Bubble Force Balance Formula for Low Reynolds Number Bubbly Flows in Pipes and Channels: Comparison of Wall Force Models
Résumé
Abstract In recent work, we investigated analytically low Reynolds number bubbly flows in pipes. We showed that the distribution of bubbles results from a balance between lift, dispersion and wall forces, and exhibited an analytical expression for this void fraction profile. We then performed a comparison of this analytical Bubble Force Balance Formula (BFBF) with an experiment from the literature. Antal’s model was used for the wall force. The objective of the present work is to compare and assess the three main wall force models in the literature: Antal’s, Tomiyama’s and Frank’s models. We begin by deriving two new BFBF, respectively with Tomiyama’s and Frank’s forces. We can see that the choice of the model impacts the velocity with which the analytical void fraction profile goes to zero at the wall. We then compare our three analytical profiles with experimental measurements and DNS simulations of laminar flows from the literature. We restrict ourselves to the near-wall region. The choice of Antal’s wall force model yields the best agreement. The data is also used to estimate the dispersion coefficient at the wall. Interestingly, we obtain the same order of magnitude with the three wall force models.