Dynamic stiffness removal for direct numerical simulations

A systematic approach was developed to derive non-stiff reduced mechanisms for direct numerical simulations (DNS) with explicit integration solvers. The stiffness reduction was achieved through on-the-fly elimination of short time-scales induced by two features of fast chemical reactivity, namely quasi-steady-state (QSS) species and partial-equilibrium (PE) reactions. The sparse algebraic equations resulting from QSS and PE approximations were utilized such that the efficiency of the dynamic stiffness reduction is high compared with general methods of time-scale reduction based on Jacobian decomposition. Using the dimension reduction strategies developed in our previous work, a reduced mechanism with 52 species was first derived from a detailed mechanism with 561 species. The reduced mechanism was validated for ignition and extinction applications over the parameter range of equivalence ratio between 0.5 and 1.5, pressure between 10 and 50 atm, and initial temperature between 700 and 1600 K for ignition, and worst-case errors of approximately 30% were observed. The reduced mechanism with dynamic stiffness removal was then applied in homogeneous and 1-D ignition applications, as well as a 2-D direct numerical simulation of ignition with temperature inhomogeneities at constant volume with integration time-steps of 5–10 ns. The integration was numerically stable and good accuracy was achieved.