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Direct simulation of unsteady axisymmetric core-annular flow with high viscosity ratio. (English) Zbl 0973.76067
Summary: 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 for up-flow. The numerical scheme is validated against linearized stability theory for perfect core-annular flow, and against weakly nonlinear saturation for 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.

76M20 Finite difference methods applied to problems in fluid mechanics
76D50 Stratification effects in viscous fluids
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