Orientation Formation in Planar Mold Filling: Theory and Numerical Predictions

Abstract

Orientation formation in a steady, Newtonian, Hele-Shaw flow containing rigid, neutrally buoyant, slender fibers is numerically analyzed. The Hele-Shaw model is used to simulate flows through mold cavities consisting of thin planar sections. In this study, orientation results are calculated for a mold cavity containing a three to one sudden contraction. The suspension is injected from a single inlet gate at constant volume flow rate. Initially, the planar stream function is numerically solved by an Eulerian finite difference method to obtain the flow field. Subsequently, a Lagrangian particle tracking method is used to calculate the orientation field from the flow kinematics. The three-dimensional orientation formation throughout the mold cavity is obtained by a new method which calculates the second-order orientation tensors directly from flow kinematics and particle aspect ratio. With this new method, time-consuming integrals and inaccurate closure approximations commonly used in orientation calculations are avoided. The rotational dynamics of each particle are described by Jeffery’s theory. The numerical results are valid for multi-particle, dilute suspensions in which the orientation field can be fully described by the second-order moment of the orientation probability density function (OPDF). The orientation results are presented at different layers through the thickness of the mold cavity, ranging from the midplane to the top wall. In addition, the second-order orientation tensor is averaged through the mold thickness at a number of points in the vicinity of sudden contraction. These averaged orientation tensors are compared with the experimental data obtained from the same flow configuration by Olivero et al. (1997).