Abstract




 
   

IJE TRANSACTIONS A: Basics Vol. 29, No. 4 (April 2016) 563-571   

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  EFFECT OF MAGNETIC FIELD ON THE ROTATING FLOW IN A SIMILAR CZOCHRALSKI CONFIGURATION
 
S. Bouabdallah, A. Atia and A. H. Boughzala
 
( Received: November 02, 2015 – Accepted in Revised Form: April 14, 2016 )
 
 

Abstract    We present a numerical study of the rotating flow generated by two rotating disks in co-/counter-rotating, inside a fixed cylindrical enclosure similar to the Czochralski configuration (Cz). The enclosure having an aspect ratio A = H/Rc equal to 2, filled with a low Prandtl number fluid (Pr = 0.011), which is submitted to a vertical temperature gradient. The finite volume method has been used to solve numerically the governing equations of the studied phenomenon.We present the steady state flow; and make a comparison between the flow generated by the co-/counter-rotating end disks. This study was caried out for different Richardson numbers; Ri = 0.01, 0.1, 0.5, 1, 2, 3, 5 and 10. The effect of orientation of the magnetic field is also taken into account for different values of the Hartmann number (Ha = 0, 5, 10, 20, 30 and 50). The obtained results show that the strongest stabilisation of the velocity field and heat transfer occurs when the flow generated byco-rotating end disks and the applied of magnetic field in radial direction provied a more stabilisation of the convective flow.

 

Keywords    Rotating flow, Czochralski, co-/counter-rotating mixed convection, magnetic field

 

چکیده    ما در حال حاضر، مطالعه عددی جریان چرخشی تولید شده را توسط دو دیسک چرخشی در چرخش همسو/ ناهمسو، در داخل محوطه یک استوانه ثابت مشابه پیکربندی Czochralski (Cz) نشان می دهیم. محوطه دارای نسبت A = H / RC برابر با 2، پر شده با سیالی با عدد پرانتل کوچک (01/0 (Pr = می باشد که به گرادیان دما عمودی نسبت داده می شود. روش حجم محدود برای حل عددی معادلات حاکم پدیده تحت مطالعه استفاده شده است. ما جریان حالت پایدار را ارائه می دهیم؛ و مقایسه ای بین جریان تولید شده توسط دیسک های انتهایی با چرخش همسو/ناهمسو نشان می دهیم. این مطالعه برای عددهای مختلف ریچاردسون Ri برابر با 01/0، 1/0، 5/0، 1، 2، 3، 5 و 10 انجام شد. اثر جهت میدان مغناطیسی نیز برای مقادیر مختلف عدد هارتمن Ha برابر با 0، 5، 10، 20، 30 و 50 به حساب می آید. نتایج به دست آمده نشان می دهد که قوی ترین تثبیت میدان سرعت و انتقال حرارت هنگامی رخ میدهد که جریان، دیسک های انتهایی چرخشbyco تولید می کند و اعمال میدان مغناطیسی در جهت شعاعی، ثبات بیشتری از جریان همرفتی را ایجاد می کند.

References   

1.     Tsitverblit, N. and Kit, E., "Numerical study of axisymmetric vortex breakdown in an annulus", Acta Mechanica,  Vol. 118, No. 1-4, (1996), 79-95.

2.     Kharicha, A., Alemany, A. and Bornas, D., "Influence of the magnetic field and the conductance ratio on the mass transfer rotating lid driven flow", International Journal of Heat and Mass Transfer,  Vol. 47, No. 8, (2004), 1997-2014.

3.     Granger, R., "Introduction to vortex dynamics", V. Karman Institute Lecture Series,  Vol. 8, (1986), 158-167.

4.     Vogel, H.U., "Experimentelle ergebnisse über die laminare strömung in einem zylindrischen gehäuse mit darin rotierender scheibe", MPIStrömungsforschung,  (1968), 342-350.

5.     Escudier, M., "Observations of the flow produced in a cylindrical container by a rotating endwall", Experiments in fluids,  Vol. 2, No. 4, (1984), 189-196.

6.     Spohn, A., Mory, M. and Hopfinger, E., "Experiments on vortex breakdown in a confined flow generated by a rotating disc", Journal of Fluid Mechanics,  Vol. 370, (1998), 73-99.

7.     Sotiropoulos, F., Webster, D.R. and Lackey, T.C., "Experiments on lagrangian transport in steady vortex-breakdown bubbles in a confined swirling flow", Journal of Fluid Mechanics,  Vol. 466, (2002), 215-248.

8.     Lopez, J., "Axisymmetric vortex breakdown part 1. Confined swirling flow", Journal of Fluid Mechanics,  Vol. 221, (1990), 533-552.

9.     Brown, G. and Lopez, J., "Axisymmetric vortex breakdown part 2. Physical mechanisms", Journal of Fluid Mechanics,  Vol. 221, (1990), 553-576.

10.   Baradaran Rahimi, A. and Yousefi, E., "Transient natural convection flow on an isothermal vertical wall at high prandtl numbers: Second-order approximation", International Journal of Engineering,  Vol. 14, No. 4, (2001), 367-376.

11.   Sheikhzadeh, G., Babaei, M., Rahmany, V. and Mehrabian, M., "The effects of an imposed magnetic field on natural convection in a tilted cavity with partially active vertical walls: Numerical approach", International Journal of Engineering-Transactions A: Basics,  Vol. 23, No. 1, (2009), 65-78.

12.   Rahmannezhad, J., Ramezani, A. and Kalteh, M., "Numerical investigation of magnetic field effects on mixed convection flow in a nanofluid-filled lid-driven cavity", International Journal of Engineering Trans. A: Basics,  Vol. 26, (2013), 1213-1224.

13.   Davidson, P., "Magnetohydrodynamics in materials processing", Annual Review of Fluid Mechanics,  Vol. 31, No. 1, (1999), 273-300.

14.   Tian, X.-Y., Zou, F., Li, B.-W. and He, J.-C., "Numerical analysis of coupled fluid flow, heat transfer and macroscopic solidification in the thin slab funnel shape mold with a new type embr", Metallurgical and Materials Transactions B,  Vol. 41, No. 1, (2010), 112-120.

15.   Cramer, A., Pal, J. and Gerbeth, G., "Experimental investigation of a flow driven by a combination of a rotating and a traveling magnetic field", Physics of Fluids (1994-present),  Vol. 19, No. 11, (2007), 109-118.

16.   Koal, K., Stiller, J. and Grundmann, R., "Linear and nonlinear instability in a cylindrical enclosure caused by a rotating magnetic field", Physics of Fluids (1994-present),  Vol. 19, No. 8, (2007), 88-107.

17.   Moreau, R.J., "Magnetohydrodynamics, Springer Science & Business Media,  Vol. 3,  (2013).

18.   Davidson, P., Kinnear, D., Lingwood, R., Short, D. and He, X., "The role of ekman pumping and the dominance of swirl in confined flows driven by lorentz forces", European Journal of Mechanics-B/Fluids,  Vol. 18, No. 4, (1999), 693-711.

19.   Ben Hadid, H., Henry, D. and Touihri, R., "Unsteady 3d buoyancy-driven convection in a circular cylindrical cavity and its damping by magnetic field", Journal of Crystal Growth,  Vol. 180, No. 3-4, (1997), 433-441.

20.   Talmage, G., Shyu, S.-H., Walker, J. and Lopez, J., "Inertial effects in the rotationally driven melt motion during the czochralski growth of silicon crystals with a strong axial magnetic field", Zeitschrift Fur Angewandte Mathematik Und Physik ZAMP,  Vol. 51, No. 2, (2000), 267-289.

21.   Bouabdallah, S. and Bessaih, R., "Magnetohydrodynamics stability of natural convection during phase change of molten gallium in a three-dimensional enclosure", Fluid Dynamics & Materials Processing,  Vol. 6, No. 3, (2010), 251-276.

22.   Mahfoud, B. and Bessaïh, R., "Stability of swirling flows with heat transfer in a cylindrical enclosure with co/counter-rotating end disks under an axial magnetic field", Numerical Heat Transfer, Part A: Applications,  Vol. 61, No. 6, (2012), 463-482.

23.   Bessaih, R., Marty, P. and Kadja, M., "Hydrodynamics and heat transfer in disk driven rotating flow under axial magnetic field", International Journal of Transport Phenomena,  Vol. 5, No., (2003), 259-278.

24.   Davidson, P. and Pothérat, A., "A note on bödewadt–hartmann layers", European Journal of Mechanics-B/Fluids,  Vol. 21, No. 5, (2002), 545-559.

25.   Mahfoud, B. and Bessaih, R., "Oscillatory swirling flows in a cylindrical enclosure with co-/counter-rotating end disks submitted to a vertical temperature gradient", Fluid Dynamics & Materials Processing,  Vol. 8, No. 1, (2012), 1-26.

26.   Ziapour, B.M. and Rahimi, F., "Numerical study of natural convection heat transfer in a horizontal wavy absorber solar collector based on the second law analysis", International Journal of Engineering,  Vol. 29, No. 1, (2016), 109-117.

27.   Patankar, S., "Numerical heat transfer and fluid flow, CRC press,  (1980).

28.   Atia, A., Bouabdallah, S., Teggar, M. and Benchatti, A., "Numerical study of mixed convection in cylindrical czochralski configuration for crystal growth of silicon", International Journal of Heat and Technology,  Vol. 33, No. 1, (2015), 39-46.

29.   Wang, B.-F., Ma, D.-J., Guo, Z.-W. and Sun, D.-J., "Linear instability analysis of rayleigh–bénard convection in a cylinder with traveling magnetic field", Journal of Crystal Growth,  Vol. 400, (2014), 49-53.

30.   Kakarantzas, S., Sarris, I., Grecos, A. and Vlachos, N., "Magnetohydrodynamic natural convection in a vertical cylindrical cavity with sinusoidal upper wall temperature", International Journal of Heat and Mass Transfer,  Vol. 52, No. 1, (2009), 250-259.

31.   Karcher, C., Kolesnikov, Y., Andreev, O. and Thess, A., "Natural convection in a liquid metal heated from above and influenced by a magnetic field", European Journal of Mechanics-B/Fluids,  Vol. 21, No. 1, (2002), 75-90.

32.   Omi, Y. and Iwatsu, R., "Numerical study of swirling flows in a cylindrical container with co-/counter-rotating end disks under stable temperature difference", International Journal of Heat and Mass Transfer,  Vol. 48, No. 23, (2005), 4854-4866.

33.   Bouabdallah, S. and Bessaїh, R., "Effect of magnetic field on 3d flow and heat transfer during solidification from a melt", International Journal of Heat and Fluid Flow,  Vol. 37, (2012), 154-166.





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