Numerical study of the unstable thermocapillary flow in a silicon float zone under mu-g condition

In this work, the problem of the hydrodynamic instabilities of the thermoca pillary flow inside a Silicon (Pr = 0.016) float zone supported by a pair o f coaxial disks and operating under g-g conditions has been investigated. T he system of the conservation equations corresponding to a three-dimensiona l transient model was directly solved by employing a finite control volumes method fully-implicit in time and a staggered spatial mesh in the cylindri cal coordinates system. Results have shown that for a low Marangoni number or a low temperature difference between the disks, the flow remains steady and consists of a perfectly axisymmetrical toroidal structure with the vort ex center located beneath the free surface near the cold disk. Beyond the f irst critical Marangoni number, say Ma(cr)(1) approximate to 48, the transi tion from the axisymmetrical to the steady three-dimensional state has been observed. The flow structure consists of a drastically distorted torus wit h its vortex centers displaced both radially and axially and is located alo ng a 'saddle-like' curve. At the second critical Marangoni number, say Ma(c r)(2) approximate to 80, the transition from this three-dimensional-steady- state to the three-dimensional-oscillatory state occurs. Under the effects of some azimuthally travelling instabilities, the entire velocity and tempe rature fields rotate around the main axis; and a dependent variable varies periodically both in time and space. The flow instabilities, which appear s imilar to,those of the theoretical 'unstable vortex ring', are believed to be of the hydrodynamic origin. A detailed description of the internal flow structure and its dynamic behavior as well as a comparison with the previou s numerical and experimental data have been given. (C) 2001 Editions scient ifiques et medicales Elsevier SAS.