Application of Heterogeneous Catalysis Models in Solving Problems of Jet Flow around Copper Models for Experimental Conditions on Induction HF Plasmatron




A stepwise model of the heterogeneous kinetics of the interaction of dissociated air with a copper surface is proposed based on the methods of quantum mechanics and the theory of the transition state. Numerical simulation of multicomponent non-equilibrium dissociated air flow past a copper water-cooled cylindrical model with a spherical nose in underexpanded supersonic jets of high-enthalpy air is performed within the framework of the Navier-Stokes equations, taking into account chemical reactions in the flow and on a cold surface for the conditions of experiments on the VGU-4 induction RF plasma torch. (IPMech RAS) on heat transfer.Comparison of numerical solutions for the chemical composition of the gas and for heat fluxes on the surface of a hemispherical sensor for various boundary conditions on the surface, based on both the Goulard model and the model proposed in this paper, is carried out.

dissociated air, heterogeneous catalysis, heat transfer, HF plasmatron


Volume 24, issue 4, 2023 year


Применение моделей гетерогенного катализа при решении задач струйного обтекания моделей из меди для условий экспериментов на индукционном ВЧ-плазмотроне

Предложена постадийная модель гетерогенной кинетики взаимодействия диссоциированного воздуха с поверхностью меди на основе методов квантовой механики и теории переходного состояния. Выполнено численное моделирование обтекания медной водоохлаждаемой цилиндрической модели со сферической носовой частью в недорасширенных сверхзвуковых струях высокоэнтальпийного воздуха в рамках уравнений Навье-Стокса многокомпонентным неравновесно-диссоциированным воздухом с учетом химических реакций в потоке и на холодной поверхности для условий экспериментов на индукционном ВЧ-плазмотроне ВГУ-4 (ИПМех РАН) по теплообмену. Проведено сравнение численных решений по химическому составу газа и по тепловым потокам на поверхности полусферического датчика для различных граничных условий на поверхности, основанных как на модели Гуларда, так и на модели, предложенной в данной работе.

диссоциированный воздух, гетерогенный катализ, теплообмен, ВЧ-плазмотрон


Volume 24, issue 4, 2023 year



1. Gordeev A.N., Kolesnikov A.F., Yakushin M.I. An Induction Plasma Application to “Bu-ran’s” Heat Protection Tiles Ground Tests // SAMPE J. 1992. Vol. 28, № 3. P. 29−33.
2. Gordeev A.N., Kolesnikov A.F., Saharov V.I. Techenie i teploobmen v nedorasshirennyh strujah indukcionnogo plazmotrona // Izvestija RAN Mehanika zhidkosti i gaza RAN. MZhG. 2011. № 4. P. 130–142.
3. Kolesnikov A.F., Gordeev A.N., Caharov V.I. Teploobmen v nedorasshirennyh neravnovesnyh strujah uglekislogo gaza: jeksperiment na indukcionnom plazmotrone i jekstrapoljacija na uslovija vhoda v atmosferu Marsa // Fiziko-himicheskaja kinetika v gazovoj dinamike. 2014. Vol. 15, № 4.
4. Galkin S.S. et al. Investigation of Influence of Model Geometry on Convective Heat Trans-fer to Cold Catalytic Surface in Supersonic Dissociated Air Flows in HF-Plasmatron // Phys. Kinet. Gas Dyn. 2021. Vol. 22, № 3. P. 21–30.
5. Umanskij S.Ja. Teorija jelementarnogo akta himicheskogo prevrashhenija v gaze. Moskva: Izd-vo MGU, 2000. 287 p.
6. Chorkendorff I., Niemantsverdriet J.W. Concepts of Modern Catalysis and Kinetics, 3rd Edition. Third. WILEY-VCH VerlagGmbH&Co.KGaA, Boschstr. 12, 69469Weinheim, Germany, 2017. 524 p.
7. Becke A.D. Density-functional exchange-energy approximation with correct asymptotic be-havior // Phys. Rev. A. 1988. Vol. 38, № 6. P. 3098–3100.
8. Lee C., Yang W., Parr R.G. Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density // Phys. Rev. B. 1988. Vol. 37, № 2. P. 785–789.
9. Hariharan P.C., Pople J.A. The influence of polarization functions on molecular orbital hy-drogenation energies // Theor. Chim. Acta. 1973. Vol. 28, № 3. P. 213–222.
10. Frisch M.J. et al. Gaussian 09 // Gaussian, Inc., Wallingford CT. 2009.
11. Glasstone S., Laidler K.J., Eyring H. The theory of rate processes // McGraw-Hill. New York, 1941. 611 p.
12. Kovalev V.L., Kroupnov A.A., Vetchinkin A.S. Quantum mechanics calculation of catalytic properties of a copper sensor for prediction of flow characteristics in plasmatron // Acta Astronaut. 2015. Vol. 117.
13. Goulard R. On Catalytic Recombination Rates in Hypersonic Stagnation Heat Transfer // J. Jet Propuls. 1958. Vol. 28, № 11. P. 737–745.
14. Kovalev V.L. Geterogennye kataliticheskie processy v ajerotermodinamike. Moskva: FIZMATLIT, 2002. 224 p.
15. Kroupnov A.A., Pogosbekian M.J. Interaction of dissociated air with the surface of β-cristobalite material // Acta Astronaut. 2023. Vol. 203. P. 454–468.
16. Afonina N.E., Gromov V.G., Sakharov V.I. HIGHTEMP technique of high temperature gas flows numerical simulations // Proc. 5th Europ. Symp. on Aerothermodyn. Spase Vehicles. Co-logne, 2004. P. 323–328.
17. Saharov V.I. Chislennoe modelirovanie termicheski i himicheski neravnovesnyh techenij i teploobmena v nedorasshirennyh strujah indukcionnogo plazmotorona // Izvestija RAN Mehanika zhidkosti i gaza RAN MZhG. 2007. № 6. P. 157–168.
18. Gurvich L.V., Vejc I.V., Medvedev V.A. Termodinamicheskie svojstva individual'nyh veshhestv. 3rd ed. Moskva: Nauka, 1978.
19. Ibragimova L.B., Smehov G.D., Shatalov O.P. Konstanty skorosti dissociacii dvuh-atomnyh molekul v termicheski ravnovesnyh uslovijah // Izvestija RAN Mehanika zhidkosti i gaza RAN MZhG. 1999. № 1. P. 181–186.
20. Losev S.A., Makarov V.N., Pogosbekyan M.Y. Model of the physico-chemical kinetics be-hind the front of a very intense shock wave in air // Fluid Dyn. 1995. Vol. 30, № 2. P. 299–309.
21. Park C. et al. Review of chemical-kinetic problems of future NASA missions. II - Mars en-tries // J. Thermophys. Heat Transf. 1994. Vol. 8, № 1. P. 9–23.
22. Losev S., Makarov V., Nikolsky V. Thermochemical nonequilibrium kinetic models in strong shock waves on air // 6th Joint Thermophysics and Heat Transfer Conference. Reston, Virigina: American Institute of Aeronautics and Astronautics, 1994.
23. Hirschfelder J.O., Curtiss C.F., Bird R.B. The Molecular Theory of Gases and Liquids. New York: John Willey and Sons, 1954. 1219 p.
24. Reid R.C., Prausnitz J.M., Sherwood T.K. The Properties of Gases and Liquids. New York: McGraw-Hil, 1977. 688 p.
25. Vasil'evskij, S.A. Kolesnikov A.F. Chislennoe modelirovanie techenij ravnovesnoj indukcionnoj plazmy v cilindricheskom kanale plazmotrona // Izvestija RAN Mehanika zhidkosti i gaza RAN. Mehanika zhidkosti i gaza. 2000. № 5. P. 164–173.