Numerical Treatment of Polymorphic Species in Multiphase Chemical-Equilibrium Solvers for Jet-Engine Applications

This article presents a phase-stability criterion for treating polymorphic condensed species in high-temperature combustion-equilibrium modeling. The aim of the article is to prevent polymorph locking, invalid coefficient usage, and unstable phase switching in Gibbs free-energy minimization when composition-identical solid phases have small free-energy differences near solid-solid transition boundaries. The methods are based on identifying composition-identical condensed candidates, separating true polymorphic families from solid-liquid phase-transition cases, and inferring solid-solid transition temperatures from thermo-chemical-database interval adjacency using a dedicated phase-transition detection procedure. The stable polymorph is selected according to the current temperature relative to the inferred boundary while preserving elemental composition and stoichiometric constraints. If no transition temperature can be reliably inferred, a temperature-validity check is applied, and out-of-range polymorphs are replaced with admissible counterparts of identical composition. This phase-admissibility layer is coupled with the condensed active-set stability test, ensuring that only thermodynamically stabilizing condensed phases remain in the equilibrium solution. The novelty of the article lies in the explicit integration of polymorph phase-stability logic into KKT-based multiphase combustion-equilibrium iterations and active-set decision procedures. The proposed criterion regularizes solid-solid switching, prevents thermodynamic-data leakage outside valid polynomial intervals, and improves convergence robustness near phase-boundary regions. Benchmark temperature-sweep cases involving Cr2O3 polymorphs demonstrate stable temperature-dependent phase selection and agreement with NASA CEA at the property level, with an average relative error of approximately 0.05%. The results show that explicit phase-stability criteria provide a physically consistent and numerically robust foundation for modeling polymorphic species in multiphase combustion-equilibrium calculations.