Begell House Inc.
Multiphase Science and Technology
MST
0276-1459
18
2
2006
MODELING WALL-INDUCED FORCES ON BUBBLES FOR INCLINED WALLS
111-133
F. J.
Moraga
Center for Multiphase Research, Rensselaer Polytechnic Institute, Troy, NY 12180-3590, USA
S.
Cancelos
Center for Multiphase Research, Rensselaer Polytechnic Institute, Troy, NY 12180-3590, USA
Richard T.
Lahey, Jr.
Center for Multiphase Research, Rensselaer Polytechnic Institute, Troy, NY 12180-3590, USA
A model for the wall- induced forces on bubbles for application in two-fluid model simulations of bubbly flows has been derived. The wall-induced force is obtained as the integral of an excess pressure calculated from the solution of the lubrication equation. Our numerical results are compared with experiments and it is shown that the wall-induced force is a function of the buoyancy and added mass forces, modulated by a smoothed Heaviside function that accounts for the proximity to the wall. This model explicitly accounts for the Reynolds, Eotvos and Weber numbers of the bubble and is valid in a larger range of these numbers than previous models.
SYSTEMATIC APPROACH TO CLOSURE RELATIONS FOR DISPERSE PARTICLE FLOWS: INTER-PHASE FORCE
135-154
A.
Prosperetti
Department of Mechanical Engineering, The John Hopkins University, Baltimore, MD 21218, USA; and Department of Applied Physics, IMPACT, University of Twente, AE 7500 Enschede, The Netherlands
K.
Ichiki
Department of Chemistry, University of Western Ontario, Ontario N6A 5B7, Canada
Q.
Zhang
Department of Mechanical Engineering, The Johns Hopkins University, Baltimore MD 21218, USA
The closure of the equations obtained by formal averaging of the microscopic laws of motion for particles in a fluid remains an important open problem in the theory of disperse flows. This paper gives a form for the particle and fluid momentum equations expressed in terms of computable quantities and derives a closure relation for the inter-phase force. It is shown that, in the derivation, it is essential to address the spatially non-uniform situation to find a valid relation and a method to carry out ensemble averaging for this situation is described.
INTERACTION AND COALESCENCE OF BUBBLES IN STAGNANT LIQUID
155-174
T.
Sanada
Dept. of Mechanical Engineering Science, Kyushu University, Fukuoka, Japan
M.
Watanabe
Dept. of Mechanical Engineering Science, Kyushu University, Fukuoka, Japan
T.
Fukano
Dept. of Environmental Symbiosis Engineering, Kurume Institute of Technology, Fukuoka, Japan
Interaction effects on the bubble motion and consequently induced coalescence were experimentally studied. A high accuracy bubble production control device enabled us to experiment various spatial configurations of a pair of bubbles. Among them, we focused on the cases where either bubbles rose in vertical line and side by side in silicone oil pool. Bubble diameter and liquid kinematic viscosity were taken as the experimental parameters. The motion of bubbles was recorded by a high-speed video camera. We observed that the Reynolds number Re significantly affected the motion of a pair of bubbles rising in both vertical line and side by side. When a pair of bubbles rose in vertical line, the trailing bubble was attracted by the wake of the leading bubble, and then it collided with leading bubble, in the case of low Re. On the other hand, in the case of intermediate Re, a pair of bubbles kept a mutual equilibrium distance due to the balance between the leading bubble wake attractive force and potential repulsive force. As Re further increased, the trailing bubble deformed and then escaped from the vertical line. When a pair of bubbles rose side by side, they separated from each other as they rose in the case of low Re. On the contrary, in the case of large Re, they attracted each other and then collided if the initial bubble horizontal distance was smaller than a critical value. At the moment of the collision of a pair of bubbles, we did not observe the significant deceleration of the bubble rising velocity. It should be noted that they collided with each other with asymmetric shape deformation. In addition, we investigate the criteria of either bouncing or coalescence of bubbles. Our experimental results show that the approach velocity is important parameter on coalescence of a pair of bubbles.
THREE DIMENSIONAL INTERACTION OF BUBBLES AT INTERMEDIATE REYNOLDS NUMBERS
175-197
Yuichi
Murai
Hokkaido University
Jian Wu
Qu
University of Fukui, Fukui 910-8507, Japan
Fujio
Yamamoto
Faculty of Engineering, University of Fukui, Fukui 910-8507, Japan
Three-dimensional bubble-bubble interaction in quiescent liquid is investigated experimentally using a stereoscopic bubble-tracking technique. An accurate labeling method and a three-dimensional stereo-matching method are applied to the measurement of the three-dimensional centroid for individual bubbles. The velocity vectors of the bubbles are measured by a 3-D four-time-step tracking algorithm and then the relative velocity vectors of two nearest-neighbor bubbles are captured with high statistic reliability. With the measurement data for intermediate Reynolds numbers ranging from 5 to 75, the vertical attraction and the horizontal repulsion are confirmed for Re < 10 as known by a past study based on Navier-Stokes simulation. The new finding of the present measurement is that bubbles of Re > 30 have more repulsive velocity both in the horizontal and the vertical directions because they rise closely. Moreover, the three-dimensional structure of the bubble-bubble interaction is discussed with the data analysis of the interaction vector fields.