Secondary and oscillatory gravitational instabilities in canonical three-dimensional models of crystal growth from the melt. Part 2: lateral heating and the Hadley circulation

Marcello Lappa

doi:10.1016/j.crme.2007.05.004

Secondary and oscillatory gravitational instabilities in canonical three-dimensional models of crystal growth from the melt. Part 2: lateral heating and the Hadley circulation
[Instabilités secondaires et oscillatoires dans des modèles 3D canoniques pour la croissance cristalline. 2ème partie : des configurations latéralement chauffées et la circulation de Hadley]

Marcello Lappa ^1,²

¹ MARS (Microgravity Advanced Research and Support) Center, Via Gianturco 31, 80146 Napoli, Italy
² Via Salvator Rosa 53, 80046 San Giorgio a Cremano (Na), Italy

Comptes Rendus. Mécanique, Melting and solidification: processes and models, Volume 335 (2007) no. 5-6, pp. 261-268.

Résumé
Abstract

La première partie 1 (C. R. Mecanique, ce numéro) de cette discussion restreinte aux systèmes de chauffage est ici étendue aux cas des configurations chauffées latéralement et au problème de la stabilité de l'écoulement de Hadley.

The focused discussion limited in Part 1 (C. R. Mecanique, this issue) to systems heated from below is now extended to the case of laterally heated configurations and the related problem of the Hadley flow stability.

Publié le : 2007-05-01

DOI : 10.1016/j.crme.2007.05.004

Keywords: Computational fluid dynamic, Thermal convection, Transitions
Mots-clés : Mécanique des fluides numérique, Transitions, Convection thermique

Affiliations des auteurs :

Marcello Lappa ^{1, 2}

¹ MARS (Microgravity Advanced Research and Support) Center, Via Gianturco 31, 80146 Napoli, Italy
² Via Salvator Rosa 53, 80046 San Giorgio a Cremano (Na), Italy

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Marcello Lappa. Secondary and oscillatory gravitational instabilities in canonical three-dimensional models of crystal growth from the melt. Part 2: lateral heating and the Hadley circulation. Comptes Rendus. Mécanique, Melting and solidification: processes and models, Volume 335 (2007) no. 5-6, pp. 261-268. doi : 10.1016/j.crme.2007.05.004. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2007.05.004/

Bibliographie
Cité par

[1] M. Lappa Thermal convection and related instabilities in models of crystal growth from the melt on earth and in microgravity: Past history and current status, Cryst. Res. Technol., Volume 40 (2005) no. 6, pp. 531-549

[2] M. Lappa On the nature and structure of possible three-dimensional steady flows in closed and open parallelepipedic and cubical containers under different heating conditions and driving forces, Fluid Dynam. Mater. Process., Volume 1 (2005) no. 1, pp. 1-19

[3] E. Semma; M. El Ganaoui; A. Cheddadi; P. Bontoux Etude numérique des instabilités de la phase fluide et de l'interface de solidification en croissance dirigée horizontale, C. R. Acad. Sci. Paris, Volume 331 (2003), pp. 631-639

[4] G.Z. Gershuni; P. Laure; V.M. Myznikov; B. Roux; E.M. Zhukhovitsky On the stability of plane-parallel advective flows in long horizontal layers, Microgravity Q., Volume 2 (1992) no. 3, pp. 141-151

[5] H.P. Kuo; S.A. Korpela Stability and finite amplitude natural convection in a shallow cavity with insulated top and bottom and heated from the side, Phys. Fluids, Volume 31 (1988), pp. 33-42

[6] J.E. Hart Stability of thin non-rotating Hadley circulations, J. Atmos. Sci., Volume 29 (1972), pp. 687-697

[7] J.E. Hart A note on the stability of low-Prandtl-number Hadley circulations, J. Fluid Mech., Volume 132 (1983), pp. 271-281

[8] A.E. Gill A theory of thermal oscillations in liquid metals, J. Fluid Mech., Volume 64 (1974) no. 3, pp. 577-588

[9] P. Laure Study of convective motion in a rectangular cavity with horizontal temperature gradient, J. Méc. Théor. Appl., Volume 6 (1987), pp. 351-382

[10] B. Roux; H. Ben Hadid; P. Laure Hydrodynamical regimes in metallic melts subject to a horizontal temperature gradient, Eur. J. Mech. B/Fluids, Volume 8 (1989), pp. 375-396

[11] A.Yu. Gelfgat; P.Z. Bar-Yoseph; A.L. Yarin Stability of multiple steady states of convection in laterally heated cavities, J. Fluid Mech., Volume 388 (1999), pp. 315-334

[12] A.Yu. Gelfgat; P.Z. Bar-Yoseph; A.L. Yarin Non-symmetric convective flows in laterally heated rectangular cavities, Int. J. Comput. Fluid Dynam., Volume 11 (1999), pp. 261-273

[13] R. Delgado-Buscalioni Convection patterns in end-heated inclined enclosures, Phys. Rev. E, Volume 64 (2001), p. 016303 (17 pp)

[14] J.C. Patterson; J. Imberger Unsteady natural convection in a rectangular cavity, J. Fluid Mech., Volume 100 (1980), pp. 65-86

[15] J.C. Patterson; S.W. Armfield Transient features of natural convection in a cavity, J. Fluid Mech., Volume 219 (1990), pp. 469-497

[16] S.G. Schladow Oscillatory motion in a side-heated cavity, J. Fluid Mech., Volume 213 (1990), pp. 589-610

[17] J.C. Patterson; J. Imberger Unsteady natural convection in a rectangular cavity, J. Fluid Mech., Volume 100 (1980), pp. 65-86

[18] J.C. Patterson; S.W. Armfield Transient features of natural convection in a cavity, J. Fluid Mech., Volume 219 (1990), pp. 469-497

[19] G.K. Batchelor Heat transfer by free convection across a closed cavity between vertical boundaries at different temperatures, Quart. Appl. Math., Volume 12 (1954), pp. 209-233

[20] R.V. Birikh On small perturbations of a plane parallel flow with cubic velocity profile, J. Appl. Math. Mech., Volume 30 (1966), pp. 432-438

[21] R.V. Birikh; G.Z. Gershuni; E.M. Zhukhovitskii; R.N. Rudakov On oscillatory instability of plane-parallel convective motion in a vertical channel, J. Appl. Math. Mech., Volume 36 (1972), pp. 707-710

[22] S.A. Korpela; D. Gözüm; C.B. Baxi On the stability of the conduction regime of natural convection in a vertical slot, Int. J. Heat Mass Transfer, Volume 16 (1973) no. 9, pp. 1683-1690

[23] G.Z. Gershuni; E.M. Zhukhovitskii; E.L. Tarunin Secondary convective steady motions in a plane vertical fluid layer, Mekh. Zhid. Gaza, Volume 5 (1968), pp. 130-136

[24] K. Fujimura; J. Mizushima Nonlinear equilibrium solutions for traveling waves in free convection between vertical parallel plates, Eur. J. Mech. B Fluids, Volume 10 (1991) no. Suppl. 2, pp. 25-30

[25] G.D. McBain; S.W. Armfield Natural convection in a vertical slot: accurate solution of the linear stability equations, ANZIAM J., Volume 45 (2004), p. C92-C105 (E)

[26] R.M. Clever; F.H. Busse Tertiary and quarternary solutions for convection in a vertical fluid layer heated from the side, Chaos Solitons Fractals, Volume 5 (1995), pp. 1795-1803

[27] A.Yu. Gelfgat Stability and slightly supercritical oscillatory regimes of natural convection in a 8:1 cavity: solution of the benchmark problem by a global Galerkin method, Int. J. Numer. Meth. Fluids, Volume 44 (2004), pp. 135-146

[28] D.A. Bratsun; A.V. Zyuzgin; G.F. Putin Non-linear dynamics and pattern formation in a vertical fluid layer heated from the side, Int. J. Heat Fluid Flow, Volume 24 (2003) no. 6, pp. 835-852

[29] R. Delgado-Buscalioni; E. Crespo del Arco; P. Bontoux; J. Ouazzani Convection and instabilities in differentially heated inclined shallow rectangular boxes, C. R. Acad. Sci. IIB, Volume 36 (1998), pp. 711-718

[30] R. Delgado-Buscalioni; E. Crespo del Arco Stability of thermally driven shear flows in long inclined cavities with end-to-end temperature gradient, Int. J. Heat Mass Transfer, Volume 42 (1999), pp. 2811-2822

[31] D.E. Melnikov; V.M. Shevtsova Liquid particles tracing in three-dimensional buoyancy-driven flows, Fluid Dynam. Mater. Process., Volume 1 (2005) no. 2, pp. 189-199

[32] M. Afrid; A. Zebib Oscillatory three dimensional convection in rectangular cavities and enclosures, Phys. Fluids, Volume 2 (1990) no. 8, pp. 1318-1327

[33] J.M. Pratte; J.E. Hart Endwall driven, low Prandtl number convection in a shallow rectangular cavity, J. Cryst. Growth, Volume 102 (1990), pp. 54-68

[34] M.C. Hung; C.D. Andereck Transitions in convection driven by a horizontal temperature gradient, Phys. Lett. A, Volume 132 (1988), pp. 253-258

[35] R. Delgado-Buscalioni; E. Crespo del Arco; P. Bontoux Flow transitions of a low-Prandtl-number fluid in an inclined 3D cavity, Eur. J. Mech. B Fluids, Volume 329 (2001), pp. 1-17

[36] M.G. Braunsfurth; T. Mullin An experimental study of oscillatory convection in liquid gallium, J. Fluid Mech., Volume 327 (1996), pp. 199-219

[37] J.P. Pulicani; E. Crespo del Arco; A. Randriampianina; P. Bontoux; R. Peyret Spectral simulations of oscillatory convection at low Prandtl number, Int. J. Numer. Meth. Fluids, Volume 10 (1990), pp. 481-517

[38] P. Bontoux; B. Roux; G.H. Schiroky; B.L. Markham; F. Rosenberger Convection in the vertical midplane of a horizontal cylinder. Comparison of two-dimensional approximations with three-dimensional results, Int. J. Heat Mass Transfer, Volume 29 (1986) no. 2, pp. 227-240

[39] S. Xin; P. Le Quéré; O. Daube Natural convection in a differentially heated horizontal cylinder: Effects of Prandtl number on flow structure and instability, Phys. Fluids, Volume 9 (1997) no. 4, pp. 1014-1033

[40] J. Baumgartl; W. Budweiser; G. Muller; G. Neumann Studies of buoyancy driven convection in a vertical cylinder with parabolic temperature profile, J. Cryst. Growth, Volume 97 (1989), pp. 9-17

[41] A.Yu. Gelfgat; P.Z. Bar-Yoseph; A. Solan Axisymmetry breaking instabilities of natural convection in a vertical Bridgman growth configuration, J. Cryst. Growth, Volume 220 (2000), pp. 316-325

[42] R. Selver; Y. Kamotani; S. Ostrach Natural convection of a liquid metal in vertical cylinders heated locally from the side, J. Heat Transfer, Volume 120 (1998), pp. 108-114

[43] D.J. Ma; D. Henry; H. Ben Hadid Three-dimensional numerical study of natural convection in vertical cylinders partially heated from the side, Phys. Fluids, Volume 17 (2005) no. 12, p. 124101 (12 pp)

[44] G. Amberg; J. Shiomi Thermocapillary flow and phase change in some widespread materials processes, Fluid Dynam. Mater. Process., Volume 1 (2005), pp. 81-95

[45] M. Lappa Review: Possible strategies for the control and stabilization of Marangoni flow in laterally heated floating zones, Fluid Dynam. Mater. Process., Volume 1 (2005) no. 2, pp. 171-188

[46] A.Yu. Gelfgat; A. Rubinov; P.Z. Bar-Yoseph; A. Solan On the three-dimensional instability of thermocapillary convection in arbitrarily heated floating zones in microgravity environment, Fluid Dynam. Mater. Process., Volume 1 (2005) no. 1, pp. 21-32

[47] C.W. Lan; B.C. Yeh Effects of rotation on heat flow, segregation, and zone shape in a small-scale floating-zone silicon growth under axial and transversal magnetic fields, Fluid Dynam. Mater. Process., Volume 1 (2005) no. 1, pp. 33-44

[48] T. Tsukada; M. Kobayashi; C.J. Jing; N. Imaishi Numerical simulation of CZ crystal growth of oxide, Fluid Dynam. Mater. Process., Volume 1 (2005) no. 1, pp. 45-62

[49] Y.R. Li; L. Peng; W.Y. Shi; N. Imaishi Convective instability in annular pools, Fluid Dynam. Mater. Process., Volume 2 (2006) no. 3, pp. 153-166

[50] K. Matsunaga; H. Kawamura Influence of thermocapillary convection on solid–liquid interface, Fluid Dynam. Mater. Process., Volume 2 (2006) no. 1, pp. 59-64

[51] M. El-Gamma; J.M. Floryan Thermocapillary effects in systems with variable liquid mass exposed to concentrated heating, Fluid Dynam. Mater. Process., Volume 2 (2006) no. 1, pp. 17-26

[52] K. Achour; S. Kaddeche; A. Gharbi; H. Ben Hadid; D. Henry On the stability of the Hadley flow under the action of an acoustic wave, Fluid Dynam. Mater. Process., Volume 1 (2006) no. 4, pp. 277-284

[53] Y. Yan; V. Shevtsova; M.Z. Saghir Numerical study of low frequency g-jitter effect on thermal diffusion, Fluid Dynam. Mater. Process., Volume 1 (2005) no. 4, pp. 315-328

[54] V.G. Kozlov; N.V. Selin Pendulum thermal vibrational convection in a liquid layer with internal heat generation, Fluid Dynam. Mater. Process., Volume 2 (2006) no. 2, pp. 107-118

[55] E.A. Semma; M. El Ganaoui; V. Timchenko; E. Leonardi Some thermal modulation effects on directional solidification, Fluid Dynam. Mater. Process., Volume 2 (2006) no. 3, pp. 191-202

[56] Y. Okano; A. Ishii; H. Miyashita; H. Minakuchi; S. Dost A numerical study of controlling the g-jitter induced convection in the solution of a crystal growth crucible under microgravity, Fluid Dynam. Mater. Process., Volume 2 (2006) no. 4, pp. 261-270

[57] N. Ma; J.S. Walker Electromagnetic stirring in crystal growth processes, Fluid Dynam. Mater. Process., Volume 2 (2006) no. 2, pp. 119-126

[58] K. Kakimoto; L. Liu Flow instability of silicon melt in magnetic fields, Fluid Dynam. Mater. Process., Volume 2 (2006) no. 3, pp. 167-174

[59] M. Sohail; M.Z. Saghir Three-dimensional modeling of the effects of misalignment on the growth of Ge1-xSix by the traveling solvent method, Fluid Dynam. Mater. Process., Volume 2 (2006) no. 2, pp. 127-140

[60] T.J. Jaber; M.Z. Saghir The effect of rotating magnetic fields on the growth of SiGe using the traveling solvent method, Fluid Dynam. Mater. Process., Volume 2 (2006) no. 3, pp. 175-190

[61] M. Mosaad; A. Ben-Nakhi; M.H. Al-Hajeri Thermal communication between two vertical systems of free and forced convection via heat conduction across a separating wall, Fluid Dynam. Mater. Process., Volume 1 (2005) no. 4, pp. 301-314

[62] N.I. Wakayama; D.C. Yin; J.W. Qi How does buoyancy-driven convection affect biological macromolecular crystallization? An analysis of microgravity and hypergravity effects by means of magnetic field gradients, Fluid Dynam. Mater. Process., Volume 1 (2005) no. 2, pp. 153-170

[63] C. Giessler; C. Sievert; U. Krieger; B. Halbedel; D. Huelsenberg; U. Luedke; A. Thess A model for electromagnetic control of buoyancy driven convection in glass melts, Fluid Dynam. Mater. Process., Volume 1 (2005) no. 3, pp. 247-266

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