### Prediction of Optimum Length to Diameter Ratio for Two-Phase Fluid Flow Development in Vertical Pipes

#### Abstract

We investigate, via numerical simulation technique, the effect of length-to-diameter ratio on transient air-water two-phase flow in vertically upward cylindrical pipe geometry for parameterisation of the pilot scale laboratory multiphase flow rig. Variables such as axial velocity along the leading Taylor bubble, Taylor bubble length and Taylor bubble velocity are considered. A hydrodynamic entrance length required to establish a fully developed two phase flow was critically evaluated. Aperiodic behaviour on time and space dictates the complexity of continuous and unstable gas liquid flow. The porous injection configuration produced small bubble sizes compared to a single gas injection configuration even at higher gas injection rates.

Average axial velocity of the leading Taylor bubble of 0.411, 0.424 and 0.451 m/s were obtained for *L*/*D* ratios of 16.6, 83.3 and 166.7 respectively. The eccentricity of the axial velocity on the leading Taylor bubble stream and on its nose is perceived from *L*/*D* ratio of 166.7. We obtained a power law function for the radial component of the axial velocity profile in the liquid film ahead of the leading Taylor bubble as , with exponent *n*=16 for *L*/*D* =16.7, *n*=8 for *L*/*D*=83.3 and *n*=6 for *L*/*D* =166.7. Despite the decrease in the exponent as *L*/*D* ratio increases, a fully parabolic profile of the axial velocity on the liquid phase ahead of the Taylor bubble is not achieved. This, suggests that further studies on higher *L*/*D* ratios should be conducted.

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