Numerical linear stability analysis of a thermocapillary-driven liquid bridge with magnetic stabilization

Abstract

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 ∈ (10 −12 , 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.

Thermocapillary instabilities in a laterally heated liquid bridge with end wall rotation

“…17 Similar regularization procedures have often been used and are widely discussed. 7,17,[32][33][34][35] A. Base flow…”