Numerical simulation of laminar natural convection in a laterally heated vertical cylindrical enclosure: application to crystal growth |
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Authors: | Subhransu Roy Abhra Roy R C Arora |
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Institution: | (1) Mechanical Engineering Department, Indian Institute of Technology, Kharagpur, 721302, India;(2) CFD Research Corporation, Huntsville, USA |
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Abstract: | Laminar natural convection has been studied in a laterally heated vertical cylindrical enclosure with a free insulated surface
and a centrally located constant temperature wall at the top. These conditions are a simplification of the conditions existing
in a Czochralski crystal pulling system. The laminar, axisymmetric flow of a Newtonian, constant physical properties fluid
under Boussinesq’s approximation has been considered. Governing equations in primitive variable form are solved numerically
by control volume method. SIMPLE algorithm due to Patankar has been used for the numerical simulation. The effects of the
constant wall heat flux boundary condition at the side wall have been investigated whereas the bottom wall is considered to
be insulated. Streamlines and isotherms are presented for various Rayleigh numbers and Prandtl numbers. Heat flux vectors
through the melt are plotted for selected cases. The axial velocity and temperature variations at different horizontal sections
of the crucible have been presented graphically to explain the transport processes inside the crucible. It has been observed
that in case of low Pr and high Ra, flow separation occurs at the vertical wall of the crucible which leads to an oscillatory flow as Ra increases. The investigation has been extended to the oscillatory regime of flow in the zone of supercritical Rayleigh numbers
and some unsteady results are also presented. Finally a heat transfer correlation has been developed for steady-state case. |
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Keywords: | Natural convection Heat transfer Steady flow Cylindrical enclosure Numerical simulation Crystal growth |
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