Analysis of natural convection in a waste glass melter Page: 5 of 23
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Rayleigh number, Ra = ppg(T2- Ti)L^|ia
Prandtl number, Pr=v/a = ^iCp'k
the continuity, momentum, and energy equations can be written,
dropping asterisks, as
Vu = 0
V'Ra/Pr U VU = -Vp + V^U + VR^P, Te
VR^FVu VT= v^r +qs
3. Base Case
The two-dimensiuna.I cross section of the melter that is being
considered in this study is one-half of the symmetric plane of the
glass melt volume across each pair of the electrodes. In Figure
2, this glass melt volume is shown with the upper and lower
recesses occupied by these electrodes. The waste slurry dropped
from the top is melted and carried away from the cavity through an
opening located on the sidewall near the bottom floor. However,
the effect of this opening on the overall convection field has
been found to be small (2). Therefore the cavity is assumed to be
completely closed for this problem.
The boundary conditions for-the. base case are displayed in Figure
2. It is assumed that the top boundary is subject to a heat sink
( 0.< x < 0.7 ) and a heat source ( 0.7 < x < 0.8). For the
bottom boundary, a constant temperature boundary condition is
used. The wall to the left is a symmetric adiabatic plane. The
wall to the right is assumed to lose heat by a constant amount of
heat flux.
Figure 3 compares the calculated results with experimental data.
The experimental data were obtained from the DWPF Scale Glass
Melter in SRS, and are presented here to show the general shape of
the vertical temperature distribution. The experimental data show
fuller parabolic profile with steeper temperature gradients in the
upper and lower region. Largest uncertainties in the measured
data take place at the top boundary as anticipated.
Shown in figure 4 are the velocity vectors and isotherms for the
base case. The most dominant convection currents take place at
the mid-height location between the upper and lower electrodes.
The maximum nondimensional velocity is 0.015 which is equivalent
to 0.93 mm/sec. These convection currents are basically
Rayleigh-Bernard type, and produced primarily by unstably
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Choi, Inn Gui. Analysis of natural convection in a waste glass melter, article, January 1, 1989; Aiken, South Carolina. (https://digital.library.unt.edu/ark:/67531/metadc1087720/m1/5/: accessed July 16, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.