The steady planar and cylindrical stick-slip flows for a viscoelastic fluid are computed using the Phan-Thien and Tanner (PTT) constitutive model. The mixed finite element method is used in combination with the elastic-viscous stress-splitting technique and the streamline upwind Petrov–Galerkin discretization for the constitutive equation. This combination of methods when applied to the PTT constitutive model allows us to compute steady state solutions up to high Weissenberg numbers; practically without an upper limit. Equally important, the global Jacobian matrix is generated in order to be able to perform a linear stability analysis of the computed steady state. The dependence of the steady solutions on all the problem parameters is examined. In the limit of a Newtonian fluid, the expansion coefficients near the singularity are computed with comparable accuracy to those from previous analytical and numerical studies, which include the singular finite element method. In the case of a viscoelastic liquid, it is shown that the computed solutions converge quadratically with mesh refinement even at the exit plane of the die and also locally very close to the singularity. The form of the converged solution near the singularity is examined as well as its dependence on various rheological parameters. It is shown that the singularity at the die exit is a logarithmic one and always integrable. Under such conditions our calculations can be extended to determine the linear stability of the herein computed steady states.
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December 2009
Research Article|
December 08 2009
On the stick-slip flow from slit and cylindrical dies of a Phan-Thien and Tanner fluid model. I. Steady state
George Karapetsas;
George Karapetsas
Department of Chemical Engineering, Laboratory of Computational Fluid Dynamics,
University of Patras
, Patras 26500, Greece
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John Tsamopoulos
John Tsamopoulos
a)
Department of Chemical Engineering, Laboratory of Computational Fluid Dynamics,
University of Patras
, Patras 26500, Greece
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a)
Author to whom correspondence should be addressed. Electronic mail: [email protected]. Fax: +(30) 2610-996-178.
Physics of Fluids 21, 123101 (2009)
Article history
Received:
April 28 2009
Accepted:
November 13 2009
Connected Content
A companion article has been published:
On the stick-slip flow from slit and cylindrical dies of a Phan-Thien and Tanner fluid model. II. Linear stability analysis
Citation
George Karapetsas, John Tsamopoulos; On the stick-slip flow from slit and cylindrical dies of a Phan-Thien and Tanner fluid model. I. Steady state. Physics of Fluids 1 December 2009; 21 (12): 123101. https://doi.org/10.1063/1.3271495
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