In this paper the one-dimensional two-fluid model is used to dynamically simulate slightly inclined fluid-fluid flow in a rectangular channel. By that, it is specifically meant that the solutions exhibit a wavy pattern arising from the inherent instability of the model. The conditions and experimental data of Thorpe (1969) are used for comparison. The linear instability of the model is regularized, i.e., made well-posed, with surface tension and axial turbulent stress with a simple turbulent viscosity model. Nonlinear analysis in an infinite domain demonstrates for the first time one-dimensional two-fluid model chaotic behavior in addition to limit cycle behavior and asymptotic stability. The chaotic behavior is a consequence of the linear instability (the long wavelength energy source) the nonlinearity (the energy transfer mechanism) and the viscous dissipation (the short wavelength energy sink). Since the model is chaotic, solutions exhibit sensitive dependence on initial conditions which results in non-convergence of particular solutions with grid refinement. However, even chaotic problems have invariants and the ensemble averaged water void fraction amplitude spectrum is used to demonstrate convergence and make comparisons to the experimental data.
- Fluids Engineering Division
Numerical Solution of Wavy-Stratified Fluid-Fluid Flow With the One-Dimensional Two-Fluid Model: Stability, Boundedness, Convergence and Chaos
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Fullmer, WD, Clausse, A, Vaidheeswaran, A, & Lopez de Bertodano, MA. "Numerical Solution of Wavy-Stratified Fluid-Fluid Flow With the One-Dimensional Two-Fluid Model: Stability, Boundedness, Convergence and Chaos." Proceedings of the ASME 2014 4th Joint US-European Fluids Engineering Division Summer Meeting collocated with the ASME 2014 12th International Conference on Nanochannels, Microchannels, and Minichannels. Volume 2, Fora: Cavitation and Multiphase Flow; Fluid Measurements and Instrumentation; Microfluidics; Multiphase Flows: Work in Progress; Fluid-Particle Interactions in Turbulence. Chicago, Illinois, USA. August 3–7, 2014. V002T20A006. ASME. https://doi.org/10.1115/FEDSM2014-22121
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