scholarly journals An Iterative Approach for the Parameter Estimation of Shear-Rate and Temperature-Dependent Rheological Models for Polymeric Liquids

Polymers ◽  
2021 ◽  
Vol 13 (23) ◽  
pp. 4185
Author(s):  
Medeu Amangeldi ◽  
Yanwei Wang ◽  
Asma Perveen ◽  
Dichuan Zhang ◽  
Dongming Wei

Numerical flow simulations play an important role in polymer processing. One of the essential prerequisites for accurate and precise flow simulations is to obtain accurate materials functions. In the framework of the generalized Newtonian fluid model, one needs to obtain shear viscosity as a function of the rate-of-shear and temperature—as determined by rheometry—and then fitted to a mathematical model. Often, many subjectively perform the fitting without paying attention to the relative quality of the estimated parameters. This paper proposes a unique iterative algorithm for fitting the rate-of-shear and temperature-dependent viscosity model under the time–temperature superposition (TTS) principle. Proof-of-concept demonstrations are shown using the five-parameter Carreau–Yasuda model and experimental data from small-amplitude oscillatory shear (SAOS) measurements. It is shown that the newly proposed iterative algorithm leads to a more accurate representation of the experimental data compared to the traditional approach. We compare their performance in studies of the steady isothermal flow of a Carreau–Yasuda model fluid in a straight, circular tube. The two sets of parameters, one from the traditional approach and the other from the newly proposed iterative approach, show considerable differences in flow simulation. The percentage difference between the two predictions can be as large as 10% or more. Furthermore, even in cases where prior knowledge of the TTS shifting factors is not available, the newly proposed iterative approach can still yield a good fit to the experimental data, resulting in both the shifting factors and parameters for the non-Newtonian fluid model.

2017 ◽  
Author(s):  
Chan-Hoo Jeon ◽  
Ben R. Hodges

Abstract. Debris flows such as avalanches and landslides are heterogeneous mixtures of solids and liquids but are often simulated as homogeneous non-Newtonian fluids using a Herschel-Bulkley model. By representing the heterogeneous debris as a homogeneous non-Newtonian fluid, it is possible to use standard numerical approaches for the Navier-Stokes equations where viscosity is allowed to vary in time and space (e.g. eddy-viscosity turbulence models). Common non-Newtonian models are time-independent so that the relationship between the time-space-varying effective viscosity and flow stress is unchanging. However, the complex behaviors of debris flows at flow initiation (jamming) and cessation (restructuralization) imply that the viscosity-stress relationships should have time-dependent behaviors, which is a feature of thixotropic non-Newtonian fluids. In this paper, both Herschel-Bulkley and thixotropic non-Newtonian fluid models are evaluated for simulating avalanches along a slope and subaqueous debris flows. A numerical solver using a multi-material level set method is applied to track multiple interfaces simultaneously. The numerical results are validated with analytical solutions and available experimental data using parameters selected based on the experimental setup and without post-hoc calibration. The thixotropic (time-dependent) fluid model shows reasonable agreement with all the experimental data. For most of the experimental conditions, the Herschel-Bulkley (time-independent) model results were similar to the thixotropic model, a critical exception being conditions with a high yield stress. Where the flow initiation is strongly dominated by the structural jamming and the initial yield behavior the time-independent model performed poorly.


Fluids ◽  
2020 ◽  
Vol 5 (3) ◽  
pp. 125
Author(s):  
Evangelos Karvelas ◽  
Giorgos Sofiadis ◽  
Thanasis Papathanasiou ◽  
Ioannis Sarris

Blood is a non-homogeneous fluid that flows inside the human artery system and provides the cells with nutrients. In this study the auto rotation effect of blood’s microstructure on its flow inside a human carotid model is studied by using a micropolar fluid model. The study aims to investigate the flow differences that occur due to its microstructure as compared to a Newtonian fluid. We focus on the vortex viscosity effect, i.e., the ratio of microrotation viscosity to the total one, because this is the only parameter that affects directly the fluid flow. Simulations in a range of vortex viscosities, are carried out in a 3D human carotid model that is computationally reconstructed. All of the simulations are conducted at the diastolic Reynolds number that occurs in the human carotid. Results indicate that micropolarity affects blood velocity in the range of parameters studied by 4%. As micropolarity is increased, higher velocities in the center of vessels and lower near the boundaries are found as compared to a Newtonian fluid consideration. This is an indication that the increase of the fluid’s micropolarity leads to an increase of the boundary layer thickness. More importantly, an increase in vortex viscosity and the resulting increase in microrotation result in decreased shear stress in the carotid’s walls; this finding can be significant in regards to the onset and the development of atherosclerosis. Finally, the flow distribution at the carotid seems to heavily be affected by the geometry and the micropolarity of the fluid.


2013 ◽  
Vol 135 (12) ◽  
Author(s):  
A. O. Nieckele ◽  
J. N. E. Carneiro ◽  
R. C. Chucuya ◽  
J. H. P. Azevedo

In the present work, the onset and subsequent development of slug flow in horizontal pipes is investigated by solving the transient one-dimensional version of the two-fluid model in a high resolution mesh using a finite volume technique. The methodology (named slug-capturing) was proposed before in the literature and the present work represents a confirmation of its applicability in predicting this very complex flow regime. Further, different configurations are analyzed here and comparisons are performed against different sets of experimental data. Predictions for mean slug variables were in good agreement with experimental data. Additionally, focus is given to the statistical properties of slug flows such as shapes of probability density functions of slug lengths (which were represented by gamma and log-normal distributions) as well as the evolution of the first statistical moments, which were shown to be well reproduced by the methodology.


1992 ◽  
Vol 114 (3) ◽  
pp. 540-551 ◽  
Author(s):  
Hsing-Sen S. Hsiao ◽  
Bernard J. Hamrock

A complete solution is obtained for elastohydrodynamically lubricated conjunctions in line contacts considering the effects of temperature and the non-Newtonian characteristics of lubricants with limiting shear strength. The complete fast approach is used to solve the thermal Reynolds equation by using the complete circular non-Newtonian fluid model and considering both velocity and stress boundary conditions. The reason and the occasion to incorporate stress boundary conditions for the circular model are discussed. A conservative form of the energy equation is developed by using the finite control volume approach. Analytical solutions for solid surface temperatures that consider two-dimensional heat flow within the solids are used. A straightforward finite difference method, successive over-relaxation by lines, is employed to solve the energy equation. Results of thermal effects on film shape, pressure profile, streamlines, and friction coefficient are presented.


1975 ◽  
Vol 97 (2) ◽  
pp. 303-310 ◽  
Author(s):  
D. S. Kodnir ◽  
R. G. Salukvadze ◽  
D. L. Bakashvili ◽  
V. Sh. Schwartzman

An approximate solution of the stationary isothermal elastohydrodynamic problem has been obtained for a Ree Eyring fluid model also the solution’s algorithm is described for a non Newtonian fluid of an arbitrary model. The solution has been obtained for the complex hydrodynamic and thermal problem for the lubricant film of a non Newtonian fluid with its specified thickness and with a relative surface slip. The diagrams have been made for velocities, temperatures, and tangential stresses in the lubricant film. The solution enables the direct estimation of the tangential stress reduction caused by the non Newtonian fluid’s behavior as well as by the nonisothermal process by means of known theological properties (Newtonian viscosity and time of relaxation) with selected values of pressure and temperature as well as with a given velocity of slip, and with the help of simple nomograms.


Author(s):  
U. P. Singh ◽  
Amit Medhavi ◽  
R. S. Gupta ◽  
Siddharth Shankar Bhatt

The present investigation is concerned with the problem of heat transfer and peristaltic flow of non-Newtonian fluid using Rabinowitsch fluid model through a channel under long wavelength and low Reynolds number approximation. Expressions for velocity, pressure gradient, pressure rise, friction force and temperature have been obtained. The effect of different parameters on velocity, pressure gradient, pressure rise, streamlines, friction force and temperature have been discussed through graphs.


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