On numerical resolution requirements in combustion modeling

We discuss one-dimensional steady laminar premixed flames in a mixture of calorically imperfect ideal gases described by detailed kinetics and multi-component transport. The required spatial discretization to capture all detailed continuum physics in the reaction zone is determined through use of a robust method developed to rigorously calculate the finest length scale a posteriori. This is accomplished by reformulating the governing equations as a nonlinear system of differential algebraic equations. Then, the solution of the steady reaction zone structure is obtained, and the generalized eigenvalues of the locally linearized system are calculated at each point in the reaction zone. Their reciprocals provide all local length scales. Application of the method to laminar flames reveals that the finest length scale is on the order of 10 ^-4 cm. Independent estimates from grid convergence studies on the continuum equations as well as from the underlying molecular collision theory verify the result. This finest length scale is orders of magnitude smaller than common engineering geometric scales, the discretization scales employed in nearly all multi-dimensional and/or unsteady laminar premixed flame simulations in the literature, and the flame thickness.