Review of potential flow solutions for velocity and shape of long isolated bubbles in vertical pipes

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Alexandre Boucher ◽  
Roel Belt ◽  
Alain Liné

Abstract The motion of elongated gas bubbles in vertical pipes has been studied extensively over the past century. A number of empirical and numerical correlations have emerged out of this curiosity; amongst them, analytical solutions have been proposed. A review of the major results and resolution methods based on a potential flow theory approach is presented in this article. The governing equations of a single elongated gas bubble rising in a stagnant or moving liquid are given in the potential flow formalism. Two different resolution methods (the power series method and the total derivative method) are studied in detail. The results (velocity and shape) are investigated with respect to the surface tension effect. The use of a new multi-objective solver coupled with the total derivative method improves the research of solutions and demonstrates its validity for determining the bubble velocity. This review aims to highlight the power of analytical tools, resolution methods and their associated limitations behind often well-known and wide-spread results in the literature.

2021 ◽  
Author(s):  
Devin F. Barcelos

A higher-order potential flow method is adapted for the aerodynamic performance prediction of small rotors used in multirotor unmanned aerial vehicles. The method uses elements of distributed vorticity which results in numerical robustness with both a prescribed and relaxed wake representation. The radial loading and wake shapes of a rotor in hover were compared to experiment to show strong agreement for three disk loadings. The advancing flight performance prediction of a single rotor was compared to a single rotor was compared to a blade element momentum theory based approach and to experiment. Comparison showed good thrust and power agreement with experiment across a range of advance ratios and angles of attack. Prediction in descending flights showed improvements in comparison to the blade element momentum theory approach. The model was extended to a quadrotorm configuration showing the differences associated to vehicle orientation and rotor rotational direction.


1998 ◽  
Vol 15 (1) ◽  
pp. 145-148
Author(s):  
A.M. Asmal

At first this book looks like another eye-catching, fear-mongering title aboutIslam. Are these books promoted by profit-hungry publishers or by underpaidfretful academics? Or has Islam become fair game for a wider unrestrainedacademia replacing the Orientalist school with newer analytical tools? Somepreliminary remarks, or a contextualization, might be useful here.Whatever its “resurgent” form, Islam is presenting something of an enigmaticchallenge for all. From the bazaars of the East to the sidewalks of the West,it refuses to lie down or go away. Attempts to discount it, ignore it or even suppressit have not succeeded. This hauntingly recurring phenomenon (p. 1) needsto be relabeled and reassessed. But the doubt lingers that representing it as “terrorism,”“theocracy,” “obscurantism,” “fundamentalism,” or “religious extremism”has muddied waters even more. Feeding popular fears with such preconfiguredterminology has neither satiated curiosity, quelled fears, nor broughtanyone closer to the truth.Compounding the picture is the “location” of the writers of such works: theworld-view, epistemology, discourse theory, or narrative framework fromwhich they approach Islam. The much-heralded objectivity of academia issacrosanct no more. Relativity, subjectivity, and the actor’s point of view are invogue. Old Orientalist views and definitions of the non-Occidental world arebeing overwhelmed by an array of (neo-Orientalist) analyses from a variety ofdiscourse perspectives.These analytical tools, even if applied with some success to their own societiesand disciplines this past century, don’t seem to have much of a shelf lifewhile some are less effective than others: positivist assertions fast give way torealist or inteqretivist ones; modernist perspectives to postmodemist ones; andstructuralist interpretations to poststructuralist ones. And when applied to Islamand Muslim societies, the results of these approaches can be bewildering (asshown by Rushdie’s Satanic Verses), and so can their effects (as shown byHuntingdon’s Clash of Civilisations prognostication).From its side, the Muslim world is all the more perplexed at the persistenceof such stereotypical labeling and analyses. Generally unfamiliar with these“new” tools, their reaction is either to ignore this “demonology of fundamentalism”(p. 16) or to interpret it as another of the West’s conspiracies against Islam.Sometimes it results in outright hostility (as shown by Khomeini’s fatwa andBradford’s book burning) or crude attempts at redress in reciprocal terms (as inAkbar Ahmed‘s Postmodernity and Islam). To western experts, such reactionscan only seem woefully inadequate.Furthermore, the apparently monolithic scenario of western experts with theirwestern critiques of the non-West is complicated by the emerging presence ofnonwestern migrants and their offspring on the westem academic scene. Taken ...


2014 ◽  
Vol 722 ◽  
pp. 97-100 ◽  
Author(s):  
Zai Shuai Ling ◽  
Wei Long ◽  
Zhang Yong Wu

The dissolution mechanism of air and formation mechanism of bubble in the scopic-scale,and the change rule of the velocity and pressure of bubble in the rising process,made the theoretical analysis and explanation. Be based on VOF model,with the help of Fluent software,For the single bubble rising in the water by numerical simulation;The results show that liquid phase flow state is a key factor affecting the speed of the bubbles rise;Pressure difference is the main reason cause the jets and bubbles deformation.Through the above process in the rising process of the bubble velocity and pressure changes, and a detailed analysis of inquiry, the pressure and velocity of the bubble rising process show up more realistic.


Author(s):  
Tohru Miyashita ◽  
Yasuo Koizumi

A bubble rising velocity in stagnant water in rectangular channels was examined. The width of the flow channels and the gap space between parallel walls were varied from 10 mm through 150 and from 1 mm through 10 mm, respectively. When the bubble had plug shape in the long side and also the short side, the bubble velocity took the same velocity as that in a circular pipe that had the same periphery. When the bubble lost the plug shape in the long side, the rising velocity became fast as the long side shape departed from the plug shape. When the long side was large enough for the bubble to have the shape of a bubble in open space, the bubble rising velocity was expressed well with the expression for the bubble rising velocity in open space. As the long side became narrow, the bubble rising velocity became slower than that for open space. When the gap spacing was quite narrow; 1 mm, and the long side was less than 20mm, the bubble stopped rising halfway in the flow channel.


1963 ◽  
Vol 16 (2) ◽  
pp. 161-176 ◽  
Author(s):  
D. W. Moore

The equations governing the boundary layer on a spherical gas bubble rising steadily through liquid of small viscosity are derived. These equations are linear are linear and are solved in closed form. The boundary layer separates at the rear stagnation point of the bubble to form a thin wake, whose structure is determined. Thus the drag force can be calculated from the momentum defect. The value obtained is 12πaaUμ, where a is the bubble radius and U the terminal velocity, and this agrees with the result of Levich (1949) who argued from the viscous dissipation in the potential flow round the bubble. The next term in an expansion of the drag in descending fractional powers of R is found and the results compared with experiment.


2015 ◽  
Vol 9 (1) ◽  
pp. 35
Author(s):  
Eneias Strakoshia ◽  
George Petrakos

<p align="center"> </p><p>Over the last decade, the whopping growth of the Chinese economy, due to the liberalization of its market, with regard to the vulnerable Eurozone’s economic activity, has led to trade disputes between the two economies. In order to best capture and describe these implications, we attempt to approach their moves and payoffs through a combination of strategic and analytical tools such as zero-sum games and multiple regression models. Data and metadata for both economies were obtained from official sources, mainly the Eurostat and the National Bureau of Statistics of China and used as input in the regression model. Subsequently, the model output was used as input in the zero-sum game. The results of this process pointed out the best strategies that the players should follow in order to avoid great losses.</p>


Author(s):  
Tohru Miyashita ◽  
Yasuo Koizumi ◽  
Hiroyasu Ohtake

Bubble rising velocity in stagnant water in rectangular channels was examined. The width of the flow channels and the gap space between parallel walls were varied from 10 mm through 150 mm and from 1 mm through 10 mm, respectively. When the bubble had plug shape in the long side and also the short side, the bubble velocity took the same velocity as that in a circular pipe that had the same periphery. When the bubble lost the plug shape in the long side, the rising velocity became fast as the long side shape departed from the plug shape. When the long side was large enough for the bubble to have the shape of a bubble in open space, the bubble rising velocity was expressed well with the expression for the bubble rising velocity in open space. As the long side became narrow, the bubble rising velocity became slower than that for open space. When the gap spacing was quite narrow; 1 mm, and the long side was less than 15 mm, the bubble stopped rising halfway in the flow channel. When the bubble took the shape of a plug, the bubble rising velocity did not depend on the film thickness between the bubble and the long-side wall in the present experimental range.


Minerals ◽  
2021 ◽  
Vol 11 (5) ◽  
pp. 452
Author(s):  
Jakub Crha ◽  
Pavlína Basařová ◽  
Marek C. Ruzicka ◽  
Ondřej Kašpar ◽  
Maria Zednikova

Multiphase flows are a part of many industrial processes, where the bubble motion influences the hydrodynamic behavior of the batch. The current trend is to use numerical solvers that can simulate the movement and mutual interactions of bubbles. The aim of this work was to study how two commercial CFD solvers, COMSOL Multiphysics and Ansys Fluent, can simulate the motion of a single rising bubble in a stagnant liquid. Simulations were performed for spherical or slightly deformed bubbles (Db = 0.6, 0.8, and 1.5 mm) rising in water or in propanol. A simple 2D axisymmetric approach was used. Calculated bubble terminal velocities and bubble shape deformations were compared to both experimental data and theoretical estimations. Solver Comsol Multiphysics was able to precisely calculate the movement of smaller and larger bubbles; due to the 2D rotational symmetry, better results were obtained for small spherical bubbles. The deformation of larger bubbles was calculated sufficiently. Solver Ansys Fluent, in the setting used, failed to simulate the motion of small bubbles due to parasitic currents but allowed for modeling of the motion of larger bubbles. However, the description of the bubble velocity and shape was worse in comparison with experimental values.


Energies ◽  
2021 ◽  
Vol 14 (3) ◽  
pp. 578
Author(s):  
Yaxin Liu ◽  
Eric R. Upchurch ◽  
Evren M. Ozbayoglu

An experimental investigation of single Taylor bubbles rising in stagnant and downward flowing non-Newtonian fluids was carried out in an 80 ft long inclined pipe (4°, 15°, 30°, 45° from vertical) of 6 in. inner diameter. Water and four concentrations of bentonite–water mixtures were applied as the liquid phase, with Reynolds numbers in the range 118 < Re < 105,227 in countercurrent flow conditions. The velocity and length of Taylor bubbles were determined by differential pressure measurements. The experimental results indicate that for all fluids tested, the bubble velocity increases as the inclination angle increases, and decreases as liquid viscosity increases. The length of Taylor bubbles decreases as the downward flow liquid velocity and viscosity increase. The bubble velocity was found to be independent of the bubble length. A new drift velocity correlation that incorporates inclination angle and apparent viscosity was developed, which is applicable for non-Newtonian fluids with the Eötvös numbers (E0) ranging from 3212 to 3405 and apparent viscosity (μapp) ranging from 0.001 Pa∙s to 129 Pa∙s. The proposed correlation exhibits good performance for predicting drift velocity from both the present study (mean absolute relative difference is 0.0702) and a database of previous investigator’s results (mean absolute relative difference is 0.09614).


2014 ◽  
Vol 763 ◽  
pp. 254-285 ◽  
Author(s):  
Damien Colombet ◽  
Dominique Legendre ◽  
Frédéric Risso ◽  
Arnaud Cockx ◽  
Pascal Guiraud

AbstractThe present work focuses on the collective effect on both bubble dynamics and mass transfer in a dense homogeneous bubble swarm for gas volume fractions${\it\alpha}$up to 30 %. The experimental investigation is carried out with air bubbles rising in a square column filled with water. Bubble size and shape are determined by means of a high-speed camera equipped with a telecentric lens. Gas volume fraction and bubble velocity are measured by using a dual-tip optical probe. The combination of these two techniques allows us to determine the interfacial area between the gas and the liquid. The transfer of oxygen from the bubbles to the water is measured from the time evolution of the concentration of oxygen dissolved in water, which is obtained by means of the gassing-out method. Concerning the bubble dynamics, the average vertical velocity is observed to decrease with${\it\alpha}$in agreement with previous experimental and numerical investigations, while the bubble agitation turns out to be weakly dependent on ${\it\alpha}$. Concerning mass transfer, the Sherwood number is found to be very close to that of a single bubble rising at the same Reynolds number, provided the latter is based on the average vertical bubble velocity, which accounts for the effect of the gas volume fraction on the bubble rise velocity. This conclusion is valid for situations where the diffusion coefficient of the gas in the liquid is very low (high Péclet number) and the dissolved gas is well mixed at the scale of the bubble. It is understood by considering that the transfer occurs at the front part of the bubbles through a diffusion layer which is very thin compared with all flow length scales and where the flow remains similar to that of a single rising bubble.


Sign in / Sign up

Export Citation Format

Share Document