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

Flow Activation Energy Estimation by Thermo‐Rheological Method

“…[8] The reduced order model. [12] is chosen as the direct model in the inverse method. Different from the full order finite element model, the reduced order model employs the power law without thermal dependence.…”

“…Virtual measurements are generated by a finite element model with « ANSYS POLYFLOW » software. The model is described in the previous study [ 12 ] and it uses the power law (Equation (1)). [ 10,11 ] $$$$\begin{equation}\eta = K{\dot{\bar{\gamma }}}^{n - 1}\end{equation}$$$$with η the dynamic viscosity, $$\dot{\bar{\gamma }}$$the generalized shear rate, K the consistency factor and n the pseudo‐plasticity index.…”

“…The output of these simulations is the change in temperature over time (due to the viscous dissipation) measured by each virtual thermocouple along the central axis (Figure 1). The positions of the virtual thermocouples are described in the previous study, [ 12 ] which names the thermocouple measurements as [ T obs ] i . Virtual measurements [ T obs ] i , i ∈ {2; 5} are presented in Figure 2 .…”

“…[ T obs ] 1 (closest to the inlet) is at the tip of the conical shape of the central axis. [ 12 ] and is not taken into account in this study, since it is also absent in the viscosity identification method, [ 8 ] which will be described in the next section.…”

“…In the finite element model, the rheological law is replaced by Equation (12) with 𝜂 0 = 3192.75 Pa.s, 𝜏* = 19996.2 Pa and n = 0.3387. In Equation ( 13), E a = 50 kJ.mol −1 and T 0 = 473.15 K. Three virtual two-second injections are simulated with the finite element model for:…”