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, |
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.