Influence de la contrainte seuil sur la stabilité de l'écoulement de Poiseuille d'un fluide viscoplastique : études modale et non modale

Abstract : The linear stability of the Poiseuille flow of a Bingham fluid is analysed. The present study is motivated by the problems encountered during the cementation of oil wells. In such situations, it is mandatory to know the structure of the flow of the different fluids involved (cement, mud of drilling). More specifically, the conditions of the transition from the laminar to the turbulent regime are important. The mean flow is essentially characterized by the presence in its central part of a plug zone, which moves as a rigid solid. The modal analysis relies upon an infinitesimal disturbance of the mean flow of exponential form, and shows that the Poiseuille flow is linearly stable. The non normal character of the linear operator demonstrates that a transient growth of the energy associated to the perturbation is possible, for short times. The optimal disturbances and the conditions of non increasing energy are determined, versus the Bingham number.
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Nadjiba Kabouya. Influence de la contrainte seuil sur la stabilité de l'écoulement de Poiseuille d'un fluide viscoplastique : études modale et non modale. Autre. Université Henri Poincaré - Nancy 1, 2005. Français. ⟨NNT : 2005NAN10025⟩. ⟨tel-01754348⟩

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