On problems of time lag and susceptibility during mathematical simulation of thermal operation of roasting furnace for production of artificial graphite

Abstract

The method of mathematical simulation has been used for examination of the effect of relationship of thermal time lag of the container (with stock material and fill) and susceptibility of the control system on the temperature pattern of stock material for obtaining artificial graphite; also the effect of computational time step value in time (Δτ) on the results of mathematical simulation has been studied. The results of simulation at any fill bed thickness are shown not to depend practically on Δτ for infinitelyfast system for control of roasting furnace, and at finite susceptibility of the control system the temperature oscillations, being generated by the system with decreasing thermal time lag of the container (fill bed depth), penetrate ever deeper and deeper inside it, however you can detect it with help of computational method only at small Δτ – because big time steps show smoothed pattern with monotonous trends that corresponds to the reality only at significant fill bed depth. The degree of convergence of iteration calculation algorithm is high enough if Δτ is significantly more or significantly less than the period of modeled periodic processes; if these values are of the same order the algorithm can run into a cyclic path or the demanded amount of iterations can increase by some orders.