Abstract
A three-dimensional numerical simulation of an Oldroyd-B fluid through a 4:1 planar contraction was performed using a time-dependent finite volume method on a staggered grid. The forward Euler scheme was employed to march in time. The non-linear terms in the momentum equations were discretized using a quadratic upstream interpolation. The program was validated on the start-up Couette flow at Reynolds number 1 and different Deborah numbers from 0.5 to 900, and the 2D 4:1 planar contraction of a Newtonian fluid. The time-dependent nature of these flows is analysed taking the solution at various times, from the initial condition to the steady-state, as frames in a motion picture. Results for vortex formation and growth are presented, then the differences between the simulated 2D and 3D planar contractions are discussed. To our knowledge, this is the first time-dependent numerical simulation of a viscoelastic fluid through a three-dimensional 4:1 contraction.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
J. Y. Yoo and Y. Na, “A numerical study of the planar contraction flow of a viscoelastic fluid using the SIMPLER algorithm,” J. Non-Newtonian Fluid Mech. 39, 89 (1991).
J. M. Marchai and M. J. Crochet, “Hermitian finite elements for calculating viscoelastic flow,” J. Non-Newtonian Fluid Mech. 20, 187 (1986).
Ch. Bodart and M. J. Crochet, “Time-Dependent Numerical Simulation of Viscoelastic Flow and Stability”, Theor. and Comput. Fluid Dynamics 5, 57 (1993).
D. V. Boger, “Viscoelastic flows through contractions”, Annu. Rev. Fluid Mech. 19, 157 (1987).
C. W. Hirt, B. D. Nichols and N. C. Romero, “SOLA — Numerical solution algorithm for transient fluid flow,” Los Alamos Laboratory, Report LA-5852 (1975).
M. Resch and U. Küster, “On viscoelastic fluid flow simulation using finite volume method,” Computational Fluid Dynamics’ 94, Eds. S. Wagner, E. H. Hirschel, J. Périaux, R. Piva, 989–993 (1994).
S. Bschorer and P. O. Brunn, “Finite volume method for simulation of non-Newtonian fluid flow,” Computational Fluid Dynamics’ 94, Eds. S. Wagner, E. H. Hirschel, J. Périaux, R. Piva, 989–993 (1994).
V. S. Patankar, Numerical heat transfer and fluid flow, (Hemisphere Publishing Corporation, New York, 1980).
D. D. Joseph, Fluid Dynamics of Viscoelastic Liquids, (Springer-Verlag, New York, 1984).
B. P. Leonard, “A stable accurate convective modelling procedure based on quadratic upstream interpolation,” Comp. Meth. Appl. Mech. Eng., 19, 59–88 (1979).
J. J. Van Schaftingen, “Méthodes d’éléments finis pour les écoulements viscoélastiques”, Thèse de Doctorat, Université Catholique de Louvain, Louvain-la-Neuve (1985).
R. Keunings and M. J. Crochet, “Numerical simulation of the flow of a viscoelastic fluid through an abrupt contraction,” J. Non-Newtonian Fluid Mech. 14, 279 (1984).
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1996 Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig/Wiesbaden
About this chapter
Cite this chapter
Mompean, G., Deville, M.O. (1996). Time-Dependent 3D Numerical Simulation of Oldroyd-B Fluid Using Finite Volume Method. In: Deville, M., Gavrilakis, S., Ryhming, I.L. (eds) Computation of Three-Dimensional Complex Flows. Notes on Numerical Fluid Mechanics (NNFM), vol 49. Vieweg+Teubner Verlag. https://doi.org/10.1007/978-3-322-89838-8_23
Download citation
DOI: https://doi.org/10.1007/978-3-322-89838-8_23
Publisher Name: Vieweg+Teubner Verlag
Print ISBN: 978-3-322-89840-1
Online ISBN: 978-3-322-89838-8
eBook Packages: Springer Book Archive