Shouichi Yasuhiro

Numerical simulation of oscillatory Marangoni flow in half-zone liquid bridge of low Prandtl number fluid

Abstract A set of numerical simulations was conducted using a finite difference method to understand the general feature of oscillatory Marangoni convection in half-zone liquid bridges of low Prandtl number fluids (Pr=0, 0.01, 0.02) with a cylindrical liquid surface over a wide aspect ratio range (As=0.6 to 2.2). The simulation results indicated that under smaller temperature differences the flow in the liquid bridge was axisymmetric but it became unstable against three-dimensional (3-D) disturbances beyond a certain threshold value of temperature difference, i.e., the flow became steady 3-D flow at and beyond the first critical Reynolds number Rec1. This steady 3-D flow became unstable against time-dependent 3-D disturbances beyond a second critical condition, Rec2. The numerical simulations revealed the critical conditions and flow structures in detail for Pr=0 fluid and rough sketches for fluids of Pr=0.01 and 0.02. The present results of Rec1 and Rec2 showed good agreements with those of linear stability analyses and with available numerical results. A stability map for low Pr fluids (Pr=0, 0.01 and 0.02) was proposed.

Three-dimensional numerical simulation of rotating spoke pattern in an oxide melt under a magnetic field

Abstract On the surface of various oxide melts under a vertical magnetic field, the rotating spoke pattern appears. In order to provide a first basic view of this phenomenon, a series of three-dimensional numerical simulations of LiNbO3 melt flow in a crucible (47 mmφ × 46 mmH) under a uniform vertical magnetic field were performed. In this model, the oxide melt was assumed to be a dielectric fluid with a uniform electric charge density ce0. The Marangoni effect was also taken into account. The simulations indicated that the spoke pattern is caused by the Marangoni instability and the rotating motion is driven by the Lorentz force caused by the interaction between the vertical magnetic field and the radial motion of charged fluid which is driven by the Rayleigh–Marangoni convection in the crucible. A charge density of 0.1 C/m3 is sufficient to express the experimentally observed rotating spoke patterns on the LiNbO3 melt which were reported by Miyazawa et al. (1996).

Numerical simulation of three-dimensional oscillatory thermocapillary flow in a half zone of Pr=1 fluid

Abstract Three-dimensional (3-D) numerical simulations of oscillatory Marangoni convection were conducted for half-zone liquid bridges of Pr=1.02 fluid with different aspect ratios (0.75–1.60) and over a wide range of Marangoni number. The multi-morphological feature of the 3-D oscillatory flow was reproduced by the simulations: i.e., pulsating and rotating oscillatory flow with azimuthal wave number m =1–4. Growth rate constants β of 3-D disturbances were determined as functions of the Marangoni number. The critical Marangoni number Ma c was determined by extrapolating β to zero. Thus determined critical Marangoni numbers show good agreement with those of linear stability analyses. A rough estimation predicts a correlation Ma a / Ma c ∝ a 2 for large liquid bridges, where a is the liquid bridge radius and Ma a is some ‘apparent critical Marangoni number’ at which the 3-D oscillatory flow can be detected experimentally within a constant observation time t o . The equation also predicts an extremely long observation time for experimental determination of the true critical Marangoni number.

Three-dimensional numerical simulation of oscillatory Marangoni flow in half-zone of low-Pr fluids

3D unsteady numerical simulations were conducted, by means of the finite difference method, to understand the characteristics of stationary and oscillatory 3D Marangoni flows in half-zone liquid bridges of low Prandtl number fluids (Pr=0.01 and 0.02) with different aspect ratios (As=1.0, 1.2 and 1.8). The results clearly explain the transition processes; first from an axisymmetric to a 3D steady flow and the second from a 3D steady to 3D oscillatory flow. Critical Marangoni numbers for each transition as well as the frequency were determined for various conditions. These results were compared with available results of both linear stability analysis and non- linear numerical simulations. The present results agreed well with previously reported values within 6%. In a short liquid bridge, the 3D flows indicate two-fold symmetry in azimuthal direction (m=2). In a longer liquid bridge, however, there appeared a 3D flow with m=1. These basic flows become unstable against time dependent disturbances at Mac2.