Abstract |
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Accurate representation of heat and mass-transfer in thermoconvective flows is of great importance in several industrial processes. In particular this study is motivated by the need to better understand molten glass circulation in glass melting furnaces.
The geometry of furnaces is rather simple : the free surface of the molten glass is horizontal and the refractory walls are parallelepipedic. However, the flow patterns in this geometry are actually 3D as the width of the tank can be restricted at the neck while the height is modified by a step. For these reasons, the solution in the plane of symmetry can no longer be regarded as representative.
For this class of problems, the convective currents are moderate amplitude, with a typical value of Reynolds number of O(1), while the Peclet number can be of order of 300 (given the low conductivity of molten glass). The numerical difficulty is therefore associated with solving of energy equation rather then that of momentum.
While a detailed, steady-state solution is important, the time evolution of the flow structure is also of great interest. Given the intensity of the thermoconvection - the Grasshof number is approximate to 5000 - no unstationary solution should be expected. However, a sensitivity, study is a variation of the solution under varying operating conditions, e.g. pull rate; thermal boundary conditions..., sheds light on the stability and the relative importance of both thermal and viscous effects.
The numerical tool developed to simulate this physical situation is an unstationnary spectral element Boussinesq solver. Spatial discretization is realized through the division of the Computational domain in a limited (<50) number of spectral elements. On each element, the unknowns are interpolated by a high-order Legendre polynomial. Depending on the value of the Prandtl number of the fluid, a greater number of degrees of freedom can be associated to the thermal problem.
The goal of this presentation is to claim the efficiency of high order methods for the numerical simulation of thermoconvection in the glass melting tank. Comparisons with finite-difference and finite-element solutions demonstrates a lower number of degrees of freedom necessary to obtain specified level of accuracy. A global increase in computing efficiency allows 30 simulations like time evolution of melting rank during change of glass. |