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    <title language="eng">A super-grid approach for LES combustion closure using the linear eddy model</title>
    <abstract language="eng">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.</abstract>
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    <author>
      <firstName>Abhilash M.</firstName>
      <lastName>Menon</lastName>
    </author>
    <submitter>
      <firstName>Helen</firstName>
      <lastName>Jacob</lastName>
    </submitter>
    <author>
      <firstName>Michael</firstName>
      <lastName>Oevermann</lastName>
    </author>
    <author>
      <firstName>Alan R.</firstName>
      <lastName>Kerstein</lastName>
    </author>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>LES</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>LEM</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Combustion closure</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Presumed PDFs</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Splicing</value>
    </subject>
    <collection role="institutes" number="1311">FG Numerische Mathematik und Wissenschaftliches Rechnen</collection>
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    <title language="eng">Investigation of coarse-graining parameters for super-grid LEM closure applied to LES of practical bluff-body flames</title>
    <abstract language="eng">Large Eddy Simulation (LES) coupled with the Linear Eddy Model (LEM) provides a robust method for studying turbulent combustion, but it is computationally expensive due to the need for highly resolved sub-grid LEM domains. These domains simulate sub-grid stirring through stochastic rearrangements of scalar fields, while large-scale transport is modelled using a Lagrangian ‘splicing’ scheme. To address the computational cost of LES-LEM, a super-grid (SG) framework for LEM closure was developed by the authors (Comb. Theor. Model. 28, 2024), which uses coarse-graining, on-the-fly chemistry tabulation and a presumed PDF approach to reconstruct thermochemical fields at LES resolution. This study applies SG-LEM to a challenging setup, Case 1 of the Volvo Validation Rig, which involves a bluff-body-stabilised turbulent premixed propane-air flame, as a stress test to identify limitations that were not revealed by the previous application, in particular that of the coarse-graining parameters used to generate the super-grid. The intent is to yield a more realistically constrained assessment of the current capabilities of the method, and insight into possible ways for improving it. Four simulations were conducted using three SG cluster sizes. The finest resolution was tested with a global 2-step mechanism, showing good agreement with experimental data for temperature and velocity, particularly near the bluff body. The two larger cluster sizes used a 66-step skeletal mechanism for more detailed chemical closure but led to unphysical quenching due to splicing inaccuracies. To mitigate these issues, two novel additions were introduced: an intra-cluster-stirring routine and a method to control SG cluster shapes to reduce numerical dissipation. These methods improved flame stability with coarser SG clusters and more detailed mechanisms. Comparison with experiments showed good agreement for temperature and velocity, though elevated CO levels were observed in the recirculation region. Potential methods for further improving SG-LEM's capabilities are discussed.</abstract>
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    <author>
      <firstName>Abhilash M.</firstName>
      <lastName>Menon</lastName>
    </author>
    <submitter>
      <firstName>Helen</firstName>
      <lastName>Jacob</lastName>
    </submitter>
    <author>
      <firstName>Alan</firstName>
      <lastName>Kerstein</lastName>
    </author>
    <author>
      <firstName>Michael</firstName>
      <lastName>Oevermann</lastName>
    </author>
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      <language>eng</language>
      <type>uncontrolled</type>
      <value>LES-LEM</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Premixed flames</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Stabilised flames</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Turbulence modelling</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Subgrid-scale closure</value>
    </subject>
    <collection role="institutes" number="1311">FG Numerische Mathematik und Wissenschaftliches Rechnen</collection>
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