate  chemistry description as well as turbulence-chemistry-interaction for accurate modelling. Auto- ignition and differential-diffusion capabilities are also  desirable features for modelling HCCI and hydrogen combustion, respectively. The Linear Eddy Model (LEM) is a mode- and regime- independent sub-grid  combustion closure for 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 using stochastic  processes. In LES-LEM an LEM-line is advanced in each LES cell which makes the approach computationally rather expensive.

In this thesis, a novel closure approach is presented using LEM which involves coarse-graining of the LES mesh to generate a coarse ‘super-grid’  comprised of ‘super-cells’. Each super-cell, instead of each LES cell, then contains a single LEM line which ad-vances the combined reaction-diffusion equations and also provides binned statistics for thermochemical scalars such as species mass fractions, the method is hence termed ‘super-grid LES- LEM’ or simply, ‘SG-LEM’. Local LES filtered states are then obtained by probability-density-function (PDF) weighted integration of binned scalars, akin to  standard presumed PDF approaches for reactive LES. The thesis also introduces a new ‘splicing’ scheme for the super-grid formulation where LES  resolved flow information is accounted for via Lagrangian transport of LEM fragments between adjacent domains. A pressure based solver was developed  using the OpenFOAM library to test the proposed model with a premixed ethylene flame stabilized over a backward facing step, a setup for which DNS  data is available for validation. The new model is able to produce LES-resolved flame structures and species mass fractions at a significantly lower cost  than standard LES-LEM. Comparison with time-averaged reaction rates show good agreement with DNS data where the model is able to correctly capture  regions of net production and consumption of highly sensitive OH. In general, SG-LEM is able to provide high fidelity reaction rate statistics with  the compute efficiency of a mapping-type closure. The encouraging results and performance of SG-LEM indicate its suitability for industrial reacting  simulations once full validation is complete. While it is yet unclear how the presented mapping strategy will cope with transient phenomena like  extinction, it retains desirable features of LES-LEM and is able to report thermochemical scalars averaged over individual LEM domains for diagnosis.