Bubble sizes and shapes in a counter-current bubble column with pure and binary liquid phases

Flow Measurement and Instrumentation 67 (2019) 55–82

Contents lists available at ScienceDirect

Flow Measurement and Instrumentation journal homepage: www.elsevier.com/locate/flowmeasinst

Bubble sizes and shapes in a counter-current bubble column with pure and binary liquid phases

T

Giorgio Besagni∗, Fabio Inzoli Politecnico di Milano, Department of Energy, Via Lambruschini 4a, 20156, Milano, Italy

ARTICLE INFO

ABSTRACT

Keywords: Homogeneous regime Ethanol Counter-current Bubble column

It is generally admitted that the “global-scale” behavior of bubble columns is imposed by the “local-scale” phenomena. For this reason, understanding the fluid dynamics in bubble columns relies on the precise knowledge of the so-called “birth and life” of bubbles. A-priori knowledge of the bubble sizes and shapes is required to characterize the “local-scale”, to understand the “global-scale”, to set-up and validate numerical models, as well as to support scaling-up methods towards the “industrial-scale”. This paper contributes to the present-day discussion by proposing an experimental research devoted to clarify the relationships between the bubble sizes and shapes, the integral flow parameters, and the liquid phase properties. The experimental study, based on a bubbleidentification methods, was performed in a “large-scale” bubble column (inner diameter equal to 0.24 m, height equal to 5.3 m) operated in the batch and in the counter-current modes with pure (deionized water) and binary (mixture of ethanol and deionized water) liquid phases. The system was operated in the pseudo-homogeneous flow regime with superficial gas velocities in the range of 0.0037–0.0188 m/s and superficial liquid velocity, in the counter-current mode, equal to −0.066 m/s. In the different experimental runs, bubble size distributions and shapes were obtained at different radial and axial locations. The experimental observations have been presented, compared with literature correlations, used to develop novel correlations (to be applied in practical applications), compared with previously obtained experimental data and interpreted in a multi-scale point of view. The comprehensive dataset obtained within this research may be used to improve the validation of numerical approaches and, in particular, to tackle the unsolved issue of developing break-up and coalescence kernels.

1. Introduction Bubble columns are employed as contacting systems in industrial applications, owing to their numerous advantages in design and operation. The typical layout of a bubble column consists of a cylinder where the dispersed phase is introduced into a pure or a binary liquid phase, which can be supplied either in a batch mode or counter-currently/co-currently with respect to the dispersed phase. Batch-mode systems are applied, for example, in fermentation or hydrogenation processes; conversely, counter-current systems are applied in water ozonation or in waste-water treatments, owing to the higher mass transfer compared with batch-mode systems [1]. Thanks to the industrial interest in designing effective and efficient multi-phase reactors and the need of rational scaling-up/scaling-down methods, an increasing amount of research activities has been carried out in the last decades to clarify the multi-scale phenomena in multi-phase fluid dynamics. Despite that an agreement regarding the multi-scale dynamics is far from being achieved, it is generally admitted that the fluid

∗

dynamics in a bubble column is determined by the connection of three “bubble-scale” parameters: the liquid velocity, the void fraction, and the bubble sizes (and shapes) [2]; an example of the “bubble-scale” research activities was proposed by Murgan et al. [3]. Unfortunately, experimental studies offering a comprehensive and multi-scale description of the fluid dynamics are missing and the connection between the “bubblescale” parameters is far from being clarified. For this reason, bubble columns are still modelled by a macroscopic point-of-view, rather than using a bottom-up approach [4]. The relationships between the three “bubble-scale” parameters (liquid velocity, void fraction, bubble sizes) physically manifests, at the “reactors-scale”, in the prevailing flow regimes: the bubble column fluid dynamics is subject to the multi-scale connection since the bubble motion drives the liquid phase, which in reverse influences the rising characteristic and coalescence/break-up of the bubbles. In particular, in “large-diameter” bubble columns, three prevailing flow regimes occur while increasing the gas superficial velocity (UG) [5]: the homogeneous, the transition and the heterogeneous flow regimes. This paper considers the homogeneous flow regime, and,

Corresponding author. E-mail address: [email protected] (G. Besagni).

https://doi.org/10.1016/j.flowmeasinst.2019.04.008 Received 31 October 2018; Received in revised form 10 April 2019; Accepted 14 April 2019 Available online 17 April 2019 0955-5986/ © 2019 Elsevier Ltd. All rights reserved.

Flow Measurement and Instrumentation 67 (2019) 55–82

G. Besagni and F. Inzoli

Nomenclature BSD CFD SSR

N ni ntot p Q u UG UL Uth

Bubble size distribution Computational Fluid Dynamics Sum of squared residuals

The non-dimensional groups

AR =

g

Eo = Fr =

We =

Aspect ratio

H0 dc k

Uth g d0 u2l L

2 j deq

List of greek letters

Eötvös number

Frounde number – Eq. (11)

εG μ ρ μ ρXY σ

Weber number – Eq. (11)

List of symbols a ai b C db dc deq do d32 dw dv E f g H0 Hc h l

The number of classes used in Eq. (3) Number of bubbles of size class i Total number of bubbles in Eq. (12) Pressure Pa Volumetric gas flow rate m3 s−1 Velocity in computation of the We number m s−1 Gas superficial velocity m s−1 Liquid superficial velocity m s−1 gas velocity at the sparger openings m s−1

Bubble semi-major axis mm Interfacial area mm−1 Bubble semi-minor axis mm Coefficient in Eq. (17) Bulk bubble diameter - Eq. (5) mm Diameter of the bubble column mm Bubble equivalent diameter – Eq. (1) mm Gas sparger openings diameter mm Sauter mean bubble diameter – Eq. (3) mm Non-dimensional bubble diameter Volumetric mean bubble diameter mm Bubble aspect ratio – Eq. (2) Class relative frequency Acceleration due to gravity m s−2 Initial liquid level m Bubble column height m Axial distance from the distributor m Characteristic length in We number m

σL

Gas holdup Mean value in Eq. (5) - log-normal distribution mm Density kg m−3 Dynamic viscosity kg m−1 s−1 Flow evolution parameter Standard deviation in Eq. (5) - the log-normal distribution mm surface tension N m−1

List of subscripts Air-water-batch mode Air-water system in batch mode Air-water-counter-current mode Air-water system in counter-current mode Air-water-ethanol Air-water-ethanol system All data All experimental data d Detaching bubble parameter (Eq. (6)) Cao Cao et al. Correlation G Property related to the gas phase L Property related to the liquid phase Miyahara Miyahara et al. Correlation Polli Polli et al. Correlation

in particular, the “pseudo-homogeneous” sub-flow regime, where the gas holdup (εG) increases linearly with UG but an inhomogeneous flow is present. This flow regime is commonly observed in “industrial-scale” systems, owing to the gas sparger with large openings. Among the “bubble-scale” parameters, the knowledge of bubble size distributions (BSDs) is essential to understand the prevailing flow regimes and to validate numerical approaches. Generally, the gas phase,

introduced through the gas sparger openings, changes in the radial/ axial directions of the column in the form of "dispersed bubbles” or in the form of “coalescence-induced” structures, depending on the flow conditions, the system design and the phase properties. Unfortunately, despite the fact that modeling of multiphase fluid dynamics in “largescale” systems is a growing area of research, there is no commonly accepted strategy to predict the above-mentioned fluid dynamics [6].

Fig. 1. The experimental setup: system layout and instrumentation. 56

Flow Measurement and Instrumentation 67 (2019) 55–82

G. Besagni and F. Inzoli

Fig. 2. Spider gas sparger: distributor design and code names.

radial changes of BSDs. Unfortunately, the experimental studies available in the literature mainly concern pure liquid phases (typically, water), a limited range of gas flow rates, limited axial positions and mostly in the batch mode: indeed, the axial and radial evolution were provided only in a very limited number of studies dealing mainly with air-water systems [9,10]. In addition, a precise description of the flow phenomena at the gas sparger is generally missing. This situation is far more complicated when considering binary liquid phases and/or cocurrent or counter-current bubble columns: in this case, the lack of knowledge regarding coalescence and break-up phenomena is much more severe. This is a major shortcoming as, in practical and industrial application, counter-current bubble columns and/or binary liquid phases are frequently used. An example of binary liquid phases concerns the use of organic substances, the so-called “positive surfactants” (i.e., ethanol [11]); these substances are attracted towards the interface of the dispersed phase where they adsorb inducing changes in the interface properties (i.e., increase of bubble rigidity [12], changes in the mobility of the bubble surface [13], change in the liquid drainage time, reduction of the rising velocity, and changes in the bubble zeta-potential [14]), leading to the coalescence suppression [15], and finally, inducing a stabilization of the homogenous flow regime [16]. Considering the state-of-the-art, this paper experimentally contributes to the present-day discussion by investigating the so-called “birth and life” of bubbles, as defined by Paolo di Marco [17] within the “pseudo-homogeneous sub-flow regime” (in the remaining of the paper, for simplicity, it is defined as flow regime). This paper proposes an experimental study regarding BSDs at the gas sparger and the axial and radial evolution of BSDs, at different flow rates, with pure and binary liquid phases. In summary, this study contributes to the existing body of knowledge by addressing the following aspects:

Table 1 Location of image acquisition – data provided in terms of the distance from the gas sparger [m]. Center region

Wall region a

Gas sparger region 0.25 m 1m 1.45 m 2.2 m –

0.35 m 1.05 m 1.55 m 2.25 m 2.75bm

a

Not available for the counter-current mode. Air-water system only. These data are not available for the air-water-Ethanol case. b

Considering the homogeneous flow regime, the rule of the thumb is to model the “mono-dispersed homogeneous sub-regime” by implementing an equivalent bubble diameter as a constant; conversely, the “pseudohomogeneous sub-regime” is more complex to be modelled, and coalescence/break-up phenomena occur [7,8]. In such a case, a population balance approach is implemented in the code to predict the local BSDs, by subdividing the dispersed phase into several bubble size classes and including coalescence and breakage kernels. Subsequently, the population balance equation for the different classes is solved using the velocity fields of each phase (eventually, multiple gas velocity fields may be considered) along with information about the BSDs at the inlet. In this modeling approach, the main shortcoming is the development and the extensive validation of coalescence and breakage kernels, owing to the lack of a comprehensive datasets (Computational Fluid Dynamics (CFD)-grade), especially for non-pure liquid phases and nonbatch operation modes. To this end, a CFD-grade dataset has to include BSDs at the gas sparger (inlet boundary conditions) as well as axial and

(a) it experimentally investigates bubble sizes and shapes in “large57

Flow Measurement and Instrumentation 67 (2019) 55–82

G. Besagni and F. Inzoli

Fig. 3. Gas sparger region: flow visualizations.

scale” gas-liquid bubble column for pure (i.e., deionized water) and binary (i.e., mixture of deionized water and ethanol) liquid phases; (b) it completes the experimental dataset proposed in our previous paper [5], where image analysis, optical probes and gas holdup measurements have been applied together; (c) it studies the influence of the liquid phase properties and operation modes on the bubble sizes and shapes.

dataset proposed in this paper, coupled with the data presented in our other studies, may serve as a basis to improve the validation process of multi-phase modeling approaches, especially considering coalescence and breakage kernels. Validated coalescence and break-up kernels at ambient conditions will be valuable tools in scaling-up methods towards high pressure and relevant operating conditions.

To the best of authors’ knowledge, this is the very first study to propose such a comprehensive dataset, especially if considering binary liquid phases and counter-current operation modes. The experimental

2. Experimental system and measurement techniques The tested system is a “large-diameter”/“large-scale” column (Hc = 5.3 m and dc = 0.24 m, see Fig. 1) made of Plexiglas®. The “large58

Flow Measurement and Instrumentation 67 (2019) 55–82

G. Besagni and F. Inzoli

Fig. 4. Developed region (h = 2.2 m): flow visualizations.

2–4 mm―“coarse-sparger”―, Fig. 2), with six arms (0.012 m diameter) and a central cylinder. The initial liquid level has been fixed to 3.0 m above the gas sparger, accordingly with the recommendations listed by Besagni et al. [18]. The experimental study proposed in this paper completes and extends our previous studies; in particular, this paper obtains BSDs at different radial/axial locations and proposes a detailed description of the size distributions at the gas sparger. To this end, the system was operated in the batch mode and in the counter-current mode (superficial liquid velocity equal to UL = – 0.066 m/s) with pure (deionized water) and binary (i.e., mixture of deionized water and ethanol, 0.05%

scale” concept within this study differs from the “industrial-scale” concept, as it refers to a vertical pipe having (i) dc larger than a critical value (related to the Rayleigh–Taylor instabilities), (ii) aspect ratio above a critical value and (iii) large gas sparger opening (see Ref. [18]). The experimental facility is equipped with a pressure reducer (to control the upstream gas pressure), two rotameters (#1 and #2 in Fig. 1, produced by ASA, Italy - accuracy ± 2% f.s.v., E5-2600/h), a pump with a bypass valve (to recirculate the liquid phase), (iv) and a rotameter (#3 in Fig. 1, produced by ASA, Italy - accuracy ± 1.5% f.s.v., G6-3100/39). The dispersed phase (filtered air) is introduced in the bubble column by a “spider-sparger” (having openings in the range of 59

Flow Measurement and Instrumentation 67 (2019) 55–82

G. Besagni and F. Inzoli

Fig. 5. Influence of UG and d0 (in terms of the distance from the column axis) on the bubble mean diameter.

in mass - detailed discussion concerning the liquid phase properties can be found in Ref. [11]) liquid phase. The experimental study was conducted by the image analysis method described in Ref. [5], which is able to detect and sample both ellipsoidal and distorted bubbles. Photos have been acquired by using a NIKON-D5000 camera (Nikon 10–24 mm lenses, 4288 × 2848 pixels, 11.8 pixel/mm - other settings as follows: ISO400; f/3.5; 1/1600s) along with a 500W LED halogen lamp. To minimize optical distortion, owing to the round shape of the bubble column, a box filled with water was placed around the bubble column. As the box and the Plexiglas® of the bubble column have similar but not equal refraction indexes, some refraction problem may remain, but can be neglected: (a) as discussed in Ref. [19], the distortion due to the round geometry in the radial direction is negligible; (b) owing to the different speed of light in water and Plexiglas®, the depth of field is not a plane but rather a bend surface: it has been estimated that the deviation to a flat depth of field is below 0.175 mm for all measuring positions. Further details concerning the image analysis, uncertainties, experimental procedure and underlying assumptions were described in our previous study [19]. Based on the experimental data obtained by the image analysis method [5], under the assumption of oblate spheroids, the equivalent bubble diameter (deq, Eq. (1)), the bubble aspect ratio (E, Eq. (2)), and, the Sauter mean bubble diameter (d32, Eq. (3)) are computed:

deq = 2 3 a2b

(1)

E= b/ a

(2)

d32 =

N 3 i n i deq, i N 2 i n i deq, i

In Eqs (1) and (2) b is the bubble semi-minor axis and a is the bubble semi-major axis. In Eq. (3), deq,i is the equivalent bubble diameter; ni is the number of bubbles sampled of the size class I; N is the number of classes used. It should be noted that the results obtained in terms of BSDs can be discussed also in terms of d32 (and vice-versa) as d32 is a statistical moment of the size distribution. In summary, d32 provides a lumped view of the BSDs, by maintaining the interfacial area per volume of the dispersed phase. At last, the interfacial area (ai, Eq. (4)), is derived:

ai = 6

G

d32

(4)

In Eq. (4), εG is the gas holdup, obtained by the bed expansion technique in Ref. [5], whereas d32 is obtained as in Eq. (1). For the sake of clarity, the application of Eq. (4) to the present case deserves a brief explanation. It is known that Eq. (4) relies on the assumption of spherical bubbles, as clearly discussed and commented by Nedeltchev et al. [20]. In the present case, Eq. (4) can be applied owing to the meaning of the Sauter mean diameter: d32 is the diameter of a sphere having the same volume/surface area ratio as our size distribution. Thus, d32 summarizes all the complexity of the BSD (obtained taking into account the bubble shape by Eq. (2), assuming an oblate spheroid) into an equivalent bubble, which maintains the interfacial area per unit of volume of the dispersed phase. The images have been acquired at different locations (listed in Table 1). At the gas sparger level, the camera has been focused on the gas sparger openings; when investigating the BSDs at different radial locations, the camera has been focused on a ruler inside/along the external wall of the column, following the proposal of ref. [5]. At the different locations, five flow rates have been considered, to cover the

(3) 60

Flow Measurement and Instrumentation 67 (2019) 55–82

G. Besagni and F. Inzoli

Fig. 6. Influence of UG on BSDs at the gas sparger.

so-called “pseudo-homogeneous” flow regime: (a) UG = 0.0037 m/s, (b) 0.0074 m/s, (c) 0.0111 m/s, (d) 0.0149 m/s, (e) 0.0188 m/s (εG in the range of 1.0%–7.0%, air-water batch; 1.7%–10.7%, air-water countercurrent; 1.2%–7.2%, air-water-ethanol). For every flow condition, approximately 800–1000 bubbles have been sampled (from, at least, two images), accordingly with the suggestion of Besagni and Inzoli [21]; in each image all bubbles in-focus have been considered. The reader may consider the flow map of Shah et al. [22], which is a graphical representation of the range of flow conditions studied.

3. Results and discussion First, the results at the gas sparger region are discussed (Fig. 3 displays the typical flow patterns and bubble sizes and shapes in this region); subsequently, the axial/radial of BSDs are discussed (Fig. 4 displays the typical flow patterns and bubble sizes and shapes in this region). The results proposed in the following sub-sections should be considered also within a practical perspective: (a) the description of the gas sparger is needed to model the inlet region of “industrial-scale” bubble columns; (b) the description of BSDs inside the column is 61

Flow Measurement and Instrumentation 67 (2019) 55–82

G. Besagni and F. Inzoli

Fig. 7. Influence of the liquid phase on BSDs at the gas sparger.

essential to validate the coalescence/break-up kernels within numerical models and to support the screening of numerical closures.

3.1.1. Experimental results The experimental observations presented in this section contribute to the discussion regarding the relationships between the design parameters of the gas sparger (i.e., the gas flowrate, UG, the hole diameters, do) and the bubble sizes. Indeed, an agreement on the relationships between these parameters is far from being reached as mentioned by Hur et al. [23], Geary and Rice [24]. and Cao et al. [25]. Owing to the opening size (see Fig. 2), the gas sparger imposes a “pseuso-homogeneous” flow regime and, on the qualitative point of view (Fig. 3), the same sparger phenomena—nucleating bubbles, channeling, clustering, coalescence, segregation of agglomerates—commented by Hur et al. [23] and described in Ref. [5] have been observed here. Figs. 5–7 display the experimental results for the pure (water, batch mode) and the binary (water-ethanol) liquid phases. In particular, Fig. 5 displays the relationship between UG and do and d32; conversely, Figs. 6 and 7 display the BSDs at different UG; please note that, in Fig. 6 and in Fig. 7, we have not distinguished between the different gas sparger openings and averaged data are displayed.

3.1. Bubble sizes at the gas sparger The presentation of the experimental data at the gas sparger (the socalled “birth of bubbles [17]”) is structured into three parts. First, the experimental observations for the air-water (batch mode) case and the air-water-ethanol case are discussed; second, an analytical description of size distributions at the gas sparger is proposed; finally, a comparison with literature correlations is presented. The sampling in this region has been obtained by considering the bubbles freshly detached from the distributor, still non-affected by the break-up/coalescence phenomena. As these bubbles have deq higher that the “critical” values (in the range of deq = 10.1–12.8 mm, ref. [21]) they will break into smaller bubbles, thus evolving into axial BSDs along the vertical coordinate of the column. Please note that, counter-current mode data are not available for the gas sparger region. 62

Flow Measurement and Instrumentation 67 (2019) 55–82

G. Besagni and F. Inzoli

Fig. 8. Influence of UG on BSDs at the gas sparger – Eq. (5) outcomes.

Regardless of the liquid phase, while increasing UG, the size distributions move towards higher bubble sizes because of the well-known nucleation mechanisms and force balance at the interface. In the airwater system, the size distributions (Fig. 6a) cover the range from low to high deq (approximately deq = 36 mm, UG = 0.0188 m/s). In general, such bubble size may appear high; however, it should be considered, that these measurements refer to the “gas sparger region” (and not the developed region); in particular, these measurements characterize the “freshly detached bubbles” (and not BSDs affected by break-up) produced

by “coarse gas sparger” at gas velocities approaching the flow regime transition (see Fig. 3). At UG = 0.0037 m/s, the size distributions (BSD and d32) are bimodal: the first peak is observed at approximately deq = 8–9 mm, whereas the second one is observed at approximately deq = 14–15 mm. Increasing the gas flowrate, at UG = 0.0074 m/s, the BSD becomes unimodal, with a peak at approximately deq = 10 mm. At higher gas flow rates, an absolute maximum appears at deq = 12–14 mm, along with different relative maxima up to deq = 38 mm. Compared with the air-water case (batch mode), when 63

Flow Measurement and Instrumentation 67 (2019) 55–82

G. Besagni and F. Inzoli

Table 2 Results of the sparger data analysis (air-water). Parameters refer to Eq. (1). Code reference for hole number refers to Fig. 2b. Hole

UG [m/s]

0.0037

0.0074

0.00111

0.0149

0.0188

0

μ σ # bubbles SSR μ σ # bubbles SSR μ σ # bubbles SSR μ σ # bubbles SSR μ σ # bubbles SSR μ σ # bubbles SSR μ σ # bubbles SSR

10.89 0.2536 108 0.00696 6.33 0.2370 9 0.02592 9.97 0.3143 11 0.03562 11.74 0.3168 23 0.09140 12.05 0.2852 18 0.03694 9.43 0.504031 11 0.091456 11.70 0.3095 11 0.05245

12.76 0.1850 80 0.00432 8.78 0.2946 13 0.05221 11.08 0.3346 25 0.03807 13.89 0.2127 35 0.01139 13.33 0.3141 23 0.04918 10.57 0.270803 15 0.115406 10.26 0.3564 13 0.03940

12.98 0.2453 70 0.00746 10.86 0.3351 16 0.04465 12.44 0.2629 15 0.01657 13.10 0.2413 30 0.01289 13.90 0.2704 32 0.01347 14.22 0.333571 23 0.016477 14.01 0.3426 17 0.09222

13.64 0.1975 59 0.00807 12.09 0.2998 13 0.02086 13.02 0.2059 20 0.05703 14.31 0.3764 19 0.04791 16.47 0.1848 31 0.02341 15.02 0.312084 31 0.034133 14.32 0.2591 34 0.00453

12.96 0.2462 56 0.03002 10.98 0.3021 11 0.06546 12.15 0.3115 20 0.03664 14.04 0.1552 24 0.03569 16.79 0.2234 35 0.02462 16.11 0.259204 31 0.029599 17.88 0.2362 26 0.02920

1

2

3

4

5

6

Fig. 9. Gas sparger operating parameters - Comparison between experimental data and correlations from the literature.

Table 3 Results of the sparger data analysis (air-water-ethanol). Parameters refer to Eq. (1). Code reference for hole number refers to Fig. 2b. Hole

UG [m/s]

0.0037

0.0074

0.00111

0.0149

0.0188

0

μ σ # bubbles SSR μ σ # bubbles SSR μ σ # bubbles SSR μ σ # bubbles SSR μ σ # bubbles SSR μ σ # bubbles SSR μ σ # bubbles SSR

11.92653 0.301071 71 0.016345 6.808004 0.277103 3 0.120355 7.472943 0.503992 7 0.054872 11.5309 0.429745 8 0.161254 9.979976 0.338221 8 0.136849 11.69791 0.224863 7 0.088467 8.438534 0.13999 2 0.075368

12.29166 0.283552 113 0.004997 8.923619 0.160716 6 0.031331 8.128916 0.292352 11 0.052283 12.09555 0.345355 21 0.0202 10.79412 0.354803 21 0.03959 11.90186 0.465504 18 0.076314 12.31052 0.397225 19 0.069274

12.3302 0.247332 68 0.006561 11.71689 0.20293 7 0.059832 9.438927 0.287838 16 0.020931 11.78918 0.348301 23 0.053986 11.55574 0.306923 29 0.04187 12.45089 0.294591 26 0.048749 12.68844 0.244146 13 0.032082

12.2861 0.275808 33 0.032566 11.74791 0.249981 5 0.109015 11.5098 0.241528 12 0.020202 12.17005 0.237319 12 0.036762 14.1186 0.375494 13 0.079437 11.78813 0.368461 12 0.056611 14.82262 0.255234 12 0.099255

12.14845 0.212293 62 0.014283 12.77073 0.234337 13 0.023949 11.41787 0.257125 25 0.014473 13.0316 0.408062 24 0.125527 14.43177 0.291453 30 0.040346 13.67751 0.269562 26 0.020343 13.72408 0.276824 26 0.033615

1

2

3

4

5

6

Fig. 10. Relationship between sauter mean diameter and UG at the gas sparger.

effects promote detachment of smaller bubbles, prevent the coalescence of two subsequent bubbles exiting the gas sparger [17,26] and inhibit the nucleation of some larger bubbles. For the sake of clarity, Fig. 7 proposed a detailed comparison between the pure and binary liquid phases. The above-mentioned results are in agreement with the ones presented in Ref. [5] and, in particular, they represent a considerable advancement in terms of available experimental dataset.

ethanol is included into the system (Fig. 5b), the size distributions (in terms of BSDs and d32) slightly shift towards lower equivalent bubble diameter (Fig. 6c and d) with multiple relative maxima (viz., BSDs are less regular in shape). This experimental observation can be explained by the changes in the interface properties of the bubbles induced by the presence of ethanol [4], thus leading to coalescence suppression. These 64

Flow Measurement and Instrumentation 67 (2019) 55–82

G. Besagni and F. Inzoli

Fig. 11. Axial evolution of air-water BSDs in the batch mode – Center of the bubble column.

65

Flow Measurement and Instrumentation 67 (2019) 55–82

G. Besagni and F. Inzoli

gas sparger (“distance from column axis” in Fig. 6 = 0.02 m) is higher compared with the one of the first hole of the sparger arm (“distance from column axis” in Fig. 6 = 0.03 m), despite d0 = 2 mm for both holes. This difference is caused by the changes in the nucleation process, as qualitatively described in Fig. 8 and quantitatively outlined in the pioneering works of Gaddis and Vogelpohl [27] or Wilkison and Dierendonck [28], as well as in the review of Kulkarni an Joshi [29]. These results agree, on the qualitatively point of view, with the research of Cao et al. [25], showing that larger bubbles are obtained by increasing the gas flow rate or by decreasing do. Finally, the comparison of the airwater system with the air-water-ethanol system (Fig. 6) is characterized by bubble sizes slightly shifted towards equivalent bubble diameters, owing to the above-discussed coalescence suppression. 3.1.2. Analytical description of the size distributions at the gas sparger This section provides a straightforward approach to support the modelling approaches of “coarse gas spargers” in “large-scale” bubble columns (as it is known that the implementation of BSDs at the gas sparger is a major shortcoming in numerical modelling). To this end, an analytical description of the bubble sizes produced by the gas sparger openings is proposed. The analytical description is build upon a preliminary assumption regarding the radial symmetry of the BSDs: the gas maldistribution is not considered and the bubble sizes do not depend on the arm of the distributor. Consequently, for every UG considered, seven BSDs are derived (viz., six for the holes on the lateral arms and one for the central holes); the obtained BSDs, were fitted by using a log-normal distribution (Eq. (5)), in agreement with the previous literature (i.e., [30]):

ln N (x; µ , ) =

1 x

2

exp

(ln x 2

µ )2 2

(5)

In Eq. (5), σ is the standard deviation and μ is the mean value of the log-normal distribution. Table 2 and Table 3 present the results of the analysis, in terms of the log-normal parameters (μ and σ). For the sake of clarity, Fig. 8 displays the BSDs obtained based on Eq. (5) for the different gas sparger openings, for the air-water and the air-water-ethanol cases. As expected, the mean bubble diameter depends on the gas sparger opening and the nucleation process. The larger the opening, the larger the standard deviation of the BSD. As previously observed, the bubble size at the center of the gas sparger (“distance from column axis” in Fig. 6 = 0.02 m) is higher compared with the one of the first hole of the sparger arm (“distance from column axis” in Fig. 6 = 0.03 m), despite the fact that d0 is equal to 2 mm for the two holes. Compared with the airwater case, the water-ethanol mixture (Fig. 5b) is characterized by BSDs slightly shifted towards lower equivalent bubble diameters, owing to the coalescence suppression [31] as well as changes at the bubble interface [4]. Future researches aiming to model a bubble column equipped with a “coarse gas sparger” may use the parameters listed in Tables 2 and 3 to implement experimental-based boundary conditions. 3.1.3. Comparison with literature correlations In the last decades, different correlations to relate the bubble size and the gas sparger design parameters (i.e., do and UG) were proposed. Unfortunately, most of the studies consider single bubbles in ideal conditions, so that reliable correlations for “large-scale” reactors are still not available. To address this lack of knowledge, four correlations (Eqs. (6)–(9)) are compared with the experimental observation to assess their validity in relevant operating conditions:

Fig. 12. Axial evolution of air-water BSDs in the batch mode – Wall region of the bubble column.

Fig. 6 further elaborates on the relationship between d0 and BSDs, by displaying the relationships between BSDs and the radial distance from the center of the gas sparger (see Fig. 2 for the details regarding the relationship between the radial distance—“distance from column axis” in Fig. 6—and the gas sparger openings). With increasing d0, the BSD shifts towards higher bubble diameters, regardless of the liquid phase considered. It is worth noting that the BSDs in the center of the

• the correlation proposed by Gaddis and Vogelpohl [27], which re-

lates the detaching equivalent bubble diameter, deq,D, to the distributor design parameters:

66

Flow Measurement and Instrumentation 67 (2019) 55–82

G. Besagni and F. Inzoli

Fig. 13. Axial evolution of air-water BSDs in the counter-current mode – Center of the bubble column.

67

Flow Measurement and Instrumentation 67 (2019) 55–82

G. Besagni and F. Inzoli

Fig. 14. Axial evolution of air-water BSDs in the counter-current mode – Wall region of the bubble column.

68

Flow Measurement and Instrumentation 67 (2019) 55–82

G. Besagni and F. Inzoli

Fig. 15. Axial evolution of air-water-ethanol BSDs – Center of the bubble column.

69

Flow Measurement and Instrumentation 67 (2019) 55–82

G. Besagni and F. Inzoli

Fig. 16. Axial evolution of air-water-ethanol BSDs – Wall region of the bubble column.

70

Flow Measurement and Instrumentation 67 (2019) 55–82

G. Besagni and F. Inzoli

Fig. 17. Relationship between sauter mean diameter and axial position in the bubble column (air-water - batch mode).

6dc

deq, D =

4 L

3

+

Lg

81µL Q Lg

+

135Q 2 4 2g

4

5

Fig. 18. Relationship between sauter mean diameter and axial position in the bubble column (air-water – counter-current mode).

volumetric mean bubble diameter, computed as follows:

0.25

(6)

dv =

In Eq. (6), Q is the gas volumetric flow rate.

• the correlations proposed by Polli et al. [32] (Eq. (7)), Cao et al.

Fr =

[30] (Eq. (8)) and Miyahara et al. [33] (Eq. (9)), relating the nondimensional bubble diameter, dw, to the parameters of the system:

1.6722Nw0.333

(7)

d w, Cao = 1.7522Nw0.362

(8)

d w, Polli =

d w, Miyahara = f (Nw )

L d0

g

L

Nw =

We Fr

g do

1 L L

1

3

ntot

(12)

Uth gd o

(13)

In Eq. (13), Uth is gas velocity at the sparger openings. Fig. 9 compares the experimental observations with the correlations. In the whole range of Nw, Eqs. (7)–(9) under-predict dw; despite that the correlations of Polli et al. [32] and Cao et al. [30] underpredict dw, they are able to capture the trend of the observations. The comparison between the correlation of Gaddis and Vogelpohl [27] and the experimental data is not shown owing to the large error committed: the flow rates in our experiments exceeded the boundaries of the correlation. In fact, in the present case, the Weber number calculated by taking into consideration the characteristics of the hole is larger than a critical value suggested by Gaddis and Vogelpohl [27], the error in the estimation of the detaching bubble diameter becomes too high and Eq. (6) is no more valid. It is worth noting these results concern the pure liquid phase; as the physical properties of the binary system are quite similar to the ones of the pure system and the operative conditions do not change significantly, the results of above-mentioned analysis are not expected to have significant variations. As above-reported correlations exhibited poor accuracy, a novel and simple correlation is derived. To this end, when displaying d32 as a function of UG, a linear relationship was found (R2 = 0.9925, Fig. 10a):

1/3

(9)

Eq. (9) was suggested by Polli et al. [32] and by Cao et al. [30], in the range between Nw = 0 and the lower boundaries of Eqs. (7) and (8). In Eq. (9), f(NW) is determined in terms of NW (accordingly with the values proposed in Ref. [33]). In Eqs. (7)–(9), the non-dimensional bubble diameter and the dimensionless hole velocity, Nw, are defined as follows:

dw = dv

3 deq

3

(10) (11)

d32, air

In Eqs. (10) and (11), Fr is the Froude number and dv is the

71

water

= 344.06UG + 12.261

(14)

Flow Measurement and Instrumentation 67 (2019) 55–82

G. Besagni and F. Inzoli

Fig. 3) break-up, leading to left-skewed BSDs (Figs. 11a, 12a and 13a, 14a, 15a and 16a); subsequently, coalescence phenomena take place and the BSDs shift towards larger equivalent diameters (Figs. 11b, 12b and 13b and 14b); finally, a “dynamic-equilibrium” is reached and, as a consequence, increasing the distance from the gas sparger does not largely affect the BSDs (the reader may compare Figs. 11c, 12c and 13c, 14c, 15c, 16c with Figs. 11d, 12d and 13d, 14d, 15d, 16d). In the “dynamic-equilibrium” condition, BSDs are characterized by an approximately constant mean diameter (viz. it does not depend on the axial position), whereas the standard deviation decreases if the axial position increases. This observation is quantitatively displayed in Fig. 17 (air-water, batch mode), Fig. 18 (air-water, counter-current mode) and Fig. 19 (air-water-ethanol), showing the relationship between the axial position and d32. Despite the three above-mentioned similarities, some differences are also observed within the different cases, thus reflecting the fundamental modifications imposed at the “local-scale” by the changes of the liquid phase properties and operation modes. Comparting the air-water case in the batch mode with air-water-ethanol, regardless of UG, at the different axial positions, BSDs in the binary system are shifted towards smaller diameters and are characterized by higher relative frequencies. This experimental observation can be easily explained by the changes induced at the bubble interface (i.e., the Marangoni effect), inducing the coalesce-suppression effects (similar considerations were reported by Gemello et al. [4], by Keitel and Onken [40] or by Shah et al. [41]). In particular, the addition of ethanol do not affect largely the break-up rate but reduces the coalescence rate [4]. A practical outcome of this effect is difference in the length requested to reach the “dynamic-equilibrium” between coalescence/break-up in the air-water case and in the air-water-ethanol case. On one hand, in the in the air-water case, after the large bubbles detached from the gas sparger broke-up, coalescence starts immediately and modifies the BSDs towards the “dynamic-equilibrium”. On the other hand, in the air-water-ethanol case, this process is delayed in time and space. Consequently, in the air-water system, “dynamic-equilibrium” BSDs have been reached at approximately h = 1 m, (viz., approaching the aspect ratio value equal to 5, in agreement with the Wilkinson scale-up criterion, ref. [42]); conversely, in the air-water–ethanol system the “dynamic-equilibrium” has not been reached completely neither at h = 1.5–2 m. These observations provide a “local-scale” representation of the “global-scale” influence of the aspect ratio (see the discussions of Sasaki et al. [43] and Besagni et al. [18]) and, for this reason, offer a rational basis to interpret the scaling-up criteria. It has not escaped our notice that our observations are in qualitative agreement with Gemello et al. [4]. Comparting the air-water case in the batch mode with the air-water case in the counter-current mode, it is noted that, when the liquid flows counter-currently with respect to the dispersed phase, BSDs are likely to have a smaller variance and are generally unimodal (the peak is at deq = 4–5 mm). The narrowing of BSDs when increasing the flowrate was also observed by Besagni and Inzoli [5] and by Sundaresan and Varma [44]. Another insight in the “local-scale” is proposed by comparing the BSDs at the wall/center of the column. In the batch mode (regardless of the liquid phase), BSDs at the wall are shifted lower equivalent bubble diameters compared with BSDs at the center; conversely, in the counter current-mode, the size distributions at the wall are slightly shifted towards larger bubbles. This observation is consistent in almost every axial position, with the exception of the first ones, where BSDs at the center exhibit smaller deq compared with the ones near the wall, possibly because of the higher flow rate at the center (imposed by the shape of the distributor). In addition, it has not escaped our notice that, in the batch mode, BSDs exhibit a different shape depending on the radial position (wall/center of the column): BSDs near the wall exhibit a smaller variance compared with BSDs at the center, and vice-versa. These observations regarding the batch and the counter-current modes

Fig. 19. Relationship between sauter mean diameter and axial position in the bubble column (air-water-ethanol).

A similar relationship was obtained for the air-water-ethanol case (Fig. 10b) and reads as follows:

d32, air

water ethanol

= 86. 797UG + 14. 474

(15)

3.2. Axial and radial development of size distribution As mentioned above, after the “birth of bubbles [17]”, from the gas sparger, their life into the system should be studied. In the following of this section, the experimental BSDs are presented in terms of the radial and axial positions, UG, the operation modes and the liquid phase properties. The experimental results are discussed in terms of similarities and differences between the different cases. First, the three main similarities are found. The first similarity concerns the nature of the flow regime: regardless of the operation mode and liquid phase, the BSDs cover a broad range of deq, which is in agreement with the definition and properties of the “pseudo-homogeneous” flow regime. Second, regardless of the axial position, the lower the flow rate is, the more leftshifted are the BSDs and vice-versa, in agreement with previous literature [34–36]. Similarly, a widespread of the size distribution while increasing of UG has been also observed by Jin et al. [37]; on the other hand, the changes in the size distributions while increasing the flow rate, for the air-water system, are in agreement with Lichti and Bart [38]. Third, for all the tested cases, the size distributions induced by the distributor change in similar ways in the axial coordinate owing to the break-up/coalescence phenomena [39]: this concept is displayed in Figs. 11and12 (air-water, batch mode), Fig. 13 – 14 (air-water, countercurrent mode) and in Figs. 15and16 (air-water-ethanol). For the different cases, the large bubbles detached from the gas sparger (see

72

Flow Measurement and Instrumentation 67 (2019) 55–82

G. Besagni and F. Inzoli

Fig. 20. Local flow properties (BSDs obtained at UG = 0.0111 m/s – h = 1.0 m).

can be interpreted considering the local flow phenomena and, to this end, a lift force interpretation was proposed in our previous studies and further discussed in the followings. As already mentioned, three parameters determine the fluid dynamics at the “local-scale”: (a) liquid velocity, (b) local gas fraction, and (c) BSDs. In this perspective, Fig. 20 couples the batch mode local liquid velocity profiles obtained in Ref. [45] (by a particle tracking velocimetry methods), with the local gas holdup profiles measured in Ref. [5]. The liquid moves upward in the center of the bubble column whereas it moves downward at the wall, becoming null at an intermediate position. The liquid velocity profiles are strictly related to the BSDs by means of the (transversal) lift force; it is known that the direction of the lift force is related to the bubble shape and size. In the case of “large bubbles”, it acts in the direction of increasing liquid velocity and vice-versa for the “small bubbles”. The distribution of the gas phase, given by the prevailing BSDs, determines the local void fraction profiles; owing to the poly-dispersed nature of the present system and given the local liquid velocity field, the local gas holdup profile is center-pecked owing to the “large bubbles” moving in the direction of the center of the column. Future study should couple these data by lift force approach and should extend the present comparison to the counter-current mode. In addition, these data may be coupled with gas disengagement measurements to propose a complete description of the non-coalescence induced bubbles [46].

3.3. The interfacial area: experimental observations and correlations Using d32 (present experimental observation) and εG (taken from Ref. [5]), the interfacial areas, ai, have been computed (Eq. (4)); as a result, Fig. 21, Fig. 22 and Fig. 23 display the relationship between ai and UG, for the different cases. Generally, ai increases with increasing UG; in the binary system, ai increases compared with the pure liquid phase (owing to the above-commented changes in BSDs) and it slightly increases in the counter-current operation (which justify the use of counter-current bubble columns, to have higher mass transfer systems [1]). In order to provide a practical outcome, five correlations were compared with our experimental observations:

• the correlation proposed by Van Dierendonck et al. [47]: ai =

6 C

1/2

L

µL UG

Lg

L

1/4

3 1/4 L L G 4 gµL

(16)

C = 2.5 (non-electrolyte system) or C = 1.45 (electrolyte system).

• the correlation proposed by Akita and Yoshida [48]:

73

Flow Measurement and Instrumentation 67 (2019) 55–82

G. Besagni and F. Inzoli

Fig. 21. Relationship between interfacial area and axial position in the bubble column (air-water - batch mode).

ai =

0.23 gdc2 dc L

1/2 L

gdc3 µL2

2 0.12 L

UG2 gdc

Fig. 22. Relationship between interfacial area and axial position in the bubble column (air-water – counter-current mode).

1/4 G

• the correlation proposed by Besagni and Inzoli [11]:

(17)

In the case of εG ≤ 0.14, Eq. (17) becomes as follows:

ai =

1 gdc2 3dc L

1/2 L

0.1 gdc3 L2 1.13 G µL2

ai =

0.3

3 L L gµL4

0.03

G

0.3

gdc2 L

1/2 L

gdc3 µL2

2 0.12 L

UG2 gd c

1/4 0.614 G

(20)

The results of this comparison are summarized in Fig. 24 and are consistent with the discussion of Besagni and Inzoli [11]. In particular, Eq. (16) overpredicts the interfacial areas regardless of the gas flow rate, as this correlation was validated in the range of UG = 0.03–0.30 m/s and for different values of AR (12.5 in this present case). Akita and Yoshida [48] correlations were obtained for “small/ intermediate-diameter” bubble columns (viz., dc = 0.077–0.15 m), which may be the reasons for the discrepancies. Conversely, Eq. (19) largely underestimates ai, possibly because it was developed for relatively low-

(18)

• the correlation proposed by Gestrich and Krauss [49]: ai = 26AR

0.23 AR dc

(19)

In Eq. (19), the aspect ratio (AR) is defined in terms of the initial liquid level, rather than column height. 74

Flow Measurement and Instrumentation 67 (2019) 55–82

G. Besagni and F. Inzoli

bubbly flows in general. Different bubble shapes induce different local flow properties (i.e., bubble wake dynamics) and, thus, different behavior and clustering phenomena (at the intermediate-scale), which influences the whole system fluid dynamics. Herein, we will not study the local interface and shape properties (i.e., bubble agitation, bubble wake, local flow fields, the shear rate around the bubble interface) but we will investigate the integral relationships between E (the aspect ratio, Eq. (2)) and the flow conditions (i.e., UG and UL). This section contributes to the existing discussion regarding bubble shape in lowMorton systems (with pure and liquid binary liquid phases) in dense bubbly flow conditions. Indeed, investigating the integral relationships between E and the flow conditions provides insight regarding the existing relationships between the influence of the flow condition and the bubble interface (viz., the determinants of the bubble shape). In this respect, despite it is recognized that small bubbles are more likely to be spherical and larger bubbles are more likely to be distorted, an analytical relationship between E and the flow conditions is still far from being reached. The experimental observations are presented in Figs. 25 – 28. Fig. 25 displays the aspect ratio distributions at different flow rates and at fixed axial location (h = 2.2 m above the gas sparger); conversely, Fig. 26 displays the aspect ratio distributions at different axial locations and fixed superficial gas velocity (0.0074 m/s); Fig. 27 displays the influence of the radial position on the aspect ratio of the bubbles. Fig. 28 displays the relationship between E and the bubble size for all the cases considered within this paper. The results are discussed in terms of similarities and differences between the different cases. Two main similarities are observed: (a) small bubbles exhibit higher E and larger bubbles exhibit lower E, (b) the bubble shapes, for a given operation mode and liquid phase do not largely depend on the superficial gas velocity. The former conclusion is quite trivial, whereas the latter supports and extends the outcomes of Ziegenhein and Lucas [50], who stated that, when E does not depend on the flow rate, the bubble shape is mostly related to the prevailing flow regime and BSDs, rather than the local gas fraction. Looking at the differences between the different systems, the influence of ethanol on the bubble shapes is easily observed: bubbles are smaller in the water-ethanol mixtures. For the sake of clarity, this concept is also shown in Fig. 4 (qualitatively) and in Figs. 25–27 (quantitatively): the aspect ratio in the binary liquid phase is higher compared with the pure liquid phase for all the different flow conditions (viz., in the binary system, bubbles are more likely to be smaller and spherical in shape). In particular, in the pure system, the mean aspect ratio is in the range of 0.6–0.7 independently of UG and sampling location. Conversely, in the binary system, the mean aspect ratio is in the range of 0.8–0.9. It is also observed that the bubble shape and prevailing aspect ratio is not significantly influenced by the operating conditions (gas flow rate) and the axial locations. Considering the influence of the counter-current mode, it has been observed that an increased liquid velocity tends to make bubbles more flattered, exhibiting a lower aspect ratio. In the counter-current mode, at higher bubble equivalent diameters, the experimental data are more scattered, which is in agreement with the discussion of Besagni and co-authors [19,21], based on smaller datasets and a more limited range of operating conditions. The analytical description of bubble shapes is of paramount importance as discussed by Ziegenhein and Lucas [50]. For example, Shi et al. [51] successfully implemented the correlation proposed in Ref. [21] in a numerical code. In the broader framework of analytical description of bubble shapes, Besagni and co-authors [19,21] discussed the need of ad-hoc E correlations valid for dense bubbly flow conditions. Given the importance of this topic, in the remaining part of this section, the aspect ratio correlation proposed in Ref. [21] (based on aspect ratio data obtained in an annular gaps counter-current bubble

Fig. 23. Relationship between interfacial area and axial position in the bubble column (air-water-ethanol).

AR bubble columns. Finally, Eq. (20) fits fairly well the experimental data in the whole range of flow rates. These results support the conclusions of Besagni and Inzoli [11]: the poor performances of literature correlations may be imputed to the distance to achieve an equilibrium size distribution (quantified by the aspect ratio) and the design of the gas sparger. 3.4. Bubble aspect ratio It is widely accepted that the bubble shapes have a profound influence in the prevailing fluid dynamics of bubble columns, and of

75

Flow Measurement and Instrumentation 67 (2019) 55–82

G. Besagni and F. Inzoli

Fig. 24. Interfacial area: comparison between experimental data and literature correlations.

column) has been extended by using the dataset obtained in this paper (the same procedure used in Ref. [21] has been applied here):

studies may extend Eq. (24) with additional experimental datasets, to derive general aspect ratio correlation to represent bubble column systems.

• when considering all the data for the air-water system (batch mode), the following correlation was obtained (Fig. 28a):

Eair

water batch mode

=

1 1 + 0.489 (Eo) 0.148

4. Conclusions, outcomes and outlooks (21)

Datasets that include the bubble size, void fraction, and liquid velocity are vital to validate numerical codes. In particular, datasets for different facility sizes are important to validate the capability of present numerical approach for upscaling. While some data exist for tabletop bubble columns, complete datasets for “large-scale” bubble columns are seldom, in particular when considering axial description of bubble sized with binary liquid phases. In the present study, prior measurements were completed with respect to the bubble sizes and shapes. The main conclusions of the proposed research are as follows:

• when considering all the data for the air-water system (countercurrent mode), the following correlation was obtained (Fig. 28a):

Eair

water counter current mode

=

1 1 + 0.777 (Eo) 0.167

(22)

• when considering all the data for the air-water-ethanol system, the following correlation was obtained (Fig. 28a):

Eair

water ethanol

=

1 1 + 0.489 (Eo)0.186

• a comprehensive experimental dataset of BSDs for different axial

(23)

Fig. 28 compares the experimental observations with Eqs. (21)–(23): despite the shape obtained by Eq. (21) and Eq. (23) is similar, in the ethanol case, the larger number of the bubbles is included in the lower bubble classes (in the air-water-ethanol system, 65% of the bubbles is below 2.5 mm; in the air-water system, only 19% of the bubbles is comprised in this range). This consideration suggests that, despite the shape of the correlations is similar, the bubble distribution in the different parts of the correlation differs. To provide a more general outcome, if considering all our available air-water data regarding bubble shape aspect ratio data from Ref. [21] and the ones obtained in this study, the following correlation has been derived, which is suggested for the future:

Eair

water all data

=

1 1 + 0.570 (Eo) 0.117

• • • • •

(24)

and radial positions, for pure and binary liquid phases, have been proposed (Section 3.1 and 3.2); size distributions at the gas sparger have been obtained and correlations to be used in modeling “coarse gas spargers” have been proposed, in order to provide experimental-based input for numerical models (Section 3.1.2); literature correlations to predict bubble sizes at the gas sparger have been tested against experimental data and novel correlations have been proposed (Section 3.1.3); “global-scale” scaling-up criteria have been related to the “bubblescale” (Section 3.2); interfacial area data have been obtained and compared with the literature (Section 3.3); the aspect ratio correlation proposed in Ref. [21] has been extended with the datasets obtained in this paper (Section 3.4)

This is the very first study providing a complete dataset for ethanolbased systems and for the counter-current flow in bubble columns. The experimental dataset proposed in this study, coupled with the data presented in our other studies, may serve as a basis to improve the validation process of multi-phase modeling approaches, especially considering coalescence and breakage kernels. In addition, the obtained data have been extensively compared with literature correlations to further assess their range of validity and to be used in practical applications.

The proposed correlation is able to fit the shape of bubbles having an equivalent diameter above 2 mm (Fig. 29) and slightly fails in the low-diameter region. This begs a fundamental issue: it appears that, correlations having only one non-dimensional group are unable to correctly reproduce the bubble shape for dense bubbly flows system with high slip ratio between the phases, possibly because two prevailing mechanisms exists: one at low equivalent bubble diameters and another one at highest equivalent diameters. This issue might be solved by either using multiple groups or by applying blending functions; future

76

Flow Measurement and Instrumentation 67 (2019) 55–82

G. Besagni and F. Inzoli

Fig. 25. Aspect ratio distributions at different flow rates and at fixed axial location (h = 2.2 m above the gas sparger).

77

Flow Measurement and Instrumentation 67 (2019) 55–82

G. Besagni and F. Inzoli

Fig. 26. Aspect ratio distributions at different axial locations and fixed flow rate (UG = 0.0074 m/s).

78

Flow Measurement and Instrumentation 67 (2019) 55–82

G. Besagni and F. Inzoli

Fig. 27. Comparison between aspect ratio distributions near the wall and at the center of the bubble column (UG = 0.0037 m/s – h = 0.3 m from the gas sparger).

79

Flow Measurement and Instrumentation 67 (2019) 55–82

G. Besagni and F. Inzoli

Fig. 28. Relationship between bubble aspect ratio and bubble size for different flow conditions.

80

Flow Measurement and Instrumentation 67 (2019) 55–82

G. Besagni and F. Inzoli

Fig. 29. Aspect ratio correlation.

Appendix A. Supplementary data

[20] S. Nedeltchev, U. Jordan, A. Schumpe, Correction of the penetration theory applied to the prediction of kLa in a bubble column with organic liquids, Chem. Eng. Technol. 29 (2006) 1113–1117. [21] G. Besagni, F. Inzoli, Bubble size distributions and shapes in annular gap bubble column, Exp. Therm. Fluid Sci. 4 (2016) 27–48. [22] Y.T. Shah, B.G. Kelkar, S.P. Godbole, W.D. Deckwer, Design parameters estimations for bubble column reactors, AIChE J. 28 (1982) 353–379. [23] Y.G. Hur, J.H. Yang, H. Jung, S.B. Park, Origin of regime transition to turbulent flow in bubble column: orifice- and column-induced transitions, Int. J. Multiph. Flow 50 (2013) 89–97. [24] N.W. Geary, R.G. Rice, Bubble size prediction for rigid and flexible spargers, AIChE J. 37 (1991) 161–168. [25] C. Cao, L. Zhao, D. Xu, Q. Geng, Q. Guo, Investigation into bubble size distribution and transient evolution in the sparger region of Gas−Liquid external loop airlift reactors, Ind. Eng. Chem. Res. 48 (2009) 5824–5832. [26] D. McCann, R. Prince, Regimes of bubbling at a submerged orifice, Chem. Eng. Sci. 26 (1971) 1505–1512. [27] E. Gaddis, A. Vogelpohl, Bubble formation in quiescent liquids under constant flow conditions, Chem. Eng. Sci. 41 (1986) 97–105. [28] P.M. Wilkinson, L.L. Van Dierendonck, A theoretical model for the influence of gas properties and pressure on single-bubble formation at an orifice, Chem. Eng. Sci. 49 (1994) 1429–1438. [29] A.A. Kulkarni, J.B. Joshi, Bubble formation and bubble rise velocity in Gas−Liquid Systems: a review, Ind. Eng. Chem. Res. 44 (2005) 5873–5931. [30] C. Cao, L. Zhao, D. Xu, Q. Geng, Q. Guo, Investigation into bubble size distribution and transient evolution in the sparger region of Gas− liquid external loop airlift reactors, Ind. Eng. Chem. Res. 48 (2009) 5824–5832. [31] J. Zahradník, M. Fialova, V. Linek, The effect of surface-active additives on bubble coalescence in aqueous media, Chem. Eng. Sci. 54 (1999) 4757–4766. [32] M. Polli, M. Di Stanislao, R. Bagatin, E.A. Bakr, M. Masi, Bubble size distribution in the sparger region of bubble columns, Chem. Eng. Sci. 57 (2002) 197–205. [33] T. Miyahara, M. Hamaguchi, Y. Sukeda, T. Takahashi, Size of bubbles and liquid circulation in a bubble column with a draught tube and sieve plate, Can. J. Chem. Eng. 64 (1986) 718–725. [34] Y. Kang, Y.J. Cho, K.J. Woo, K.I. Kim, S.D. Kim, Bubble properties and pressure fluctuations in pressurized bubble columns, Chem. Eng. Sci. 55 (2000) 411–419. [35] K. Muroyama, K. Imai, Y. Oka, J.i. Hayashi, Mass transfer properties in a bubble column associated with micro-bubble dispersions, Chem. Eng. Sci. 100 (2013) 464–473. [36] J. Xue, M. Al-Dahhan, M.P. Dudukovic, R.F. Mudde, Bubble velocity, size, and interfacial area measurements in a bubble column by four-point optical probe, AIChE J. 54 (2008) 350–363. [37] H. Jin, Y. Lian, S. Yang, G. He, Z. Guo, The parameters measurement of air–water two phase flow using the electrical resistance tomography (ERT) technique in a bubble column, Flow Meas. Instrum. 31 (2013) 55–60. [38] M. Lichti, H.-J. Bart, Bubble size distributions with a shadowgraphic optical probe, Flow Meas. Instrum. 60 (2018) 164–170. [39] F. Lehr, M. Millies, D. Mewes, Bubble‐Size distributions and flow fields in bubble columns, AIChE J. 48 (2002) 2426–2443. [40] G. Keitel, U. Onken, The effect of solutes on bubble size in air-water dispersions, Chem. Eng. Commun. 17 (1982) 85–98. [41] Y.T. Shah, S. Joseph, D.N. Smith, J.A. Ruether, On the behavior of the gas phase in a bubble column with ethanol-water mixtures, Ind. Eng. Chem. Process Des. Dev. 24 (1985) 1140–1148. [42] P.M. Wilkinson, A.P. Spek, L.L. van Dierendonck, Design parameters estimation for scale-up of high-pressure bubble columns, AIChE J. 38 (1992) 544–554. [43] S. Sasaki, K. Uchida, K. Hayashi, A. Tomiyama, Effects of column diameter and liquid height on gas holdup in air-water bubble columns, Exp. Therm. Fluid Sci. 82 (2017) 359–366. [44] A. Sundaresan, Y. Varma, Dispersed phase holdup and bubble size distributions in gas–liquid concurrent upflow and countercurrent flow in reciprocating plate

Supplementary data to this article can be found online at https:// doi.org/10.1016/j.flowmeasinst.2019.04.008. References [1] C. Leonard, J.H. Ferrasse, O. Boutin, S. Lefevre, A. Viand, Bubble column reactors for high pressures and high temperatures operation, Chem. Eng. Res. Des. 100 (2015) 391–421. [2] T. Ziegenhein, A. Tomiyama, D. Lucas, A new measuring concept to determine the lift force for distorted bubbles in low Morton number system: results for air/water, Int. J. Multiph. Flow 108 (2018) 11–24. [3] I. Murgan, F. Bunea, G.D. Ciocan, Experimental PIV and LIF characterization of a bubble column flow, Flow Meas. Instrum. 54 (2017) 224–235. [4] L. Gemello, C. Plais, F. Augier, A. Cloupet, D.L. Marchisio, Hydrodynamics and bubble size in bubble columns: effects of contaminants and spargers, Chem. Eng. Sci. 184 (2018) 93–102. [5] G. Besagni, F. Inzoli, Comprehensive experimental investigation of counter-current bubble column hydrodynamics: holdup, flow regime transition, bubble size distributions and local flow properties, Chem. Eng. Sci. 146 (2016) 259–290. [6] D.D. McClure, J.M. Kavanagh, D.F. Fletcher, G.W. Barton, Characterizing bubble column bioreactor performance using computational fluid dynamics, Chem. Eng. Sci. 144 (2016) 58–74. [7] Y. Liao, T. Ma, L. Liu, T. Ziegenhein, E. Krepper, D. Lucas, Eulerian modelling of turbulent bubbly flow based on a baseline closure concept, Nucl. Eng. Des. 337 (2018) 450–459. [8] O.C. Adetunji, R. Rawatlal, Prediction of bubble size and axial position distribution through hybridization of population balance modelling and dynamic gas disengagement, Flow Meas. Instrum. 59 (2018) 181–193. [9] D.D. McClure, C. Wang, J.M. Kavanagh, D.F. Fletcher, G.W. Barton, Experimental investigation into the impact of sparger design on bubble columns at high superficial velocities, Chem. Eng. Res. Des. 106 (2016) 205–213. [10] P. Tyagi, V.V. Buwa, Experimental characterization of dense gas–liquid flow in a bubble column using voidage probes, Chem. Eng. J. 308 (2017) 912–928. [11] G. Besagni, F. Inzoli, The effect of liquid phase properties on bubble column fluid dynamics: gas holdup, flow regime transition, bubble size distributions and shapes, interfacial areas and foaming phenomena, Chem. Eng. Sci. 170 (2017) 270–296. [12] P. Dargar, A. Macchi, Effect of surface-active agents on the phase holdups of threephase fluidized beds, Chem. Eng. Process: Process Intensification 45 (2006) 764–772. [13] A.S. Najafi, J. Drelich, A. Yeung, Z. Xu, J. Masliyah, A novel method of measuring electrophoretic mobility of gas bubbles, J. Colloid Interface Sci. 308 (2007) 344–350. [14] M. Takahashi, ζ potential of microbubbles in aqueous Solutions: electrical properties of the Gas−Water interface, J. Phys. Chem. B 109 (2005) 21858–21864. [15] G. Keitel, U. Onken, Inhibition of bubble coalescence by solutes in air/water dispersions, Chem. Eng. Sci. 37 (1982) 1635–1638. [16] R. Krishna, M.I. Urseanu, A.J. Dreher, Gas hold-up in bubble columns: influence of alcohol addition versus operation at elevated pressures, Chem. Eng. Process: Process Intensification 39 (2000) 371–378. [17] P. Di Marco, Birth, life and death of gas bubbles rising in a stagnant liquid, Heat Technol. 23 (2005) 17–26. [18] G. Besagni, A. Di Pasquali, L. Gallazzini, E. Gottardi, L.P.M. Colombo, F. Inzoli, The effect of aspect ratio in counter-current gas-liquid bubble columns: experimental results and gas holdup correlations, Int. J. Multiph. Flow 94 (2017) 53–78. [19] G. Besagni, F. Inzoli, T. Ziegenhein, H. Hessenkemper, D. Lucas, Bubble aspect ratio in dense bubbly flows: experimental studies in low Morton-number systems, J. Phys. Conf. Ser. 923 (2017) 012014.

81

Flow Measurement and Instrumentation 67 (2019) 55–82

G. Besagni and F. Inzoli column, Can. J. Chem. Eng. 68 (1990) 560–568. [45] G. Besagni, I. Fabio, Z. Thomas, L. Dirk, Experimental study of liquid velocity profiles in large-scale bubble columns with particle tracking velocimetry, 36TH UIT HEAT TRANSFER CONFERENCE, Catania, 2018. [46] O. Adetunji, R. Rawatlal, Estimation of bubble column hydrodynamics: imagebased measurement method, Flow Meas. Instrum. 53 (2017) 4–17. [47] L. Van Dierendonck, J. Fortuin, D. Venderbos, The specific contact area in gas-liquid reactors, Proceedings on the 4th European Symposium on Chemical Reactor Engineering, Brussels, 1968, pp. 205–215.

[48] K. Akita, F. Yoshida, Bubble size, interfacial area, and liquid-phase mass transfer coefficient in bubble columns, Ind. Eng. Chem. Process Des. Dev. 13 (1974) 84–91. [49] W. Gestrich, W. Krauss, Die spezifische phasengrenzfläche in blasenschichten, Chem. Ing. Tech. 47 (1975) 360–367. [50] T. Ziegenhein, D. Lucas, Observations on bubble shapes in bubble columns under different flow conditions, Exp. Therm. Fluid Sci. 85 (2017) 248–256. [51] W. Shi, J. Yang, G. Li, X. Yang, Y. Zong, X. Cai, Modelling of breakage rate and bubble size distribution in bubble columns accounting for bubble shape variations, Chem. Eng. Sci. 187 (2018) 391–405.

82