Elongated bubble velocities in horizontal pipes with different viscous fluids and pipe diameters

Accurate prediction of elongated bubble velocity in horizontal pipes holds significant importance for the development of transient multiphase flow models and the optimization of pipeline transport systems. In this study, experimental investigations were conducted on elongated bubble velocities in both short-distance (65 mm inner diameter, 215 D length) and long-distance (46 mm inner diameter, 35957 D length) horizontal pipes. A comprehensive database of elongated bubble velocities was established, covering a wide range of pipe diameters (25.8 – 300 mm) and liquid viscosities (0.001 – 5.5 Pa s). The dimensionless bubble drift velocity in quiescent liquids is primarily governed by the Eötvös number and the dimensionless viscosity number. Under conditions involving gas-liquid flow, the dimensionless elongated bubble nose position was found to effectively distinguish whether the bubble velocity includes the drift component in quiescent liquid. Quantitative correlations between the dimensionless bubble nose position, mixture Froude number, and gas-liquid velocity ratio were developed for three liquid viscosity regimes, with all data falling within ±20% error bands. By incorporating the bubble nose position and the radial velocity profiles under varying flow intensities, accurate predictions of elongated bubble velocity across different pipe diameters and liquid viscosities were achieved, approximately 93.6% of the data lie within ±25% error bands, with a mean absolute percentage error as low as 9.47%. The empirical correlation was integrated as a physical constraint to develop a physics-guided neural network PGNN model, demonstrating a 15.40% reduction in root mean square error on an independent test dataset.