Using the Merson Method to Study the Dust-Air Mixture Self-Ignition Process
DOI:
https://doi.org/10.20998/2078-774X.2017.10.10Анотація
The numerical integration of differential equations on the self-ignition of dust-air mixtures taking into consideration almost abrupt changes in the mixture temperature and the fuel concentration in it requires substantiation of the choice of integration step. Many step-by-step numerical methods used for the integration of ordinary differential equations are available; however special attention should be paid to the Merson method, because it provides the most effective algorithm for the automatic selection of the step of integration. The purpose of this scientific paper was to study the opportunities of the Merson method for the integration of differential equations on the self-ignition of dust-air mixture taking into consideration actually abrupt changes in the mixture temperature and the fuel concentration in it. The common mathematical models of the self-ignition of dust-air mixtures that move in the cylindrical channel were used. The obtained data show that in the case of self-ignition the mixture temperature can be increased 8 times. It has been shown that the integration step should be reduced more than 100 times to take into consideration such abrupt temperature drops and the fuel concentration in the dust-air mixture during the integration of differential self-ignition equations. The Merson method is efficient for the investigation of self-ignition due to the automatic selection of the step of integration. The Merson method is recommended for the integration of differential equations that describe the self-ignition of dust-air mixtures and it can be used for the investigation of ignition and combustion processes.Посилання
Wu, D., Schmidt, M., Huang, X. and Verplaetsen, F. (2017), "Self-ignition andsmolderingcharacteristicsofcoaldustaccumulations in O2/N2 and O2/CO2 atmospheres", Proceedings of theCombustionInstitute, Vol.36,Issue 2,pp.3195–3202, ISSN 1540-7489, doi: 10.1016/j.proci.2016.08.024.
Muto, M., Yuasa, K. and Kurose, R. (2017), "Numerical simulation of ignition in pulverized coal combustion withdetailedchemical reaction mechanism", Fuel, Vol. 190, pp. 136–144, ISSN 0016-2361, doi: 10.1016/j.fuel.2016.11.029.
Zhang, J., Ren, T., Liang, Y. and Wang, Z. (2016), "A review on numerical solutions to self-heating of coalstockpile:Mechanism, theoretical basis, and variable study", Fuel, Vol. 182, pp. 80–109, ISSN 0016-2361,doi:10.1016/j.fuel.2016.11.029.
Butcher, J. C. (1996), "A history of Runge-Kutta methods", Applied numerical mathematics, Vol. 20, pp. 247–260.
Hoffman, J. D. and Frankel, S. (2001), Numerical Methods for Engineers and Scientists, Marcel Dekker Inc., New York-Basel.
Morachkovskii, O. K. and Romashov, Yu. V. (2009), "Solving initial-boundary-value creep problems", InternationalAppliedMechanics, Vol. 45, No. 10, pp. 1061–1070.
Colannino, J. (2006), Modeling of Combustion Systems: A Practical Approach, CRC Press.
Glassman, I., Yetter, R. A. and Glumac, N. G. (2008), Combustion, Academic Press.
Vilenskii, T. V. and Hzmalyan, D. M. (1978), Dinamika goreniya pylevidnogo topliva (Issledovaniya naelektronnyhvychislitelnyh mashinah) [Dynamics of combustion of pulverized fuel: (Research on electroniccomputers)],Energiya,Moscow,Russia.
