Simulation of viscoelastic fluids: Couette-Taylor flow

Journal Article · Fri Nov 20 04:00:00 EST 1998 · Journal of Computational Physics

DOI:https://doi.org/10.1006/jcph.1998.5934· OSTI ID:320964

Kupferman, R ^[1]

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1. Lawrence Berkeley National Lab., CA (United States). Mathematics Dept.

The author presents a numerical scheme for viscoelastic flow based on a second-order central differencing method recently introduced in the context of incompressible newtonian flow; the incompressibility constraint is treated with the projection method. The result is a simple and efficient scheme that is readily adaptable to a wide class of differential constitutive equations and flow geometries. He implements the new method on Couette-Taylor flow for a fluid governed by the Oldroyd-B constitutive equations. He simulates transient flow in a domain that includes at least eight wavelengths during many hundreds of natural periods. For weak elasticity, a stationary instability leading to Taylor vortices is observed. For a regime; of parameters where both inertia and elasticity are important, the instability is oscillatory. In both cases the early stage growth rates are compared to linear stability calculations, showing good agreement. The oscillatory instability is fourfold degenerate and gives rise to two bifurcating ranches: an axially traveling wave and a standing wave; only one of these solutions is stable. In the early stages of the instability, there is generally a combination of traveling and standing waves, depending on the initial conditions. As nonlinearities become important, the flow spontaneously breaks into coexisting regions of upward and downward-going waves. Such flow can persist for long times, until the globally stable traveling wave takes over and a limit cycle is reached.

• Sponsoring Organization: USDOE Office of Energy Research, Washington, DC (United States)
• DOE Contract Number: AC03-76SF00098
• OSTI ID: 320964
• Journal Information: Journal of Computational Physics, Journal Name: Journal of Computational Physics Journal Issue: 1 Vol. 147; ISSN JCTPAH; ISSN 0021-9991
• Country of Publication: United States
• Language: English

Related Subjects

42 ENGINEERING
99 GENERAL AND MISCELLANEOUS
BIFURCATION
COUETTE FLOW
FINITE DIFFERENCE METHOD
STANDING WAVES
TRAVELLING WAVES
VORTICES