A new approach in modeling phase distribution in fully developed bubbly pipe flow

Turbulent two-phase flow equations are derived and solved for fully developed pipe flow using a composite eddy-viscosity model and a new void-fraction equation. The void fraction profile is first specified from experiments and the velocity field is calculated to validate the eddy viscosity model. Consequently, a new equation is presented for calculation of the void fraction. This void-fraction equation incorporates the gradient of turbulent normal stresses in the radial direction, the conventional lift force, and a contribution from the unsteady drag force. The implications of this new equation, for the bubbly flow regime, are investigated by calculating the void-fraction distribution for a given velocity field. Inclusion of the normal turbulent stresses in the radial direction is shown to simulate correctly the experimentally observed trends of the phase distribution, both for upward and downward bubbly flow, without the need for a fictitious term such as the so called "lubrication force".