On thermal and mass dispersion effect on barium titanate synthesis via CCSO
Abstract This paper reports a study on thermal and mass dispersion in carbon combustion synthesis of oxides (CCSO) in a porous media. A well known volume averaging procedure of the microscopic conservation equations over an elementary volume is applied to derive the macroscopic conservation equations in a porous media. The approach allows us to account for the dispersion, convective and conductive heat and mass transfer in a porous media consisting of gas components mixture and solid particles of reactant species. The model developed in dimensionless variables using the similarity parameters is applied to numerical simulation of barium titanate micron particles synthesis using the thermal and mass dispersion effect. Three different kinetic schemes of synthesis are explored. The results are in satisfactory agreement with experimental measurements. The modeling with allowance for dispersion is compared to that one neglecting the dispersion. The data presented demonstrates the significant influence of the dispersion on CCSO process such as the combustion speed, the rate of synthesis and the uniformity of reagents and product distribution in the reactor.
Аннотация Излагаются результаты исследования воздействия тепловой и концентрационной дисперсии на синтез сложных оксидов при горении углерода (CCSO) в пористой среде. Применен известный в литературе метод получения макроуравнений сохранения в пористой среде, основанный на усреднении по элементарному объему уравнений сохранения на микроуровне. Получены макроскопические уравнения сохранения, включающие дисперсионный, конвективный и кондуктивный механизм тепло- и массопереноса в среде, состоящей из реагирующих компонент газовой и твердой фаз. Безразмерные уравнения с параметрами подобия применены к численному моделированию воздействия тепловой и массовой дисперсии на синтез микронных частиц титаната бария. Исследуются три кинетики синтеза. Результаты удовлетворительно согласуются с данными экспериментов. Сопоставлены расчеты, включающие воздействие дисперсии при заданной пористости с расчетами, пренебрегающими дисперсией. Представленные данные позволяют моделировать и оценить влияние дисперсии на CCSO, таких как фронт горения, скорость синтеза и однородность распределения в реакторе реагентов и продукта синтеза.
References 1. Whitaker S 1973 Transport equations for multi-phase systems Chemical Engineering Science, vol. 28 pp 139-147 2. Quintard M and Whitaker S 2000 Theoretical Analysis of Transport in Porous Media (ed Marcel Dekker, New York) 3. Amhalhel G A and Furmański P 1997 Problems of modeling flow and heat transfer in porous media Biuletyn Inst Tech Cieplnej Politechniki Warszawskiej No 85 pp 56-87 4. Hsu C T and Cheng P 1990 Thermal dispersion in a porous medium Int J Heat Mass Transf 33 pp 1587–97 5. Oliveiral A A M and Kaviany M 2001 Nonequilibrium in the transport of heat and reactants in combustion in porous media Progress in Energy and Combustion Science 27 pp 523-45 6. Rubens S T and Osvair V 1992 Dispersion in heat and mass transfer natural convection along vertical bounaries in porous media Faculdade de Engenharia Mecanica, Universidade Estadual de Campinas, 1308 I Campinas-SP Brazil 7. Chen K, Martirosyan K S and Luss D 2011 Hot Zones Formation During Regeneration of Diesel Particulate Filters AIChE J. February 57 2 pp 497-506 8. Fatehi M and Kaviany M 1997 Role of gas-phase reaction and gas-solid thermal nonequilibrium in reverse combustion Int. Heat Mass Transfer 11 pp 2607-20 9. Merzhanov A G 1990 Self-propagating high-temperature synthesis: Twenty years of research and findings In: Combustion and Plasma Synthesis of High-Temperature Materials eds Munir ZA, Holt JB (New York, NY: VCH) 10. Martirosyan K S and Luss D Carbon 2005 Combustion Synthesis of Oxides: Process Demonstration and Features AIChE J 51 10 pp 2801-10 11. Dobrego K V and Zhdanok S A 1998 Engineering calculation of the characteristics of a filtration-combustion wave based on a one-dimensional two-temperature model J. of Engineering Physics and Thermophysics 71 No 3 12. Wahle C W, Matkowsky B J and Aldushin A P 2003 Effects of Gas-Solid Nonequilibrium in Filtration Combustion Comb Sci and Tech 175 pp 1389-99 13. Markov A A, Filimonov I A and Martirosyan K S 2019 Two-Temperature Model and Simulation of Induced Electric Field During Combustion Synthesis of Zinc Sulfide in Argon Int. J. of Thermophysics 40 (1) 14. Markov A A 2014 Jump-Slip simulation technique for combustion in submicron tubes and submicron pores Computers and Fluids 99 C pp 8392 15. Markov A A , Filimonov I A and Martirosyan K S 2013 Carbon Combustion Synthesis of Oxides: Effect of Mach, Peclet, and Reynolds Numbers on Gas Dynamics Int. J. of Self Propagating High Temperature Synthesis 22 No 1 pp 11–17 16. Markov A A, Hobosyan M A and Martirosyan K S 2015 Simulation of heat and mass transfer in pores as applied to synthesis of magnesium−zinc and nickel−zinc ferrite nanoparticles Nanomechanics Science and Technology: An Int. J. 6 (3) pp 209-22 DOI: 101615/NanomechanicsSciTechnolIntJv6i340 17. Markov A A, Filimonov I A and Martirosyan K S 2017 Modeling the Synthesis of Submicron-Sized Complex Oxides Theoretical Foundations of Chemical Eng. 51 No 1 pp 27–37 18. Brzozowski E, Sanchez J and Castro1 M S 2002 BaCO3–TiO2 Solid State Reaction: A Kinetic Study J. of Materials Synthesis and Processing 10 No 1 19. Beauger A, Mutin J C and Niepce J C 1983 Synthesis reaction of metatitanate BaTi03 Part 1 Effect of the gaseous atmosphere upon the thermal evolution of the system BaCO3-Ti02 J. of materials science 18 pp 3041-46 20. Frank-Kamenetskii D A 1987 Diffusion and Heat Transfer in Chemical Kinetics (Moscow: Nauka Press) p 491 21. Bird R B, Sewart W E and Iightfoot F N I960 Transport phenomena (New York: Wiley) p 750
