Mathematical modelling of sand dissolution in a glass melting channel with controlled glass flow

Abstract This work presents the results of a mathematical modelling of sand dissolution in a horizontal glass-melting channel with circulation flows when varying the length of the channel and the time needed for the dissolution of the sand particles. The recently found optimal combination of intensive transversal circulations with forward flow, slowed down by a positive longitudinal temperature gradient near the glass level, has been set in the melting channel. The results of the modelling were projected into the values of the space utilisation for the sand-dissolution process. The high values of space utilisation were repeatedly attained under these conditions in a broad interval of channel lengths and sand-dissolution times. Both the growing length of the channel and the growing sand-dissolution time increased the ratio of the transversal to longitudinal temperature gradient necessary for attaining the maximum space utilisation. The pull rate of the channel grew linearly with the growing ratio of the channel length to the sand-dissolution time. The results provide a theoretical base for the design of glass-melting segments with controlled glass flow, characterised by lower energy consumption and higher melting performance.