(422e) Simplification and Application of An Interfacial Area Concentration Balance by Order Arguments
Two approaches have been developed for dealing with two phase systems. In the first approach mass balances for the two phases with no source or exchange terms, a total momentum balance for the two phase mixture, and a gas phase momentum balance with source term models for forces based on a two fluid approach have been developed. In effect, the action of the liquid on the gas phase has been included, but the effect of the gas on the liquid pahse hase been neglected. The results obtained are very good in modeling gas-liquid flow in a vertical tube. One significant limitation is that in the total momentum balance used in this approach, the gas phase momentum is neglected, so that the appoximation is only valid over a constrained range of two phase flows. Clearly, the dispersed phase momentum being neglected would introduce much larger errors at a given phase fraction if both fluids were liquids. Thus, this aproch is limited to gas-liquid systems.
In the second approach (actually developed first) mass balances with no source or exchange terms were combined with a momentum balance for each fluid phase and with exchange terms between the phases and an interfacial energy balnce with a source term from the continuous phase mechanical energy balance was developed. Computations with this apporach have continued to show problems. Because of these problems, an effort was made to simplify the approach by simplifying the source term in the interfaial energy balance with order arguments and a simple macro model for the two fluid friction factor. Results are encouraging.