A comprehensive multi-scale method of model reduction and analysis for reactive flow*

The numerical simulation for reactive flow with detailed chemistry is challenging, one of the main reasons is that the highly nonlinear chemical source term together with diffusion and convection terms in Navier-Stokes equation contributes to a wide range of time scales, which impose a severe stiffness in the simulations. The traditional approaches to resolve the stiffness problem focus on chemistry aspect. However, those methods assume combustion under homogeneous ignition condition which lose the generality for various combustion scenario and conditions. The current work develops a comprehensive method to analyze characteristic time scales for reaction, convection and diffusion. Firstly, using the G-Scheme Participation Index (GPI) the chemical mechanism is analyzed and simplified. Then, the capability of GPI in analyzing chemical mechanisms is enriched with the introduction of a new Participation Index for convection and diffusion processes and the definition of their characteristic time scales, which provides more physics insights into the flow-reaction coupling system. This leads to a criterion for the automatic discrimination of combustion modes.