Применение метода Мерсона для исследования процесса самовоспламенения пылевоздушной смеси

Abstract

Рассмотрено применение метода Мерсона для численного интегрирования системы обыкновенных дифференциальных уравнений, описывающих процесс самовоспламенения воздушной смеси пылевидного топлива, движущейся в цилиндрическом канале. Показано, что за счет автоматического выбора шага интегрирования метод Мерсона позволяет исследовать процессы практически скачкообразных изменений температуры пылевоздушной смеси и концентрации топлива в ней, характерных для самовоспламенения.

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.