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

A three-dimensional Direct Numerical Simulation (DNS) database of statistically planar H2- 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 Sd∗. It has been found that the correlation between Sd∗ and curvature remains negative and a significantly non-linear interrelation between Sd∗ 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 Sd∗ but allows for a non-linear stretch rate dependence of Sd∗, has been found to be more successful in capturing local behaviour of the density-weighted displacement speed. The extrapolation relations, which express Sd∗ 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 Sd∗ more satisfactorily than the linear extrapolation relations. However, the improvement comes at the cost of additional tuning parameter. The Markstein lengths LM for all the extrapolation relations show dependence on the choice of reaction progress variable definition and for some extrapolation relations LM 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 Sd∗, has been shown to exhibit promising predictions of Sd∗ for all cases considered here.