Model for radial gas fraction profiles in vertical pipe flow

One-dimensional codes are frequently used for the simulation of two phase flow in the field of design, optimization and safety analysis of nuclear and chemical plants. Most of the correlations used by these codes e.g. for pressure drop or heat and mass transfer are valid only for a given flow regime. Steady flow maps are not able to predict the flow pattern in case of transient flows. Recently attempts were made to solve this problem by the introduction of additional equations for the bubble density or corresponding parameters like bubble diameter, bubble volume or interfacial area. Bubble coalescence and break-up rates, which form the source terms in these equations, are determined by local events. That means, they depend on local parameters of turbulence as well as on the local bubble size distribution.

Experimental and theoretical investigations for vertical pipes have shown, that the probability of radial residence of a bubble strongly depends on their diameter. Whereas smaller bubbles tend to move towards the wall, large bubbles are preferably found in the centre of the tube. For the water-air system at ambient conditions a change of the maximum in the radial profiles was found to occur at a bubble diameter of about 5 - 6 mm. This change is very important for the development of the flow.

A one-dimensional model is presented, which predicts the radial volume fraction profiles from a given bubble size distribution. It bases on the assumption of an equilibrium of the forces acting on a bubble perpendicularly to the flow path (non drag forces). For the prediction of the flow pattern this model could be used within an procedure together with appropriate models for local bubble coalescence and break-up.