KSME Journal

, Volume 4, Issue 1, pp 54–61 | Cite as

Numerical simulation of the hydrodynamically developing flow of a viscoelastic fluid

  • Y. Na
  • J. Y. Yoo


Hydrodynamically developing flow of OldroydB 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 distributions 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 the development of the flow characteristics from extensional flow to shear flow.

Key Words

Hydrodynamically Developing Flow Viscoelastic Fluid OldroydB Fluid SIMPLER Algorithm Modified Hybrid Scheme 



Rate of strain tensor

\(\bar L\)

Slit halfheight


Pressure, indeterminate part of the Cauchy stress tensor


The Reynolds number




Average velocity in the slit

\(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{u} \)

Velocity vector

u, v

Velocity components


The Wissenberg number based on the difference between stress relaxation time and retardation time


The Weissenberg number based on stress relaxation time


Tectangular Cartesian coordinates


Tatio of retardation time to stress relaxation time


Zero-shear-rate viscosity,η 1+η 2


Non-Newtonian contribution to η


Newtonian contribution to η


Stress relaxation time


Ratardation time



(σ, γ, π)

xx, yy andxy components of\(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\tau } _1 \), respectively

\(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\tau } \)

Determinate part of the Cauchy stress tensor

\(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\tau } _1 \)

Non-Newonian contribution to\(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\tau } \)

\(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\tau } _2 \)

Newtonian contribution to\(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\tau } \)


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Copyright information

© The Korean Society of Mechanical Engineers (KSME) 1990

Authors and Affiliations

  • Y. Na
    • 1
  • J. Y. Yoo
    • 1
  1. 1.Department of Mechanical EngineeringSeoul National UniversitySeoulKorea

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