Analyse non linéaire de la stabilité de l'écoulement de Poiseuille plan d'un fluide rhéofluidifiant

Abstract : The aim of this study is to understand the influence of the nonlinear rheological behaviour of the shear-thinning fluids on the flow stability and transition to turbulence. First, a linear stability analysis using modal approach was carried out. Results clearly highlight the stabilizing effect of shear-thinning. Then, as a first approach to take into account nonlinear effects of viscosity perturbation on the flow stability, a weakly nonlinear stability analysis is performed in the neighbourhood of the critical conditions. Results indicate that shear-thinning reduces the viscous dissipation and, in contrast to inertial terms, the nonlinear viscous terms tend to accelerate the flow and act in favour of supercritical bifurcation. Finally, a nonlinear stability analysis is done by following solution branches in the parameter space using continuation techniques. To deal with highly nonlinear viscous terms, a pseudo-spectral code is developed. Nonlinear equilibrium solutions was found and characterized for various values of the rheological parameters
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Abdelfateh Chekila. Analyse non linéaire de la stabilité de l'écoulement de Poiseuille plan d'un fluide rhéofluidifiant. Autre [cond-mat.other]. Université de Lorraine, 2014. Français. ⟨NNT : 2014LORR0022⟩. ⟨tel-01750714⟩

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