Numerical Modeling of Non-Isothermal Viscoelastic Fluids

• Main Author: Meburger, Stefanie
• Format: Others
• Language: en
• Published: 2021
• Online Access: https://tuprints.ulb.tu-darmstadt.de/18521/1/Dissertation_Meburger_final.pdf; Meburger, Stefanie <http://tuprints.ulb.tu-darmstadt.de/view/person/Meburger=3AStefanie=3A=3A.html> (2021): Numerical Modeling of Non-Isothermal Viscoelastic Fluids. (Publisher's Version)Darmstadt, Technische Universität, DOI: 10.26083/tuprints-00018521 <https://doi.org/10.26083/tuprints-00018521>, [Ph.D. Thesis]

A numerical solution procedure for non-isothermal viscoelastic fluids is developed, based on the Finite Volume method on general unstructured meshes. Stable solutions in experimentally relevant conditions, i.e. at high fluid elasticity, are ensured with the root conformation approach. The temperature dependence of the Oldroyd-B type constitutive equations is accounted for with the time-temperature superposition principle with WLF and Arrhenius shift factor. The energy equation considers energetic and entropic energy conversion with a constant partitioning factor. The verification by comparison to an analytical solution of a simplified set of equations proves the correct solution of the numerical framework. Detailed comparison of the numerical solution to experimental data from the literature provides an insight into the advantages and shortcomings of the chosen thermo-rheological model. Evaluation of the differences between simulation and experimental data in a Weissenberg number range from Wi = 4 − 14.8 shows that the suggested thermal and rheological model are suitable for a good qualitative agreement to experimental data, without encountering any stability issues at high Weissenberg numbers. The comparison with the more complex exponential PTT model with regard to the reproduction of experimental data suggests that the chosen rheological model has less influence on the considered temperature field than the thermal model, even though the differences in the stress fields can be large. At all considered Weissenberg numbers and wall temperatures, viscous dissipation, which is regarded as the main source for temperature changes in the flow, is reproduced. The magnitude of the heat production by viscous dissipation is smaller than in the experimental setup, especially in regions of low velocity gradients, where the deviations between simulation results and experimental data are highest. Comparison of results to numerical studies from the literature shows good qualitative and, in case the same fluid is analyzed, also good quantitative agreement. Small deviations are present, which suggest that the stabilization approach influences the computed flow field. The employed energy equation accounts for energetic and entropic energy conversion mechanisms, the partitioning between both is achieved with a constant factor. In natural flow, the conversion changes locally with the flow situation, so that pure energy and pure entropy elasticity provide the bounds in which the solution can be located. Computations for these two limiting cases are performed and the flow fields compared in two different flow regimes, one of low viscosity and low temperature and one of high viscosity and high temperature. In both regimes the deviation between pure entropic and pure energetic energy conversion, and thus the importance of energy elastic effects, increases with increasing elasticity of the fluid. An additional dependence on the thermal boundary conditions is found, yet of different nature in the two considered flow regimes: in case of the fluid of low viscosity and low temperature, energetic effects are found to increase with heating of the walls. The magnitude of the deviations and thus the importance of energetic effects is only very small. High deviations and a high influence of the energetic effects is encountered in the fluid of high viscosity and temperature. Unlike at the low viscosity, the deviations are found to increase with decreasing energy supply and thus are highest for the coolest wall. An alternative Oldroyd-B type constitutive equation with explicit temperature dependent terms that account for the thermal history of the fluid is proposed and investigated in different flow regimes and flow geometries. An analysis of the alternative model in comparison to the ’normal’ Oldroyd-B model and experimental data in the low viscosity regime suggests that also an explicit inclusion of temperature in the constitutive equation does not alleviate the deviations between simulation and experimental data. In case of the high viscosity and high temperature fluid, deviations between the two constitutive equations are found in all field variables, and are most pronounced for temperature and stress. The predicted peak values differ significantly, and the difference grows with growing elasticity of the fluid and magnitude of the temperature difference between (initial) fluid temperature and wall temperature. The highest deviations are found at the coolest walls. Differences in the temperature fields are found to be especially pronounced in regions where the fluid is expanded, irrespective of the considered flow geometry.