A computationally-efficient method for flamelet calculations

A new open-source code for the simulation of the diffusion flamelet equations is proposed. Emphasis is placed on using an approximate Jacobian to reduce the computational cost of the matrix operations. Performance of the proposed solvers is tested by performing flamelet calculations with kinetic mechanisms of varying sizes. For the unity Lewis number equations, the present iterative Newton solver using an approximate Jacobian greatly outperforms direct Newton solvers using exact Jacobians. The computation cost scales linearly with the number of species, leading to a reduction in solution times by two orders of magnitude for mechanisms containing thousands of species. The applicability of the Jacobian approximations to the solution of the non-unity Lewis number flamelet equations is assessed. The approximations are generally inadequate to solve the full non-unity Lewis number equations but can be used in some applications depending on the balance of terms in the flamelet equations. As an example, the flamelet solver is applied to the study of sooting tendencies in laminar co-flow diffusion flames where modified non-unity Lewis number flamelet equations, previously shown to accurately reproduce experimentally-measured Yield Sooting Indices (YSI), are solved. The accelerated flamelet solver is well suited for sensitivity analysis and uncertainty quantification with large detailed kinetic mechanisms, tasks for which the computational cost was previously prohibitive.