A study of the rate-controlled constrained-equilibrium dimension reduction method and its different implementations

Abstract

The Rate-Controlled Constrained-Equilibrium (RCCE) method is a thermodynamic based dimension reduction method which enables representation of chemistry involving n _s species in terms of fewer n _r constraints. Here we focus on the application of the RCCE method to Lagrangian particle probability density function based computations. In these computations, at every reaction fractional step, given the initial particle composition (represented using RCCE), we need to compute the reaction mapping, i.e. the particle composition at the end of the time step. In this work we study three different implementations of RCCE for computing this reaction mapping, and compare their relative accuracy and efficiency. These implementations include: (1) RCCE/TIFS (Trajectory In Full Space): this involves solving a system of n _s rate-equations for all the species in the full composition space to obtain the reaction mapping. The other two implementations obtain the reaction mapping by solving a reduced system of n _r rate-equations obtained by projecting the n _s rate-equations for species evaluated in the full space onto the constrained subspace. These implementations include (2) RCCE: this is the classical implementation of RCCE which uses a direct projection of the rate-equations for species onto the constrained subspace; and (3) RCCE/RAMP (Reaction-mixing Attracting Manifold Projector): this is a new implementation introduced here which uses an alternative projector obtained using the RAMP approach. We test these three implementations of RCCE for methane/air premixed combustion in the partially-stirred reactor with chemistry represented using the n _s=31 species GRI-Mech 1.2 mechanism with n _r=13 to 19 constraints. We show that: (a) the classical RCCE implementation involves an inaccurate projector which yields large errors (over 50%) in the reaction mapping; (b) both RCCE/RAMP and RCCE/TIFS approaches yield significantly lower errors (less than 2%); and (c) overall the RCCE/TIFS approach is the most accurate, efficient (by orders of magnitude) and robust implementation.

Keywords:

• RCCE
• dimension reduction
• invariant manifold
• RAMP
• projections

Acknowledgments

This work is supported by Office of Energy Research, Office of Basic Energy Sciences, Chemical Sciences, Geosciences and Biosciences Division of the US Department of Energy (DOE) under Grant No. DE-FG02-90ER. This research was also supported in part by the National Science Foundation through TeraGrid resources provided by the Texas Advanced Computing Center under Grant No. TG-CTS090020.

Notes

1. The residence time was misreported in [25] to be  ms.