scholarly journals Buoyancy-driven bubbly flows: ordered and free rise at small and intermediate volume fraction

2017 ◽  
Vol 816 ◽  
pp. 94-141 ◽  
Author(s):  
Aurore Loisy ◽  
Aurore Naso ◽  
Peter D. M. Spelt
Keyword(s):  
Volume Fraction ◽  
Bubbly Flows ◽  
Rise Velocity ◽  
Rising Bubble ◽  
Moderate Reynolds Number ◽  
Wake Interactions ◽  
New Strategy ◽  
Monotonically Decreasing Function ◽  
Freely Moving ◽  
Dilute Limit

Various expressions have been proposed previously for the rise velocity of gas bubbles in homogeneous steady bubbly flows, generally a monotonically decreasing function of the bubble volume fraction. For suspensions of freely moving bubbles, some of these are of the form expected for ordered arrays of bubbles, and vice versa, as they do not reduce to the behaviour expected theoretically in the dilute limit. The microstructure of weakly inhomogeneous bubbly flows not being known generally, the effect of microstructure is an important consideration. We revisit this problem here for bubbly flows at small to moderate Reynolds number values for deformable bubbles, using direct numerical simulation and analysis. For ordered suspensions, the rise velocity is demonstrated not to be monotonically decreasing with volume fraction due to cooperative wake interactions. The fore-and-aft asymmetry of an isolated ellipsoidal bubble is reversed upon increasing the volume fraction, and the bubble aspect ratio approaches unity. Recent work on rising bubble pairs is used to explain most of these results; the present work therefore forms a platform of extending the former to suspensions of many bubbles. We adopt this new strategy also to support the existence of the oblique rise of ordered suspensions, the possibility of which is also demonstrated analytically. Finally, we demonstrate that most of the trends observed in ordered systems also appear in freely evolving suspensions. These similarities are supported by prior experimental measurements and attributed to the fact that free bubbles keep the same neighbours for extended periods of time.

Phase Distribution in Buoyancy-Driven Bubbly Flows

2002 ◽  
Author(s):  
Asghar Esmaeeli ◽  
Chan Ching ◽  
Mamdouh Shoukri
Keyword(s):  
Pair Distribution Function ◽  
Phase Distribution ◽  
Liquid Velocity ◽  
Momentum Equation ◽  
Bubbly Flows ◽  
Bubble Coalescence ◽  
Rise Velocity ◽  
Topology Change ◽  
Moderate Reynolds Number ◽  
Average Rise

This study aims to investigate the effect of topology change on the rise velocity of bubbly flows and the phase distribution in a channel at a moderate Reynolds number. A front tracking/finite difference method is used to solve the momentum equation inside and outside deformable bubbles. It is found that bubble/bubble coalescence enhances the average rise velocity of the bubbles dramatically and also increases the fluctuations of the liquid velocity. Examination of the pair distribution function shows that the flow becomes more non-homogeneous as a result of topology change.

SIMULATION OF AN AXISYMMETRIC RISING BUBBLE BY A MULTIPLE RELAXATION TIME LATTICE BOLTZMANN METHOD

2009 ◽  
Vol 23 (24) ◽  
pp. 4907-4932 ◽  
Author(s):  
ABBAS FAKHARI ◽  
MOHAMMAD HASSAN RAHIMIAN
Keyword(s):  
Free Surface ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Rise Velocity ◽  
Rising Bubble ◽  
Wide Range ◽  
Theoretical Predictions ◽  
Multiple Relaxation Time ◽  
Bubble Rising ◽  
Boltzmann Method

In this paper, the lattice Boltzmann method is employed to simulate buoyancy-driven motion of a single bubble. First, an axisymmetric bubble motion under buoyancy force in an enclosed duct is investigated for some range of Eötvös number and a wide range of Archimedes and Morton numbers. Numerical results are compared with experimental data and theoretical predictions, and satisfactory agreement is shown. It is seen that increase of Eötvös or Archimedes number increases the rate of deformation of the bubble. At a high enough Archimedes value and low Morton numbers breakup of the bubble is observed. Then, a bubble rising and finally bursting at a free surface is simulated. It is seen that at higher Archimedes numbers the rise velocity of the bubble is greater and the center of the free interface rises further. On the other hand, at high Eötvös values the bubble deforms more and becomes more stretched in the radial direction, which in turn results in lower rise velocity and, hence, lower elevations for the center of the free surface.

Experimental investigation into the drag volume fraction correction term for gas-liquid bubbly flows

2017 ◽  
Vol 170 ◽  
pp. 91-97 ◽  
Author(s):  
Dale D. McClure ◽  
John M. Kavanagh ◽  
David F. Fletcher ◽  
Geoffrey W. Barton
Keyword(s):  
Experimental Investigation ◽  
Volume Fraction ◽  
Correction Term ◽  
Bubbly Flows

Dynamics of homogeneous bubbly flows Part 2. Velocity fluctuations

2002 ◽  
Vol 466 ◽  
pp. 53-84 ◽  
Author(s):  
BERNARD BUNNER ◽  
GRÉTAR TRYGGVASON
Keyword(s):  
Kinetic Energy ◽  
Reynolds Stress ◽  
Void Fraction ◽  
Three Dimensional ◽  
Bubbly Flows ◽  
Rise Velocity ◽  
Velocity Fluctuations ◽  
Kinetic Energy Spectrum ◽  
Average Rise ◽  
High Wavenumbers

Direct numerical simulations of the motion of up to 216 three-dimensional buoyant bubbles in periodic domains are presented. The bubbles are nearly spherical and have a rise Reynolds number of about 20. The void fraction ranges from 2% to 24%. Part 1 analysed the rise velocity and the microstructure of the bubbles. This paper examines the fluctuation velocities and the dispersion of the bubbles and the ‘pseudo-turbulence’ of the liquid phase induced by the motion of the bubbles. It is found that the turbulent kinetic energy increases with void fraction and scales with the void fraction multiplied by the square of the average rise velocity of the bubbles. The vertical Reynolds stress is greater than the horizontal Reynolds stress, but the anisotropy decreases when the void fraction increases. The kinetic energy spectrum follows a power law with a slope of approximately −3.6 at high wavenumbers.

An Experimental Investigation for Bubble Rising in Non-Newtonian Fluids and Empirical Correlation of Drag Coefficient

2010 ◽  
Vol 132 (2) ◽  
Author(s):  
Fan Wenyuan ◽  
Ma Youguang ◽  
Jiang Shaokun ◽  
Yang Ke ◽  
Li Huaizhi
Keyword(s):  
Reynolds Number ◽  
Aqueous Solutions ◽  
Drag Coefficient ◽  
Bubble Diameter ◽  
Video Camera ◽  
Solution Concentration ◽  
Terminal Velocity ◽  
Newtonian Fluids ◽  
Rising Bubble ◽  
Moderate Reynolds Number

The velocity, shape, and trajectory of the rising bubble in polyacrylamide (PAM) and carboxymethylcellulose (CMC) aqueous solutions were experimentally investigated using a set of homemade velocimeters and a video camera. The effects of gas the flowrate and solution concentration on the bubble terminal velocity were examined respectively. Results show that the terminal velocity of the bubble increases with the increase in the gas flowrate and the decrease in the solution concentration. The shape of the bubble is gradually flattened horizontally to an ellipsoid with the increase in the Reynolds number (Re), Eötvös number (Eo), and Morton number (Mo). With the increase in the Re and Eo, the rising bubble in PAM aqueous solutions begin to oscillate, but there is no oscillation phenomena for CMC aqueous solutions. By dimensional analysis, the drag coefficient of a single bubble in non-Newtonian fluids in a moderate Reynolds number was correlated as a function of Re, Eo, and Archimedes number (Ar) based on the equivalent bubble diameter. The predicted results by the present correlation agree well with the experimental data.

Moderate Reynolds number flows through periodic and random arrays of aligned cylinders

1997 ◽  
Vol 349 ◽  
pp. 31-66 ◽  
Author(s):  
DONALD L. KOCH ◽  
ANTHONY J. C. LADD
Keyword(s):  
Reynolds Number ◽  
Pressure Gradient ◽  
Volume Fraction ◽  
Unit Length ◽  
Reynolds Numbers ◽  
Moderate Reynolds Number ◽  
Random Arrays ◽  
Flow Through ◽  
The Mean ◽  
Square Array

The effects of fluid inertia on the pressure drop required to drive fluid flow through periodic and random arrays of aligned cylinders is investigated. Numerical simulations using a lattice-Boltzmann formulation are performed for Reynolds numbers up to about 180.The magnitude of the drag per unit length on cylinders in a square array at moderate Reynolds number is strongly dependent on the orientation of the drag (or pressure gradient) with respect to the axes of the array; this contrasts with Stokes flow through a square array, which is characterized by an isotropic permeability. Transitions to time-oscillatory and chaotically varying flows are observed at critical Reynolds numbers that depend on the orientation of the pressure gradient and the volume fraction.In the limit Re[Lt ]1, the mean drag per unit length, F, in both periodic and random arrays, is given by F/(μU) =k1+k2Re2, where μ is the fluid viscosity, U is the mean velocity in the bed, and k1 and k2 are functions of the solid volume fraction ϕ. Theoretical analyses based on point-particle and lubrication approximations are used to determine these coefficients in the limits of small and large concentration, respectively.In random arrays, the drag makes a transition from a quadratic to a linear Re-dependence at Reynolds numbers of between 2 and 5. Thus, the empirical Ergun formula, F/(μU) =c1+c2Re, is applicable for Re>5. We determine the constants c1 and c2 over a wide range of ϕ. The relative importance of inertia becomes smaller as the volume fraction approaches close packing, because the largest contribution to the dissipation in this limit comes from the viscous lubrication flow in the small gaps between the cylinders.

Nutrient uptake in a suspension of squirmers

2016 ◽  
Vol 789 ◽  
pp. 481-499 ◽  
Author(s):  
Takuji Ishikawa ◽  
Shunsuke Kajiki ◽  
Yohsuke Imai ◽  
Toshihiro Omori
Keyword(s):  
Nutrient Uptake ◽  
Sherwood Number ◽  
Volume Fraction ◽  
Industrial Applications ◽  
Hydrodynamic Interactions ◽  
Energetic Cost ◽  
Unit Energy ◽  
Micro Organisms ◽  
Dilute Limit ◽  
Good Agreement

Nutrient uptake is one of the most important factors in cell growth. Despite the biological importance, little is known about the effect of cell–cell hydrodynamic interactions on nutrient uptake in a suspension of swimming micro-organisms. In this study, we numerically investigate the nutrient uptake in an infinite suspension of squirmers. In the dilute limit, our results are in good agreement with a previous study by Magar et al. (Q. J. Mech. Appl. Maths, vol. 56, 2003, pp. 65–91). When we increased the volume fraction of squirmers, the nutrient uptake of individual cells was enhanced by the hydrodynamic interactions. The average nutrient concentration in the suspension decayed exponentially as a function of time, and the relaxation time could be scaled using the Sherwood number, the Péclet number and the volume fraction of cells. We propose a fitting function for the Sherwood number, which is useful in predicting nutrient uptake in the non-dilute regime. Furthermore, we analyse the swimming energy consumed by individual cells. The results indicate that both the energetic cost and the nutrient uptake increased as the volume fraction of cells was increased, and that the uptake per unit energy was not significantly affected by the volume fraction. These findings are important in understanding the mass transport and metabolism of swimming micro-organisms in nature and for industrial applications.

The anomalous wake accompanying bubbles rising in a thin gap: a mechanically forced Marangoni flow

1997 ◽  
Vol 352 ◽  
pp. 283-303 ◽  
Author(s):  
JOHN W. M. BUSH
Keyword(s):  
Surface Tension ◽  
Bubble Surface ◽  
Surface Flow ◽  
Surface Tension Gradient ◽  
Marangoni Flow ◽  
Wake Structure ◽  
Rising Bubble ◽  
Moderate Reynolds Number ◽  
Mechanical Analogue ◽  
Order Of Magnitude

A novel wake structure, observed as penny-shaped air bubbles rise at moderate Reynolds number through a thin layer of water bound between parallel glass plates inclined at a shallow angle relative to the horizontal, is reported. The structure of the wake is revealed through tracking particles suspended in the water. The wake completely encircles the rising bubble, and is characterized by a reverse surface flow or ‘edge jet’ which transports fluid in a thin boundary layer along the bubble surface from the tail to the nose at speeds which are typically an order of magnitude larger than the bubble rise speed. A consistent physical explanation for the wake structure is proposed. The wake is revealed to be a manifestation of the three-dimensionality of the flow in the suspending fluid. The bubble surface advances through a rolling motion, thus generating regions of surface divergence and convergence at, respectively, the leading and trailing edges of the bubble. A nose-to-tail gradient in surfactant concentration is thus established, and the associated surface tension gradient drives the edge jet. The dependence of the wake structure on the suspending fluid is examined experimentally.Surfactants play an anomalous role in the reported flow, serving to promote rather than suppress surface motions. The wake structure is an example of a mechanically forced Marangoni flow, and so represents a mechanical analogue of that accompanying thermocapillary drop motion in microgravity. A theoretical model is developed which reproduces the salient features of the flow, and on the basis of which an estimate is made of the mechanically induced surface tension gradient along the bubble surface.

Direct numerical simulations of bubbly flows Part 2. Moderate Reynolds number arrays

1999 ◽  
Vol 385 ◽  
pp. 325-358 ◽  
Author(s):  
ASGHAR ESMAEELI ◽  
GRÉTAR TRYGGVASON
Keyword(s):  
Reynolds Number ◽  
Numerical Simulations ◽  
Volume Fraction ◽  
Three Dimensional ◽  
Direct Numerical Simulations ◽  
Dimensional System ◽  
Two Dimensional ◽  
Reynolds Stresses ◽  
Bubble Distribution ◽  
Moderate Reynolds Number

Direct numerical simulations of the motion of two- and three-dimensional finite Reynolds number buoyant bubbles in a periodic domain are presented. The full Navier–Stokes equations are solved by a finite difference/front tracking method that allows a fully deformable interface between the bubbles and the ambient fluid and the inclusion of surface tension. The rise Reynolds numbers are around 20–30 for the lowest volume fraction, but decrease as the volume fraction is increased. The rise of a regular array of bubbles, where the relative positions of the bubbles are fixed, is compared with the evolution of a freely evolving array. Generally, the freely evolving array rises slower than the regular one, in contrast to what has been found earlier for low Reynolds number arrays. The structure of the bubble distribution is examined and it is found that while the three-dimensional bubbles show a tendency to line up horizontally, the two-dimensional bubbles are nearly randomly distributed. The effect of the number of bubbles in each period is examined for the two-dimensional system and it is found that although the rise Reynolds number is nearly independent of the number of bubbles, the velocity fluctuations in the liquid (the Reynolds stresses) increase with the size of the system. While some aspects of the fully three-dimensional flows, such as the reduction in the rise velocity, are predicted by results for two-dimensional bubbles, the structure of the bubble distribution is not. The magnitude of the Reynolds stresses is also greatly over-predicted by the two-dimensional results.

Hydrodynamic Drag and Electrophoresis of Suspensions of Fractal Aggregates

Fractals ◽  
1997 ◽  
Vol 05 (03) ◽  
pp. 507-522 ◽  
Author(s):  
D. Coelho ◽  
J.-F. Thovert ◽  
R. Thouy ◽  
P. M. Adler
Keyword(s):  
Fractal Dimension ◽  
Stokes Equations ◽  
Volume Fraction ◽  
Mean Field ◽  
Three Dimensional ◽  
Fractal Dimensions ◽  
Hydrodynamic Drag ◽  
Hydrodynamic Properties ◽  
Fractal Aggregates ◽  
Dilute Limit

The hydrodynamic properties of fractal aggregates are investigated numerically by solving the three-dimensional Stokes equations. Aggregates are built with a variety of sizes and fractal dimensions. Their hydraulic radii conductivities and mobilities are evaluated as functions of their volume fraction in the suspension. An influence of the fractal dimension is visible on the hydrodynamic and electrokinetic characteristics of the aggregates. In the dilute limit, our results compare well with the predictions of various mean-field arguments.

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