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

Next-generation combustion technology such as ‘lean burn’ and HCCI (Homogeneous Charge Compression Ignition) present new challenges for\ua0 combustion modelling. The presence of locally varying combustion modes (premixed vs. non-premixed) and regimes (fast/non-fast chemistry vs.\ua0 turbulent time scales) belie a need for combustion models that make few assumptions of the underlying combustion process and can also incorporate\ua0 turbulent stirring. Lean burn for gas-turbines introduce complex ignition sequences and phenomena like blowout which requires both a finite-rate\ua0 chemistry description as well as turbulence-chemistry-interaction for accurate modelling. Auto- ignition and differential-diffusion capabilities are also\ua0 desirable features for modelling HCCI and hydrogen combustion, respectively. The Linear Eddy Model (LEM) is a mode- and regime- independent sub-grid\ua0 combustion closure for Large Eddy Simulation (LES). LEM resolves, along a one-dimensional line, all spatial and temporal scales, provides on-the-fly\ua0 local turbulent flame statistics, captures finite rate chemistry effects, and directly incorporates turbulence-chemistry interaction using stochastic\ua0 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’\ua0 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\ua0 standard presumed PDF approaches for reactive LES. The thesis also introduces a new ‘splicing’ scheme for the super-grid formulation where LES\ua0 resolved flow information is accounted for via Lagrangian transport of LEM fragments between adjacent domains. A pressure based solver was developed\ua0 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\ua0 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\ua0 than standard LES-LEM. Comparison with time-averaged reaction rates show good agreement with DNS data where the model is able to correctly capture\ua0 regions of net production and consumption of highly sensitive OH. In general, SG-LEM is able to provide high fidelity reaction rate statistics with\ua0 the compute efficiency of a mapping-type closure. The encouraging results and performance of SG-LEM indicate its suitability for industrial reacting\ua0 simulations once full validation is complete. While it is yet unclear how the presented mapping strategy will cope with transient phenomena like\ua0 extinction, it retains desirable features of LES-LEM and is able to report thermochemical scalars averaged over individual LEM domains for diagnosis