Abstract
Dynamic algebraic closure of scalar dissipation rate (SDR) of reaction progress variable in the context of Large Eddy Simulations (LES) of turbulent premixed combustion has been addressed here using a power-law based expression and a model, which was originally proposed for Reynolds Averaged Navier Stokes (RANS) simulations, but has recently been extended for LES. The performances of these models have been assessed based on a-priori analysis of a Direct Numerical Simulations (DNS) database of statistically planar turbulent premixed flames with a range of different values of heat release parameter t, turbulent Reynolds number R e t and global Lewis number L e. It has been found that the power-law model with a single constant exponent a D does not adequately capture the volume-averaged behaviour of density-weighted SDR and this problem is particularly severe especially for L e < < 1 flames. The deficiency of the power-law model with a single power-law exponent arises due to multi-fractal nature of SDR. The dynamic evaluation of the model parameter for the algebraic model, which was originally proposed in the context of RANS and has been extended here for LES, has been shown to capture the local behaviour of SDR better than the power-law model. It has been demonstrated that the empirical parameterisation of a model parameter for the static version of the RANS-extended SDR model can be avoided using a dynamic formulation which captures the local behaviour of SDR either comparably or better than the static formulation for a range of different values of t, L e and R e t , without sacrificing the prediction of the volume-averaged SDR.
Highlights
The Scalar Dissipation Rate (SDR) characterises the rate of micro-mixing in turbulent reacting flows and its importance is well-recognised for turbulent non-premixed combustion modelling and interested readers are referred to Refs. [1,2,3,4] and references therein for a detailed account of the relevance of SDR modelling in both single and multi-phase non-premixed combustion
To assess a power-law based closure of SDR for Large Eddy Simulations (LES) by dynamically evaluating the power-law exponent. These objectives have been addressed here by a-priori analysis based on a single-step Arrhenius type chemistry Direct Numerical Simulations (DNS) database of statistically planar turbulent premixed flames with a range of different values of τ, Le and Ret
In order to assess the performances of the SDR models it is useful to compare the predictions of the volume-averaged value of density-weighted SDR as this quantity is expected to be proportional to the volume-averaged reaction rate w V under the flamelet assumption according to w = 2ρNc/(2cm − 1) where . . . V indicates a volume-averaging operation
Summary
The Scalar Dissipation Rate (SDR) characterises the rate of micro-mixing in turbulent reacting flows and its importance is well-recognised for turbulent non-premixed combustion modelling and interested readers are referred to Refs. [1,2,3,4] and references therein for a detailed account of the relevance of SDR modelling in both single and multi-phase non-premixed combustion. [7] demonstrated that the RANS-extended algebraic closure of SDR for LES (see Eq 5i for the expression which will be referred to as the LES-G model) satisfactorily captures both volume-averaged and local behaviours of Nc for a range of different filter widths for flames with a range of different values of τ , Le and Ret. it has been found that one of the model parameters (i.e. see βc later in Eq 5i) in the LES-G model increases with increasing τ and an empirical parameterisation was proposed by Gao et al [7] to account for this τ dependence. To assess a power-law based closure of SDR for LES by dynamically evaluating the power-law exponent These objectives have been addressed here by a-priori analysis based on a single-step Arrhenius type chemistry DNS database of statistically planar turbulent premixed flames with a range of different values of τ , Le and Ret. The rest of the paper will be organised as follows.
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