Simulations of Fibre Orientation in Dilute Suspensions with Front Moving in the Filling Process of a Rectangular Channel Using Level Set Method

摘要

The simulation of fibre orientation in dilute suspension with a front movingis carried out using the projection and level set methods. The motion of fibresis described using the Jeffery equation and the contribution of fibres to theflow is accounted for by the configuration field method. The governingNavier-Stokes equation for the fluid flow is solved using the projection methodwith finite difference scheme, while the fibre-related equations are directlysolved with the Runge-Kutta method. Our findings indicate that the fibre motionhas strong influence on the distributions of the streamwise and transversevelocities in the fountain flow. Fibre motion produces strong normal stressnear the wall which leads to the reduction of transversal velocity as comparedto the Newtonian flow without fibres and in turn the streamwise velocity nearthe wall is increased. Thus, the fibre addition to the flow weakens thestrength of the fountain flow. It is also found that the fibre orientation isnot always along the direction of velocity vector in the process of moldfilling. In the region of the fountain flow, the fibre near the centerline ismore oriented cross the streamwise direction comparing to that in the regionfar behind the flow front. This leads to that the fibre near the centreline inthe region of fountain flow is more extended along the transverse direction.Since fibre orientation in the suspension flow and the shape of the flow fronthave great bearing on the quality of the product made from injection molding,this study has much implications for engineering applications. These resultscan also be useful in other field dealing with fibre suspensions.