Modelling and esxperimental databases on poly-dispersed bubbly flows

In dispersed flows particle sizes play an important role on the evolution of the flow along the flow path. Flow situations where the dispersed phase is liquid or gas as e.g. in dispersed oil-water or in bubbly flows can frequently be found. Coalescence and breakup become important as soon as the dispersed phase volume fraction exceeds several percent. In the result a spectrum of bubble or drop sizes occurs. The momentum exchange between the continuous and dispersed phase strongly depend on the bubble respective drop size, i.e. the resulting velocity fields differ for particles with different sizes. In following the discussion is focused on poly-dispersed bubbly flows, but the phenomena are similar for dispersed oil-water flows in which oil or water may be the dispersed phase, respectively.

The momentum transfer between bubbles and the continuous liquid phase is usually considered by so-called bubble forces. The most important ones are drag, virtual mass, lift, turbulent dispersion and wall forces. All of them depend on the bubble size and the lateral lift force even may change its sign depending on the bubble size. This was found experimentally for single bubbles rising in a laminar linear shear flow [1] and confirmed by several DNS simulations. Lucas & Tomiyama showed that the change of the sign of the lift force predicted by the correlation obtained by Tomiyama et al. even holds turbulent poly-dispersed for air-water and steam flows with high gas volume fraction. In case of air-water flows at ambient conditions the critical bubble diameter for the change is 5.8 mm. In consequence for modeling poly-dispersed flows in a liquid shear flow, e.g. in a vertical tube a spatial separation of large and small bubbles occur and local bubble size distributions differ clearly from tube cross section averaged ones. For this reason the evolution of poly-dispersed flows is characterized by a complex interaction between local and bubble size effects.
To consider the different behavior of particles with different sizes the so-called Inhomogeneous MUSIG-Model was developed jointly by HZDR and ANSYS. It is implemented in the CFX-code and allows the representation of the dispersed phase by a (small) number of velocity groups (phases) and larger number of bubbles size classes (MUSIG groups).

For the validation of the model concept and appropriate closure models experimental data in high resolution in space and time are required. Vertical pipe flow is a suitable configuration to investigate such flows. Detailed data were obtained in several experiments at HZDR using the wire-mesh sensor technique. A high quality data base was established from experiments in a 8 m long pipe with an inner diameter of 195.3 mm. Measurements were done for 48 combinations of air and water superficial velocities varying from 0.04 m/s to 1.6 m/s for liquid and 0.0025 m/s to 3.2 m/s for air. Data were obtained for 12 different L/D in case of gas injection via 1 mm orifices in the pipe wall and for 6 different L/D in case of 4 mm orifices. From the raw data three-dimensional matrices of the instantaneous void fraction were obtained by calibration. These matrices were used for the calculation of time averaged data as: radial gas volume fraction profiles, bubble size distributions, radial volume fraction profiles decomposed according to the bubble size, interfacial area density and from a cross correlation between two sensors also the radial profiles of the gas velocity. All data are checked regarding their consistency. An estimation of errors was done by comparing the gas volume flow rates obtained from the measured radial profiles of void fraction and gas velocity with the setting values.

Within the same experimental setup also databases for condensing and evaporation steam-water flows were generated. They allow to validate the transferability of the models for different combinations of fluids. All these data bases are used in house and by different groups worldwide to develop, test and validate closure models for bubble forces and coalescence and break-up. At HZDR a standard model combining the closure models most suitable for wide range of flow conditions was developed. It will now be improved step by step.