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A three-dimensional Direct Numerical Simulation (DNS) database of statistically planar    $$H_{2} -$$  H 2 - air turbulent premixed flames with an equivalence ratio of 0.7 spanning a large range of Karlovitz number has been utilised to assess the performances of the extrapolation relations, which approximate the stretch rate and curvature dependences of density-weighted displacement speed    $$S_{d}^{*}$$  S d ∗ . It has been found that the correlation between    $$S_{d}^{*}$$  S d ∗ and curvature remains negative and a significantly non-linear interrelation between    $$S_{d}^{*}$$  S d ∗ and stretch rate has been observed for all cases considered here. Thus, an extrapolation relation, which assumes a linear stretch rate dependence of density-weighted displacement speed has been found to be inadequate. However, an alternative extrapolation relation, which assumes a linear curvature dependence of    $$S_{d}^{*}$$  S d ∗ but allows for a non-linear stretch rate dependence of    $$S_{d}^{*}$$  S d ∗ , has been found to be more successful in capturing local behaviour of the density-weighted displacement speed. The extrapolation relations, which express    $$S_{d}^{*}$$  S d ∗ as non-linear functions of either curvature or stretch rate, have been found to capture qualitatively the non-linear curvature and stretch rate dependences of    $$S_{d}^{*}$$  S d ∗ more satisfactorily than the linear extrapolation relations. However, the improvement comes at the cost of additional tuning parameter. The Markstein lengths  L   M   for all the extrapolation relations show dependence on the choice of reaction progress variable definition and for some extrapolation relations  L   M   also varies with the value of reaction progress variable. The predictions of an extrapolation relation which involve solving a non-linear equation in terms of stretch rate have been found to be sensitive to the initial guess value, whereas a high order polynomial-based extrapolation relation may lead to overshoots and undershoots. Thus, a recently proposed extrapolation relation based on the analysis of simple chemistry DNS data, which explicitly accounts for the non-linear curvature dependence of the combined reaction and normal diffusion components of    $$S_{d}^{*}$$  S d ∗ , has been shown to exhibit promising predictions of    $$S_{d}^{*}$$  S d ∗ for all cases considered here.

flow, turbulence and combustion

Assessment of Extrapolation Relations of Displacement Speed for Detailed Chemistry Direct Numerical Simulation Database of Statistically Planar Turbulent Premixed Flames