Towards a priori models for differential diffusion in turbulent non-premised flames

In this work, progress is made towards the correct modeling of differential diffusion, both for resolved simulations, and for reduced-order combustion models. In simulations with resolved scalar transport, the validity and the limitations of the constant non-unity Lewis number approach in the description of molecular mixing in laminar and turbulent flames is studied. Three test cases are selected, including a lean, highly unstable, premixed hydrogen/air flame, a lean turbulent premixed n-heptane/air flame, and a laminar ethylene/air-coflow diffusion flame. For the hydrogen flame, both a laminar and a turbulent configuration are considered. The three flames are characterized by Lewis numbers which are less than unity, greater than unity, and close to unity, respectively. For each flame, mixture-averaged transport simulations are carried out and used as reference data. The analysis suggests that, for numerous combustion configurations, the constant non-unity Lewis number approximation leads to small errors when the set of Lewis numbers is chosen properly. Next, modeling of differential diffusion for reduced order combustion models, is analyzed. The flamelet- based chemistry tabulation technique is a popular reduced-order chemical model for non-premixed turbulent flames. In this approach, the correct choice of the species Lewis numbers in the flamelet equations plays an important role. Experimental results have highlighted that, in turbulent non-premixed jet flames, turbulent transport becomes gradually dominant over molecular mixing with (i) increasing axial distance from the burner exit plane, and (ii) increasing jet Reynolds number. In the current work, this transition is characterized and a priori models for the effective species Lewis numbers in turbulent non- premixed flames are assessed. First, a flamelet-based methodology is proposed to extract these effective Lewis numbers from data sets of turbulent non-premixed flames. This methodology is then applied to the Sandia flames B, C, D, and E. The effective Lewis numbers are found to transition from their laminar values, close to the burner exit plane, to unity further downstream. Models for the effective Lewis numbers, based on the local Reynolds and Karlovitz numbers, are then assessed. To overcome the limitations associated with the experimental data, a campaign of Direct Numerical Simulations (DNS) of Sandia flame B (Rejet≈8200) is carried out. A baseline grid is carefully designed, and grid independence is assessed through simulations using refined grids in the axial, radial and azimuthal directions. Radiation and differential diffusion effects are systematically isolated by considering radiating and unity Lewis number cases, respectively. The DNS database is then validated using available measurement data. Finally, effective Lewis numbers are extracted from the DNS data, and comparisons with the analysis of the experimental data are carried out.