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Titre: | Analytical and numerical analysis of bifurcations in thermal convection of viscoelastic fluids saturating a porous square box |
Auteur(s): | Taleb, A. BenHamed, H. Ouarzazi, M. N. Beji, H. |
Mots-clés: | Thermal convection Viscoelastic fluids Analytical |
Date de publication: | 2016 |
Editeur: | American Institute of Physics |
Collection/Numéro: | Physics of fluids/ Vol. 28 (2016);pp. 1-20 |
Résumé: | We report theoretical and numerical results on bifurcations in thermal instability for a
viscoelastic fluid saturating a porous square cavity heated from below. The modified
Darcy law based on the Oldroyd-B model was used for modeling the momentum
equation. In addition to Rayleigh number ℜ, two more dimensionless parameters
are introduced, namely, the relaxation time λ1 and the retardation time λ2. Temporal
stability analysis showed that the first bifurcation from the conductive state may be
either oscillatory for sufficiently elastic fluids or stationary for weakly elastic fluids.
The dynamics associated with the nonlinear interaction between the two kinds of
instabilities is first analyzed in the framework of a weakly nonlinear theory. For
sufficiently elastic fluids, analytical expressions of the nonlinear threshold above
which a second hysteretic bifurcation from oscillatory to stationary convective pattern
are derived and found to agree with two-dimensional numerical simulations of the
full equations. Computations performed with high Rayleigh number indicated that
the system exhibits a third transition from steady single-cell convection to oscillatory
multi-cellular flows. Moreover, we found that an intermittent oscillation regime may
exist with steady state before the emergence of the secondary Hopf bifurcation. For
weakly elastic fluids, we determined a second critical value ℜOsc
2 (λ1, λ2) above
which a Hopf bifurcation from steady convective pattern to oscillatory convection
occurs. The well known limit of ℜOsc
2 (λ1 = 0, λ2 = 0) = 390 for Newtonian fluids is
recovered, while the fluid elasticity is found to delay the onset of the Hopf bifurcation.
The major new findings were presented in the form of bifurcation diagrams as
functions of viscoelastic parameters for ℜ up to 420. Published by AIP Publishing |
URI/URL: | http://dlibrary.univ-boumerdes.dz:8080/handle/123456789/2934 |
ISSN: | 1070-6631 |
Collection(s) : | Publications Internationales
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