Numerical simulation of the stability of flowing glass steadily cooled by radiation

Abstract

The stability limit of longitudinal roll cells in a flowing glass steadily cooled by radiation is investigated using an unsteady SIMPLER code with a periodic boundary condition. The P, approximation is used for analysis of the radiative heat transfer. The upper surface is subject to radiative cooling and the rigid bottom is insulated. This study is focused on the occurrence of longitudinal roll cells aside from the overall back flow. The critical Rayleigh number and associated wavenumber are obtained as a function of the Prandtl number dimensionless mass flow, rate, optical thickness, emissivity of the bottom wall and environmental temperature. The flow is stabilised with decreasing the Prandtl number; increasing the dimensionless mass flow, rate, increasing the optical depth and increasing the environmental temperature. If the emissivity of the bottom wall is greater than 0.6 the emissivity has little effect on the stability of the flow. The critical Rayleigh number of the radiative cooling problem is larger than that of the nonradiative case thus providing more room in the design of forehearth and shallow forming and refining processes.