Experimental and theoretical bubble growth comparison at the initial stages of horizontal injection

Two-phase liquid-gas injection constitutes an important industrial process that is used in most separators. At the early step of injection, a cylindrical bubble is formed. As time elapses, the bubble shape becomes more complex and very difficult to analyze. In this study, a simple analytical model is developed to explain bubble shape changes. The analytical model was developed based on water flow inertia that continually pushes the bubble while the drag force resists it so that the frontal area of the bubble increases. The bubble size and frontal area were estimated using the assumption of the equilibrium between inertia force and drag force neglecting viscous force. From the estimation, the role of the vortex ring from the difference between theoretical and experimental results can be identified. The analytical model was verified through experimental data collected on the shape deformation induced by bubble motion at the beginning of injection. The experimental data used as verification were measured from the bubble nose image with ten times repetition having the uncertainty of ±6 %. The experimental method is conducted by injecting a bubble along the horizontal direction into a water pool. The inertial force of the water flow in front of the bubble nose generates the bubble. The bubble suddenly changes its shape, moves in the form of a bubble jet, and undergoes gradual shape changes. The frontal area of the bubble increases and reaches a maximum at the terminal velocity point. The bubble shape deformation is affected by the inertial force of the water flow that pushes the bubble forward. Accordingly, the bubble changes its shape from cylindrical to spherical, and then to an ellipsoidal disk. When the bubble attains terminal velocity, the inertial force becomes equal to the drag force. The edge of the ellipsoidal disk bubble exhibits increased surface tension. The difference between experimental data and the analytical model is due to the complex fluid and dynamic flow surrounding the bubble. The mathematical framework proposed in this work is envisaged to be an important tool for the prediction of the bubble frontal area