Abstract
Hydrodynamically developing flow of Oldroyd B fluid in the planar die entrance region has been investigated numerically using SIMPLER algorithm in a non-uniform staggered grid system. It has been shown that for constant values of the Reynolds number, the entrance length increases as the Weissenberg number increases. For small Reynolds number flows the center line velocity distribution exhibit overshoot near the inlet, which seems to be related to the occurrence of numerical breakdown at small values of the limiting Weissenberg number than those for large Reynolds number flows. The distributions of the first normal stress difference display clearly the development of the flow characteristics from extensional flow to shear flow.
Similar content being viewed by others
Abbreviations
- D:
-
rate of strain tensor
- L :
-
slit halfheight
- P :
-
pressure, indeterminate part of the Cauchy stress tensor
- R:
-
the Reynolds number
- t :
-
time
- U :
-
average velocity in the slit
- u:
-
velocity vector
- u,v :
-
velocity components
- W :
-
the Weissenberg number based on the difference between stress relaxation time and retardation time
- W 1 :
-
the Weissenberg number based on stress relaxation time
- x,y :
-
rectangular Cartesian coordinates
- ε:
-
ratio of retardation time to stress relaxation time
- η:
-
zero-shear-rate viscosity, η1 + η2
- η1 :
-
non-Newtonian contribution to η
- η2 :
-
Newtonian contribution to η
- λ1 :
-
stress relaxation time
- λ2 :
-
retardation time
- ϱ:
-
density
- (σ, γ, τ):
-
xx, yy and xy components of τ1, respectively
- τ:
-
determinate part of the Cauchy stress tensor
- τ1 :
-
non-Newtonian contribution to τ
- τ2 :
-
Newtonian contribution to τ
References
Ahrens, M.; Yoo, J. Y.; Joseph, D. D. (1987): Hyperbolicity and change of type in the flow of viscoelastic fluids through pipes. J. Non-Newtonian Fluid Mech., 24, 67–83
Chang, P.-W.; Pattern, T. W.; Finlayson, B. A. (1979): Collocation and Galerkin finite element methods for viscoelastic fluid flow-I. Comput. Fluids, 7, 267–283
Choi, H. C.; Song, J. H.; Yoo, J. Y. (1988): Numerical simulation of the planar contraction flow of a Giesekus fluid. J. Non-Newtonian Fluid Mech., 29, 347–379
Gaidos, R. E.; Darby, R. (1988): Numerical simulation and change in type in the developing flow of a nonlinear viscoelastic fluid. J. Non-Newtonian Fluid Mech., 29, 59–79
Joseph, D. D.; Renardy, M.; Saut, J.-C. (1985): Hyperbolicity and change of type in the flow of viscoelastic fluids. Arch. Rat. Mech. Anal. 87, 213–251
Lagnado, R. R.; Phan-Thien, N.; Leal, L. G. (1985): The stability of two-dimensional linear flows of an Oldroyd-type fluid, J. Non-Newtonian Fluid Mech. 18, 25–59
Mendelson, M. A.; Yeh, P.-W. Brown, R. A.; Armstrong, R. C. (1982): Approximation error in finite element calculation of viscoelastic fluid flows. J. Non-Newtonian Fluid Mech., 10, 31–54
Na, Y. (1989): Numerical study on channel flows of viscoelastic fluid, M.S. thesis, Department of Mechanical Engineering, Seoul National University
Patankar, S. V. (1980): Numerical heat transfer and fluid flow. McGraw-Hill, New York, 120–134
Peyret, R.; Taylor, T. D. (1983): Computational methods for fluid flow. Springer-Verlag, Berlin
Song, J. H.; Yoo, J. Y. (1987): Numerical simulation of viscoelastic flow through a sudden contraction using a type dependent difference method. J. Non-Newtonian Fluid Mech., 24, 2, 221–243
Yoo, J. Y.; Ahrens, M.; Joseph, D. D. (1985): Hyperbolicity and change of type in sink flow. J. Fluid Mech., 153, 203–214
Yoo, J. Y.; Joseph, D. D. (1985): Hyperbolicity and change of type in the flow of viscoelastic fluid through channels. J. Non-Newtonian Fluid Mech., 19, 15–41
Yoo, J. Y.; Na, Y. (1990): A numerical study of the planar contraction flow of a viscoelastic fluid using SIMPLER algorithm. submitted to J. Non-Newtonian Fluid Mech.
Author information
Authors and Affiliations
Additional information
Communicated by J. Y. Yoo, September 13, 1990
Rights and permissions
About this article
Cite this article
Na, Y., Yoo, J.Y. A finite volume technique to simulate the flow of a viscoelastic fluid. Computational Mechanics 8, 43–55 (1991). https://doi.org/10.1007/BF00370547
Issue Date:
DOI: https://doi.org/10.1007/BF00370547