Multi-scale analysis of bubbly flows

Bubbly flow has multiple structures in time and spatial scales. The macro-scale flow structure in bubbly flow is affected by both Che mezzo-scale and micro-scale phenomena. It is well known that a very small amount of surfactant can drastically change the terminal velocity of a bubble. When the liquid is contaminated, the bubble motion is affected by the Marangoni effect due to the variation of surface tension along the bubble surface caused by the gradient of the contaminant concentration. The numerical results reveal that the drag coefficient increases due to the Marangoni effect and the drag coefficient of a contaminated bubble approaches that of a rigid particle. The behavior of rising bubbles in quiescent liquid is simulated by the direct numerical simulation (DNS), as the sample of a bubbly flow, where the mezzo-scale phenomena in bubbly flow is clearly observed. The Navier-Stokes equation is solved by the finite difference method (FDM) and the bubble motion is tracked with the rectangular grid system. The turbulent energy in the surround ng liquid increases with the void fraction. The relation between drag coefficient, Reynolds number and void fraction is investigated at the moderate Reynolds number. Present results of the void fraction dependence on the drag coefficients show an interesting agreement with the experimental and theoretical ones. (C) 2001 Elsevier Science B.V. All rights reserved.