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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

Chakraborty N, Hartung G, Katragadda M, Kaminski CF, "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", Comb. Flame, 158 (7), pp 1372-1390, (2011), , DOI:10.1016/j.combustflame.2010.11.014, | pdf


Abstract

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 , which is the two-dimensional projection of the actual density-weighted displacement speed  for turbulent premixed flames. Here the statistics of and  are compared using a direct numerical simulation database of statistically planar turbulent premixed flames. It is found that the probability density functions (pdfs) of  approximate the pdfs of satisfactorily for small values of root-mean-square turbulent velocity fluctuation u′, though the  pdfs are wider than the  pdfs. Although the agreement between the pdfs and the standard-deviations of  and  deteriorate with increasing u′, the mean values of  correspond closely with the mean values of for all cases considered here. The pdfs of two-dimensional curvature  and the two-dimensional tangential-diffusion component of density-weighted displacement speed  are found to be narrower than their three-dimensional counterparts (i.e. κm and  respectively). It has been found that the pdfs, mean and standard-deviation of  and  faithfully capture the pdfs, mean and standard-deviation of the corresponding three-dimensional counterparts, κm and  respectively. The combination of wider  pdfs in comparison to  pdfs, and narrower  pdfs in comparison to  pdfs, leads to wider  pdfs than the pdfs of combined reaction and normal-diffusion components of density-weighted displacement speed . This is reflected in the higher value of standard-deviation of , than that of its three-dimensional counterpart . However, the mean values of  remain close to the mean values of . The loss of perfect correlation between two and three-dimensional quantities leads to important qualitative differences between the  and , and between the  and  correlations. For unity Lewis number flames, the  correlation remains strongly negative, whereas a weak correlation is observed between  and . 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.