Vol. 6, No. 7-8, 2011

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ISSN: 1559-3959
Numerical linear stability analysis of a thermocapillary-driven liquid bridge with magnetic stabilization

Yue Huang and Brent C. Houchens

Vol. 6 (2011), No. 7-8, 995–1016
Abstract
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A full-zone model of a thermocapillary-driven liquid bridge exposed to a steady, axial magnetic field is investigated using a global spectral collocation method for low-Prandtl number (Pr) fluids. Flow instabilities are identified using normal-mode linear stability analyses. This work presents several numerical issues that commonly arise when using spectral collocation methods and linear stability analyses in the solution of a wide range of partial differential equations. In particular, effects such as discontinuous boundary condition regularization, identification of spurious eigenvalues, and the use of pseudospectra to investigate the robustness of the stability analysis are addressed. Physically, this work provides simulations in the practical range of experimentally utilized magnetic field stabilization in optically heated float-zone crystal growth. A second-order vorticity transport formulation enables modeling of the liquid bridge up to these intermediate magnetic field strength ranges, measured by the Hartmann number (Ha). The thermocapillary driving and magnetic stabilization effects are observed up to Ha = 500 for Pr = 0.001 and up to Ha = 300 for Pr = 0.02. Prandtl number effects on temperature and flow fields are investigated within Pr (1012,0.0667) and indicate that Pr = 0.001 is a good representation of the base state in the Pr 0 limit, at least up to Ha = 300.

Keywords
magnetic stabilization, thermocapillary, liquid bridge, linear stability, regularization, pseudospectra
Milestones
Received: 30 June 2010
Revised: 1 March 2011
Accepted: 10 April 2011
Published: 21 December 2011
Authors
Yue Huang
Department of Mechanical Engineering and Materials Science
Rice University
6100 Main Street
Houston, TX 77005-1827
United States
Brent C. Houchens
Department of Mechanical Engineering and Materials Science
Rice University
6100 Main Street
Houston, TX 77005-1827
United States