Transition in plane parallel shear flows heated internally

Masato Nagata; Sotos Generalis

doi:10.1016/j.crme.2003.10.011

Transition in plane parallel shear flows heated internally

Presented by: Évariste Sanchez-Palencia

Masato Nagata ¹; Sotos Generalis ²

¹ Department of Aeronautics and Astronautics, Graduate School of Engineering, Kyoto University, Kyoto 606-8501, Japan
² School of Engineering and Applied Sciences, Division of Chemical Engineering and Applied Chemistry, Aston University, UK

Comptes Rendus. Mécanique, Volume 332 (2004) no. 1, pp. 9-16.

Abstract
Résumé

The stability of internally heated inclined plane parallel shear flows is examined numerically for the case of finite value of the Prandtl number, Pr. The transition in a vertical channel has already been studied for 0⩽Pr⩽100 with or without the application of an external pressure gradient, where the secondary flow takes the form of travelling waves (TWs) that are spanwise-independent (see works of Nagata and Generalis). In this work, in contrast to work already reported (J. Heat Trans. T. ASME 124 (2002) 635–642), we examine transition where the secondary flow takes the form of longitudinal rolls (LRs), which are independent of the steamwise direction, for Pr=7 and for a specific value of the angle of inclination of the fluid layer without the application of an external pressure gradient. We find possible bifurcation points of the secondary flow by performing a linear stability analysis that determines the neutral curve, where the basic flow, which can have two inflection points, loses stability. The linear stability of the secondary flow against three-dimensional perturbations is also examined numerically for the same value of the angle of inclination by employing Floquet theory. We identify possible bifurcation points for the tertiary flow and show that the bifurcation can be either monotone or oscillatory.

On présente une étude numérique de la stabilité d'écoulements parallèles cisaillés plans, chauffés intérieurement, dans le cas du nombre de Prandtl Pr fini. On a déjà étudié la transition dans un conduit vertical pour 0⩽Pr⩽100 avec ou sans application d'un gradient de pression extérieure, quand l'écoulement secondaire prend la forme d'ondes progressives (TW), indépendantes de l'envergure de l'écoulement (voir les publications de Nagata et Generalis). Dans le travail présent, contrairement aux résultats déjà rapportés (J. Heat Trans. T. ASME 124 (2002) 635-642), on examine la transition pendant laquelle l'écoulement secondaire prend la forme des rouleaux longitudinaux (LRs), indépendants de la direction du flux, pour Pr=7 et pour une valeur spécifique de l'angle d'inclinaison de la couche fluide, sans application du gradient de pression extérieure. Nous trouvons les points de bifurcation possibles de l'écoulement secondaire en effectuant une analyse de stabilité linéaire permettant de déterminer la courbe neutre, sur laquelle l'écoulement de base peut présenter deux points d'inflexion, perdant sa stabilité. La stabilité linéaire de l'écoulement secondaire par rapport aux perturbations tri-dimensionnelles a été examinée également pour une valeur constante de l'angle d'inclinaison, à l'aide de la théorie de Floquet. On identifie les points de bifurcation possibles pour l'écoulement tertiaire ; on montre aussi que cette bifurcation peut être soit monotone, soit oscillatoire.

Received: 2003-08-11
Accepted: 2003-10-21
Published online: 2003-12-18

DOI: 10.1016/j.crme.2003.10.011

Keywords: Heat transfer, Shear flow, Internal heat, Secondary instability, Transition, Floquet theory
Mots-clés : Transferts thermiques, Écoulement cisaillé, Chaleur interne, Instabilité secondaire, Théorie de Floquet

Author's affiliations:

Masato Nagata ¹; Sotos Generalis ²

¹ Department of Aeronautics and Astronautics, Graduate School of Engineering, Kyoto University, Kyoto 606-8501, Japan
² School of Engineering and Applied Sciences, Division of Chemical Engineering and Applied Chemistry, Aston University, UK

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Masato Nagata; Sotos Generalis. Transition in plane parallel shear flows heated internally. Comptes Rendus. Mécanique, Volume 332 (2004) no. 1, pp. 9-16. doi : 10.1016/j.crme.2003.10.011. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2003.10.011/

References
Cited by

[1] M. Nagata; S. Generalis Transition in convective flows heated internally, J. Heat Trans. T. ASME, Volume 124 (2002), pp. 635-642

[2] S. Generalis; M. Nagata Transition in homegeneously heated inclined plane-parallel shear flows, J. Heat Trans. T. ASME, Volume 125 (2003), pp. 795-803

[3] S. Generalis; M. Nagata Transition in internally heated shear flows in a vertical channel, heat transfer in unsteady and transitional flows, Eurotherm, Volume 74 (2003), pp. 117-122

[4] A. Kljenak; I. Horvat; J. Marn Two-dimensional large-eddy simulation of turbulent natural convection due to internal heat generation, Int. J. Heat Mass Trans., Volume 44 (2001), pp. 3985-3995

[5] U. Ehrenstein; W. Koch Three-dimensional wavelike equilibrium states in plane Poiseuille flow, J. Fluid Mech., Volume 228 (1991), pp. 111-148

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