Thermo-rheological reduced order models for non-Newtonian fluid flows with power-law viscosity via the modal identification method

Abstract

In the framework of melted polymer flows characterization, this study deals with the formulation, construction and validation of thermo-rheological Reduced Order Models (ROMs) for incompressible flows of pseudoplastic fluids. The dynamic viscosity is described by a shear rate power law defined by consistency index K and pseudoplastic index n. The flow dynamics are assumed to be quasi-static whereas the thermal state is unsteady. Viscous dissipation acts as a heat source term in the energy equation. ROMs are built through the Modal Identification Method (MIM). First, their general form is derived from governing local conservation equations and the viscosity power-law, with an original approach to handle the issues related to the pseudoplastic index n. Then ROMs are identified using Particle Swarm Optimization and Ordinary Least Squares, from simulations coming from a reference Full Order Model (FOM). The approach is applied to a polymer flow in an annular duct, corresponding to an experimental lab apparatus. ROMs allow computing temperature at chosen locations of interest whatever the applied inputs, here parameters K, n and inlet flowrate as well as a time-varying volumetric heat source power in the central axis. Compared to the reference Finite Elements FOM, computing time is considerably reduced with limited loss of accuracy.