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Math. Comput. Appl. 2018, 23(2), 26; https://doi.org/10.3390/mca23020026

A New Analytical Procedure to Solve Two Phase Flow in Tubes

1
School of Applied Science and Technology, Fanshawe College, 1001 Fanshawe College Blvd, London, ON N5Y 5R6, Canada
2
Department of Medical Biophysics, Schulich School of Medicine and Dentistry, Western University, London, ON N6A 5C1, Canada
Received: 8 April 2018 / Revised: 21 May 2018 / Accepted: 21 May 2018 / Published: 23 May 2018
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Abstract

A new formulation for a proposed solution to the 3D Navier-Stokes Equations in cylindrical co-ordinates coupled to the continuity and level set convection equation is presented in terms of an additive solution of the three principle directions in the radial, azimuthal and z directions of flow and a connection between the level set function and composite velocity vector for the additive solution is shown. For the case of a vertical tube configuration with small inclination angle, results are obtained for the level set function defining the interface in both the radial and azimuthal directions. It is found that the curvature dependent part of the problem alone induces sinusoidal azimuthal interfacial waves whereas when the curvature together with the equation for the composite velocity is considered oscillating radial interfacial waves occur. The implications of two extremes indicate the importance of looking at the full equations including curvature. View Full-Text
Keywords: fluid dynamics; two phase flow; level set function; cylindrical coordinates; continuity equation fluid dynamics; two phase flow; level set function; cylindrical coordinates; continuity equation
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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Moschandreou, T.E. A New Analytical Procedure to Solve Two Phase Flow in Tubes. Math. Comput. Appl. 2018, 23, 26.

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