Bubbly Turbulent Flow Research Articles

A New Bubble Image Model Based on the Recognition of Bubble Flow

AbstractIn this study, a new ellipse‐fitting algorithm is proposed to achieve the reconstruction of bubble shapes in bubbly flow captured by a high‐speed camera in the gas–liquid two‐phase column reactor. Bubble flow patterns and geometric parameters in the experimental images are recognized and identified successfully, represented by means of the topological parameters. Three logical steps are carried out in detail. First, the area threshold and the circularity factors are established to identify the bubbles whether belonging to a single bubble or not. The overlapping bubbles in images can be separated from single bubbles based on a watershed segmentation algorithm. Second, a single bubble image and an overlapping bubble image are combined into one image. After that, statistical analysis for the size distributions and ellipse area bubbles is performed for further analysis and discussion. The advantage of this algorithm is that it can make use of a set of major and minor axes of an ellipse to capture the ellipse parameters more effectively. Simulation results are well agreed with experimental measurements. Moreover, it can be used to detect many ellipse‐like bubbles that are dispersed in high‐speed camera images, indicating that it is a better strategy for the recognition and identification of bubbly turbulent flow accurately.

An investigation of anisotropy in the bubbly turbulent flow via direct numerical simulations

We investigated the effects of bubble count, flow direction, and Eötvös number on deformable bubbles in turbulent channel flow. For a given shear Reynolds number Re = 180 and fixed bubble volume fractions (1.263% and 2.525%), we conducted a series of direct numerical simulations using a coupled level-set and volume-of-fluid solver to evaluate their impact on bubble volume fraction distribution, velocity fields, and turbulence characteristics. Each aspect was studied based on the microscopic equations of two-phase flow, and the accuracy of the modeling terms used in current Reynolds-averaged Navier–Stokes equation (RANS) models was assessed. The influence on the anisotropic state was analyzed using the Lumley triangle, and the anisotropy of Reynolds stresses was captured through the exact balance equations. The results indicate that in upward flow, bubbles tend to accumulate near the wall, with smaller Eötvös numbers leading to closer proximity to the wall and greater attenuation of the liquid-phase velocity. This distribution enhances energy dissipation and turbulence isotropy. In downward flow, bubbles cluster in the channel center, generating additional pseudo-turbulence and attenuating energy in the buffer layer. Moreover, the interfacial transfer of turbulent energy, as currently modeled in RANS, is found to be inadequate for upward flows.

Vortex ring and bubble interaction: Effects of bubble size on vorticity dynamics and bubble dynamics

Bubbly turbulent flows involve complex interactions between bubbles and vortices, in which their size ratio plays a critical role. The present work investigates an idealization, namely, the interaction of a single air bubble with a (water) vortex ring, with the focus being on the effects of the bubble-to-vortex core size ratio (Db/Dc,o) on the bubble and ring dynamics (Db = bubble diameter and Dc,o = initial vortex core diameter). The interaction is studied for size ratio, Db/Dc,o, of 0.6–1.7, over a large Weber number range from 10 to 500 [We=0.87ρ(Γ/πDc,o)2/(σ/Db), Γ = circulation]. On the bubble dynamics side, in the initial stages of the interaction after the bubble's capture by the ring, the bubble's radial equilibrium position, its azimuthal elongation, and breakup pattern are influenced by both Db/Dc,o and We. However, at longer times, the results show that the We alone decides the broken bubbles to Db ratio and scales as We−0.13, which can be contrasted with the scaling of We−0.6 in isotropic turbulence [R. Shinnar, J. Fluid Mech. 10, 259–275 (1961)]. On the ring dynamics side, increasing Db/Dc,o leads to larger deformation of the vortex ring core at low We, and these effects are significant above a critical Db/Dc,o of about 1.2. Under these conditions, the vortex core can fragment, leading to large reductions in the ring's measured convection speed and axial enstrophy, both of which follow a similar scaling, (Db/Dc,o)2/We; the reduction in enstrophy being reminiscent of bubbly turbulent flows. These results and scalings should help us to better understand and model bubble–turbulence interactions.

The interfacial modes and modal causality in a dispersed bubbly turbulent flow

While data-driven analysis has demonstrated significant success in single-phase flow systems, its application to multi-phase flows has been relatively limited with fewer examples. In this study, we present a modal analysis and modal causality analysis of dispersed bubbly turbulent flow, with the aim of providing new insights into the interfacial gas–liquid interaction. Our study employs an in-house coupled level-set volume-of-fluid solver, which is combined with a modified fast Fourier transforms algorithm to perform interface-resolved direct numerical simulations in a turbulent channel flow with 96 bubbles occupying 5.4% volume. In the downward flow orientation, we observe that bubbles are mainly clustered in the channel center, producing pseudo-turbulence with isotropic characteristics. We apply the proper orthogonal decomposition method to the phase-resolved, three-dimensional velocity field, radius of the bubble as well as the surface tension force in order to extract the dominant modes. Notably, our results reveal the presence of two energetic modes in both the gas and liquid phases, as well as the interface, namely, the vortex-ring mode and the quadrupolar mode. We further investigate the causal relationship across the gas–liquid interface using the modal information transfer entropy. Our findings demonstrate a strong causality between the gas phase and the surface tension, whereas the causality between the liquid phase and surface tension is comparatively weak due to the multi-scale characteristics of the turbulent fields. Overall, our novel approach to investigating the interfacial gas–liquid interaction in dispersed bubbly turbulent flow provides valuable insights that enhance physical understanding and could lead to improved flow control and efficiency in a range of industrial processes. The identification of previously unidentified energetic modes using the POD method has the potential to advance research in this field, with potential implications for future design of control strategies in complex systems.

The role of breakup and coalescence in fine-scale bubble-induced turbulence. I. Dynamics

We study the effect of bubble breakup and coalescence on fine-scale dynamics of bubbly turbulent flows using direct numerical simulations. We perform two different simulations of dilute bubbly flows of void fraction 0.5%: one with bubbles breaking up and coalescing and the other without these physical processes. The volume of the fluid method is used for simulating bubbles undergoing breakup and coalescence while the bubbles are treated as rigid spheres in the immersed boundary method simulation. The energy spectrum in both types of simulation, consistent with previous studies, exhibits a −3 slope. We follow a single infinitesimal fluid element as it evolves to understand velocity gradient dynamics using conditional mean trajectories. We note finite-time divergence when the fluid element evolves under the action of inertial and pressure dynamics. The inertial, pressure, and viscous velocity gradient dynamics, when considered individually, produce the same results for bubble-induced turbulence (BIT) as with the classical homogeneous isotropic turbulence (HIT). Yet when the overall velocity gradient dynamics is considered, BIT results in non-cyclic trajectories moving toward stable node and unstable saddle while classical HIT shows cyclic behavior in their trajectories that move toward the origin. Interestingly, both the volume of fluid and immersed boundary simulations produce similar results. Therefore, there are two main takeaways from this research. First, new velocity gradient models are needed for BIT as their velocity gradients behavior is entirely different from the HIT. Second, we can neglect the bubble topology, breakup, and coalescence while studying or modeling the fine-scale dynamics of BIT.

Experimental and Numerical Study of the Flow and Heat Transfer in a Bubbly Turbulent Flow in a Pipe with Sudden Expansion

The flow patterns and heat transfer of a downstream bubbly flow in a sudden pipe expansion are experimentally and numerically studied. Measurements of the bubble size were performed using shadow photography. Fluid phase velocities were measured using a PIV system. The numerical model was employed the Eulerian approach. The set of RANS equations was used for modelling two-phase bubbly flows. The turbulence of the carrier liquid phase was predicted using the Reynolds stress model. The peak of axial and radial fluctuations of the carrier fluid (liquid) velocity in the bubbly flow is observed in the shear layer. The addition of air bubbles resulted in a significant increase in the heat transfer rate (up to 300%). The main enhancement in heat transfer is observed after the point of flow reattachment.

Experimental investigation of the turbulence induced by a bubble swarm rising within incident turbulence

This work reports an experimental characterisation of the flow properties in a homogeneous bubble swarm rising at high Reynolds numbers within a homogeneous and isotropic turbulent flow. Both the gas volume fraction $\unicode[STIX]{x1D6FC}$ and the velocity fluctuations $u_{0}^{\prime }$ of the carrier flow before bubble injection are varied, respectively, in the ranges $0\,\%<\unicode[STIX]{x1D6FC}<0.93\,\%$ and $2.3~\text{cm}~\text{s}^{-1}<u_{0}^{\prime }<5.5~\text{cm}~\text{s}^{-1}$. The so-called bubblance parameter ($b=V_{r}^{2}\unicode[STIX]{x1D6FC}/u_{0}^{\prime 2}$, where $V_{r}$ is the bubble relative rise velocity) is used to compare the ratio of the kinetic energy generated by the bubbles to the one produced by the incident turbulence, and is varied from 0 to 1.3. Conditional measurements of the velocity field downstream of the bubbles in the vertical direction allow us to disentangle three regions that have specific statistical properties, namely the primary wake, the secondary wake and the far field. While the fluctuations in the primary wake are similar to that of a single bubble rising in a liquid at rest, the statistics of the velocity fluctuations in the far field follow a Gaussian distribution, similar to that produced by the homogenous and isotropic turbulence at the largest scales. In the secondary wake region, the conditional probability density function of the velocity fluctuations is asymmetric and shows an exponential tail for the positive fluctuations and a Gaussian one for the negative fluctuations. The overall agitation thus results from the combination of these three contributions and depends mainly on the bubblance parameter. For $0<b<0.7$, the overall velocity fluctuations in the vertical direction evolve as $b^{0.4}$ and are mostly driven by the far-field agitation, whereas the fluctuations increase as $b^{1.3}$ for larger values of the bubblance parameter ($b>0.7$), in which the significant contributions come both from the secondary wake and the far field. Thus, the bubblance parameter is a suitable parameter to characterise the evolution of liquid agitation in bubbly turbulent flows.

Energy spectra in turbulent bubbly flows

We conduct experiments in a turbulent bubbly flow to study the nature of the transition between the classical $-5/3$ energy spectrum scaling for a single-phase turbulent flow and the $-3$ scaling for a swarm of bubbles rising in a quiescent liquid and of bubble-dominated turbulence. The bubblance parameter (Lance & Bataille J. Fluid Mech., vol. 222, 1991, pp. 95–118; Rensen et al., J. Fluid Mech., vol. 538, 2005, pp. 153–187), which measures the ratio of the bubble-induced kinetic energy to the kinetic energy induced by the turbulent liquid fluctuations before bubble injection, is often used to characterise bubbly flow. We vary the bubblance parameter from $b=\infty$ (pseudoturbulence) to $b=0$ (single-phase flow) over 2–3 orders of magnitude (0.01–5) to study its effect on the turbulent energy spectrum and fluctuations in liquid velocity. The probability density functions (PDFs) of the fluctuations in liquid velocity show deviations from the Gaussian profile for $b>0$, i.e. when bubbles are present in the system. The PDFs are asymmetric with higher probability in the positive tails. The energy spectra are found to follow the $-3$ scaling at length scales smaller than the size of the bubbles for bubbly flows. This $-3$ spectrum scaling holds not only in the well-established case of pseudoturbulence, but surprisingly in all cases where bubbles are present in the system ($b>0$). Therefore, it is a generic feature of turbulent bubbly flows, and the bubblance parameter is probably not a suitable parameter to characterise the energy spectrum in bubbly turbulent flows. The physical reason is that the energy input by the bubbles passes over only to higher wavenumbers, and the energy production due to the bubbles can be directly balanced by the viscous dissipation in the bubble wakes as suggested by Lance & Bataille (1991). In addition, we provide an alternative explanation by balancing the energy production of the bubbles with viscous dissipation in the Fourier space.

Interaction of a vortex ring with a single bubble: bubble and vorticity dynamics

The interaction of a single bubble with a single vortex ring in water has been studied experimentally. Measurements of both the bubble dynamics and vorticity dynamics have been done to help understand the two-way coupled problem. The circulation strength of the vortex ring (${\it\Gamma}$) has been systematically varied, while keeping the bubble diameter ($D_{b}$) constant, with the bubble volume to vortex core volume ratio ($V_{R}$) also kept fixed at about 0.1. The other important parameter in the problem is a Weber number based on the vortex ring strength $(\mathit{We}=0.87{\it\rho}({\it\Gamma}/2{\rm\pi}a)^{2}/({\it\sigma}/D_{b});a=\text{vortex core radius},{\it\sigma}=\text{surface tension})$, which is varied over a large range, $\mathit{We}=3{-}406$. The interaction between the bubble and ring for each of the $\mathit{We}$ cases broadly falls into four stages. Stage I is before capture of the bubble by the ring where the bubble is drawn into the low-pressure vortex core, while in stage II the bubble is stretched in the azimuthal direction within the ring and gradually broken up into a number of smaller bubbles. Following this, in stage III the bubble break-up is complete and the resulting smaller bubbles slowly move around the core, and finally in stage IV the bubbles escape. Apart from the effect of the ring on the bubble, the bubble is also shown to significantly affect the vortex ring, especially at low $\mathit{We}$ ($\mathit{We}\sim 3$). In these low-$\mathit{We}$ cases, the convection speed drops significantly compared to the base case without a bubble, while the core appears to fragment with a resultant large decrease in enstrophy by about 50 %. In the higher-$\mathit{We}$ cases ($\mathit{We}>100$), there are some differences in convection speed and enstrophy, but the effects are relatively small. The most dramatic effects of the bubble on the ring are found for thicker core rings at low $\mathit{We}$ ($\mathit{We}\sim 3$) with the vortex ring almost stopping after interacting with the bubble, and the core fragmenting into two parts. The present idealized experiments exhibit many phenomena also seen in bubbly turbulent flows such as reduction in enstrophy, suppression of structures, enhancement of energy at small scales and reduction in energy at large scales. These similarities suggest that results from the present experiments can be helpful in better understanding interactions of bubbles with eddies in turbulent flows.

Numerical simulation of secondary flow in bubbly turbulent flow in sub-channel

Secondary flow in bubbly turbulent flow in sub-channel was simulated by using an algebraic turbulence stress model. The mass, momentum, turbulence energy and bubble diffusion equations were used as fundamental equation. The basis for these equations was the two-fluid model: the equation of liquid phase was picked up from the equation system theoretically derived for the gas–liquid two-fluid turbulent flow. The fundamental equation was transformed onto a generalized coordinate system fitted to the computational domain in sub-channel. It was discretized for the SIMPLE algorithm using the finite-volume method. The shape of sub-channel causes a distortion of the computational mesh, and orthogonal nature of the mesh is sometimes broken. An iterative method to satisfy a requirement for the contra-variant velocity was introduced to represent accurate symmetric boundary condition. Two-phase flow at a steady state was simulated for different magnitudes of secondary flow and void fraction. The secondary flow enhanced the momentum transport in sub-channel and accelerated the liquid phase in the rod gap. This effect was slightly mitigated when the void fraction increased. The acceleration can contribute to effective cooling in the rod gap. The numerical result implied a phenomenon of industrial interest. This suggested that experimental approach is necessary to validate the numerical model and to identify the phenomenon.

503 気泡乱流における気泡分布の数値モデル(OS5-1 混相流の微細流動構造(相間作用),OS5 混相流の微細流動構造,オーガナイズドセッション)

503 気泡乱流における気泡分布の数値モデル(OS5-1 混相流の微細流動構造(相間作用),OS5 混相流の微細流動構造,オーガナイズドセッション)

K-1616 ガスリフト効果を利用した二酸化炭素海洋固定システムの性能シミュレーション(J10-2 地球温暖化問題への熱・環境工学の役割(2))(J10 地球温暖化問題への熱・環境工学の役割)

GLAD (Gas Lift Advanced Dissolution) System has been investigated to mitigate the estimated peak of atmospheric CO_2 concentration over the next few hundreds years. The system is a practical use of bubbly turbulent flows to a deep-ocean sequestration of CO_2. Unsteady characteristics of the system are discussed by computational simulation on the basis of experimental results using a large diameter pipe. First, outline of experiment and the results are described. Second, the numerical method based on the Drift Flux Model and the experimental results is employed, and finally the performance and characteristics at the starting operation are discussed.

2824 チャネル内気泡流乱流における流動特性の解明

2824 チャネル内気泡流乱流における流動特性の解明