A Model Based Closure Approach For Turbulent Combustion Using The One Dimensional Turbulence Model

A new model-based closure approach for turbulent combustion using the One-Dimensional turbulence model (ODT) is developed and validated in context to a turbulent jet diffusion flame. The interaction of turbulence and chemistry provides interesting finite rate chemistry effects including the phenomena of extinction and re-ignition. The ODT model resolves both spatially and temporally all the scales in a turbulent reaction flow problem, thus, combining the accuracy of a DNS like solver with efficiency by reduction in the number of dimensions. The closure approach is based on identifying the mechanisms responsible for the above mentioned effects and parameterizing the ODT results with a minimum set of scalars transported in the coarse grained solvers like the Reynolds-Averaged Navier-Stokes (RANS) or Large Eddy Simulation (LES). Thus, the closure from ODT is based on a "one-way" coupling between the coarse grained solvers and ODT. Two approaches for closure are developed in the present work with respect to a RANS solver; however, they can be easily extended to LES. The first approach relies on ODT to provide the history effects associated with the geometry, which represent the interactions of turbulence and chemistry, by tabulating scalar statistics (first and second moments) on two parameters measuring, the extent of mixing, the radial mean mixture fraction, and the extent of entrainment, the centerline mean mixture fraction. However, based on the above parameterization, the approach is limited to jet diffusion flame geometry. Furthermore, the closure requires a one to one correspondence between the flames simulated in the coarse grained solver and ODT. As a second approach, the results from ODT are parameterized based on general representative scalars; mixture fraction, which specifies the mixedness of the mixture and temperature, which specifies the reactedness of the mixture. The history effects associated with the flow geometry are provided by the RANS solver in t.