Dynamics of homogeneous bubbly flows Part 2. Velocity fluctuations

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.

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Dynamics of homogeneous bubbly flows Part 1. Rise velocity and microstructure of the bubbles

Journal of Fluid Mechanics ◽

10.1017/s0022112002001179 ◽

2002 ◽

Vol 466 ◽

pp. 17-52 ◽

Cited By ~ 131

Author(s):

BERNARD BUNNER ◽

GRÉTAR TRYGGVASON

Keyword(s):

Void Fraction ◽

Stokes Equations ◽

Three Dimensional ◽

Navier Stokes ◽

Rise Velocity ◽

Navier Stokes Equations ◽

Front Tracking Method ◽

Deformable Interface ◽

The Individual ◽

Average Rise

Direct numerical simulations of the motion of up to 216 three-dimensional buoyant bubbles in periodic domains are presented. The full Navier–Stokes equations are solved by a parallelized finite-difference/front-tracking method that allows a deformable interface between the bubbles and the suspending fluid and the inclusion of surface tension. The governing parameters are selected such that the average rise Reynolds number is about 12–30, depending on the void fraction; deformations of the bubbles are small. Although the motion of the individual bubbles is unsteady, the simulations are carried out for a sufficient time that the average behaviour of the system is well defined. Simulations with different numbers of bubbles are used to explore the dependence of the statistical quantities on the size of the system. Examination of the microstructure of the bubbles reveals that the bubbles are dispersed approximately homogeneously through the flow field and that pairs of bubbles tend to align horizontally. The dependence of the statistical properties of the flow on the void fraction is analysed. The dispersion of the bubbles and the fluctuation characteristics, or ‘pseudo-turbulence’, of the liquid phase are examined in Part 2.

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Pseudo-turbulent gas-phase velocity fluctuations in homogeneous gas–solid flow: fixed particle assemblies and freely evolving suspensions

Journal of Fluid Mechanics ◽

10.1017/jfm.2015.146 ◽

2015 ◽

Vol 770 ◽

pp. 210-246 ◽

Cited By ~ 43

Author(s):

M. Mehrabadi ◽

S. Tenneti ◽

R. Garg ◽

S. Subramaniam

Keyword(s):

Kinetic Energy ◽

Phase Velocity ◽

Turbulent Kinetic Energy ◽

Gas Phase ◽

Reynolds Stress ◽

Slip Velocity ◽

Volume Fraction ◽

Velocity Fluctuations ◽

The Mean ◽

Particle Assemblies

Gas-phase velocity fluctuations due to mean slip velocity between the gas and solid phases are quantified using particle-resolved direct numerical simulation. These fluctuations are termed pseudo-turbulent because they arise from the interaction of particles with the mean slip even in ‘laminar’ gas–solid flows. The contribution of turbulent and pseudo-turbulent fluctuations to the level of gas-phase velocity fluctuations is quantified in initially ‘laminar’ and turbulent flow past fixed random particle assemblies of monodisperse spheres. The pseudo-turbulent kinetic energy $k^{(f)}$ in steady flow is then characterized as a function of solid volume fraction ${\it\phi}$ and the Reynolds number based on the mean slip velocity $\mathit{Re}_{m}$. Anisotropy in the Reynolds stress is quantified by decomposing it into isotropic and deviatoric parts, and its dependence on ${\it\phi}$ and $Re_{m}$ is explained. An algebraic stress model is proposed that captures the dependence of the Reynolds stress on ${\it\phi}$ and $Re_{m}$. Gas-phase velocity fluctuations in freely evolving suspensions undergoing elastic and inelastic particle collisions are also quantified. The flow corresponds to homogeneous gas–solid systems, with high solid-to-gas density ratio and particle diameter greater than dissipative length scales. It is found that for the parameter values considered here, the level of pseudo-turbulence differs by only 15 % from the values for equivalent fixed beds. The principle of conservation of interphase turbulent kinetic energy transfer is validated by quantifying the interphase transfer terms in the evolution equations of kinetic energy for the gas-phase and solid-phase fluctuating velocity. It is found that the collisional dissipation is negligible compared with the viscous dissipation for the cases considered in this study where the freely evolving suspensions attain a steady state starting from an initial condition where the particles are at rest.

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On the Spectra of Turbulent Velocity Field in a Stably Stratified Flow

Zeitschrift für Naturforschung A ◽

10.1515/zna-1991-0514 ◽

1991 ◽

Vol 46 (5) ◽

pp. 462-468

Author(s):

A. K. Chakraborty ◽

B. E. Vembe ◽

H. P. Mazumdar

Keyword(s):

Heat Flux ◽

Energy Spectrum ◽

Kinetic Energy ◽

Turbulent Kinetic Energy ◽

Eddy Viscosity ◽

Three Dimensional ◽

Inertial Subrange ◽

Coefficient Function ◽

One Dimensional ◽

Kinetic Energy Spectrum

Abstract This paper describes a method to solve the spectral equation for the balance of turbulent kinetic energy in a stably stratified turbulent shear flow. The cospectra of vertical momentum and heat flux arc modelled with the aid of a basic eddy-viscosity (or turbulent exchange coefficient) function. For the term representing the inertial transfer of turbulent kinetic energy, Pao's [Phys. Fluids 8 (1965)] form is assumed. Analytical expressions for the three-dimensional kinetic energy spectrum as well as the cospectra of momentum and heat flux are obtained over the range of wave numbers k≥kb, which includes the inertial subrange kb≪k≪ks and the viscous subrange k>ks (kb and ks are the buoyancy and Kolmogorov wavenumbers, respectively). The two one-dimensional spectra, e.g., the kinetic energy spectra of the horizontal and vertical components of turbulence are derived from the three-dimensional kinetic energy spectrum. These one-dimensional spectra are compared with the measured data of Gargett et al. [J. Fluid Mech. 144 (1984)] for the case I ( = ks/kb) = 630. Finally, we compute the basic eddy-viscosity function and discuss its behavio

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Phase Distribution in Buoyancy-Driven Bubbly Flows

Volume 2: Symposia and General Papers, Parts A and B ◽

10.1115/fedsm2002-31236 ◽

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.

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Turbulence modulation in buoyancy-driven bubbly flows

Journal of Fluid Mechanics ◽

10.1017/jfm.2021.942 ◽

2021 ◽

Vol 932 ◽

Author(s):

Vikash Pandey ◽

Dhrubaditya Mitra ◽

Prasad Perlekar

Keyword(s):

Numerical Simulation ◽

Large Scale ◽

Bubble Diameter ◽

Bubbly Flows ◽

Air Bubbles ◽

Rise Velocity ◽

Turbulence Modulation ◽

Budget Analysis ◽

Average Rise ◽

Turbulence Scaling

We present a direct numerical simulation (DNS) study of buoyancy-driven bubbly flows in the presence of large-scale driving that generates turbulence. On increasing the turbulence intensity: (a) the bubble trajectories become more curved and (b) the average rise velocity of the bubbles decreases. We find that the energy spectrum of the flow shows a pseudo-turbulence scaling for length scales smaller than the bubble diameter and a Kolmogorov scaling for scales larger than the bubble diameter. We conduct a scale-by-scale energy budget analysis to understand the scaling behaviour observed in the spectrum. Although our bubbles are weakly buoyant, the statistical properties of our DNS are consistent with the experiments that investigate turbulence modulation by air bubbles in water.

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Experiments and Modeling in Bubbly Flows at Elevated Pressures

Volume 1: Fora, Parts A, B, C, and D ◽

10.1115/fedsm2003-45793 ◽

2003 ◽

Author(s):

R. Kumar ◽

T. A. Trabold ◽

C. C. Maneri

Keyword(s):

Void Fraction ◽

Bubble Size ◽

Bubbly Flow ◽

Bubble Diameter ◽

Bubbly Flows ◽

Rise Velocity ◽

Two Phase ◽

Flow Models ◽

Gamma Densitometer ◽

Visualization Techniques

Measurements of local void fraction, rise velocity and bubble diameter have been obtained for cocurrent, wall-heated, upward bubbly flows in a pressurized refrigerant. The instrumentation used was the gamma densitometer and the hot-film anemometer. Departure bubble size and bulk size measurements were also made and correlated with appropriate parameters. Flow visualization techniques have also been used to understand the two-phase flow structure and the behavior of the bubbly flow for different bubble shapes and sizes, and to obtain the rise velocity. Such insight, coupled with quantitative local and averaged data on void fraction and bubble size at different pressures, has aided in developing bubbly flow models applicable to heated two-phase flows at high pressure.

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Direct numerical simulations of bubbly flows. Part 1. Low Reynolds number arrays

Journal of Fluid Mechanics ◽

10.1017/s0022112098003176 ◽

1998 ◽

Vol 377 ◽

pp. 313-345 ◽

Cited By ~ 169

Author(s):

ASGHAR ESMAEELI ◽

GRÉTAR TRYGGVASON

Keyword(s):

Reynolds Number ◽

Numerical Simulations ◽

Stokes Flow ◽

Stokes Equations ◽

Three Dimensional ◽

Direct Numerical Simulations ◽

Two Dimensional ◽

Rise Velocity ◽

Regular Array ◽

Average Rise

Direct numerical simulations of the motion of two- and three-dimensional buoyant bubbles in periodic domains 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 governing parameters are selected such that the average rise Reynolds number is O(1) and deformations of the bubbles are small. The rise velocity of a regular array of three-dimensional bubbles at different volume fractions agrees relatively well with the prediction of Sangani (1988) for Stokes flow. A regular array of two- and three-dimensional bubbles, however, is an unstable configuration and the breakup, and the subsequent bubble–bubble interactions take place by ‘drafting, kissing, and tumbling’. A comparison between a finite Reynolds number two-dimensional simulation with sixteen bubbles and a Stokes flow simulation shows that the finite Reynolds number array breaks up much faster. It is found that a freely evolving array of two-dimensional bubbles rises faster than a regular array and simulations with different numbers of two-dimensional bubbles (1–49) show that the rise velocity increases slowly with the size of the system. Computations of four and eight three-dimensional bubbles per period also show a slight increase in the average rise velocity compared to a regular array. The difference between two- and three-dimensional bubbles is discussed.

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Experiments and Modeling in Bubbly Flows at Elevated Pressures

Journal of Fluids Engineering ◽

10.1115/1.1567308 ◽

2003 ◽

Vol 125 (3) ◽

pp. 469-478 ◽

Cited By ~ 6

Author(s):

Ranganathan Kumar ◽

Thomas A. Trabold ◽

Charles C. Maneri

Keyword(s):

Void Fraction ◽

Bubble Size ◽

Bubbly Flow ◽

Bubble Diameter ◽

Bubbly Flows ◽

Rise Velocity ◽

Two Phase ◽

Flow Models ◽

System Pressure ◽

Eotvos Number

Measurements of local void fraction, rise velocity, and bubble diameter have been obtained for cocurrent, wall-heated, upward bubbly flows in a pressurized refrigerant. The instrumentation used are the gamma densitometer and the hot-film anemometer. Departure bubble size is correlated in terms of liquid subcooling and bulk bubble size in terms of void fraction. Flow visualization techniques have also been used to understand the two-phase flow structure and the behavior of the bubbly flow for different bubble shapes and sizes, and to obtain the bubble diameter and rise velocity. The lift model is provided explicitly in terms of Eotvos number which is changed by changing the system pressure. In general, Eotvos number plays a strong role in determining both bubbly lift and drag. Such insight coupled with quantitative local and averaged data on void fraction and bubble size at different pressures has aided in developing bubbly flow models applicable to heated two-phase flows at high pressure.

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