Approximate analytical results for two-fluid model of laminar bubbly flow

The two-fluid model is usually taken to predict the bubbly flow. The direct numerical calculation is often used for it, because it can not get the analytical results. In this paper, the results in integration type (i.e. the approximate analytical results) of the most simple type of bubbly flow and fully developed laminar bubbly flow in vertical pipe, are derived by symbol integration of the two-fluid model. Then they are calculated in numerical integration and compared with the experimental data. The numerical results coincide with the experimental data. Though the integration type results are not the analytical results of two-fluid model of bubbly flow, they can show what influences the flow field of bubbly flow. So they are good approximation of analytical results and have an advantage over direct numerical calculation.