Comptes Rendus
Identification of the convective instability in a multi-component solution by 3D simulations
Comptes Rendus. Mécanique, Volume 333 (2005) no. 10, pp. 739-745.

Three-dimensional calculations have been done to simulate the onset of convective motion in ternary nondilute solution under phase transition conditions. The process is considered for Rayleigh number in the range [1×103,1.4×104], where subcritical convective motion with hexagonal flow pattern is identified. The results are in good agreement with the linear and finite amplitude theory of hydrodynamics instability.

Le présent papier concerne les résultats numériques des instabilités de convection naturelle dans un système ternaire en changement de phase. Les simulations sont effectuées en configuration tridimensionnelle. Une bifurcation sous critique avec des cellules hexagonales est identifiée dans la gamme des nombres de Rayleigh [1×103,1,4×104]. Les résultats de simulation sont en bon accord avec les prédictions de la théorie de stabilité linéaire et d'amplitude finie.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crme.2005.08.004
Keywords: Computational fluid mechanics, Instability and transitions
Mot clés : Mécanique des fluides numérique, Instabilité et transition

Viatcheslav V. Kolmychkov 1; Olga S. Mazhorova 1; Yurii P. Popov 1; Patrick Bontoux 2; Mohammed El Ganaoui 3

1 Keldysh Institute of Applied Mathematics RAS, 4, Miusskaya pl., Moscow 125047, Russia
2 UMR CNRS 6181, les universités d'Aix–Marseille, 38, rue F. Joliot Curie, 13451 Marseille, France
3 SPCTS UMR CNRS 6638, université de Limoges, 123, avenue Albert-Thomas, 87060 Limoges, France
@article{CRMECA_2005__333_10_739_0,
     author = {Viatcheslav V. Kolmychkov and Olga S. Mazhorova and Yurii P. Popov and Patrick Bontoux and Mohammed El Ganaoui},
     title = {Identification of the convective instability in a multi-component solution by {3D} simulations},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {739--745},
     publisher = {Elsevier},
     volume = {333},
     number = {10},
     year = {2005},
     doi = {10.1016/j.crme.2005.08.004},
     language = {en},
}
TY  - JOUR
AU  - Viatcheslav V. Kolmychkov
AU  - Olga S. Mazhorova
AU  - Yurii P. Popov
AU  - Patrick Bontoux
AU  - Mohammed El Ganaoui
TI  - Identification of the convective instability in a multi-component solution by 3D simulations
JO  - Comptes Rendus. Mécanique
PY  - 2005
SP  - 739
EP  - 745
VL  - 333
IS  - 10
PB  - Elsevier
DO  - 10.1016/j.crme.2005.08.004
LA  - en
ID  - CRMECA_2005__333_10_739_0
ER  - 
%0 Journal Article
%A Viatcheslav V. Kolmychkov
%A Olga S. Mazhorova
%A Yurii P. Popov
%A Patrick Bontoux
%A Mohammed El Ganaoui
%T Identification of the convective instability in a multi-component solution by 3D simulations
%J Comptes Rendus. Mécanique
%D 2005
%P 739-745
%V 333
%N 10
%I Elsevier
%R 10.1016/j.crme.2005.08.004
%G en
%F CRMECA_2005__333_10_739_0
Viatcheslav V. Kolmychkov; Olga S. Mazhorova; Yurii P. Popov; Patrick Bontoux; Mohammed El Ganaoui. Identification of the convective instability in a multi-component solution by 3D simulations. Comptes Rendus. Mécanique, Volume 333 (2005) no. 10, pp. 739-745. doi : 10.1016/j.crme.2005.08.004. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2005.08.004/

[1] I.A. Denisov; V.M. Lakeenkov; O.S. Mazhorova; Yu.P. Popov Numerical study for liquid phase epitaxy of CdxHg1xTe solid solution, J. Crystal Growth, Volume 245 (2002), pp. 21-30

[2] I.A. Denisov; O.S. Mazhorova; Yu.P. Popov; N.A. Smirnova Numerical modelling for convection in growth/dissolution of solid solution CdXHg1XTe by liquid phase epitaxy, J. Crystal Growth, Volume 269 (2004), pp. 284-291

[3] F.H. Busse The stability of finite amplitude cellular connection and its relation to an extremum principle, J. Fluid Mech., Volume 30 (1967) no. 4, pp. 625-649

[4] R. Krishnamurti Finite amplitude convection with changing mean temperature. Part I. Theory, J. Fluid Mech., Volume 33 (1968) no. 3, pp. 445-455

[5] R. Krishnamurti Finite amplitude convection with changing mean temperature. Part II. An experimental test of the theory, J. Fluid Mech., Volume 33 (1968) no. 3, pp. 457-463

[6] A.V. Getling Rayleigh–Bernard Correction Structures and Dynamics, World Scientific, Singapore, 1998

[7] V.V. Kolmychkov, O.S. Mazhorova, Yu.P. Popov, On the solution of Navier–Stokes equations in primitive variables, Preprint No. 60, Keldysh Institute of Applied Mathematics, Moscow, 2001, 39 p

[8] D.B. White The planforms and onset of convection with a temperature-dependent viscosity, J. Fluid Mech., Volume 191 (1988) no. 3, pp. 247-286

[9] M. Medale; P. Cerisier Numerical simulation of Benard–Marangoni convection in small aspect ratio containers, Numer. Heat Transfer A, Volume 42 (2002), p. 5572

[10] V.V. Kolmychkov, O.S. Mazhorova, Yu.P. Popov, Mathematical modelling for convective mass transfer in 3D case, part 1, Preprint No. 92, Keldysh Institute of Applied Mathematics, Moscow, 2003, 28 p

[11] V.V. Kolmychkov, O.S. Mazhorova, Yu.P. Popov, Mathematical modelling for convective mass transfer in 3D case, part 2, Preprint No. 98, Keldysh Institute of Applied Mathematics, Moscow, 2003, 34 p

Cited by Sources:

Comments - Policy