Pipe flow of shear-thinning fluids

Abstract

Pipe flow of purely viscous shear-thinning fluids is studied using numerical simulations. The rheological behavior is described by the Carreau model. The flow field is decomposed as a base flow and a disturbance. The perturbation equations are then solved using a pseudo-spectral Petrov–Galerkin method. The time marching uses a fourth-order Adams–Bashforth scheme. In the case of an infinitesimal perturbation, a three-dimensional linear stability analysis is performed based on modal and non-modal approaches. It is shown that pipe flow of shear-thinning fluids is linearly stable and that for the range of rheological parameters considered, streamwise-independent vortices are optimally amplified. Nonlinear computations are done for finite amplitude two-dimensional disturbances, which consist of one pair of longitudinal rolls. The numerical results highlight a strong modification of the viscosity profile associated with the flow reorganization. For a given wall Reynolds number, shear-thinning reduces the energy gain of the perturbation. This is due to a reduction of the exchange energy between the base flow and the perturbation. Besides this, viscous dissipation decreases with increasing shear-thinning effects.