NUMERICAL TREATMENT OF POLYMORPHIC SPECIES IN MULTIPHASE CHEMICAL-EQUILIBRIUM SOLVERS

Nijat Parviz oglu Abdulla

Abstract


This article presents a phase-stability criterion for treating polymorphic condensed species in high-fidelity chemical 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 exhibit small free-energy differences near solid-solid transition boundaries. The methods are rooted in identifying compositionally identical condensed candidates, separating true polymorphic families from solid-liquid phase-transition cases, and inferring solid-solid transition temperatures from thermochemical-database interval adjacency using a dedicated phase-transition detection procedure. The stable polymorph is selected based on 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 scientific 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 robust foundation for modeling polymorphic species in multiphase chemical equilibrium calculations.


Keywords


chemical equilibrium modeling; polymorphic species; phase stability; Gibbs free-energy minimization; con-densed phases; solid-solid phase transition; active-set method; thermochemical database; high-temperature combustion; KKT-based equilibrium solver

Full Text:

PDF

References


Catana, R. M., Badea, G. P. Experimental analysis on the operating line of two gas turbine engines by testing with different exhaust nozzle geometries, Energies, 2023, vol. 16, iss. 15. 20 p. DOI: 10.3390/en16155627

Abdulla, N., Abdullayev, P. S. The generalized tensor model for numerical investigation of combustion and flow processes in liquid rocket engine chamber, Journal of Aeronautics and Space Technologies, 2023, vol. 16, iss. 1, pp. 15–40. Available at: https://jast.hho.msu.edu.tr/index.php/JAST/article/view/514

Abdulla, N. Numerical investigation of combustion equilibrium in thrust chambers of liquid rocket engines. Proceedings of the 73rd International Astronautical Congress, Paris, France, 18–22 Sep-tember 2022. Available at: https://dl.iafastro.directory/event/IAC-2022/paper/68767/

Moreno-Pacheco, L.A., Sánchez-López, F., Bar-bosa-Saldaña, J. G., Martínez-Trinidad, J., Carpinteyro-Pérez, M. A., Wong-Ángel, W., García-León, R.A. Design and numerical analysis of an annular combustion chamber, Fluids, 2024, vol. 9, iss. 7. 26 p. DOI: 10.3390/fluids9070161

Kulczycki, A., Przysowa, R., Białecki, T., Gawron, B., Jasiński, R., Merkisz, J., Pielecha, I. Empirical modeling of synthetic fuel combustion in a small turbofan, Energies, 2024, vol. 17, iss. 11. 19 p. DOI: 10.3390/en17112622

Zhu, Y., Wang, S., Wang, K., Liu, Y., Liu, C., Liu, F., Yang, J., Mu, Y., Xu, G. A review of ignition characteristics and prediction model of combustor under high-altitude conditions, Energies, 2025, vol. 18, iss. 3. 26 p. DOI: 10.3390/en18030527

Zhao, W., Yang, X., Wang, J., Zheng, Y. and Zhou, Y. Evaluation of thermodynamic and chemical kinetic models for hypersonic and high-temperature flow simulation, Applied Sciences, 2023, vol. 13, iss. 17, 20 p. DOI: 10.3390/app13179991

Saccone, G., Marini, M. Chemical kinetic analysis of high-pressure hydrogen ignition and combustion toward green aviation, Aerospace, 2024, vol. 11, iss. 2, 17 p. DOI: 10.3390/aerospace11020112

Gordon, S., McBride, B. J. Computer program for calculation of complex chemical equilibrium compositions and applications. Part 1: Analysis. NASA Reference Publication 1311. Washington, DC: NASA, 1994. Available at: https://ntrs.nasa.gov/citations/19950013764

McBride, B. J., Gordon, S. Computer program for calculation of complex chemical equilibrium compositions and applications II. Users manual and program description. NASA Reference Publication 1311. Washington, DC: NASA, 1996. Available at: https://ntrs.nasa.gov/citations/19960044559

National Aeronautics and Space Administration Chemical equilibrium with applications. NASA Glenn Research Center, 2025. Available at: https://www.nasa.gov/glenn/research/chemical-equilibrium-with-applications/

Cantera Developers Cantera: an object-oriented software toolkit for chemical kinetics, thermodynamics, and transport processes, 2026. Available at: https://cantera.org/

RP Software+Engineering UG Rocket Propulsion Analysis, 2026. Available at: https://www.rocket-propulsion.com/index.htm

Herranz, M., Benito, J., Foteinopoulou, K., Karayiannis, N. C., Laso, M. Polymorph stability and free energy of crystallization of freely-jointed polymers of hard spheres, Polymers, 2023, vol. 15, iss. 6. 20 p. DOI: 10.3390/polym15061335

Al-Rawe, S. K., Baranov, D., Bronowska, A. K., Cano, C., Carroll, M. A., Waddell, P. G. Polymorphism in N-(3-hydroxyphenyl)-3-methoxybenzamide’, Crystals, 2024, vol. 14, iss. 12. 13 p. DOI: 10.3390/cryst14121070

Kaptay, G. The generalized phase rule, the extended definition of the degree of freedom, the component rule and the seven independent non-compositional state variables: to the 150th anniversary of the phase rule of Gibbs, Materials, 2024, vol. 17, iss. 24. 34 p. DOI: 10.3390/ma17246048

Chi, Z., Ji, Y., Liu, N., Jiang, T., Liu, X., Zhang, W. Algorithms for solving the equilibrium composition model of arc plasma, Entropy, 2025, vol. 27, iss. 1, 24 p. DOI: 10.3390/e27010024

Moravvej, Z., Bazargani, Z., Esmaeilzadeh, F. Thermodynamic modeling and optimization of biomass and bio-renewable organic source gasification in supercritical water using Gibbs free energy minimization, Water, 2024, vol. 16, iss. 15. 17 p. DOI: 10.3390/w16152123

dos Santos Junior, J. M., dos Reis, L. P., Vidotti, A. D. S., de Freitas, A. C. D., Mariano, A. P., Guirardello, R. Thermodynamic modeling of low-temperature Fischer–Tropsch synthesis: a Gibbs free energy minimization study for hydrocarbon production, Processes, 2025, vol. 13, iss. 8. 22 p. DOI: 10.3390/pr13082373

Lopez-Zamora, S., Escobedo, S. and de Lasa, H. A machine learning approach for phase-split calculations in n-octane/water and PASN/water systems, Processes, 2022, vol. 10, iss. 4. 26 p. DOI: 10.3390/pr10040710

Bains, W., Petkowski, J. J., Zhan, Z., Seager, S. A data resource for prediction of gas-phase thermo-dynamic properties of small molecules, Data, 2022, vol. 7, iss. 3. 19 p. DOI: 10.3390/data7030033

Moreno, D. E., Hargather, C. Z. Thermodynamic properties as a function of temperature of AlMoNbV, NbTaTiV, NbTaTiZr, AlNbTaTiV, HfNbTaTiZr, and MoNbTaVW refractory high-entropy alloys from first-principles calculations, Solids, 2023, vol. 4, iss. 4, pp. 327–343. DOI: 10.3390/solids4040021

McBride, B. J., Zehe, M. J., Gordon, S. NASA Glenn coefficients for calculating thermodynamic properties of individual species. NASA/TP-2002-211556. Cleveland, OH: NASA Glenn Research Center, 2002. Available at: https://ntrs.nasa.gov/citations/

Luo, H., Xin, Q., Yao, C., Li, C., Yang, T., Wu, X., Chahine, R., Xiao, J. Effect of real gas equations on calculation accuracy of thermodynamic state in hydrogen storage tank, Applied Sciences, 2025, vol. 15, iss. 20. 13 p. DOI: 10.3390/app152011151

Ren, J., Yang, F., Ma, D., Le, G., Zhong, J. Pneumatic performance study of a high-pressure ejection device based on real specific energy and specific enthalpy, Entropy, 2014, vol. 16, iss. 9, pp. 4801–4817. DOI: 10.3390/e16094801

Madana Gopal, J. V., Morgan, R., De Sercey, G., Vogiatzaki, K. Overview of common thermophysical property modelling approaches for cryogenic fluid simulations at supercritical conditions,

Energies, 2023, vol. 16, iss. 2. 30 p.

DOI: 10.3390/en16020885

Hosseini, A., Hage, J. L. T., Meijer, K., Offerman, E.,Yang, Y. On the importance of model selection for CFD analysis of high-temperature gas-solid reactive flow; case study: post combustion chamber of HIsarna off-gas system, Processes, 2023, vol. 11, iss. 3. 38 p. DOI: 10.3390/pr11030839

Korukçu, M. Ö. A graphical user interface for calculating exergy destruction for combustion reactions, Processes, 2024, vol. 12, iss. 2. 17 p. DOI: 10.3390/pr12020294

Gao, J., Zhang, K., Lyu, W., Zhang, Y., Wang, M., Cheng, Y., Li, A., Chen, X. Molecular dynamics simulation of phase behavior of fluid in confined nanopores, Processes, 2025, vol. 13, iss. 2. 13 p. DOI: 10.3390/pr13020506

Kocherginsky, N. M. Physicochemical mechanics and nonequilibrium chemical thermodynamics, Entropy, 2023, vol. 25, iss. 9. 13 p. DOI: 10.3390/e25091332

Arabczyk, W., Pelka, R., Wilk, B., Lendzion-Bieluń, Z. Kinetics and thermodynamics of the phase transformation in the nanocrystalline substance--gas phase system’, Crystals, 2024, vol. 14, iss. 2. 21 p. DOI: 10.3390/cryst14020129

Abdulla, N. CEAPlugins.py [Source code]. CEA-Thermochemical-Analysis. GitHub, 2026. Available at: https://github.com/nijatabdulla/CEA-Thermochemical-Analysis/blob/main/CEAPlugins.py




DOI: https://doi.org/10.32620/aktt.2026.4.04