Analysis of subgrid scale phenomena of premixed turbulent combustion of methane and hydrogen in comparable regimes

Computational simulation of turbulent combustion has the potential to play a very important role in fundamental research and in the design of combustion devices, yet it remains problematic for many practical applications. Although it is certainly possible to perform fully resolved direct numerical simulations (DNS) with detailed chemistry and transport on idealized centimeter-scale domains, even these " toy " applications require massive computing resources. For the study of practical devices, the huge disparity in spatial and temporal scales renders such studies infeasible now and for the foreseeable future. A more manageable approach to simulating combustion devices at the device scale can be developed by dramatically reducing the degrees of freedom used to represent the solution. Reynolds Averaged Navier Stokes (RANS) methods, for example, replace the detailed model with one based on a set of time-averaged variables. Since fastest time scales are no longer evolved in this reduced system explicitly, their effects on the resolved scales, if significant, must be incorporated through explicit models. Similarly, Large Eddy Simulation (LES) methods are based on a spatial filtering of the equations that eliminates small length scales. Unfortunately, most combustion processes of interest involve coupling across these scales, and the coupling is both strong and highly nonlinear. Modeling terms are essential to adequately account for subgrid processes on the resolved fields. The goal of the present work is to explore the applicability of yet another reduction approach, the presumed probability density function (PDF) method. Presumed PDF methods are based on the use of an efficient representation for flow or thermodynamic variable distributions (or joint distributions) that use parameterized functional forms. We consider the β-PDF form in particular, and explore its utility to capture key aspects of a class of turbulent premixed lean combustion problems by evaluating actual distributions taken from numerically resolved DNS solutions. The β-PDF (reviewed in more detail in Section 2) can be used to parameterize the distribution of a variety of scalar fields in reacting flow problems. Candidate fields are typically bounded on physical grounds to values arbitrarily between 0 and 1. For example, early combustion-related applications of β-PDF methods include the work by Cook & Riley (2004), where the β-PDF was used to represent the mixture fraction field in a diffusion flame configuration. In premixed flames, a natural candidate to use is " reaction progress " , a scalar which rises from 0 in the cold fuel to 1 in …