Bubble-induced Turbulence Research Articles

A numerical study on the turbulence characteristics in an air–water upward bubbly pipe flow

A high-resolution numerical simulation of an air–water turbulent upward bubbly flow in a pipe is performed to investigate the turbulence characteristics and bubble interaction with the wall. We consider three bubble equivalent diameters and three total bubble volume fractions. The bulk and bubble Reynolds numbers are $Re_{bulk}= u_{bulk} D/\nu _w = 5300$ and $Re_{bub}= (\langle u_{bub}\rangle - u_{bulk}) d_{eq}/\nu _w = 533\unicode{x2013}1000$ , respectively, where $u_{bulk}$ is the water bulk velocity, $\langle u_{bub}\rangle$ is the overall bubble mean velocity, $D$ is the pipe diameter and $\nu _w$ is the water kinematic viscosity. The mean water velocity near the wall significantly increases due to bubble interaction with the wall, and the root-mean-square water velocity fluctuations are proportional to $\bar {\psi }(r)^{0.4}$ , where $\bar {\psi } (r)$ is the mean bubble volume fraction. For the cases considered, the bubble-induced turbulence suppresses the shear-induced turbulence and becomes the dominant flow characteristic at all radial locations including near the wall. Rising bubbles near the wall mostly bounce against the wall rather than slide along the wall or hang around the wall without collision. Low-speed streaks observed in the near-wall region in the absence of bubbles nearly disappear due to the bouncing bubbles. These bouncing bubbles generate counter-rotating vortices in their wake, and increase the skin friction by sweeping high-speed water towards the wall. We also suggest an algebraic Reynolds-averaged Navier–Stokes model considering the interaction between shear-induced and bubble-induced turbulence. This model provides accurate predictions for a wide range of liquid bulk Reynolds numbers.

Euler-Euler simulation of a bubble column flow up to high gas fraction

This study investigates homogeneous flow in a bubble column up to 50% gas holdup. For low to medium gas holdup below ∼20%, the good performance of an established baseline model is confirmed. In this range, the mixture pressure gradient is decisive in determining the relative velocity, resulting in good predictions without considering swarm effects. However, beyond a gas holdup of ∼20%, a swarm corrector to the drag force becomes necessary, for which several proposals from the literature are evaluated. In addition, the lift force influences the shape of the gas fraction profile depending on the bubble size, which has a significant impact on the liquid flow inside the column. For wall-peaked profiles, the liquid flow remains moderate, while center-peaked profiles strongly boost the liquid velocity. Finally, several mechanisms proposed in the literature for inducing unstable flow based on the lift force, bubble-induced turbulence or flooding are investigated. Of these only the first gave qualitative agreement with the observed gas holdup.

Investigation of equivalent spherical bubble diameter at high inlet velocity pool scrubbing conditions

This study investigates Equivalent Spherical Diameter (ESD) estimation at high inlet velocity pool scrubbing conditions using the Interfacial Area Transport Equation (IATE) diameter model including bubble-induced turbulence and interphase modeling. The compatibility of area-averaged Sauter Mean Diameter (SMD), area-averaged Local Equivalent Diameter (LED) and void-weighted area-averaged LED approaches to estimate the ESD are explored and the proposed model is validated against available experimental data. The study reveals that the prevalent constant ESD assumption in pool scrubbing codes is not universal by showcasing a decreasing trend along the column due to intensive bubble breakup. The area-averaged LED approach fails to capture this trend, while the area-averaged SMD and void-weighted area-averaged LED approaches provide accurate estimations aligned with experimental data. Turbulence parameters, interfacial forces, and diameter modeling are identified as crucial for accurate predictions of flow and geometrical variables by setting up the OpenFOAM framework. A sensitivity analysis indicates that the inlet velocity has an acceptable effect on the ESD along the column. The ESD increases near the exit and decreases in the swarm region by increasing the inlet velocities. Turbulent intensity reduces ESD across all column sections while changes in aspect ratio minimally impact ESD. The study shows promise in developing correlations that take into account the spatial variation of ESD in pool scrubbing conditions.

Numerical modeling of turbulent air-water mixture flows in spilling breaking waves

This paper presents a numerical study of turbulent air-water mixture flows under spilling breaking waves by using a mixture-flow model. The model is extended from the earlier 2D numerical framework NEWFLUME, which solves the Reynolds-averaged Navier-Stokes (RANS) equations for mean flow motions. The turbulence closure is accomplished by a modified k−ε two-equations model, in which the effect of entrained bubbles on turbulence production and dissipation is considered by incorporating additional buoyancy terms. A transient equation based on two-fluid formulation is solved for air bubble transport. The present model is validated by comparing the simulated free surface displacement, void fraction, mean velocity and turbulence kinetic energy against existing experimental data and the previous numerical results. The effects of the additional convective term in transient equation of void fraction and the bubble-induced turbulence term in turbulence transport equation are further explored. The results reveal that the additional convective term in the transient equation of void fraction plays an essential role of suppressing unphysical turbulence growth and bringing correct amount of air entrainment into water during wave breaking processes. The additional bubble-induced turbulence production and dissipation terms become effective after wave breaks when the void fraction has been appropriately modeled, and they can further reduce the simulated turbulence intensities in spilling breaking wave, rendering a better agreement with the experimental measurements.

Revisiting RANS turbulence modelling for bubble-induced turbulence: Effects of surfactants

Recent experiments of dispersed bubbly flow (Ma et al., 2023) show that contamination of the carrier phase plays a considerable role in bubble-induced turbulence (BIT): although the bubbles rise slower with adding surfactants, the BIT increases. This trend, however, cannot be reproduced by any current BIT models in the framework of Euler–Euler Reynolds-averaged Navier–Stokes two-equation turbulence model, including the model proposed by Ma et al. (2017). The present work revisits this widely used model (Ma et al., 2017) as a representative, which considers the BIT with an additional source term in the k- and ɛ (or ω) - equation, respectively. We have systematically investigated the reason why such a BIT model is unable to capture the BIT modulation caused by different degrees of contamination and discuss the new possibility for the prefactor in the source term of the ɛ-equation that may improve the results.

Direct numerical simulation of bubble collision, bounce and coalescence in bubble-induced turbulence

A direct numerical simulation study has been carried out to better understand the dynamics of deformable bubbles in bubble-induced turbulence. A mathematical model for bubble collision, bounce and coalescence is developed based on the Volume-of-Fluid (VoF) method. A surface-tension-holding film thickness δc is introduced to determine whether the bubbles will coalesce or bounce after collision. Bubbly flows with the gas volume fractions αg=5.6% (low), 11.2% (medium) and 22.1% (high) are considered in the study. The DNS results show that the dissipation of turbulent kinetic energy in the cases under consideration takes place when the wavenumber κ is smaller than twice the wavenumber for the bubble diameter 2κd. The bubble-induced turbulence is anisotropic at the length scales close to the bubble diameter due to the elongated turbulent structures in the bubble-rising direction. The bubbles collide intensively with each other when they are in a cluster surrounded by the liquid with low pressure. Parallel clustering of bubbles is found when the gas volume fraction has a low or medium value. Three-dimensional clustering is found when the bubbles are densely populated. Two different mechanisms of bubble collision have been identified from the DNS results, termed parallel collision and vertical collision. Parallel collision is often observed when bubbles are sparsely populated. In a parallel collision, the relative velocity of the bubbles slows down as two bubbles approach each other due to the jet flow between them, while the relative velocity increases sharply after the bounce. In a vertical collision, by contrast, the relative velocity of bubbles accelerates as two bubbles approach each other, while it slows down during the collision. Vertical collisions occur when the bubbles are more densely populated. The numerical results also show the significant effects of δc on bubble coalescence.

Experimental investigation on distribution of boric acid in a vertical 1 × 2 rod array channel

During the reactor operation, the mixing mass flow of boron acid caused by diversion cross-flow, turbulent mixing and void drift changes the boron concentration distribution in the coolant and affects the amount of boron in the Chalk River Unidentified Deposit (CRUD). Accumulation of boron within the porous crud layer on the fuel rods in the cores of pressured water reactors (PWR) results in the crud-induced power shift (CIPS), threatening the operation safety of reactors. In order to obtain the mixing mass flow of boric acid between adjacent channels, a vertical test channel containing two subchannels simulating a PWR fuel rod bundle is constructed. Using this channel, flow distributions and mixing mass flow of boric acid are measured for single-phase and two-phase air–water flows. The measurements show that the boric acid distribution is affected by turbulent mixing for single-phase flow and the mixing mass flow of boric acid increases with the Reynolds number. For two-phase flow, the bubble-induced turbulence enhances the turbulence intensity of the liquid flow, the mixing mass flow of boric acid increases with the increase of void drift and reaches the maximum in the slug flow. The experimental data is used to support the development and validation of a new transverse source term model of boron mixing. The comparison result shows the significant improvement of the code prediction.

Polarization Multiplexing Based UOWC Systems Under Bubble Turbulence

High-speed and turbulence-tolerant transmission links are required to meet the growing demand for underwater optical wireless communication (UOWC). However, most previous works were implemented in statically simulated underwater channels with uniform temperature and salinity gradients irrespective of bubble motion. This paper presents an experimental demonstration of a polarization multiplexing (PolMux) based UOWC system considering bubble-induced turbulence. A theoretical transmission model is built and experiments are carried out to investigate the impact of bubble turbulence on PolMux transmission. The general rules of bubble impairments are summarized by manipulating different bubble flow rates, positions and bubble-effected region thicknesses. Moreover, to mitigate these effects, subchannel pairwise coding is implemented to address the subchannel signal-to-noise-ratio (SNR) imbalance issue, and subcarrier pairwise coding is utilized to overcome the subcarrier SNR imbalance, reaching a sum data rate of 8.58 Gbps. This work evaluates the performance of PolMux-UOWC links in the presence of air bubbles and demonstrates the feasibility of pairwise coding to achieve high-speed transmission in UOWC systems with bubble turbulence.

Effects of surfactants on bubble-induced turbulence

We use experiments to explore the effect of surfactants on bubble-induced turbulence (BIT) at different scales, considering how the bubbles affect the flow kinetic energy, anisotropy and extreme events. To this end, high-resolution particle shadow velocimetry measurements are carried out in a bubble column in which the flow is generated by bubble swarms rising in water for two different bubble diameters (3 and 4 mm) and moderate gas volume fractions (0.5 %–1.3 %). We use tap water as the base liquid and add 1-Pentanol as an additional surfactant with varying bulk concentration, leading to different bubble shapes and surface boundary conditions. The results reveal that with increasing surfactant concentration, the BIT generated increases in strength, even though bubbles of a given size rise more slowly with surfactants. We also find that the level of anisotropy in the flow is enhanced with increasing surfactant concentration for bubbles of the same size, and that for the same surfactant concentration, smaller bubbles generate stronger anisotropy in the flow. Concerning the intermittency quantified by the normalized probability density functions of the fluid velocity increments, our results indicate that extreme values in the velocity increments become more probable with decreasing surfactant concentration for cases with smaller bubbles and low gas void fraction, while the effect of the surfactant is much weaker for cases with larger bubble and higher void fractions.

A Note on Modeling the Effects of Surfactants on Bubble‐Induced Turbulence

AbstractRecent experimental results reveal that with rising concentration of surfactants, the generated bubble‐induced turbulence (BIT) increases as well, although the bubbles rise slower. Herein, it is shown that this phenomenon has not be considered so far in the standard Reynolds‐averaged Navier‐Stokes (RANS) modeling for BIT, using the Ansatz with source terms added to the transport equation of turbulent kinetic energy and dissipation, respectively. Some problematic issues related to the common concepts for closure of the liquid‐phase turbulence kinetic energy equation are also discussed. Furthermore, this issue is demonstrated by simulating the experiments using two‐fluid approach.

Effects of bubble-induced turbulence on interfacial species transport: A direct numerical simulation study

A direct numerical simulation (DNS) study is carried out to understand the effects of bubble-induced turbulence on the interfacial species transport. A volume-of-fluid (VOF) method is used in the DNS to simulate the multiphase flow in a box containing one or two deformable bubbles. The bubbly flows with Schmidt numbers 1≤Sc≤64, Reynolds numbers 100≤ReB≤750, Eötvös number Eo=1.21 and gas volume fractions 2.8%≤αg≤22.1% have been investigated. The DNS results indicate that the one-dimensional energy spectra evolve as the power −3 of the wavenumber at large scales. At a high Schmidt number, an inertial subrange characterized by the -5/3 slope can be found in the power spectra of species concentration. The power spectra of species concentration for different Schmidt numbers become close to each other when the wavenumber is scaled with Sc0.5. The bubble-induced turbulence enhances the oscillation of the transient Sherwood number, however, it has marginal effects on the time-averaged value. By contrast, the time-averaged Sherwood number for a fixed Peclet number increases with an increase of αg, indicating that convection plays a more important role in species transport when the bubbles are more densely populated. A possible reason is that, the neighboring bubbles enhance the spatial fluctuations of the velocity, which favor the interfacial species transfer. The energy spectrum confirms that an increase of αg leads to stronger spatial fluctuations of the vertical velocity component at low wavenumbers.

Assessing passive scalar dynamics in bubble-induced turbulence using direct numerical simulations

By using direct numerical simulations (DNS) of bubbly flows with passive scalars, we show a transition in the scalar spectra from a $k^{-5/3}$ to a $k^{-3}$ scaling with the wavenumber $k$ , in contrast with those of single-phase isotropic turbulence. For cases with a mean scalar gradient in the horizontal direction, the scalar spectrum decays faster than $k^{-3}$ at high wavenumbers. While the $k^{-3}$ scaling is well established in the bubbly flow velocity spectrum, the scalar spectrum behaviour is not fully understood. We find that the transition length scale of the scalar spectra is comparable to or below the bubble diameter and decreases with the molecular diffusivity of the scalar in the liquid. We use DNS to compute the scalar spectrum budget and show that the scalar fluctuations are produced by the mean scalar gradient at length scales above the bubble diameter, contrary to the velocity fluctuations. At length scales below the bubble diameter, the net scalar transfer scales as $k^{-1}$ inducing the $k^{-3}$ scaling of the scalar spectra. This finding is consistent with the hypothesis proposed by Dung et al. (J. Fluid Mech., vol. 958, 2023, p. A5) about the physical mechanism behind the $k^{-3}$ scaling. We also show dependencies of the bubble suspension's convective scalar diffusivity on the gas volume fraction and molecular diffusivity that differ based on the direction of the mean scalar gradient. For a mean scalar gradient in the vertical direction, we find and qualitatively explain a significant effect of the molecular diffusivity in the gas on the convective scalar diffusivity.

Bubble-induced turbulence in CFD simulation of bubble columns. Part I: Coupling of SIT and BIT

One of the challenges in CFD simulation of gas–liquid flow is the modeling of shear-induced turbulence (SIT) and bubble-induced turbulence (BIT). Although many BIT models have been proposed, there is no consensus on the effect of BIT models. This paper aims to investigate this issue and the coupling mechanisms of SIT and BIT. When activating BIT, we find a marginal effect of Simonin model, yet a significant effect of the Sato or TH model. In addition, the coupling mechanisms of BIT and SIT are different when applying various SIT models. For the RNG k-ε model, the Sato model generates a snowball effect that greatly increases the SIT viscosity, but this effect is lacking in the standard k-ε model. In summary, the role of BIT in CFD simulation depends on its formulation and the coupling mechanisms with various SIT models. These findings would be helpful to the future study of BIT.

Computational Fluid Dynamics Modelling of Two-Phase Bubble Columns: A Comprehensive Review

Bubble columns are used in many different industrial applications, and their design and characterisation have always been very complex. In recent years, the use of Computational Fluid Dynamics (CFD) has become very popular in the field of multiphase flows, with the final goal of developing a predictive tool that can track the complex dynamic phenomena occurring in these types of reactors. For this reason, we present a detailed literature review on the numerical simulation of two-phase bubble columns. First, after a brief introduction to bubble column technology and flow regimes, we discuss the state-of-the-art modelling approaches, presenting the models describing the momentum exchange between the phases (i.e., drag, lift, turbulent dispersion, wall lubrication, and virtual mass forces), Bubble-Induced Turbulence (BIT), and bubble coalescence and breakup, along with an overview of the Population Balance Model (PBM). Second, we present different numerical studies from the literature highlighting different model settings, performance levels, and limitations. In addition, we provide the errors between numerical predictions and experimental results concerning global (gas holdup) and local (void fraction and liquid velocity) flow properties. Finally, we outline the major issues to be solved in future studies.

A mesoscale bubble-induced turbulence model and simulation of gas–liquid flows

In gas–liquid two-phase flows, bubble motion significantly affects liquid phase turbulence, and adding bubble-induced turbulence (BIT) source term is widely used to improve the simulation accuracy. This paper presents a new BIT model based on the energy-minimization multi-scale (EMMS) methodology. The model was constructed by considering two mesoscale factors, i.e., the sub-grid structures through analyzing the slip velocity and the gas holdup gradient, and the equivalent diameter of turbulent eddies calculated by the EMMS-based turbulence model. In order to verify its performance, the model was incorporated to the Eulerian–Lagrangian simulating framework and applied to two typical experimental systems. Both mean flow characteristics and turbulence quantities were well predicted, and the new model showed advantages over traditional BIT models, especially at higher gas velocities. Moreover, a strategy for counting energy dissipation in the simulation was devised and performed whereby the dual effects of promotion and suppression on liquid phase turbulence by bubbles can be reflected. The simulations demonstrated that BIT dominated the energy dissipation and turbulence was enhanced by BIT at higher gas velocities, while shear-induced turbulence dominated the energy dissipation and turbulence is reduced due to the suppression by bubbles at lower gas velocities.

Analysis of two-phase flow regimes and parameter distribution in 5 x 5 rod bundle using image processing techniques

With the recent developments in image processing and analysis, this paper presents bubble characteristics distribution in adiabatic air-water two-phase flow through a 5 × 5 rod bundle. The experiment covered water superficial velocities (Jl = 0.012 m/s – 0.421 m/s) and air superficial velocities (Jg = 0.042 m/s – 0.987 m/s) in which three distinct flow regimes were identified. The flow regime map was compared with existing flow regime transition criteria for vertical rod bundles. Distinct features from the two-phase flow images were extracted to train a classifier model to distinguish between regimes from a separate experiment. The model distinguishes between the bubbly flow regime and others accurately. The void fraction and velocity distributions were also extracted from the R–CCN masked images. Bubble-induced turbulence that was dominant in the subchannel at (Jl = 0.28 m/s) shifted to the outer subchannels and gaps when the flow rate increased (Jl = 0.42 m/s). These methods over-predicted the void faction around the surfaces of the inner rods.

An experimental study on the liquid phase properties of a bubble column operated in the homogeneous and in the heterogeneous regimes

We present an experimental study on the liquid phase properties in a bubble column. The reactor, that has a diameter of 40 cm, can be operated in both the homogeneous and the heterogeneous regimes, reaching superficial gas velocities and void fractions up to 23.2 cm/s and 30%, respectively.Our measurements, obtained with a Pavlov tube, have a temporal resolution of 20 Hz, and cover different superficial gas velocities and axial and radial positions. The moderate temporal resolution achieved allowed to quantify the liquid velocity via probability density functions, standard deviations, spectra and spatial and temporal integral scales.Spectral analysis was performed to study the validity of bubble-induced turbulence models. While such models were developed for the homogeneous regime, we show that they can be applied, with some limitations, to the heterogeneous one. In particular, a -3 power law is found in the liquid velocity spectra, with integral scales related to the column’s diameter.

CFD simulation of mass transfer in bubble columns: Detailed study of mass transfer models

The accuracy of the computational fluid dynamics simulations of mass transfer process in bubble columns is significantly influenced by the mass transfer models. Various mass transfer models have been developed based on different theories. However, it is still confusing on the choice of mass transfer models when performing the simulations of mass transfer in bubble columns. In the present work, the applicability and accuracy of three types of widely-used mass transfer models, including the single bubble-based models, the slip velocity model, and the surface renewal stretch model, were assessed with the spatially resolved data of gas holdup and species concentration in the literature. By comparing simulation results with experimental data, the present work provided suggestions on choosing a proper mass transfer model when performing simulations of the mass transfer process in bubble columns. The influence of bubble-induced turbulence and its different modeling approaches on different mass transfer models were investigated.

Bubbles generate their own kind of turbulence

Simulations of bubble-induced turbulence, while fundamentally different from those of classical homogeneous isotropic turbulence, do not need to account for bubble shape, topology, or breakup and coalescence.

Experimental Investigations and Numerical Assessment of Liquid Velocity Profiles and Turbulence for Single- and Two-phase Flow in a Constricted Vertical Pipe

In this work, the capabilities of state-of-the-art turbulence models are compared for a three-dimensional flow (3D) field within a constricted vertical pipe. The considered flow domain is a vertical pipe section with a baffle-shaped flow constriction which leads to the development of a jet flow through and a recirculation flow region behind the constriction. Different Reynolds-Averaged Navier-Stokes (RANS) and Large Eddy Simulation (LES) models were tested for single- and two-phase flow simulations. In the two-phase simulations, bubble-induced turbulence (BIT) was also considered by adding source terms in the k and ε/ω equations. The results are validated against experimental data. We employed hot-film anemometry (HFA) for liquid velocity measurement and combined it with ultrafast X-ray computed tomography (UFXCT), which provides gas phase data. Based on the local phase-indicator function obtained from the tomographic image data, we can correct HFA signals, which become corrupted by bubble contacts. We found that for single-phase flow all RANS models predict axial velocity well while radial velocity prediction is inadequate. LES models, however, achieve a better prediction of the latter. For two-phase flow, the axial component of the liquid velocity is well captured by all RANS models and the radial component of the liquid velocity is predicted better than for single-phase flow. In general, the computationally less costly RNG k-ε model performs similar to the SSG RSM model and can therefore be recommended for simulation of complex flow scenarios.