Improved model of orthotropic closure approximation for flow induced fiber orientation

Abstract

We developed improved models (called ORW and ORW3) of existing "orthotropic fitted" closure approximations (ORF or ORL) for use with a wide range of fiber-fiber interaction coefficients. Closure approximation refers to the approximation of a higher order tensor in terms of a lower order tensor. Principal values of the 4th order tensor are assumed in terms of polynomial expansions of the eigenvalues of the 2nd order tensor. Unknown parameters are determined by a least-square fitting technique with assumed exact solutions. Flow data for the optimal fitting were designed to cover the entire domain of the orientation triangle as uniformly as possible to eliminate non-physical oscillation. Shear/biaxial stretching combined flow turns out to play an important role in covering the orientation triangle, thereby increasing the accuracy of fiber orientation prediction. When tested for a variety of flow cases, neither ORW nor ORW3 shows any of the non-physical oscillatory behaviors that ORF and ORL frequently suffer from.