A more accurate projection in the rate-controlled constrained-equilibrium method for dimension reduction of combustion chemistry

Abstract

The rate-controlled constrained-equilibrium (RCCE) method for dimension reduction of combustion chemistry is revisited from a geometric viewpoint. A constrained equilibrium manifold (CEM) is defined as all compositions that satisfy the maximum-entropy or minimum-free energy conditions of the gas mixture, subject to specified constraints. The RCCE method is based solely on thermodynamics, and it is shown that this method contains a hidden assumption of an orthogonal projection that projects the rate equation of the chemical system onto the CEM. An extension of the RCCE method is constructed by making an alternative projection based on the conjecture that, near the CEM, there is a close parallel inertial manifold (CPIM). The CPIM assumption introduces the chemical kinetics directly through the local Jacobian and hence leads to greater accuracy than RCCE. The comparison between the RCCE method and its extension is made in the test calculations of hydrogen–air and methane–air autoignition.