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Simulation of viscoelastic stagnation flow. (English) Zbl 0589.76024

A finite element simulation for the steady flow in a planar stagnation die was used to compute the velocity, pressure and stress fields. It is predicted that a region surrounds the stagnation point where the flow approximates a planar extension. This region is circular for the Newtonian liquid and becomes an ellipse for the Maxwell fluid. An isotropic point in the stress field is found for the Newtonian case as well as for the Maxwell fluid. Lubrication of the die wall, modeled as a finite slip, increases the size of extensional flow region by as much as 100%, while causing a migration of the isotropic stress point towards the die wall.

MSC:

76A10 Viscoelastic fluids
76M99 Basic methods in fluid mechanics
Full Text: DOI

References:

[1] Dealy JM (1978) J Non-Newtonian Fluid Mech 4:9 · Zbl 0381.76001 · doi:10.1016/0377-0257(78)85003-4
[2] Winter HH, Macosko CW, Bennett KE (1979) Rheol Acta 18:323 · doi:10.1007/BF01515825
[3] Macosko C, Ocansey MA, Winter HH (1982) J Non-Newtonian Fluid Mech 11:301 · doi:10.1016/0377-0257(82)80037-2
[4] Park HS (1984) Planar Extension of Polystyrene Melts in Stagnation Flow Dies. MS Thesis, Univ. of Massachusetts
[5] Malone MF (1979) Numerical Simulation of Hydrodynamics Problems in Polymer Processing. PhD Thesis, Univ. of Massachusetts
[6] Baker AJ (1983) Finite Element Computational Fluid Mechanics. Hemisphere Publishing Corporation, Washington D.C. · Zbl 0515.76001
[7] LeBlanc JV (1985) Analysis of an Upper-Convected Maxwell Model in Viscoelastic Polymer Flow Simulation. PhD Thesis, Univ. of Massachusetts
[8] Navier M (1827) Memoire Sur Les Du Mouvement Des Fluides. Academie des Sciences, Series 2, TV1: 389 · ERAM 002.0052cj
[9] Silliman WJ, Seriven LE (1980) J Comput Phys 34:287 · Zbl 0486.76064 · doi:10.1016/0021-9991(80)90091-1
[10] Strang G, Fix GE (1974) An Analysis of the Finite Element Method. Prentice-Hall, Englewood Cliffs, NJ
[11] Berker A, Lilleleht LU (1977) Ind Eng Chem Fund 16:425 · doi:10.1021/i160064a006
[12] Crochet MJ, Davies AR, Walters K (1984) Numerical Simulation of Non-Newtonian Flows. Elsevier, New York · Zbl 0583.76002
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