Numerical Simulation of a Small Bubble Impinging Onto an Inclined Wall

2006 ◽  
Author(s):  
Be´renge`re Podvin ◽  
Francisco Moraga ◽  
Daniel Attinger
Keyword(s):  
Weber Number ◽  
Classical Mechanics ◽  
Vertical Axis ◽  
Terminal Velocity ◽  
Excess Pressure ◽  
Small Bubble ◽  
Film Drainage ◽  
Bubble Deformation ◽  
Horizontal Wall ◽  
Comparison With Experiments

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]

Analysis of dynamic characteristics of bubble rise under a free surface

2020 ◽  
Vol 98 (11) ◽  
pp. 981-992
Author(s):  
Ying Zhang ◽  
Qiang Liu ◽  
Wenbin Li ◽  
Xiaolong Lian ◽  
Jinglun Li ◽  
...  
Keyword(s):  
Free Surface ◽  
Immersed Boundary Method ◽  
Weber Number ◽  
Front Tracking ◽  
Terminal Velocity ◽  
Immersed Boundary ◽  
Tracking Method ◽  
Free Interface ◽  
Front Tracking Method ◽  
Moving Interface

The rising process of a bubble occurs in several natural and industrial apparatuses. This process is computationally studied using the front tracking method for a moving interface whose surface properties are solved in terms of an immersed-boundary method. The results show that the free interface does not influence the bubble before the centroid velocity of the bubble reaches the terminal velocity, which reaches a stable value or fluctuates at it, with the distance h (between the centroid of the bubble and the free surface) reaching a certain value. When the Reynolds number increases, the time to reach terminal velocity will decrease, and the influence of the viscous factor on the terminal velocity is also weakened. The dramatic interaction between a bubble and free surface is beneficial to accelerate film draining out. It is also shown that the shape of the bubble gradually becomes an ellipse as the Weber number (We) decreases, and it is beneficial to reduce the resistance of the bubble. The free surface could accelerate the bubble breaking at high We values.

On the instability of small gas bubbles moving uniformly in various liquids

1957 ◽  
Vol 3 (1) ◽  
pp. 27-47 ◽  
Author(s):  
R. A. Hartunian ◽  
W. R. Sears
Keyword(s):  
Surface Tension ◽  
Weber Number ◽  
Gas Bubbles ◽  
Hydrodynamic Pressure ◽  
Terminal Velocity ◽  
Approximate Methods ◽  
Stability Calculation ◽  
Fluid Medium ◽  
Critical Weber Number ◽  
The Stability

The instability of small gas bubbles moving uniformly in various liquids is investigated experimentally and theoretically.The experiments consist of the measurement of the size and terminal velocity of bubbles at the threshold of instability in various liquids, together with the physical properties of the liquids. The results of the experiments indicate the existence of a universal stability curve. The nature of this curve strongly suggests that there are two separate criteria for predicting the onset of instability, namely, a critical Reynolds number (202) and a critical Weber number (1.26). The former criterion appears to be valid for bubbles moving uniformly in liquids containing impurities and in the somewhat more viscous liquids, whereas the latter criterion is for bubbles moving in pure, relatively inviscid liquids.The theoretical analysis is directed towards an investigation of the possibility of the interaction of surface tension and hydrodynamic pressure leading to unstable motions of the bubble, i.e. the existence of a critical Weber number. Accordingly, the theoretical model assumes the form of a general perturbation in the shape of a deformable sphere moving with uniform velocity in an inviscid, incompressible fluid medium of infinite extent. The calculations lead to divergent solutions above a certain Weber number, indicating, at least qualitatively, that the interaction of surface tension and hydrodynamic pressure can result in instabilities of the bubble motion.A subsequent investigation of the time-independent equations, however, shows the presence of large deformations in shape of the bubble prior to the onset of unstable motion, which is not compatible with the approximation of perturbing an essentially spherical bubble. This deformation and its possible effects on the stability calculation are therefore determined by approximate methods. From this it is concluded that the deformation of the bubble serves to introduce quantitative, but not qualitative, changes in the stability calculation.

scholarly journals Free-fall experiments of volcanic ash particles using a 2-D video disdrometer

2019 ◽  
Vol 12 (10) ◽  
pp. 5363-5379 ◽  
Author(s):  
Sung-Ho Suh ◽  
Masayuki Maki ◽  
Masato Iguchi ◽  
Dong-In Lee ◽  
Akihiko Yamaji ◽  
...  
Keyword(s):  
Volcanic Ash ◽  
Free Fall ◽  
Oblate Spheroid ◽  
Vertical Axis ◽  
Prolate Spheroid ◽  
Terminal Velocity ◽  
Atmospheric Conditions ◽  
Axis Ratio ◽  
Mean Values ◽  
Ash Fall

Abstract. Information of aerodynamic parameters of volcanic ash particles, such as terminal velocity, axis ratio, and canting angle, are necessary for quantitative ash-fall estimations with weather radar. In this study, free-fall experiments of volcanic ash particles were accomplished using a two-dimensional video disdrometer under controlled conditions. Samples containing a rotating symmetric axis were selected and divided into five types according to shape and orientation: oblate spheroid with horizontal rotating axis (OH), oblate spheroid with vertical axis (OV), prolate spheroid with horizontal rotating axis (PH), prolate spheroid with vertical rotating axis (PV), and sphere (Sp). The horizontally (OH and PH) and vertically (OV and PV) oriented particles were present in proportions of 76 % and 22 %, and oblate and prolate spheroids were in proportions of 76 % and 24 %, respectively. The most common shape type was OH (57 %). The terminal velocities of OH, OV, PH, PV, and Sp were obtained analyzing 2-D video disdrometer data. The terminal velocities of PV were highest compared to those of other particle types. The lowest terminal velocities were found in OH particles. It is interesting that the terminal velocities for OH decreased rapidly in the range 0.5<D<1 mm, corresponding to the decrease in axis ratio (i.e., smaller the particle, the flatter the shape). The axis ratios of all particle types except Sp were found to be converged to 0.94 at D>2 mm. The histogram of canting angles followed unimodal and bimodal distributions with respect to horizontally and vertically oriented particles, respectively. The mean values and the standard deviation of entire particle shape types were close to 0 and 10∘, respectively, under calm atmospheric conditions.

Liquid Droplet Impact Over Hydrophobic Mesh Surfaces and Assessment of Weber Number Dependent Characteristics

2022 ◽  
Author(s):  
Abba Abdulhamid Abubakar ◽  
Bekir Sami Yilbas ◽  
Hussain Al-Qahtani ◽  
Anwaruddin Siddiqui Mohammed
Keyword(s):  
Weber Number ◽  
Liquid Droplet ◽  
Droplet Diameter ◽  
Mesh Size ◽  
Vertical Axis ◽  
Capillary Length ◽  
Flat Surfaces ◽  
Mesh Surface ◽  
Droplet Behavior ◽  
Fluid Penetration

Abstract Impacting droplets and droplet ejection from hydrophobic mesh surfaces have interest in biomedicine, heat transfer engineering, and self-cleaning of surfaces. The rate and the size of newborn droplets can vary depending on, the droplet fluid properties, Weber number, mesh geometry, and surface wetting states. In the present study, impacting water droplets onto hydrophobic mesh surface is investigated and impact properties including, spreading, rebounding, and droplet fluid penetration and ejection rates are examined. Droplet behavior is assessed using high recording facilities and predicted in line with the experiments. The findings reveal that the critical Weber number for droplet fluid penetrating/ejecting from mesh screen mainly depends on the droplet fluid capillary length, and hydrophobic mesh size. The contact time of impacting droplet over mesh surface reduces with increasing droplet Weber number, which opposes the case observed for impacting droplets over flat hydrophobic surfaces. The restitution coefficient attains lower values for impacting droplets over mesh surfaces than that of flat surfaces. The rate and diameter of the ejected droplet from the mesh increases as droplet Weber increases. At the onset of impact, streamline curvature is formed inside droplet fluid, which creates a stagnation zone with radially varying pressure at the droplet fluid mesh interface. This reduces the ejected droplet diameter from mesh cells as mesh cells are located away from the impacting vertical axis.

Axisymmetric bubble or drop in a uniform flow

1981 ◽  
Vol 108 ◽  
pp. 89-100 ◽  
Author(s):  
Michael Miksis ◽  
Jean-Marc Vanden-Broeck ◽  
Joseph B. Keller
Keyword(s):  
Constant Velocity ◽  
Weber Number ◽  
Reynolds Numbers ◽  
Added Mass ◽  
Terminal Velocity ◽  
Bubble Surface ◽  
Uniform Flow ◽  
Axially Symmetric ◽  
Maximum Value ◽  
Nonlinear Integrodifferential System

The deformation of an axisymmetric bubble or drop in a uniform flow of constant velocity U is computed numerically. The flow is assumed to be inviscid and incompressible. The problem is formulated as a nonlinear integrodifferential system of equations for the bubble surface and for the potential function on the surface. These equations are discretized and the resulting algebraic system is solved by Newton's method. For U = 0 the bubble is a sphere. The results show that as U increases the bubble becomes oblate, spreading out in the direction normal to the flow and contracting in the direction of the flow. Then the poles get pushed in and ultimately they touch each other. The results also show that there is a maximum value of the Weber number above which there is no steady axially symmetric bubble. This value is somewhat smaller than the approximate value obtained by Moore (1965) but close to that found by El Sawi (1974). We also compute the added mass, the drag on the bubble, and its terminal velocity in a gravitational field, for large Reynolds numbers.

Spatial Representations as an Emergent Feature of Perceptual Processing

2010 ◽  
Vol 24 (3) ◽  
pp. 161-172 ◽  
Author(s):  
Edmund Wascher ◽  
C. Beste
Keyword(s):  
Common Ground ◽  
Event Related Potentials ◽  
Vertical Axis ◽  
Relevant Information ◽  
Sources Of Information ◽  
Integrated Network ◽  
Perceptual Maps ◽  
Emergent Feature ◽  
Related Potentials ◽  
Selection Of

Spatial selection of relevant information has been proposed to reflect an emergent feature of stimulus processing within an integrated network of perceptual areas. Stimulus-based and intention-based sources of information might converge in a common stage when spatial maps are generated. This approach appears to be inconsistent with the assumption of distinct mechanisms for stimulus-driven and top-down controlled attention. In two experiments, the common ground of stimulus-driven and intention-based attention was tested by means of event-related potentials (ERPs) in the human EEG. In both experiments, the processing of a single transient was compared to the selection of a physically comparable stimulus among distractors. While single transients evoked a spatially sensitive N1, the extraction of relevant information out of a more complex display was reflected in an N2pc. The high similarity of the spatial portion of these two components (Experiment 1), and the replication of this finding for the vertical axis (Experiment 2) indicate that these two ERP components might both reflect the spatial representation of relevant information as derived from the organization of perceptual maps, just at different points in time.

Particle motion with air resistance

2012 ◽  
Vol 8 (1) ◽  
pp. 1-15
Author(s):  
Gy. Sitkei
Keyword(s):  
Basic Equation ◽  
Initial Conditions ◽  
Equation Of Motion ◽  
Terminal Velocity ◽  
Dimensionless Form ◽  
Wood Industry ◽  
Acceptable Error ◽  
General Validity ◽  
Practical Applications ◽  
Air Resistance

Motion of particles with air resistance (e.g. horizontal and inclined throwing) plays an important role in many technological processes in agriculture, wood industry and several other fields. Although, the basic equation of motion of this problem is well known, however, the solutions for practical applications are not sufficient. In this article working diagrams were developed for quick estimation of the throwing distance and the terminal velocity. Approximate solution procedures are presented in closed form with acceptable error. The working diagrams provide with arbitrary initial conditions in dimensionless form of general validity.

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