Numerical modeling of chemistry and gas dynamics during shock-induced ethylene combustion

We present the results of a numerical study of shock-induced ethylene combustion. As in other reactive flow problems the computational time increases significantly when finite rate chemistry is included. We compare the accuracy and efficiency of a variety of methods when applied to this combustion problem. For a full kinetics scheme we consider the speed of a range of alternative ordinary differential equation solvers. We find that for the coupled ODE-hydrodynamic problem an extrapolated linearly implicit Euler method is the fastest of the methods used, but that otherwise a fourth-order Rosenbrock scheme is the fastest solution method. The identity of the fastest method changes because of the start up conditions having to be recalculated at the start of every step in a coupled ODE-hydrodynamics module. The faster methods in a static simulation, where the values of the variables can be carried over between time-steps without recalculation, generally have higher start-up penalties, and as a consequence are generally slower in a reactive flow model. We then apply a detailed reduction strategy to a chemical kinetics reaction data set and find that it cannot be reduced by many reactions as it is already a fairly compact set. We then introduce an induction parameter model based on the two parameter model of Taki and Fujiwara [1] and the work of Oran et al. [2]. We derive functions that model the induction times and the energy release rates predicted using the chemical kinetics data set. We show some results of coupled gas dynamics and reactive how calculations using these models and compare with experiment. We find that the induction parameter model reproduces the experimental results well whilst using less than 5% of the computational time of the chemical kinetics model.