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Research Papers

Modeling and Simulation of the Cooling Process of Borosilicate Glass

[+] Author and Article Information
Nicolas Barth, Daniel George, Yves Rémond

 Institut de Mécanique des Fluides et des Solides, Université de Strasbourg, CNRS, 2 rue, Boussingault, 67000 Strasbourg, France

Saïd Ahzi1

 Institut de Mécanique des Fluides et des Solides, Université de Strasbourg, CNRS, 2 rue, Boussingault, 67000 Strasbourg, Franceahzi@unistra.fr

Véronique Doquet

Laboratoire de Mécanique des Solides, UMR CNRS 7649, Ecole Polytechnique, 91128, Palaiseau Cedex, France

Frédéric Bouyer

CEA Centre de Marcoule DTCD/SECM, 30207 Bagnols-Sur-Cèze Cedex, France

Sophie Bétremieux

AREVA, Direction Innovation Recherche et Projets, 1 place Jean Millier, 92084 Paris-La Défense 6, France

1

Corresponding author.

J. Eng. Mater. Technol 134(4), 041001 (Jun 29, 2012) (10 pages) doi:10.1115/1.4006132 History: Received June 30, 2011; Revised February 02, 2012; Published June 27, 2012; Online June 29, 2012

For a better understanding of the thermomechanical behavior of glasses used for nuclear waste vitrification, the cooling process of a bulk borosilicate glass is modeled using the finite element code Abaqus. During this process, the thermal gradients may have an impact on the solidification process. To evaluate this impact, the simulation was based on thermal experimental data from an inactive nuclear waste package. The thermal calculations were made within a parametric window using different boundary conditions to evaluate the variations of temperature distributions for each case. The temperature differences throughout the thickness of solidified glass were found to be significantly non-uniform throughout the package. The temperature evolution in the bulk glass was highly responsive to the external cooling rates applied; thus emphasizing the role of the thermal inertia for this bulky glass cast.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 1

External temperatures during the filling and cooling of inert glass in the experimental two casting process (positions are near the bottom and the top of the nominal cast, outside on the container). The “heterogeneous” temperature simulations begin from point S onwards – the heterogeneity in the glass being induced mainly by this particular process in two castings.

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Figure 2

Geometry approximations made for the finite element design of the canister, rendered as a half-cylinder, and symmetry considered in the model (which could have been reduced to an axisymmetry). The arrow points to the cylinder center whose height delimits the two glass castings. The gray shades are the 16 layers of stacked plates used to simulate the glass casting process.

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Figure 3

External temperatures applied after the filling process for the different cooling down periods. Ref., quench and linear BC simulations begin at point S in Fig. 1 (here this Fig. is at the end of Fig. 1). The ref. simulation follows closely experimental thermocouple values between point A and point B. (I) all simulations are represented in this particular time window, where different temperatures are prescribed. (II) the internal temperature homogenization moment is given by the filled symbols for the corresponding simulations, which then follow the experimental data. (III) the external temperature alteration simulations (linear or quench BC) follow the linear paths marked by an open symbol (in the case of linear BC: chord A–B; in the case of quench BC: the initially vertical path from point A).

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Figure 4

Series of temperature profiles at reference times (i) to (iv) during solidification for each BC case. The experimental temperatures on the edges are taken for each reference time as the mean value of the experimental curves from the two thermocouples at the same moment on the time axis (see Fig. 3).

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Figure 5

Temperature differences evolution over constant radius positions; the solidification front in the three simulations modeled is progressing from 0 up to its end between 251–349 min

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Figure 6

Maximum radial temperature differences averaged in the solid glass (over the relevant radial distance d) for the reference and homogeneous simulations. The three consecutive first points are respectively at reference times (ii), (iii) and (iv); the continuous lines being used for the totally solidified package only (d = 0.2 m).

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Figure 7

Maximum radial temperature differences averaged in the solid glass (over the relevant radial distance d) for the reference and altered boundary conditions simulations. The three consecutive first points are respectively at reference times (ii), (iii) and (iv); the continuous lines being used for the totally solidified package only.

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