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Comparison of the 4th Order Stream Function and 2nd Order Vorticity Transport Representations for Modeling Float-Zone Crystal Growth With a Constant Magnetic Field

[+] Author Affiliations
Yue Huang, Brent C. Houchens

Rice University, Houston, TX

Paper No. IMECE2008-66716, pp. 425-434; 10 pages
doi:10.1115/IMECE2008-66716
From:
  • ASME 2008 International Mechanical Engineering Congress and Exposition
  • Volume 10: Heat Transfer, Fluid Flows, and Thermal Systems, Parts A, B, and C
  • Boston, Massachusetts, USA, October 31–November 6, 2008
  • Conference Sponsors: ASME
  • ISBN: 978-0-7918-4871-5 | eISBN: 978-0-7918-3840-2
  • Copyright © 2008 by ASME

abstract

During optically heated float-zone crystal growth processing, a cylindrical melting zone forms from a polycrystalline rod by lateral heating, then re-solidifies into single crystal rod. Thermocapillary forces drive a flow in the melt region. This base flow is susceptible to instabilities, which lead to nonuniformities and defects in the crystal. In order to minimize these imperfections, a magnetic field is employed to damp the base flow within the melt region. Modeling this base flow has proven challenging, and two representations are discussed here. The float-zone crystal growth base flow under the influence of a constant magnetic field and neglecting buoyancy is investigated with a full-zone model. The flow field and temperature distributions are calculated by a steady state, axisymmetric spectral collocation method using Chebyshev polynomials as basis functions. A 2nd order vorticity transport representation is compared with a 4th order stream function formulation. The results show high consistency between the models.

Copyright © 2008 by ASME

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