Numerical Simulation of a Small Bubble Impinging Onto an Inclined Wall

Abstract

This paper presents a numerical modeling of the collision between a small bubble -of a few hundred microns, initially moving at terminal velocity, and an inclined wall, with relevance to drag reduction schemes. The theoretical model uses the lubrication theory to describe the film drainage as the bubble approaches the wall, and compute the force exerted by the wall as the integral of the excess pressure due to the bubble deformation. The model is solved using finite differences. The trajectory of the bubble is then determined using equations of classical mechanics. This study is an extension of previous work by Moraga, Cancelos and Lahey, [Multiphase Science and Technology, 18,(2),2006] where the simulation and comparison with experiments was carried out for a horizontal wall. In the present study where the wall is inclined, the bubble trajectory is no longer onedimensional and axisymmetry around the vertical axis is lost, allowing for more complex behavior. The influence of various parameters (Reynolds number, Weber number) is examined. Numerical results are compared with the experimental data from Tsao and Koch [Physics Fluids 9, 44, 1997]

High-Speed Visualization of Bubbles Interacting With a Solid Surface

“…Our results may be used to study the physical mechanism behind drag reduction. The acquired results will be used in a numerical study for predicting bubble rebounds [7].…”

“…The corresponding Reynolds Number and Weber Number are in the range 40 to 560 and 0.04 to 1.80, a case where the motion of the surrounding fluid can be approximated as a potential flow [4]. Therefore our results can be readily used by other theoretical and numerical study [7]. The paper reports the experimental results of the interaction.…”

“…As a result, we observed some sliding motion even at larger angles. Our measured data for inclined wall study can be used in numerical simulations [7] to find the critical angle of different sized bubbles. We now analyze a specific case of the bouncing motion.…”

“…Most bubbles with diameters 0.8 to 2 mm rebound two to three times before the amplitude of the motion dampens away due to fluid's viscosity and cannot be observed. The data obtained from the horizontal wall study will be used in numerical simulations developed in our laboratory [7].…”

“…The magnitude of the achieved drag reduction depends on the compressibility of the fluid [3]. Also, there is still a lack of modeling for the force between a wall and a bouncing bubble [7], while it seems reasonable to think that bubbles close to the wall influence drag reduction the most. Our contribution to this complex problem is to study the rebound of bubbles against a solid surface.…”