Mathematical and Experimental Modeling of the Circulation Patterns in Glass Melts

Abstract

Natural convection currents in a rectangular two-dimensional enclosure representative of the longitudinal section of an industrial glass-melting furnace have been established by both model experiments and numerical calculation. For the latter a finite-difference method has been employed to solve the time-dependent coupled flow and energy equations. The highly generalized mathematical model makes allowance for buoyancy, temperature-dependent viscosity, and diffusive radiation. Generalized boundary conditions are employed to permit specification of any combination of temperature, flux, or mixed thermal boundary conditions. Representative temperature and flow contour maps obtained from the calculations are shown to agree well with experimental results obtained with a 1/20 scale model in which glycerine was employed as the modeling fluid.

Glass Furnace Combustion and Melting Research Facility.

“…The requirements for realistic glass depth and mean residence time in the relatively short research tank are the factors largely responsible for the lower velocity in the smaller tank. The Reynolds numbers in both tanks are very low (Table 2-2), supporting the conclusion of Noble et al (1972) that the effect of the through-flow is negligible. Because the Reynolds number in the industrial tank is already so small, the factor of 4 decrease in Reynolds number in the research tank will have minimal impact on the flow field.…”

“…Noble et al (1972) noted that for values of the Prandtl number, Pr >> 1, which is the case in glass tanks, Equations (7) and (8) imply that the inertial forces in the flow are negligible compared with the buoyant and viscous forces, and that the solution is therefore not a function of the Prandtl number. This was confirmed by Wright and Rawson (1973), who found that solutions for the streamlines and temperature distribution in their two-dimensional model were independent of Prandtl number over the range of values of practical interest.…”

“…The non-dimensionalization of Equations (2) and (3) was discussed by Noble et al (1972), Wright and Rawson (1973), and Leyens (1974a). These authors wrote the momentum balance in the form of a vorticity transport equation (Schlichting, 1979, pp.…”

“…Possible dimensionless variables and their definitions are listed in Table 2-1. Noble et al (1972) and Wright and Rawson (1973) defined the time scale using the thermal diffusivity. Following these authors and introducing the corresponding dimensionless variables, Equations (2), (3), and (4), become:…”

Experimental and mathematical modeling of three‐dimensional natural convection in an enclosure

“…Further, the velocities and temperature profiles near the sources and sinks exhibited the features of boundary layer flows. Although good agreement was obtained between the measured and computed velocity fields for a single longitudinal plane, the computed temperature outside the boundary layer predicted a systematically lower temperature than the experimental observation (Noble et al, 1972).…”