Please enter verification code
Numerical Approximation of a Non-Newtonian Flow with Effect Inertial
Engineering Mathematics
Volume 3, Issue 1, June 2019, Pages: 9-12
Received: Jun. 12, 2019; Accepted: Jul. 3, 2019; Published: Jul. 13, 2019
Views 1003      Downloads 203
Giovanni Minervino Furtado, Department of Mechanical Engineering, Federal University of Rio Grande do Sul, Porto Alegre, Brazil; Department of Engineering Federal, University of Santa Maria, Cachoeira do Sul Campus, Brazi
Renato da Rosa Martins, Department of Mechanical Engineering, Federal University of Rio Grande do Sul, Porto Alegre, Brazil
Article Tools
Follow on us
V iscoplastic fluids are materials of great interest both in industry and in our daily lives. These applications range from food and cosmetics products to industrial applications such as plastics in the industry of polymers and drilling muds the oil industry. This class of material is characterized by having a yield stress that must be exceeded to the material starts to flow. These fluids are classically predicted by purely viscous models with yield stress. In the last decade, however, there some experimental visualizations has reported that the unyielded regions exhibit elasticity inside. This work is an attempt to investigate the effect of elasticity and inertia in those materials. We will studied, therefore, inertia flow of elastic-viscoplastic materials with no thixotropic behavior, according to the material equation introduced in de Souza Mendes (2011). The mechanical model is approximated by a stabilized finite element method in terms of extra stress, pressure and velocity. Due to its fine convergence feature, the method allows the use of equal-order finite elements and generates stable solutions in high advective-dominated flows. In this study is considered the geometry of a biquadratic cavity, in which the top wall moves to the right at constant velocity. In all computations is used biquadratic Lagrangian (Q1) elements. Results focuses in determining the influence of elasticity and inertia on the position and shape of unyielded. These results proved to be physically meaningful, indicating a strong interlace between elasticity and inertia on determining of the topology of yield surfaces.
Elastic-viscoplastic Marerials, Finite Element, Biquadratic Cavity, Elasticity and Inertia
To cite this article
Giovanni Minervino Furtado, Renato da Rosa Martins, Numerical Approximation of a Non-Newtonian Flow with Effect Inertial, Engineering Mathematics. Vol. 3, No. 1, 2019, pp. 9-12. doi: 10.11648/j.engmath.20190301.13
Copyright © 2019 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License ( which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
N. Alexandrou, T. M. McGilvreay, G. Burgos, Steady Herschel-Bulkley fluid flow in three-dimensional expansions. J. Non-Newtonian Fluid Mech. 100 (2001) 77–96.
Behr, M., Franca, L. P., Tezduyar, T. E., 1993. Stabilized Finite Element Methods for the Velocity-Pressure-stress Formulation of Incompressible Flows. Comput. Methods Appl. Mech. Engrg., vol. 104, pp. 31–48.
Bird, R. B., Armstrong, R. C., Hassager, O., 1987. Dynamics of polymeric liquids. vol. 1, John Wiley and Sons, U.S.A.
R. P. Chhabra and J. F. Richardson, 1999. Non-Newtonian Flow in the Process Industries. Editora Butterworth Heinemann.
Franca, L. P., Frey, S., 1992. Stabilized Finite Element Methods: II. The Incompressible Navier-Stokes Equations. Computer Methods in Applied Mechanics and Engineering, vol. 99, pp. 209–233.
H. A. Barnes. A brief history of the yield stress. Appl. Rheol. 9 (1999) 262–266.
H. A. Barnes. The yield stress - a review. J. Non-Newtonian Fluid Mech. 81 (1999a) 133–178.
J. Mewis, N. J. Wagner. Thixotropy, Adv. Colloid Interface Sci. 147-148 (2009) 214-227.
M. Bercovier, M. Engelman. A finite element method for incompressible non-Newtonian flows. J. Comput. Phys. 36 (1980) 313–326.
Nassar, B., de Souza Mendes, M. F. Naccache, 2011. Flow of elasto- viscoplastic liquids through an axisymmetric expansion–contraction. J. Non-Newtonian Fluid Mech. vol. 166, pp. 386–394.
P. R. de Souza Mendes. Dimensionless non-Newtonian fluid mechanics. J. Non-Newtonian Fluid Mech. 147 (12) (2007) 109-116.
P. R. de Souza Mendes, M. F. Naccache, Bruno Nassar. Flow of viscoplastic liquids through axisymmetric expansions-contractions. J. Non- Newtonian Fluid Mech. 166 (2011) 386-394.
Renato da R. Martins, Giovanni M. Furtado, Daniel D. dos Santos, Sérgio Frey, Mônica F. Nacacche, Paulo R. de Souza Mendes. Elastic and viscous effects on flow pattern of elasto-viscoplastic fluids in a cavity. Mechanics Research Communications. 53 (2013) 36-42.
Zinani, F. S. F. e Frey, S. L., 2008. Galerkin Least-Squares Multifield Approximations for Flows of Inelastic Non-Newtonian Fluids. Journal of Fluids Engineering, vol. 130, pp. 1-14.
Science Publishing Group
1 Rockefeller Plaza,
10th and 11th Floors,
New York, NY 10020
Tel: (001)347-983-5186