A numerical study is presented for dilute to semi-concentrated fibre s
uspension flows in a Newtonian solvent through various contraction and
expansion geometries. A time-stepping Taylor-Galerkin/pressure correc
tion numerical scheme is employed to obtain steady solutions. We cover
ranges of fibre concentrations and inertia beyond those in the litera
ture, giving consideration to co-linear and orthogonal fibre alignment
constitutive models adopting a quadratic closure approximation. Close
agreement is obtained with both experimental and, where available, ot
her numerical results for these problems.