Primary and Secondary Instabilities in a Glass Melting Furnace

Abstract

The transition from steady laminar to chaotic convection in a glass-melting furnace specified by upper surface temperature distribution has been studied by direct numerical analysis of two- and three-dimensional time dependent Navier-Stokes equations. Thermal instability of the convection roll may take place when the modified Rayleigh number Ra_m is larger than 9.71*10^4. It is shown that the basic flow patterns in a glass-melting furnace are steady laminar, unsteady periodic, quasi-periodic, and chaotic flow. The instabilities have the characteristic (viscous diffusion, t_d=H^2/nu_0) timescales observed in the typical transitions. Through primary (2-D) and secondary (3-D) instability analyses, the fundamental unsteady feature in a glass-melting furnace is well defined as an unsteady periodic or a weak chaotic flow with typical periods of 1-3 times t_d. The results strongly imply the possibility of unsteady or chaotic flow in glass melters.