Liquid Turbulence Kinetic Energy Budget of Co-Current Bubbly Flow in a Large Diameter Vertical Pipe

The liquid turbulence kinetic energy transfer between the liquid and gas phases was investigated for upward air-water bubbly flow in a 200 mm diameter pipe. The liquid and gas axial momentum equations were analyzed to estimate the interfacial drag from experimental measurements, and hence the liquid turbulence production due to the relative velocity of the bubbles. The liquid turbulence production due to the bubbles was significantly higher than that due to the liquid shear. The liquid turbulence kinetic energy budget indicates that the turbulence production due to the bubbles is approximately balanced by the viscous dissipation, estimated assuming an isotropic turbulence structure, with negligible dissipation due to the bubbles. The liquid turbulence kinetic energy spectra showed an addition of energy at length scales in the range corresponding to the bubble diameter. A model for the turbulence energy production spectra due to the bubbles is proposed and used to investigate the spectral turbulence energy budget. The model indicates that when there is a liquid turbulence augmentation, most of the production occurs in the low wave number range with only a small overlap with the viscous dissipation region. In the case of a turbulence suppression, most of the bubble production occurs in the same wave number range as the viscous dissipation.