Three-Dimensional Flow and Thermal Structures in Glass Melting

This paper presents a study of the flow and thermal structures in the molten glass bath of a typical glass melting furnace with a throat but without air bubblers or electric boosting. Different separate effects on the flow structure of the glass melt are simulated, but only the glass melt is considered. The net heat flux distribution is imposed at the combustion space/glass melt interface, and its effects on the flow and thermal structures of the glass melt are analyzed in a systematic manner by changing the heat flux distribution while keeping the total heat input to the glass bath constant. The main purpose of the work is to evaluate the capability of the furnace operators to control the glass flow and temperature fields by adjusting the firing in the combustion space. The physical phenomena affecting the flow structure in the glass melt are analyzed and discussed in detail. The major results of the study indicate that (i) the heat flux distribution has no significant effect on the flow structure of the glass melt under the batch blanket where several RayleighBenard cells develop in the spanwise direction, (ii) a heat flux gradient in the longitudinal direction is required to generate two recirculation loops in the direction, and (iii) steep heat flux gradient in the refining part of the tank increase significantly the size of the refining recirculation loop near the front wall. NOMENCLATURE c Specific heat ∆Hmelt Total enthalpy of melting of the batch g Specific gravity h Depth within the glass melt ~i,~j,~k Unit vectors in the physical space k Thermal conductivity Lb Length of the batch blanket Lmax Longitudinal location of the maximum heat flux L0 Longitudinal location of the zero heat flux ṁb Batch mass flow rate ṁpull Glass mass flow rate at the throat p Pressure q′′ Heat flux q′′ 0 Heat flux at the back wall (x = 0 m) q∗(y) Dimensionless multiplying factor of the heat flux Qmelt→batch Heat transfer rate from the glass melt to the batch per unit length of batch Ṡ Volumetric heat source T Temperature T0 Reference temperature t Time u Velocity vector in the x-direction v Velocity vector in the y-direction ~v Velocity vector w Velocity vector in the z-direction W Glass tank width x Longitudinal location (see Figure 3) y Spanwise location (see Figure 3) z Local depth within the glass melt (see Figure 3) Greek symbols α Thermal diffusivity β Thermal expansion coefficient ρ Density μ Dynamic viscosity φ Local volumetric gas fraction Subscripts b Refers to the batch bubbles Refers to the depth under the batch where bubbles are present