Drag coefficient in one-dimensional two-group two-fluid model

Recently, the concept of the interfacial area transport equation has been proposed to predict the dynamic change of interfacial structure in transient and developing flows. In this approach, bubbles are categorized into two groups (group 1: spherical/distorted bubbles; group 2: cap/slug/churn-turbulent bubbles) due to the considerable difference in their transport characteristics. In this paper, the equations for calculating drag coefficients of both groups under developing flow conditions are derived based on the momentum equations in the one-dimensional two-group two-fluid model. It is found that void fraction of both groups should be taken into account in determining drag coefficient of each group. The shape factor is important for group 2 bubbles even though it can be approximated to be unity for group 1 bubbles. Experimental data of air–water upward bubbly flows in various sizes of pipes are used to examine the existing drag coefficient model of group 1 bubbles. It is shown that the Ishii and Chawla’s models for spherical and distorted bubbles can predict the experimental data in the forced convective flow systems satisfactorily, which confirms their applicability to bubbly flow systems.