Gradient trajectory analysis in a Jet flow for turbulent combustion modelling

Based on planar high-speed Rayleigh scattering measurements of the mixture fraction Z of propane discharging from a turbulent round jet into co-flowing carbon dioxide at nozzle-based Reynolds numbers Re-0 = 3000-8600, we use scalar gradient trajectories to investigate the local structure of the turbulent scalar field with a focus on the scalar turbulent/non-turbulent interface. The latter is located between the fully turbulent part of the jet and the outer flow. Using scalar gradient trajectories, we partition the turbulent scalar field into these three regions according to an approach developed by Mellado et al. (J.P. Mellado, L. Wang, and N. Peters, Gradient trajectory analysis of a scalar field with external intermittency, J. Fluid Mech. 626 (2009), pp. 333-365.). Based on these different regions, we investigate in a next step zonal statistics of the scalar probability density function (pdf) P(Z) as well as the scalar difference along the trajectory Delta Z and its mean scalar value Z(m), where the latter two quantities are used to parameterize the scalar profile along gradient trajectories. We show that the scalar pdf P(Z) can be reconstructed from zonal gradient trajectory statistics of the joint pdf P(Z(m), Delta Z). Furthermore, on the one hand we relate our results for the scalar turbulent/non-turbulent interface to the findings made in other experimental and numerical studies of the turbulent/non-turbulent interface, and on the other hand discuss them in the context of the flamelet approach and the modelling of pdfs in turbulent non-premixed combustion. Finally, we compare the zonal statistics for P(Z) with the composite model of Effelsberg and Peters (E. Effelsberg and N. Peters, A composite model for the conserved scalar pdf, Combust. Flame 50 (1983), pp. 351-360) and observe a very good qualitative and quantitative agreement.