Direct Numerical Simulations of Premixed Turbulent Combustion: Relevance and Applications to Engineering Computational Analyses

Abstract

Analysis of turbulent flows is one of the most difficult and challenging topics in physical sciences because of the nonlinearity of the governing equations, which is manifested by a large range of length and time scales. Resolution of this large range of scales is difficult to address using both experimental and numerical means. This problem is further exacerbated in turbulent reacting flows due to the nonlinearity of the temperature dependence of burning rate in typical combustion processes. Moreover, the interaction of flow and chemistry in turbulent premixed combustion (where reactants are homogeneously mixed prior to the combustion process) necessitates simultaneous measurements of fluid velocity and flame propagation in three dimensions with adequate spatial resolution. Such an experimental analysis is either impossible in most configurations or extremely expensive to carry out. The advances in high-performance computing have made it possible to carry out three-dimensional Direct Numerical Simulations (DNS) of turbulent premixed combustion by resolving all the relevant length and time scales of turbulent reacting flows without any recourse to physical approximations. The cost of DNS for non-reacting flows is immense where one only has to resolve the Kolmogorov scale, and it is more expensive for premixed combustion because it requires additional resolution of the internal flame structure. It can be shown that for simulating homogeneous non-reacting turbulence the number of grid points varies with Reynolds number as $Re_{t}^{9/4}$, where $Re_{t}$ is the large-scale turbulent Reynolds number, which is why DNS is limited by computer capacity and the application of DNS remains limited to research problems in simple configurations for moderate turbulent Reynolds numbers. However, the data obtained from DNS circumvents the aforementioned limitations of experimental data and can be considered as an equivalent to experimental data with a spatial resolution up to the Kolmogorov length scale (i.e. the smallest significant length scale of turbulence). Although DNS does not require turbulence and combustion modelling (and thus avoids physical inaccuracies associated with them), the chemical aspect of premixed combustion is often simplified for the sake of computational economy in order to conduct a detailed parametric analysis. The simplification of chemistry and the specification of ‘soft’ boundary conditions often significantly affect the results and determine the aspects which can be analysed using DNS data. In spite of these constraints, DNS data can be explicitly Reynolds-averaged/filtered to extract the ‘exact’ behaviour of the unclosed terms in the Reynolds-averaged/ filtered transport equations of momentum, energy and species. This makes it possible to compare the predictions of existing models with respect to the ‘exact’ unclosed terms extracted from DNS data and propose either model modifications or new models, wherever necessary, in the light of physical insights obtained from DNS data. Thus, even though the DNS of premixed combustion remains mostly limited to canonical configurations, the physical insights obtained from it contribute significantly to the development of the high-fidelity models for Reynolds-Averaged Navier–Stokes (RANS) and Large Eddy Simulations (LES), which are used for engineering calculations for designing industrial burners. As an example, this chapter will illustrate how DNS data can contribute to the model development for the Reynolds flux of sensible enthalpy in head-on quenching of statistically planar turbulent premixed flames by an inert isothermal wall.