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.

scholarly journals Analytical solution of settling behavior of a particle in incompressible Newtonian fluid by using Parameterized Perturbation Method

2014 ◽  
Vol 33 (2) ◽  
pp. 145-160
Author(s):  
Reza Mohammadyari ◽  
Mazaher Rahimi Esboee ◽  
Majid Rahgoshay
Keyword(s):  
Perturbation Method ◽  
Newtonian Fluid ◽  
Mass Term ◽  
Reynolds Numbers ◽  
Added Mass ◽  
Unsteady Motion ◽  
High Rate ◽  
Settling Behavior ◽  
Analytical Expressions ◽  
Parameterized Perturbation Method

The problem of solid particle settling is a well known problem in mechanic of fluids. The parametrized Perturbation Method is applied to analytically solve the unsteady motion of a spherical particle falling in a Newtonian fluid using the drag of the form given by Oseen/Ferreira, for a range of Reynolds numbers. Particle equation of motion involved added mass term and ignored the Basset term. By using this new kind of perturbation method called parameterized perturbation method (PPM), analytical expressions for the instantaneous velocity, acceleration and position of the particle were derived. The presented results show the effectiveness of PPM and high rate of convergency of the method to achieve acceptable answers.

scholarly journals Fluid Dynamics Properties of Barium Hexaferrite Particle

2014 ◽  
Vol 17 (49) ◽  
Author(s):  
Perdamean Sebayang ◽  
Muljadi ◽  
Anggito Tetuko ◽  
Priyo Sardjono
Keyword(s):  
Particle Size ◽  
Bulk Density ◽  
Barium Hexaferrite ◽  
Reynolds Numbers ◽  
Terminal Velocity ◽  
Size Estimation ◽  
Floc Size ◽  
Ethanol Medium ◽  
Lower Bulk Density ◽  
Relationship Of

Particle size distribution of Barium Hexaferrite sample has been performed with commonly used methods of mathematical models by Rosin-Rammler (RR model) distribution. By using sieving method from 20-400 mesh, the basis of network analysis distribution function F(d) and density function, f(d) were obtained. Particle size estimation was performed using sedimentation gravitation based on Stokes law to obtained Reynolds numbers and terminal velocity of flocs in medium value has been calculated. The results of Reynolds numbers shows that Barium hexaferrite flocs in ethanol medium in laminar flow, whereas terminal velocity increases as larger particle size and density, however, bulk density reduce due to contained highly porous in the sample which yields lower bulk density. The relationship of turbidity with the floc size has been evaluated. The results show that turbidity and bulk density increases as smaller particle size, meanwhile, terminal velocity reduced. Differences in turbidity for each sample (20-400 mesh) has been determined which shows two region instead, with first region from 150-850 µm yields larger differences compared to the second region: 37-105 µm.  

scholarly journals An experimental study on the effects of swirling oxidizer flow and diameter of fuel nozzle on behaviour and light emittance of propane-oxygen non-premixed flame

2017 ◽  
Vol 21 (3) ◽  
pp. 1453-1462 ◽  
Author(s):  
Alireza Javareshkian ◽  
Sadegh Tabejamaat ◽  
Soroush Sarrafan-Sadeghi ◽  
Mohammadreza Baigmohammadi
Keyword(s):  
Reynolds Numbers ◽  
Flame Length ◽  
Nozzle Diameter ◽  
Fuel Flow ◽  
Maximum Value ◽  
Fuel Nozzle ◽  
Flame Shape ◽  
The Stability ◽  
Blue Flame

In this study, the stability and the light emittance of non-premixed propane-oxygen flames have been experimentally evaluated with respect to swirling oxidizer flow and variations in fuel nozzle diameter. Hence, three types of the vanes with the swirl angles of 30?, 45?, and 60? have been chosen for producing the desired swirling flows. The main aims of this study are to determine the flame behaviour, light emittance, and also considering the effect of variation in fuel nozzle diameter on combustion phenomena such as flame length, flame shape, and soot free length parameter. The investigation into the flame phenomenology was comprised of variations of the oxidizer and fuel flow velocities (respective Reynolds numbers) and the fuel nozzle diameter. The results showed that the swirl effect could change the flame luminosity and this way could reduce or increase the maximum value of the flame light emittance in the combustion zone. Therefore, investigation into the flame light emittance can give a good clue for studying the mixing quality of reactants, the flame phenomenology (blue flame or sooty flame, localized extinction), and the combustion intensity in non-premixed flames.

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.

scholarly journals Breakup of the Water Sheet Formed by Two Liquid Impinging Jets

2019 ◽  
Vol 2019 ◽  
pp. 1-8
Author(s):  
Yakang Xia ◽  
Lyes Khezzar ◽  
Shrinivas Bojanampati ◽  
Arman Molki
Keyword(s):  
Weber Number ◽  
Reynolds Numbers ◽  
Impinging Jets ◽  
Liquid Jets ◽  
Liquid Jet ◽  
Impingement Angle ◽  
Number Range ◽  
Breakup Length ◽  
Sheet Breakup ◽  
Visualization Experiments

Flow visualization experiments are carried out to study the flow regimes and breakup length of the water sheet generated by two impinging liquid jets from an atomizer made of two identical tubes 0.686 mm in diameter. These experiments cover liquid jet Reynolds numbers based on the pipe diameter in the range of 1541 to 5394. The effects of the jet velocities and impingement angle between the two jets on the breakup performance are studied. Four spray patterns are recognized, which are presheet formation, smooth sheet, ruffled sheet, and open-rim sheet regimes. Water sheet breakup length is found to be consistent with previous experimental and theoretical results in the lower Weber number (based on water jet diameter and velocity) range. In the relatively high Weber number range, the breakup length tends to a constant value with increasing Weber number, and some discrepancies between experimental and theoretical predictions do exist. Measured water sheet area increases with increasing liquid jet Reynolds numbers and impingement angle within the range of the current study.

Laminar to Turbulent Buoyant Vortex Ring Regime in Terms of Reynolds Number, Bond Number, and Weber Number

2018 ◽  
Vol 140 (5) ◽  
Author(s):  
Xueying Yan ◽  
Rupp Carriveau ◽  
David S. K. Ting
Keyword(s):  
Reynolds Number ◽  
Vortex Ring ◽  
Weber Number ◽  
High Speed ◽  
Reynolds Numbers ◽  
Bond Number ◽  
Vortex Rings ◽  
Transition Regime ◽  
Turbulent Vortex ◽  
Buoyant Vortex Rings

When buoyant vortex rings form, azimuthal disturbances occur on their surface. When the magnitude of the disturbance is sufficiently high, the ring will become turbulent. This paper establishes conditions for categorization of a buoyant vortex ring as laminar, transitional, or turbulent. The transition regime of enclosed-air buoyant vortex rings rising in still water was examined experimentally via two high-speed cameras. Sequences of the recorded pictures were analyzed using matlab. Key observations were summarized as follows: for Reynolds number lower than 14,000, Bond number below 30, and Weber number below 50, the vortex ring could not be produced. A transition regime was observed for Reynolds numbers between 40,000 and 70,000, Bond numbers between 120 and 280, and Weber number between 400 and 800. Below this range, only laminar vortex rings were observed, and above, only turbulent vortex rings.

Added Mass and In-Line Steady Drag Coefficient of Multiple Risers

1985 ◽  
Vol 107 (1) ◽  
pp. 2-11 ◽  
Author(s):  
T. Overvik ◽  
G. Moe
Keyword(s):  
Reynolds Number ◽  
Drag Coefficient ◽  
Reynolds Numbers ◽  
Added Mass ◽  
Central Cylinder ◽  
Lock In

Part of the results of an investigation with multiple rise configuration exposed to steady currents are presented. These tests were performed on smooth sectional riser models in a water flume at Reynolds numbers in the range 0.5 × 104 to 0.5 × 105. Reynolds number is based upon the diameter of the central cylinder (DC). Both the added mass, the frequency of vibration and the in-line steady drag coefficient are discussed both for vibration in the lock-in range and in the galloping mode.

Reynolds Number Effects on Hydrodynamic Coefficients for Pure In-Line and Pure Cross-Flow Forced Vortex Induced Vibrations

2009 ◽  
Author(s):  
Jamison L. Szwalek ◽  
Carl M. Larsen
Keyword(s):  
Reynolds Number ◽  
Prediction Models ◽  
Current Knowledge ◽  
Cross Flow ◽  
Reynolds Numbers ◽  
Added Mass ◽  
Hydrodynamic Coefficients ◽  
Vortex Induced Vibrations ◽  
Reynolds Number Effects ◽  
Sinusoidal Oscillations

In-line vibrations have been noted to have an important contribution to the fatigue of free spanning pipelines. Still, in-line contributions are not usually accounted for in current VIV prediction models. The present study seeks to broaden the current knowledge regarding in-line vibrations by expanding the work of Aronsen (2007) to include possible Reynolds number effects on pure in-line forced, sinusoidal oscillations for four Reynolds numbers ranging from 9,000 to 36,200. Similar tests were performed for pure cross-flow forced motion as well, mostly to confirm findings from previous research. When experimental uncertainties are accounted for, there appears to be little dependence on Reynolds number for all three hydrodynamic coefficients considered: the force in phase with velocity, the force in phase with acceleration, and the mean drag coefficient. However, trends can still be observed for the in-line added mass in the first instability region and for the transition between the two instability regions for in-line oscillations, and also between the low and high cross-flow added mass regimes. For Re = 9,000, the hydrodynamic coefficients do not appear to be stable and can be regarded as highly Reynolds number dependent.

Average Flow Inside and Around Fish Cages With and Without Fouling in a Uniform Flow

2010 ◽  
Author(s):  
Lars Gansel ◽  
Thomas A. McClimans ◽  
Dag Myrhaug
Keyword(s):  
Flow Field ◽  
Numerical Models ◽  
Fish Farming ◽  
Reynolds Numbers ◽  
Uniform Flow ◽  
Metal Mesh ◽  
Average Flow ◽  
Fish Cages ◽  
Farming Industry ◽  
Porous Cylinders

The average flow field inside and around the bottom of porous cylinders in a uniform flow is explored using Particle Image Velocimetry (PIV). Tests were conducted on six cylinders with porosities of 0%, 30%, 60%, 75%, 82% and 90% in a flume tank where the flow field inside and around the models is time averaged over 180 seconds. The models had a height-to-diameter ratio of 3 and were made from metal mesh. The Reynolds numbers ranged from 5,000 to 20,000 based on the diameter of the models and from 75 to 300 based on the diameter of individual strands of the mesh, which corresponds to the Reynolds numbers occurring at salmon fish cage netting used along the Norwegian coast. The porosities of 82%, 75% and 60% correspond to those of a fish cage netting in Norwegian Salmon farming with no, light and heavy biofouling, respectively. The results from this study are discussed with respect to the instantaneous flow field in and around the same cylinders at identical Reynolds numbers. The focus is on the effect of porosity on the ventilation inside the cages and the vertical transports within the near wake. It is shown that heavy fouling of aquacultural nettings can lead to internal circulation inside fish cages and therefore has the potential to reduce the ventilation of the net pens dramatically. The description of the time-averaged flow field inside and around porous cylinders can be used as benchmarks to validate and adjust numerical models of the flow past porous cylinders. The results from this study can be valuable also for the fish farming industry, as bio-fouling and the reduced porosity of fish cages can be monitored and controlled directly by fish farmers.

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