# Transition vers la turbulence pour un fluide à seuil en écoulement dans une conduite cylindrique

Abstract : The transition to turbulence for shear-thinning fluid with a yield-stress in a cylindrical pipe flow is studied. A linear stability analysis is performed using modal and non-modal approches. The numerical results show that the Hagen-Poiseuille flow of yield stress fluid is linearly stable. The effect of rheological behavior of the fluid on the characteristics of the optimal perturbation is clearly highlighted. At very low Herschel-Bulkley number (Hb << 1), the optimal perturbation consists of almost streamwise vortices, and the amplification of the kinetic energy is provided by the lift-up mechanism. In contrast for sufficiently large values of $Hb$, the optimal perturbation is axisymmetric and the growth of the kinetic energy is provided by the Orr-mechanism. From experimental point of view, the flow of 0.2 wt % aqueous solution of Carbopol 940 in a pipe is investigated from the measurement of the mean, i.e., time-averaged, axial velocity profiles as well as the statistical analysis of the fluctuations. It is observed that the velocity profiles are axisymmetric in the laminar and turbulent regimes, and present an increasing asymmetry with increasing Reynolds number in the transitional regime. A three-dimensional description of this asymmetry is provided from velocity profiles measurements at different azimuthal positions. The observed transitional flow suggest the existence of a robust non-linear coherent structure characterized by two weakly modulated counter-rotating longitudinal vortices, which length is comparable to that of the test section. The statistical analysis of the axial velocity fluctuations indicate that the transition occurs essentially in two stages. The first stage corresponds to the transition from the laminar regime to a stable non linear asymmetric state, where the spectra of axial velocity fluctuations are similar to those obtained in the case of two-dimensional turbulence. The second stage corresponds to the transition from this non linear asymmetric state to the hydrodynamic turbulence with the apparition of the classical spots of turbulence.
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• HAL Id : tel-01748511, version 1

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Ahmed Esmael. Transition vers la turbulence pour un fluide à seuil en écoulement dans une conduite cylindrique. Autre. Université Henri Poincaré - Nancy 1, 2008. Français. ⟨NNT : 2008NAN10103⟩. ⟨tel-01748511⟩

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