Non-newtonian viscous elongation and shear fluid model based on optimal triple tensor decomposition

Abstract

The modeling of the distinct non-Newtonian fluid properties is an essential prerequisite for the computational simulation of associated flow fields. In particular, some non-Newtonian fluids reveal strong diverse viscosity response behaviours to pure elongational and simple shearing flows. Therefore, it is necessary to be able to distinguish between these flow types even in complex flow configuration. Unfortunately flow types are naturally mixed and this distinction becomes quite difficult. Only in a Lagrangian framework the tracking of the Lagrangian fluid element deformation allows an accurate strain related deformation type assignment. However, most CFD approaches prefer the Eulerian framework accepting the loss of the natural flow path alignment of the moving fluid particles. Consequently shear and elongation rates are barely separable without particular assignment methods. In this work a tensor decomposition method from vortex dynamics is discussed which allows to distinguish between these flow types. In vortex dynamics the problem occurred to separate shearing from purely rotational flows because different hydro- and aerodynamic flow phenomena are caused by shear and vortex related flow types. Thereto, various methods were proposed, among others the optimal triple tensor decomposition method which is able to separate vortical from shearing flows but also, after some modification, elongational from shearing flows. This tensor decomposition is now used to calculate elongation and shearing rates as input variables into non-Newtonian fluid models for the calculation of the local elongational and shear viscosity. The application case is a cross slot channel flow often used as reference. In this numerical simulation study the impact of the elongation rate modeling on the contraction flow topology is shown and discussed. It is shown that the modeling of different viscous elongational and shear-thinning affects the resulting flow significantly