Finite element analysis of fibre suspension flows

The numerical simulation of the flow of fluids containing short, slender fi bres is investigated. The orientations of the fibres are represented in an averaged sense by a second-order orientation tensor A. The governing equati ons contain, in addition to velocity, pressure and second-order orientation , a fourth-order orientation tensor which is approximated in terms of A thr ough the use of various closure rules. Discretisation is carried out using the standard Galerkin method for the momentum equation, and the discontinuo us Galerkin method for the evolution equation. Numerical results focus on t wo areas. Firstly, the behaviour of the evolution equation is investigated for simple shear flows, and for various closure rules and choices of parame ters. Earlier studies by others, in which the use of the linear closure lea ds to oscillatory behaviour, is confirmed in the present study, though it i s shown that a steady state is ultimately achieved. The second study in thi s work is concerned with the influence fibres on fluid flow in the benchmar k 4:1 contraction problem. The necessity of using upwinding is confirmed, a t least for the limiting case of zero rotary diffusivity, in that unrealist ic fibre orientations are obtained in the absence of upwinding. Experimenta l results show an increase in the magnitude of the zone of recirculation wi th increase in fibre concentration; this behaviour is reproduced in the num erical results presented here. (C) 2001 Elsevier Science B.V. All rights re served.