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L. Sun, [email protected]; H. Liu, [email protected]

A review on bubble generation and transportation in Venturi-type bubble generators

Jiang Huang, Licheng Sun (), Hongtao Liu (), Zhengyu Mo, Jiguo Tang, Guo Xie, Min Du

State Key Laboratory of Hydraulics and Mountain River Engineering, College of Water Resource & Hydropower, Sichuan University, Chengdu, China Abstract Venturi-type bubble generators own advantages of simplicity in structure, high efficiency, low power consumption, and high reliability, exhibiting a broad application potential in various fields. This work presents a literature review of recent progress in the research concerning Venturi-type bubble generators, with a focus on the performance evaluation, bubble transportation, and breakup mechanisms. Experimental studies employing flow visualization techniques have played an important role in exploring the bubble transportation and breakup phenomena, which is vitally necessary for clarifying the bubble breakup mechanisms and understanding the working principle and performance of a Venturi channel as a bubble generator. A summarization was carried out on both experimental and theoretical work concerning parameters influencing the bubble breakup and the performance of Venturi-type bubble generators. Based on the geometric parameter optimization combined with appropriate flow conditions, it is expected that Venturi-type bubble generators can produce bubbles with controllable size and concentration to satisfy the application requirements, while a further work is required to illustrate the interaction between the liquid and gas bubbles.

Keywords Venturi-type bubble generator

performance

bubble transportation

bubble breakup mechanism

Article History Received: 6 August 2019

Revised: 7 September 2019

Accepted: 8 September 2019

Review Article © Tsinghua University Press 2019

1 Introduction

Bubbly flow is a typical and fundamental flow pattern of gas–liquid flow, characterized by the gas or vapor phase dispersed in a liquid continuum. Due to the large gas–liquid interfacial area beneficial to heat and mass transfer and efficient mixing processes, bubbly flow is immensely important in many applications, such as bubble columns, flotation cells, spargers, fluidized beds, and electrochemical reactors, etc. With the increasing applications of bubbly flow, a well control of bubble size and concentration has become a key issue and attracts much attention (Fujikawa et al., 2003; Mills and Schlegel, 2019a). For flotation technology, microbubbles with diameter of 100 μm or less tend to remove numerous pollutants (e.g., colloids, metal ions, microorganisms, proteins, oil emulsions, fine and ultrafine particles) in waste water treatment (Rodrigues and Rubio, 2007); however, com-paratively large bubbles with diameter of 500–2000 μm are employed for lifting many large particles in mineral flotation (Reay and Ratcliff, 1973; Rodrigues and Rubio, 2003). To satisfy various application requirements, many methods for

the generation of fine bubbles have been developed so far. Venturi structure is employed by many devices for generating bubbles in a gas–liquid flow system, it can provide a wide size range of bubbles from tens of microns to millimeters (Fujiwara et al., 2003; Yoshida et al., 2008; Sun et al., 2017; Zhao et al., 2019).

A classic Venturi structure consists three main parts: a converging section, a throat, and a diverging section. It operates on the Bernoulli principle of the conservation of energy. When a fluid flows through a Venturi channel, its increase in velocity (kinetic energy) in the throat is accompanied by a fall in pressure (pressure energy), while in the diverging section, it regains most of its pressure energy by the reduction in kinetic energy. In practical applications, Venturi structure can apply to short contact time and high intensity gas–liquid reactions, and usually takes the two forms. One is the above- mentioned conventional Venturi (Gabbard, 1972; Fujiwara et al., 2007; Sun et al., 2017; Zhao et al., 2018), with which the introduced gas bubbles or cavitation bubbles are well-broken into finely dispersed bubbles in the divergent section. The other is jet-Venturi or Venturi ejector (Jackson, 1964;

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J. H, L. Sun, H. Liu, et al.

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Kandakure et al., 2005; Balamurugan et al., 2007; Sharma et al., 2018), mainly consisting of a throat and a diverging section. A typical jet-Venturi or Venturi ejector consists of a liquid nozzle, a suction chamber, a mixing tube, and a divergent section (Gourich et al., 2007). Liquid is pumped into the system at high velocity through the nozzle, and the gas phase is sucked into the chamber. The two phases get mixed in the chamber and the mixing tube and bubbly flow is subsequently created in the divergent section. Versatility in applications has been well proved for Venturis. Venturis have been suggested to be as gas absorption devices (Bauer et al., 1963; Zhou and Smith, 2000; Baawain et al., 2007), bubble generators or gas distributors (Kress, 1972; Huynh et al., 1991; Briens et al., 1992; Havelka et al., 2000; Kawamura et al., 2004), and chemical reactors for the fast reaction inside (Cramers and Beenackers, 2001; Gourich et al., 2005). Liquid-driven type Venturi is often used as gas-inducing devices, such as bubble generators and gas distributors, while gas-driven type Venturi is used as scrubbers (Ali et al., 2013; Gulhane et al., 2015; Zhou et al., 2016; Bal et al., 2019).

Recently, Venturi bubble generators receive increasingly attention in the fields of application and research, and the performance is the most important concern. The size and distribution of generated bubbles are the primary indexes for its performance. In a Venturi channel, it takes advantage of the intensified interaction between the gas and liquid two phases to produce a large number of fine bubbles. In view of increasingly concern to Venturi bubble generators, this paper reviews the progress of fundamental research involved, for a better understanding of complex interaction between gas and liquid in Venturi channels.

2 Bubble generation methods

Bubble technology is expected to be a cost-effective and environmentally friendly technology with great potential in many applications. In order to meet the application requirements mentioned above, an appropriate method for generating bubbles becomes the key, on which extensive research has been motivated. Generally, hydrodynamic method (Agarwal et al., 2011), acoustic or sonication (Xu et al., 2008), electrochemical method (Wu et al., 2008), and mechanical agitation (Xu et al., 2008) are the four basic ways for generating fine bubbles. For all these methods, much smaller and higher number density bubbles are desired, and moreover, they are controllable in size according to purposes of practical applications. Duo to low-energy consumption and widely applicable to various application environments, the hydro-dynamic method is the most frequently encountered in industrial applications and several typical bubble generators have been developed, such as spiral liquid flow type, pressurized dissolution type, ejector type, and Venturi type (Terasaka

et al., 2011), as shown in Fig. 1. For a spiral liquid flow type bubble generator, micro or fine bubbles are generated due to centrifugation effect and strong shear force caused by a high-speed rotating liquid flow (Fig. 1(a)). When the gas in saturated high-pressure water is released into ordinary pressure water, a large number of bubbles will be formed, so that a pressurized dissolution type bubble generator is named consequently. The ejector type and Venturi type bubble generators take advantage of intensified pressure change of high-speed flow arsing from the variation in the cross-section area to generate fine bubbles. With these principles, a variety of bubble generators have been inves-tigated. Sadatomi et al. (2005, 2012) placed a spherical body and an orifice plate in the flow paths, respectively, taking advantage of the throttling effect to accelerate the fluid and cause a highly-turbulent and shear flow, thus breaking bubbles into pieces.

A Venturi type bubble generator, as shown in Fig. 1(d), owns advantages of simple structure, installation convenience, having no internal moving parts, less maintenance, and good reliability. Most importantly, low power consumption makes it an economic alternative for enhancing gas–liquid mass transfer (Terasaka et al., 2011; Basso et al., 2018). A Venturi bubble generator is capable of generating a high number density of micro or fine bubbles normally with a mean diameter below 100 μm (Fujiwara et al., 2003; Kawamura et al., 2004; Yoshida et al., 2008; Kaneko et al., 2012), and the concentration and size of produced bubbles in a wide range from tens of microns to millimeters are controllable by operating the liquid and gas flow rates. For a Venturi bubble generator, gas is normally introduced through the throat under conditions of free gas suction and forced gas supply. The latter can provide larger gas feed rate, but limit the gas dispersion efficiency at high gas flow rates

Fig. 1 Several typical bubble generators.


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(Zahradnik et al., 1997). While for the former, the gas supply circuit is open to the environments, making the system simpler and more flexible, and adaptive to various complex environments. Venturi bubble generator attracts increasingly attention in recent years and shows potential in many applications. Being as an aeration device, it can increase the concentration of dissolved oxygen in the water to promote the growth of fish and plants, and has been successfully applied to fish farming (Akhtar et al., 2018) and agriculture production (Bagatur, 2014; Dahrazma et al., 2019). With the ability of supplying a large number of fine bubbles, Venturi bubble generator has a good prospect in waste water treatment (Mitra et al., 2016; Kaya et al., 2017), mineral flotation (Ahmadi et al., 2014; Reis and Barrozo, 2016), ship drag reduction (Kawamura et al., 2004; Hashim et al., 2015), and bioreactors (Krusong et al., 2015; Kayaalp and Ozturkmen, 2016).

3 Performance of Venturi-type bubble generators

3.1 Evaluation method of performance

The ability of the Venturi-type bubble generator in generating fine bubbles is crucial for practical applications. Probability size distribution of the generated bubbles and their average diameter are the two key parameters in the evaluation of the performance of a Venturi-type bubble generator (Yin et al., 2015; Gordiychuk et al., 2016; Li et al., 2017; Sun et al., 2017; Huang et al., 2019a; Zhao et al., 2019). With measuring the produced bubble sizes (Mills and Schlegel, 2019b), the probability density function (PDF) or the cumulative dis-tribution function (CDF) are often employed in the statistical analysis. A log-normal distribution is the most common in experimental work for a Venturi-type bubble generator (Gordiychuk et al., 2016; Li et al., 2017; Zhao et al., 2019).

The average diameter of the produced bubbles reflects the ability of a Venturi-type bubble generator in generating fine bubbles to a great extent. Fujiwara et al. (2007) suggested that the throat velocity was the main parameter controlling the size of the generated bubbles in Venturi tubes, and pro-posed that the average diameter of the generated bubbles had a −1.0 power dependence on the throat velocity by fitting experimental data. In fact, tiny bubbles are mainly generated in the divergent section of the Venturi as a result of interaction of the gas with the turbulent flow, causing difficulties in correlating the average bubble size with flow parameters. Kolmogorov-Hinze assumed that bubble breakup occurred when the maximum hydrodynamic force in the liquid is larger than the surface tension force. With this assumption, a dimensionless correlation was proposed by Gabbard (1972). His experimental work showed that the volume averaged bubble diameter was about 0.6 power dependence

for the surface tension term, and −0.8 power dependence for the Reynolds number term. Similar relationship was also found by Yin et al. (2015) and Sun et al. (2017). An approximate correlation was found:

3/5

v c 1 th 1.11,th2

th 1

d g σρ D ReD μ

-æ ö÷çµ ÷ç ÷çè ø (1)

where dv, Dth, and ρ1 represent average diameter of bubbles, diameter of throat, and liquid density, respectively. gc, σ, μ1, and Rel,th are dimensional proportionality constant relating force to the product of mass and acceleration, surface tension, dynamic viscosity of liquid and liquid Reynolds number of throat, respectively. Yin et al. (2015) and Sun et al. (2017) obtained a fitting formula from the experimental results and presented the exponents of –1 and –1.3 for Reynolds number term, separately.

It should be noted that the performance of a Venturi-type bubble generator depends on the flow conditions and the geometry configuration, the combination of which will generate different bubble size distribution characteristics. Comprehensively investigations have to be conducted to elucidate the effect of these factors on the bubble size and distribution, by which a more appropriate correlation might be achievable.

3.2 Effects of flow parameters

The size distribution of the generated bubbles and their average diameter are closely correlated with the gas and liquid flow rates in a Venturi-type bubble generator. Extensive investigation has been carried out to illustrate effect of the flow rates on the bubble size and distribution.

Gordiychuk et al. (2016) carried out an investigation on the factors influencing the size distribution of bubbles in a Venturi-type bubble generator, including air/water Reynolds number and volume fraction. They found that the bubble size was inversely proportional to the water flow rate and got increased with the increase in the volume fraction, which was confirmed by the subsequent works (Sun et al., 2017; Majid et al., 2018; Huang et al., 2019a, 2019b). As shown in Fig. 2, increasing the liquid flow rate leads to a more uniform bubble size distribution, but increasing the gas flow rate has an opposite effect. The effects of water and air flow rates on the average diameter are shown in Fig. 3. As the gas flow rate increased at a specified water flow rate, the average diameter of the bubble also increased. In order to generate reasonable bubble sizes to meet the application requirement, besides providing a strong turbulent flow field with sufficient liquid flow rates, gas flow rates need to be strictly controlled (Sun et al., 2017; Huang et al., 2019a). Sun et al. (2017) designed a Venturi-type bubble generator for the xenon removal in


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the Molten Salt Breeder Reactor. With the void fraction covering in a reasonable range of 0.2%–0.3%, the generated bubbles had an average diameter about 0.5–0.6 mm, which was able to meet the bubble size requirement. Huang et al. (2019a) carried out experiments with a small-scale Venturi bubble generator with rectangular cross-section to produce fine bubbles. With a liquid Reynolds number in the throat of (0.7–1.2)×104, the bubble generator can produce fine bubbles with average diameters of approximately 0.2–0.4 mm under the condition of void fraction below 10%. A higher void fraction, above which large bubbles from the throat can escape the breakup region (recirculation flow region) of the diverging section.

Since the bubble breakup mainly depends on the flow turbulence, researchers agree that the liquid flow rate has a significant effect on the bubble size and distribution (Fujiwara et al., 2007; Reichmann et al., 2017a). While the gas flow rate has less effect on the bubble size and distribution com-pared with that of the liquid flow rate. At high liquid flow rates, Huang et al. (2019b) pointed out that the sensitivity of the bubble size and distribution to the gas flow rate is reduced compared with that at low liquid flow rates. Poh et al. (2014) has designed a Venturi-type bubble generator with free gas suction. The liquid flow rate became the only factor to determine the size and distribution of produced bubbles. Fujiwara et al. (2003) and Kawamura et al. (2004)

conducted experiments with a Venturi bubble generator that can easily generate the microbubble with the diameter of 100 μm. As shown in Fig. 4, it was available for a wide range of void fraction (Ql = 5.3 L/min), and the bubble size distribution was quite independent of the void fraction up to 20%. This was an important advantage for the bubble generator to obtain better performance in applications.

3.3 Effects of geometric parameters

Besides the flow rates, performance of a Venturi-type bubble

Fig. 4 Bubble size distribution with different void fractions (Ql = 5.3 L/min) (Fujiwara et al., 2003; reproduced with permission © Elsevier Science Ltd. 2003).

Fig. 2 Bubble size distributions under different flow conditions (Huang et al., 2019a; reproduced with permission © Elsevier B.V. 2019).

Fig. 3 Bubble size distributions (a) and average diameters (b) under different flow conditions (Sun et al., 2017; reproduced with permission © Elsevier Ltd. 2017).


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generator is highly dependent on its geometric parameters, especially the diverging angle (β). Controllable size distribution of generated bubbles is the primary objective, which spurs a great effort to investigate the effects of geometric parameters, inclusive of convergent angle (α), divergent angle (β), throat length (l), throat diameter (d), outlet diameter (D), and gas feeding hole diameter (dg), as shown in Fig. 5. An appropriate combination of the geometric parameters becomes the key for a Venturi-type bubble generator to satisfy the application requirements.

Reichmann et al. (2017a) investigated the influence of the divergent angle, throat length, hydraulic diameter of the throat, and the hydraulic diameter of the outlet on the produced bubble sizes. Their results showed that increasing the throat length and divergent angle or decreasing the throat diameter and outlet diameter resulted in the reduction of the produced bubble sizes. However, they were barely influenced

Fig. 5 Characteristic geometric parameters of the Venturi channel.

by the convergent angle and the diameter and number of the gas feeding holes (Li et al., 2017; Lee et al., 2019). The throat diameter and divergent angle play key roles in determination of the performance of a Venturi-type bubble generator. Unyaphan et al. (2017) designed three Venturi tubes with the fixed inlet and outlet diameters (D = 12 mm) but different throat diameters (d = 2, 5, and 8 mm). Con-sidering that bubble coalescence led to the increase of the final bubble size in the case of d = 2 mm, the Venturi tube with a throat diameter of 5 mm (corresponding to the throat ratio d/D = 0.42) produced the smallest bubble with average diameter of 197 μm at the velocity of 5.6 m/s in the throat. Huang et al. (2019b) made a comparative study of two rectangular Venturi channels with the throat sizes of 1 mm × 1 mm and 1 mm × 2 mm, respectively. Figure 6 presents the bubble size distributions in the two Venturi channels. Under the conditions of the throat velocity in the range of 6.0–10.0 m/s, the two Venturi channels produced fine bubbles with average diameters of 0.2–0.3 mm and 0.3–0.4 mm, respectively. The Venturi channel with smaller throat size exhibited a better performance in producing fine bubbles. Lee et al. (2019) compared five Venturi tubes with different divergent angles (15°, 22°, 30°, 38°, and 45°) to show the effect of the divergent angle on produced bubble size. They

Fig. 6 Comparisons of the bubble size distributions in two Venturi channels with different throat sizes (Wth) (Huang et al., 2019b; reproduced with permission © Tsinghua University Press 2019).

Fig. 7 Bubble size distributions (a) and average bubble diameters (b) in Venturi-type bubble generators with different divergent angles (Zhao et al., 2019; reproduced with permission © Elsevier Ltd. 2019).


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also found increasing the divergent angle is beneficial to decreasing the size of the produced bubbles, except the cases of the divergent angle greater than 30° at high liquid flow rates (260–300 L/min).

Zhao et al. (2019) conducted experiments with rectangular cross-section Venturi bubble generators with three divergent angles (7.5°, 10.0°, and 12.5°). By fitting experimental data, a modified correlation for predicting the average bubble size in Venturi channels was proposed with the consideration of the effect of the divergent angles:

/90v [1.1 (1 e )]1,th

th

βd CReD

- - + -= (2)

where C equals to 3.7×104. Figure 7 shows the significant effect of the divergent angles on the bubble size distributions and the average bubble size, although it was weakened at a higher the liquid flow rate. It was also suggested that an appropriate increase in the divergent angle was an efficient way for improving the performance of the Venturi-type bubble generator.

4 Bubble transportation in Venturi-type bubble generators

Strong turbulence and vortexes in the diverging section intensifies the interaction between the bubble and liquid, and the bubbles through a Venturi channel always experience a complex transportation process involving deceleration, deformation, and breakup, etc. Over the past years, the bubble transportation in a Venturi channel has received extensive attention and has been the subject of considerable experimental and theoretical studies. A detailed study of the bubble transportation process helps to further explore bubble breakup mechanisms and the reason for high efficiency in producing fine bubbles.

4.1 Phenomenological observation in experiments

In visual experiments, the bubble transportation processes in Venturi channels are usually recorded by a high-speed camera, from which parameters including bubble size, shape, trajectory, and velocity can be obtained for further analysis.

Zhao et al. (2017, 2018) conducted visualized experiments to investigate motions of individual bubbles in rectangular Venturi channels. They found that bubbles underwent a dramatic deformation and rapid deceleration in the divergent section. The deceleration of bubbles had a magnitude of dozens or even hundreds of times gravity, which played a key role in their breakup. Increasing the liquid flow rate resulted in a greater deceleration of a bubble and led to bubble breakup position shifted to upstream, but hardly influenced the maximum magnitude and termination positions of the bubble deceleration. Additionally, Zhao et al. (2019) also studied the effects of different divergent angles (7.5°, 10.0°, and 12.5°) on bubble deceleration, as shown Fig. 8. Both of the maximum deceleration and deformation rate in the case of β = 12.5° were twice as much as that of β = 7.5°. With a larger divergent angle, it took a shorter distance and time for bubbles to be decelerated to their minimum velocities. Moreover, bubble breakup positions were brought forward and bubble breakup was intensified. Huang et al. (2018) and Zhao et al. (2019) pointed out that bubble deceleration led to an increase of void fraction in local regions of the divergent section, and the bubbles aggregated to coalesce into a larger plug or slug in the case of high gas flow rates. Uesawa et al. (2011, 2012) measured the fluctuation of void fraction along the flow direction in a Venturi tube. They found that the void fraction increased downstream of the throat due to bubbles expansion and decreased around the bubble breakup position due to bubble shrinkage and collapse. Moreover, increasing the flow velocity led to the

Fig. 8 Bubble movements in the Venturi channels with different diverging cone angles: Ql=4.6 m3/h (Zhao et al., 2019; reproduced with permission © Elsevier Ltd. 2019).


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increase of the maximum value of void fraction and the shift of its position downstream. Mansour et al. (2018) carried out experiments on an air–water two-phase flow in a horizontal, divergent channel. The air bubbles were trapped and accumulated in the recirculation zone even under very small air volume fractions. Increasing the gas flow rate made more gas accumulated. While as the liquid flow rate increased to a certain value, the accumulated gas would start to decrease. The accumulated gas strongly affected the velocity field and the pressure recovery in the diverging section.

4.2 Theoretical analysis and numerical simulation

In spite of many experimental observations on performance of a Venturi bubble generator, whereas the bubble tran-sportation process is still poorly to be understood. Theoretical analysis and numerical simulation provide valuable insights into the understanding of bubble transportation in Venturi channels.

Kuo (1978) and Kuo and Wallis (1988) studied the motion of individual bubbles in Venturi-type nozzles based on force balance and made a comparison with the experimental results. The trajectory of individual bubbles could be presented by an equation of bubble motion only including the drag force and the added mass force, which was expected to be significant for individual bubble through the nozzle. In the accelerating and decelerating flows, the turbulence of the fluid and the bubble shape oscillation had a significant influence on the drag force, corresponding to the variation of the unsteady-state drag coefficient in the range of ±50% from the steady-state drag coefficient. The added mass coefficient (Cm) was also modified and varied in the range of 2–3. In accelerating flows, the motion of a single bubble at high Reynolds number was also analysed by Kowe et al. (1988), who recommended the added mass coefficient (Cm) of 0.5. In a Venturi channel, a similar analysis of force balance for predicting trajectories of individual bubbles was reported by Soubiran and Sherwood (2000), assuming the various forces acting on the bubble being added linearly. They discussed the deceleration of a bubble under different magnitude of drag. The results indicated that the sensitivity of the predictions to the choice of drag law and the steady drag law was inappropriate for the condition of bubble oscillation along the flow direction. Van der Geld et al. (2001) investigated the effect of the acceleration of a carrier liquid on the motion of a spherical bubble in Venturi with Reynolds number in the range of 50 ≤ Reb ≤ 200. They suggested that spatial acceleration resulted in a significant increase in drag, which was also reported by Magnaudet et al. (1995). Based on the liquid velocity field and the bubble trajectory from the experimental measurements, an empirical fitting correlation of the drag coefficient was

deduced with consideration of the bubble Reynolds number Reb and acceleration number Ac:

d b 1 d b 2( , ) (1 ) ( , 0)C Re Ac C Ac C Re Ac C Ac= + = + (3)

Van der Geld et al. (2001) derived the parameters C1 and C2 of 1.2 and 0.9, respectively, which were higher than the numerical results (C1 = 0.25, C2 = 0.55) obtained by Magnaudet et al. (1995). Zhao et al. (2018) estimated the values of various forces acting on individual bubbles undergoing deceleration in the divergent section of Venturi channel. Only the forces along the main flow direction (x-direction) were taken into account, including pressure gradient force, added mass force, and drag force. Based on the order of magnitude analysis for the forces, they suggested that the pressure gradient force played the most significant role in the bubble deceleration.

Ishii et al. (1993) numerically simulated the bubbly flow through a converging–diverging nozzle. A new model of governing the motion of a dispersed bubble was proposed, including the particle diffusion force and the repulsive force. The bubble and liquid velocities and the void fraction distribution along the flow direction were calculated. As the time increased, the velocity difference between the bubbles and the liquid produced a strong fluctuation of the void fraction, especially near the nozzle throat. For the steady flow, the numerical simulation results agree well with experimental results. Wang and Chen (2002) numerically computed the flow characteristics for bubbly flows through converging– diverging nozzles using a two-fluid model. It considered both translational and radial relative motions between the bubbles and the liquid. The relative motion between the two phases could be calculated for both subsonic and critical flow situations, showing a good agreement with the experimental data. The strength of the shock waves was pronounced at low gas volume fraction but weakened with the increase of the void fraction. The bubbly flow through convergent/ divergent channels was investigated in details by Ahmadpour et al. (2016) with Computational Fluid Dynamic (CFD) method. When the gas–liquid mixture flowed through the convergent/divergent section, a drastic increase in drag and virtual mass forces were obtained, especially higher drag force for the divergent section. They suggested that the recirculation flow led to a high void fraction region near the wall of the divergent section and increasing the liquid Reynolds number intensified this phenomenon.

5 Bubble breakup mechanisms in Venturi-type bubble generators

Generally, the bubble breakup mechanism can be expressed as a balance between external stresses from the liquid phase


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attempting to destroy the bubble, and the surface tension of the bubble tending to restore its form. Up to now, the bubble breakup in a turbulent flow has been widely investigated and well predicted by theoretical breakup models. In turbulent flow, four dominant bubble breakup mechanisms have been confirmed: (1) turbulent fluctuation and collision; (2) viscous shear stress; (3) shearing-off process; (4) interfacial instability (Liao and Lucas, 2009). They also can be observed in Venturi channels (Huang et al., 2019a; Zhao et al., 2019). Compared with straight channels or columns, the turbulent field in the divergent section of the Venturi channel is much more complex, which has received more and more attention in recent years. However, the mechanisms dominating bubble breakup in Venturi channels are not made clear, which motivates researchers to conduct extensive experimental studies.

Fujiwara et al. (2007) and Nomura et al. (2011) carried out experiments to observe the bubble behaviours in a Venturi tube in detail by using a high-speed camera. As shown in Fig. 9(a), they observed a liquid jet induced by pressure difference penetrating the entire bubble after it flowed into the diverging section of Venturi tube, and the bubble was broken into pieces by the shear flow at the low flow velocity and unsteady surface wave on its surface at the high velocity. It was particularly noteworthy that bubbles eventually collapsed after experiencing a drastic expansion and shrinkage process under supersonic flow at the throat, which had a strong dependence on the pressure recovery caused by the shock wave in the divergent section (Sandhu and Jameson, 1979; Fujiwara et al., 2003, 2007; Nomura

et al., 2011; Uesawa et al., 2012), as shown in Fig. 9(b). In a certain range of divergent angles and liquid Reynolds numbers, recirculation flow regions caused by flow separation occurs in the divergent section (Sparrow et al., 2009). The recir-culation flow hinders the bubbles or slugs from moving forward once they are discharged from the throat, leading to a deceleration and accumulation of the bubbles or slugs in the diverging section, in return resulting in more intensified interaction between the gas and the liquid (Huang et al., 2018; Zhao et al., 2018). The interaction between the bubbles and liquid is significantly intensified and consequently bubbles collapse intensively in the recirculation flow region. Moreover, the increase of the divergent angle causes the recirculation region moving towards upstream, causing the bubble breakup position to be closer to the entrance of the divergent section. Song et al. (2019) studied the effect of the position of bubble flow through the divergent section on the bubble breakup. In the diverging section, bubbles flowed toward two main directions: (1) the center of mainstream, where bubbles were broke up by the shear stress at the interface of gas and liquid; (2) neighbourhood of the wall in the diverging section with highest turbulent kinetic energy, where bubbles experienced a spiral motion under the vortex action of the liquid phase and were broken up by high turbulent fluctuation. It was also found that the critical Weber of bubble breakup criterion was in the range of 7–11. Wilkinson et al. (1993) studied the influence of various factors (gas density, horizontal or vertical configuration, pipe length) on bubble breakup in a Venturi tube. The results showed that Freon-114 bubbles (high gas density) broke up

Fig. 9 Bubble collapse behaviours at the divergent section (Nomura et al., 2011; reproduced with permission © JSME 2011).


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more frequently than helium bubbles (low gas density), and bubble breakup frequencies for horizontal pipe were 1.5–2.5 times higher than that for vertical pipe. A longer bubble residence time in the turbulent flow for longer pipe length was also beneficial to bubble breakup.

In a micro-scale Venturi with the throat section of 150 μm × 300 μm, Li et al. (2016) suggested that the shearing-off process for the relatively low liquid flow rate but the turbulence fluctuation for the high liquid flow rate was the dominating mechanisms for bubble breakup. Reichmann et al. (2017b) reported two different bubble breakup processes in micro Venturi channels: a binary breakup of relatively large bubbles or numerous small daughter bubbles that were sheared off the instable rear part of large bubbles in laminar flow; a bubble breakup owing to contraction itself or a collision between two bubbles under turbulent flow. Reichmann et al. (2017c) observed that Rayleigh–Taylor instability occurred on a bubble when a slug bubble flowed into the divergent section. When bubbles flowing through the throat were squeezed and elongated, the accelerated bubble (the lighter fluid) pushed the decelerated liquid (the heavier fluid) moving forward, and bubbles were broken up eventually due to surface instability. They also found that increasing the length of the throat caused a lower critical Reynolds number for bubble breakup, and a bend throat with 90° had the same or even better effect compared with a straight throat of the Venturi channel.

6 Conclusions

Venturi-type bubble generator is one of the promising methods for producing fine bubbles, which motivates researchers to carry out extensive experimental and theoretical studies. This article reviewed published papers concerning the performance of Venturi-type bubble generators as well as the bubble transportation and breakup mechanisms in Venturi channels. Several consensuses are summarized as follows:

1) The probability size distribution of the generated bubbles and their average diameter are the main parameters reflecting the performance of the Venturi-type bubble generator, which depends primarily upon the flow conditions (the gas and liquid flow rates) and the geometry configuration. In particular, the liquid flow rate and divergent angle are the most important factors, an appropriate combination of flow conditions and geometry configuration will generate well-controlled bubble size for practical applications.

2) Bubbles passing through a Venturi channel experience a more complex transportation process than that in a conventional channel. In the divergent section, the rapid bubble deceleration and the dramatic bubble expansion and shrinkage have significant effects on the final bubble breakup.

3) In the divergent section, the pressure recovery and the recirculation flow lead to the bubble breakup to a great extent. However, the mechanisms dominating bubble breakup in Venturi channels are not clarified yet due to the complex flow structure in the divergent section of the Venturi channel. Further work is required on the bubble transportation process and elucidates the bubble breakup mechanisms in Venturi-type bubble generators.

Acknowledgements

The authors are profoundly grateful to the financial supports of the National Natural Science Foundation of China (Grant Nos. 51706149, 51709191, 51606130) and Sichuan Science and Technology Program (Grant No. 19ZX0148Z090101001).

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