Development of a thermal Reduced Order Model with explicit dependence on viscosity for a generalized Newtonian fluid

This work falls within the general framework of melted polymers flows characterization. It deals with the development of a thermo-rheological Reduced Order Model (ROM) which could be used in future works for on-line estimation of viscosity from temperature measurements in the flow, especially in high shear zones. A steady incompressible flow of a pseudo-plastic fluid in a circular runner is considered. The dynamic viscosity is thus described by a shear rate power law defined by consistency index K and flow behavior index n. An approach is developed for building a ROM able to compute a radial temperature profile at the channel outlet for any (K, n) couple in a predefined range. Assuming the temperature field approximation on a reduced set of m space functions, the general form of the ROM is obtained through a Galerkin projection of the energy equation. The ROM constitutive parameters are then identified through an optimization procedure using temperature data for a set of (K, n) couples in the construction ranges Kϵ[5000;20,000] and nϵ[0.3;0.6]. These data are computed by a Finite Elements reference model experimentally validated on an instrumented apparatus. A series of ROMs of order m = 1 to 5 is identified and then tested for a second set of (K, n) couples. The order 5 ROM is able to reproduce the temperature profile computed by the reference model with a r.m.s. error of about 10−2 °C. The temperature profile computed with ROMs is also compared to the profile measured for a real flow.