Control of thermo- and solutocapillary flows in fz crystal growth by high-frequency vibrations
DOI:
https://doi.org/10.7242/1999-6691/2016.9.1.10Keywords:
Marangoni flow, high-frequency vibrations, liquid bridge, linear stabilityAbstract
The paper deals with the numerical investigation of the possibilities to control convective flows in the liquid bridge in zero gravity conditions by applying axial vibrations. The surface tension is assumed to be dependent on both the temperature and solute concentration. The free surface deformations and the curvature of phase change surfaces are neglected but pulsating deformation of free surface are accounted for. The first part of the paper concerns axisymmetric steady flows. The calculations show that the evolution of convective flow with the variation of thermal Marangoni number at fixed value of the solutal Marangoni number is accompanied by the hysteresis phenomenon, which is related to the existence of two stable steady regimes in certain parameter range. One of these regimes is thermocapillary dominated, it corresponds to the two-vortex flow, and the other is solutocapillary dominated, it corresponds to the single-vortex flow. Under vibrational influence the range of hysteresis becomes narrower and is shifted to the area of larger Marangoni numbers. The second part of the paper concerns the stability of axisymmetric thermo- and solutocapillary flows and the transition to three-dimensional regimes. Significant mutual influence of flows generated by each of mechanisms on the stability of each other is discovered. Stability maps in the parameter plane thermal Marangoni number - solutal Marangoni number are obtained for different values of vibration parameters. It is shown, that vibrations exert a stabilizing effect due to increasing critical Marangoni numbers for all modes of instability. However, the character of this influence is different for different modes and at high intensity of vibrations destabilization is possible. Consequently, vibrations can modify a scenario of transition to three-dimensional modes.
Downloads
References
Avdonin N.A., Zarikov E.V., Kalis H.E., Storozev N.R. Analiz vtoricnyh tecenij v zidkosti vblizi vibriruusej poverhnosti: Preprint No 90 / IOF AN SSSR. - Moskva,1989. - 17 s.
2. Zharikov E.V., Prihod’ko L.V., Storozhev N.R. Fluid flow formation resulting from forced vibration of a growing crystal // J. Cryst. Growth. - 1990. - Vol. 99, no. 1-4, part 2. - P. 910-914. DOI
3. Dold P., Croll A., Benz K.W. Floating-zone growth of silicon in magnetic fields. I. Weak static axial fields // J. Cryst. Growth. - 1998. - Vol. 183, no. 4. - P. 545-553. DOI
4. Dold P., Croll A., Lichtensteiger M., Kaiser Th., Benz K.W. Floating-zone growth of silicon in magnetic fields. IV. Rotating magnetic fields // J. Cryst. Growth. - 2001. - Vol. 231, no. 1-2. - P. 95-106. DOI
5. Anilkumar A.V., Grugel R.N., Shen X.F., Lee C.P., Wang T.G. Control of thermocapillary convection in a liquid bridge by vibration // J. Appl. Phys. - 1993. - Vol. 73, no. 9. - 41654170. DOI
6. Lyubimov D., Lyubimova T., Roux B. Mechanisms of vibrational control of heat transfer in a liquid bridge // Int. J. Heat Mass Transfer. - 1997. - Vol. 40, no. 17. - P. 4031-4042. DOI
7. Lyubimova T.P., Scuridin R.V., Croll A., Dold P. Influence of high frequency vibrations on fluid flow and heat transfer in a floating zone // Cryst. Res. Technol. - 2003. - Vol. 38, no. 7-8. - P. 635-653. DOI
8. Lubimova T.P., Skuridin R.V., Fajzrahmanova I.S. Vlianie magnitnogo pola na gisterezisnye perehody pri vyrasivanii kristallov metodom plavausej zony // PZTF. - 2007. - T. 33, No 17. - S. 61-68. DOI
9. Lyubimova T.P., Skuridin R.V., Faizrakhmanova I.S. Thermo- and soluto-capillary convection in the floating zone process in zero gravity conditions // J. Cryst. Growth. - 2007. - Vol. 303, no. 1. - P. 274-278. DOI
10. Gershuni G.Z., Lyubimov D.V. Thermal vibrational convection. - New York: John Wiley & Sons, 1998. - 358 p.
11. Longuet-Higgins M.S. Mass transport in water waves // Philos. T. Roy. Soc. A. - 1953. - Vol. 245. - P. 535-581. DOI
12. Lyubimov D.V., Lyubimova T.P., Skuridin R.V., Chen G., Roux B. Numerical investigation of meniscus deformation and flow in an isothermal liquid bridge subject to high-frequency vibrations under zero gravity conditions // Comput. Fluids. - 2002. - Vol. 31, no. 4-7. - P. 663-682. DOI
13. Lyubimov D.V. Thermovibrational flows in non-uniform systems // Microgravity Quarterly. - 1994. - Vol. 4, no. 2. - P. 221-225.
14. Walker J.S., Dold P., Croll A., Volz M.P., Szofran, F.R. Solutocapillary convection in the float-zone process with a strong magnetic field // Int. J. Heat Mass Transfer. - 2002. - Vol. 45, no. 23. - P. 4695-4702. DOI
15. Campbell T.A., Schweizer M., Dold P., Croll A., Benz K.W. Float zone growth and characterization of Ge1-xSix (x ⩽ 10 at%) single crystals // J. Cryst. Growth. - 2001. - Vol. 226, no. 2-3. - P. 231-239. DOI
16. Lyubimov D.V., Lyubimova T.P., Morozov V.A. Software package for numerical investigation of linear stability of multi-dimensional flows // Bulletin of Perm University. Information Systems and Technologies. - 2001. - No. 5. - R. 74-81.
17. Witkowski L.M., Walker J.S. Solutocapillary instabilities in liquid bridges // Phys. Fluids. - 2002. - Vol. 14, no. 8. - P. 2647. DOI
Downloads
Published
Issue
Section
License
Copyright (c) 2016 Computational Continuum Mechanics
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.