Axisymmetric flow simulations of fiber suspensions as described by 3D probability distribution function

Abstract

Numerical models are developed to examine fiber suspension flows through axisymmetric geometries, such as a circular pipe, a center-gated disk and a die exit. The fiber orientation micro-structure is fully described by using the entire probability distribution function (PDF) in 3D instead of the second and fourth moments of the PDF, which introduce errors due to the closure approximation when using orientation tensor descriptions. A Newtonian suspending fluid is considered for the constitutive relationship and simulations are performed with and without coupling the flow and fiber orientation. Results are compared with numerical simulations obtained by using the standard evolution equation for the second-order orientation tensor and the IBOF closure approximation. It is found that the IBOF closure approximation does a relatively good job of matching the exact orientation results given by the probability distribution function. For the three explored flows, the difference between the predicted orientation results using the coupled and decoupled approaches is not significant. There is a noticeable difference in the velocity field solutions, specifically at the die exit where the coupled approach increases the die swell ratio when the fibers enter the inlet with random orientation state.