An analytical relation for the void fraction distribution in a fully developed bubbly flow in a vertical pipe

The analytical void fraction profile vanishes at the wall, as a result of the balance between dispersion and wall forces. It presents a peak near the wall for upward flows, whereas its maximum is reached in the center of the pipe for downward flows. This is illustrated by calculations performed for upward and downward bubbly flows with the NEPTUNE_CFD code.