Effect of dispersed phase fraction on the drag coefficient of a droplet or a bubble in an idealized two-phase flow

Abstract In the present work, the drag force on a fluid sphere surrounded by a second is determined. This information is essential to characterize dispersed flows. Most of two-phase flow models are empirically obtained from experiments involving isolated bubbles or droplets. Their applicability to flows with a high number of bubbles or droplets is questionable. Moreover, correlations that take into account the effect of local dispersed phase fraction, the ratio of occupied volume by the dispersed phase, are sparse. This paper explores the drag on a fluid sphere inside an idealized flow. All spheres are assumed identical having the same velocity and equidistributed in space. We propose a new relation for the drag coefficient of a sphere (bubbles or droplets) depending on Reynolds number Re , dispersed phase fraction e , viscosity ratio μ ∗ and density ratio ρ ∗ . Analytical and numerical results are compared with previous studies including experimental measurements. The results lead to a proposal for a general relation of the drag coefficient for a sphere inside a cloud of spheres. In the idealized bubbly/droplet flow considered, the slip ratio is very small, and the flow around a sphere can often be characterized by Stokes approximation. In addition, dispersed phase fraction, e , has a strong effect on drag essentially through confinement. The wake and hydrodynamic interactions between spheres are comparatively small. The proposed relation can be used to elaborate a two-phase flow model for bubbly or annular flows. This work proposes an improvement on the closure relations for the drag coefficient ( C D ). The dependence of the drag coefficient ( C D ) with void fraction is of utmost importance to evaluate the stability of two-phase flows. The drag coefficient is a source term of the averaged Navier–Stokes equation. The main conclusion is that dispersed phase fraction extends the range for which Stokes flow represents accurately the flow around bubbles/droplets.