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Direct simulation of unsteady axisymmetric core–annular flow with high viscosity ratio

Published online by Cambridge University Press:  25 July 1999

JIE LI
Affiliation:
Department of Mathematics and Interdisciplinary Center for Applied Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061-0123, USA
YURIKO RENARDY
Affiliation:
Department of Mathematics and Interdisciplinary Center for Applied Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061-0123, USA

Abstract

Axisymmetric pipeline transportation of oil and water is simulated numerically as an initial value problem. The simulations succeed in predicting the spatially periodic Stokes-like waves called bamboo waves, which have been documented in experiments of Bai, Chen & Joseph (1992) for up-flow. The numerical scheme is validated against linearized stability theory for perfect core–annular flow, and weakly nonlinear saturation to travelling waves. Far from onset conditions, the fully nonlinear saturation to steady bamboo waves is achieved. As the speed is increased, the bamboo waves shorten, and peaks become more pointed. A new time-dependent bamboo wave is discovered, in which the interfacial waveform is steady, but the accompanying velocity and pressure fields are time-dependent. The appearance of vortices and the locations of the extremal values of pressure are investigated for both up- and down-flows.

Type
Research Article
Copyright
© 1999 Cambridge University Press

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