Analysis of drag and lift coefficient expressions of bubbly flow system for low to medium Reynolds number

It is very significant to calculate interphase forces correctly in bubbly flow systems. Compared with other interphase forces, drag and lift forces are of special importance, which have direct influences on terminal velocities and lateral distribution of bubbles. Many drag and lift coefficient expressions were developed in the past. In the face of numerous expressions of the drag and lift coefficients, it is very difficult for one to choose a pertinent expression to correctly compute the drag and lift forces. To solve this problem, some common drag and lift coefficient expressions, to the best of the authors' knowledge, were collected and summarized in this paper. From the physical viewpoint of forming mechanisms of the drag and lift forces, we performed a deeply comparative analysis of each drag and lift coefficient expression. Analyses showed that most of the existing drag coefficients are simply dependent on bubble Reynolds number (Re_b) and display similar profiles on Re _b. It is discovered that the critical Re_b corresponding to the inertial region are different, magnitude variations of the drag coefficients with changing Re_b are different too, and even some profiles show discontinuation. In comparison with the drag coefficient, the lift coefficient expressions (C_L) are much more complicated, and they are mainly dependent on the bubble Reynolds number (Re_b) and dimensionless shear rate (Sr_b). The different lift coefficient expressions display quite different profiles with the change of Re_b or Sr_b, and even some expressions of C_L are independent of Sr_b. It appears that the drag coefficient of Zhang and VanderHeyden (2002) and the lift coefficient of Legendre and Magnaudet (1998) are better applied to compute the drag and lift forces of bubbles in bubbly flows.