Preprint Article Version 2 Preserved in Portico This version is not peer-reviewed

# A New Analytical Procedure to Solve Two Phase Flow in Tubes

Version 1 : Received: 8 April 2018 / Approved: 10 April 2018 / Online: 10 April 2018 (08:14:04 CEST)
Version 2 : Received: 17 April 2018 / Approved: 17 April 2018 / Online: 17 April 2018 (11:46:39 CEST)

A peer-reviewed article of this Preprint also exists.

Moschandreou, T.E. A New Analytical Procedure to Solve Two Phase Flow in Tubes. Math. Comput. Appl. 2018, 23, 26. Moschandreou, T.E. A New Analytical Procedure to Solve Two Phase Flow in Tubes. Math. Comput. Appl. 2018, 23, 26.

Journal reference: Math. Comput. Appl. 2018, 23, 26
DOI: 10.3390/mca23020026

## 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 wheras 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.

## Keywords

fluid dynamics; two phase flow; level set function; cylindrical coordinates; continuity equation

## Subject

MATHEMATICS & COMPUTER SCIENCE, Applied Mathematics

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