Comparison of 2D and 3D density-weighted displacement speed statistics and implications for laser based measurements of flame displacement speed using direct numerical simulation data

0010-2180/$ see front matter 2010 The Combust doi:10.1016/j.combustflame.2010.11.014 ⇑ Corresponding author. Fax: +44 1517944848. E-mail addresses: [email protected] [email protected] (G. Hartung), m.katragadda@liver [email protected] (C.F. Kaminski). In a recent study, a light sheet imaging approach has been proposed (Hartung et al., J. Appl. Phys. B 96 (2009) 843–862) which permits measurement of a quantity S 2D d , which is the two-dimensional projection of the actual density-weighted displacement speed S d for turbulent premixed flames. Here the statistics of S d and S 2D d are compared using a direct numerical simulation database of statistically planar turbulent premixed flames. It is found that the probability density functions (pdfs) of S 2D d approximate the pdfs of S d satisfactorily for small values of root-mean-square turbulent velocity fluctuation u 0, though the S 2D d pdfs are wider than the S d pdfs. Although the agreement between the pdfs and the standard-deviations of S 2D d and S d deteriorate with increasing u 0, the mean values of S 2D d correspond closely with the mean values of S d for all cases considered here. The pdfs of two-dimensional curvature j2D m and the twodimensional tangential-diffusion component of density-weighted displacement speed S 2D t are found to be narrower than their three-dimensional counterparts (i.e. jm and S t respectively). It has been found that the pdfs, mean and standard-deviation of p=2 j2D m and p=2 S 2D t faithfully capture the pdfs, mean and standard-deviation of the corresponding three-dimensional counterparts, jm and S t respectively. The combination of wider S 2D d pdfs in comparison to S d pdfs, and narrower S 2D t pdfs in comparison to S t pdfs, leads to wider S r þ S n 2D 1⁄4 S 2D d S 2D t pdfs than the pdfs of combined reaction and normal-diffusion components of density-weighted displacement speed S r þ S n . This is reflected in the higher value of standard-deviation of S r þ S n , than that of its three-dimensional counterpart S r þ S n . However, the mean values of S r þ S n 2D remain close to the mean values of S r þ S n . The loss of perfect correlation between two and three-dimensional quantities leads to important qualitative differences between the S r þ S n 2D j2D m and S r þ S n jm , and between the S 2D d j2D m and S d jm correlations. For unity Lewis number flames, the S d jm correlation remains strongly negative, whereas a weak correlation is observed between S 2D d and j2D m . The study demonstrates the strengths and limitations of the predictive capabilities of the planar imaging techniques in the context of the measurement of density-weighted displacement speed, which are important for detailed model development or validation based on experimental data. 2010 The Combustion Institute. Published by Elsevier Inc. All rights reserved.