Mathematical Modeling of Multiphase Chemical Equilibrium

Abstract

Prediction of chemical equilibrium conditions is fundamental to modeling in many aerospace applications including rocket performance and ablation heat transfer. Although legacy equilibrium approaches have been in place for some time, improved methodologies are needed to address solution limitations, instabilities, and better code coupling. In support of this, we have developed general mathematical formulations that provide solutions for chemical composition in equilibrium states. Our methods consider both linear and nonlinear objective functions, allowing for any combination of gas- and condensed-phase products, a generality not available in other codes. Our methods are based on the minimization of Gibb’s function subject to mass balance constraints of element conservation. Standard linear programming methods are used for linear problems, and the method of Lagrange multipliers is used for nonlinear problems. We provide unique mathematical derivations in consistent matrix-vector form to provide clarity and to support modern program implementation. This mathematical clarity has allowed us to identify and correct solution instabilities common in other equilibrium codes. We have implemented our approach into a computer code named Chemics, and we provide demonstration cases to verify accuracy and stability. This code provides a stable platform for improved modeling capabilities for important aerospace applications.