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Petrov-Galerkin computation of nonlinear waves in pipe flow of shear-thinning fluids: first theoretical evidences for a delayed transition

Abstract : A pseudospectral Petrov-Galerkin code is developed in order to compute nonlinear traveling waves in pipe flow of shear-thinning fluids. The framework is continuum mechanics and the rheological model used is the purely viscous Carreau model. The code is validated, and a study of its convergence properties is made. It is shown that exponential convergence is obtained, despite the highly nonlinear nature of the viscous diffusion terms. Physical computations show that, as compared with the case of a constant-viscosity fluid, i.e., a Newtonian fluid, in the case of shear-thinning fluids the critical Reynolds number of the saddle-node bifurcation where the waves with an azimuthal wavenumber m 0 = 3 appear increases significantly when the non-Newtonian effects come into play.
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https://hal-cnrs.archives-ouvertes.fr/hal-03792139
Contributor : Chérif Nouar Connect in order to contact the contributor
Submitted on : Thursday, September 29, 2022 - 6:53:03 PM
Last modification on : Saturday, October 8, 2022 - 3:30:38 AM

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Nicolas Roland, Emmanuel Plaut, Chérif Nouar. Petrov-Galerkin computation of nonlinear waves in pipe flow of shear-thinning fluids: first theoretical evidences for a delayed transition. Computers and Fluids, 2010, 39 (9), pp.1733-1743. ⟨10.1016/j.compfluid.2010.06.011⟩. ⟨hal-03792139⟩

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