Morphology and flow behavior of buoyant bubble plumes

Highlights

• Lagrangian tracking of captured bubbles to obtain the morphology and flow behavior

• Bubble coalescence found to be more dominant than bubble breakup

• A novel correlation proposed to estimate the bubble shape by accounting all forces

• Current correlation applicable for a wider range of bubble sizes than existing ones

Abstract

The morphological and hydrodynamic behavior of bubbles in air–water plumes was studied by employing Particle Tracking Velocimetry (PTV) techniques. Individual bubbles were identified by analyzing the instantaneous high-speed camera images of the plume. The bubble velocities were then obtained by Lagrangian tracking of each bubble, based on its size and location. The nature of bubble coalescence and breakup was also investigated based on the change in the projected area of the parent and daughter bubbles. The effect of the bubble position and the air inflow rate on the bubble properties like diameter, aspect ratio, velocity, number flux, etc., and on the coalescence and breakup behavior was investigated. A novel correlation is proposed to estimate the bubble aspect ratio as a function of bubble Reynolds number and Eotvos number, for a wide range of flow conditions, and is compared with existing correlation from the literature.

Introduction

Buoyant plumes are encountered in many processes of environmental and engineering significance like wastewater treatment, petrochemical processing, destratification of lakes and reservoirs, mineral and froth flotation, and in metallurgical refining operations. In bubbly flows, the presence of bubbles enhances the mass transfer in the liquid. For this reason, bubble-driven flows are often employed in industries to obtain better mixing.

Experiments were performed on gas purged liquid baths, to understand the bubble behavior (Leibson et al., 1956, Davidson and Schuler, 1960, Ishii and Zuber, 1979, Sahajvalla et al., 1990, Xie et al., 1992, Krishnapisharody and Irons, 2010). These experiments were conducted on cylindrical vessels of different sizes. The dynamic similarity was maintained between the various systems based on different dimensionless numbers like the inlet Reynolds number, Weber number, Froude number, Morton number, etc. It was observed that the bubble flow behavior in the liquid bath is buoyancy dominated. It was also concluded that the Froude number is the dominant dimensionless group for assessing the similarity between different systems.

The injected gas penetrates the liquid bath up to a certain distance, after which it disintegrates into several bubbles. These bubbles formed after the penetration distance entrain the liquid and create a two-phase plume region, which rises to the bath surface (Fruehan, 1985). The plume radially expands as it rises and escapes the bath. The bubble formation is classified into various regimes, based on the degree of bubble interaction within the plume (Muller and Prince, 1972, Clift et al., 1978, Badam et al., 2007, Chakraborty et al., 2015, Wang et al., 2017, Capponi and Llewellin, 2019). At lower flow rates, distinct bubbles are formed, with regular periodicity and little to no interaction with the neighboring bubbles. As the flow rate increases, the bubble frequency increases, and more bubbles appear to interact and collide with each other without coalescence. These clashed bubbles group together as they rise to the free surface. A further rise in the flow rate causes strong interaction between bubbles and leads to bubble coalescence and splitting. At even higher flow rates, bubble chains are formed, and the plume behaves as a continuous gas jet, with occasional detachment and reattachment of the bubble chains.

Experiments have also been conducted to measure the bubble velocity and turbulence in the plume, using several techniques like Laser Doppler Velocimetry, electro-resistivity probe measurements, etc. (Castillejos and Brimacombe, 1987, Sheng and Irons, 1993, Shuai et al., 2018). Based on the velocity fluctuations, in the plume, it was concluded that the turbulence in the flow is nearly isotropic (Sheng and Irons, 1993). Further studies indicated the turbulence in the flow is affected by both the path oscillations and the shape oscillations of the bubbles during rising (Kataoka et al., 1993, Stover et al., 1997, Basaran, 1997, Liao et al., 2019, Owusu et al., 2018). At different airflow rates, the axial profiles of the bubble rise velocities were obtained (Castillejos and Brimacombe, 1987, Owusu et al., 2018). Based on the velocity profiles, the plume was divided into four zones along the axial direction: momentum, transition, buoyancy, and surface region. The momentum region is observed near the gas inlet orifice, characterized by a rapid increase in the bubble axial velocity. There is a transition from the momentum region to a buoyancy region, where the bubble velocity remains stable, and the velocity fluctuations are minimum. Finally, as the bubbles reach the surface region, the axial bubble velocity drops rapidly as the liquid flows radially out of the plume. Among the four zones, the buoyancy region is the largest of the bubble plume.

The nature of the bubble plume flow is unsteady, evidenced by the transversely oscillating bubble swarms. The plume radially expands as it rises to the free surface, and its boundary is approximated as a cone (Krishna Murthy et al., 1988). The angle of divergence of the plume (cone angle) and its oscillation behavior are essential parameters that affect the mixing and mass transfer in the liquid bath (Krishna Murthy et al., 1988, Delnoij et al., 1997, Liu et al., 2019). The frequency of the plume oscillations was studied at different gas flow rates in liquid baths with different aspect ratios. Empirical correlations were proposed for the same in terms of the gas velocity, liquid viscosity, and the orifice diameter (Delnoij et al., 1997, Haberman and Morton, 1954, Lin et al., 1996). The plume cone angle also depends on the inflow rate, orifice diameter, and the aspect ratio of the liquid bath (Szekely et al., 1976). The plume cone angle was experimentally measured, and the obtained data were used to obtain an empirical correlation for estimating the same, in terms of the Froude number, orifice diameter and the aspect ratio of the bath (Krishna Murthy et al., 1988).

Experiments were also performed to obtain the gas fraction in the plume, bubble frequency, bubble size, etc. (Vejrazka et al., 2017, Wellek et al., 1966, Kumar and Kuloor, 1970, Jamialahmadi et al., 2001, Joshi et al., 2002, Di Bari and Robinson, 2013, Schafer et al., 2019, Li et al., 2015, Tran et al., 2019). Various experimental techniques like high-speed imaging, Laser Doppler Velocimetry, Hotwire anemometry, electro-resistivity probing, etc., were employed for the same (Li et al., 2015, Krishnapisharody and Irons, 2007). It was observed that all the significant plume properties like the extent of plume spreading, the gas fraction of the plume, the mean diameter and the rise velocity of the bubbles in the plume, etc., can be estimated from the bubble position in the liquid bath, as well as the gas purging rate (Krishnapisharody and Irons, 2007). Empirical correlations were proposed to estimate the plume velocity, gas volume fraction, velocity slip at the bubble interface, plume shape, and bubble diameter (Krishnapisharody and Irons, 2007, Sahai and Guthrie, 1982, Joo and Guthrie, 1992).

The understanding of bubble columns at different fluid dynamic scales is essential for efficient design, scale-up, and operation of industrial reactors. The local void fraction, bubble size, shape, and local liquid velocity are essentially the local-scale parameters. The large-scale phenomena are the gas holdup, the total rate of heat and mass transfer, etc., and are enforced by the local-scale parameters (Mudde, 2005). The local-scale parameters like the bubble shape and size affect the interphase momentum and energy exchange, which determine the reactor size for given heat and mass transfer requirements. The local and large-scale fluid dynamic properties are related to the prevailing flow regime: homogeneous, transitional, and heterogeneous. The homogeneous flow regime is associated with low superficial gas velocity and only contain non-coalescence induced bubbles. The heterogeneous flow regime contains coalescence-induced bubbles, and the coalescence, breakup affect the bubble size and shape. A detailed discussion on the flow regimes and their characteristics is available in the literature (Shah et al., 1982, Montoya et al., 2016, Besagni et al., 2017, Besagni et al., 2017).

Several studies are available in the literature that attempt to relate the bubble shape to the local-scale fluid dynamic properties (Haberman and Morton, 1954, Tadaki and Maeda, 1961, Wellek et al., 1966, Grace et al., 1976, Delnoij et al., 1997, Sanada et al., 2008, Liu et al., 2015, Ziegenhein et al., 2015, Aoyama et al., 2016, Besagni and Inzoli, 2016, Besagni and Inzoli, 2017, Besagni and Inzoli, 2019, Ziegenhein and Lucas, 2017, Aoyama et al., 2018, Huang et al., 2018, Tian et al., 2019). Various gas–liquid systems like air–water, air-ethylene glycol solution, Nitrogen-silicon oil, carbon dioxide-turpentine and pine resin solution, etc., were used as the operating fluids (Wellek et al., 1966, Sanada et al., 2008, Liu et al., 2015, Aoyama et al., 2016, Besagni and Inzoli, 2016, Besagni and Inzoli, 2017, Besagni and Inzoli, 2019, Ziegenhein and Lucas, 2017, Huang et al., 2018, Tian et al., 2019). Several empirical correlations were also proposed to estimate the bubble aspect ratio, in terms of bubble Eotvos number, Reynolds number, Weber number, etc (Tadaki and Maeda, 1961, Wellek et al., 1966, Okawa et al., 2003, Sugihara et al., 2007, Aoyama et al., 2016, Besagni and Inzoli, 2016). Most of these correlations are limited to spherical and ellipsoidal regimes of the bubbles, i.e., lower ranges of bubble Reynolds number(${10}^{-1}-{10}^2$), Eotvos number (${10}^{-2}-{10}^2$), and Weber number (${10}^{-4}-10$), and are only applicable in a specific range of these dimensionless numbers. The applicability of the existing empirical correlations is validated over a wide range of Morton numbers (${10}^{-11}-10$), and a novel empirical correlation is proposed to obtain a better estimate of the bubble aspect ratio, as a function of the product of the bubble Eotvos and Reynolds numbers (Besagni and Deen, 2020). It has been shown that the bubble aspect ratio decreases with the product of Eotvos and Reynolds numbers, and then starts increasing when the product of Eotvos and Reynolds numbers is about ${10}^4-{10}^5$. High values of the product of Eotvos and Reynolds numbers indicate a dense bubbly flow, and a high gas fraction has a positive effect on the bubble aspect ratio (Roghair, 2012, Besagni and Inzoli, 2016, Besagni and Inzoli, 2017, Besagni and Inzoli, 2019).

Along with the experimental studies, numerical modeling of gas–liquid flows is also done to investigate the flow behavior and improve the heat and mass transfer in the surrounding liquid. Several phenomenological and quasi-steady state models are available in the literature, but they fail to provide detailed information about the bubbly flow behavior (Myers et al., 1987, Kantak et al., 1995, Shimizu et al., 2000, Jakobsen et al., 2005). Computational Fluid Dynamics (CFD) based modeling, using the Eulerian-Eulerian approach and Eulerian–Lagrangian approach, is the most used technique to simulate the two-phase flows (Delnoij et al., 1997, Ekambara et al., 2005, Buwa et al., 2006, Besbes et al., 2015, Ziegenhein et al., 2015, Rzehak and Krepper, 2016, Liu and Li, 2018). Both these approaches have their advantages and limitations, which are discussed elaborately in the literature(Buwa et al., 2006, Besbes et al., 2015, Jakobsen et al., 2005, Besagni et al., 2018). These techniques are often coupled with the Population Balance Modeling (PBM) method, which provides a statistical formulation to describe the bubble motion in the two-phase flow (Krishna et al., 2000, Chen et al., 2004, Cheung et al., 2007, Solsvik and Jakobsen, 2016, Vik et al., 2018). The bubble interactions, i.e., collision, coalescence, and breakup, are also modeled together with the above models, the details of which are available in the literature (Colella et al., 1999, Chen et al., 2005, Liao and Lucas, 2009, Liao and Lucas, 2010, Solsvik and Jakobsen, 2016). A detailed review of the numerical modeling of gas–liquid flows is available in the literature(Jakobsen et al., 2005, Besagni et al., 2018).

Modeling of the bubbly flows requires detailed information about the bubble shape and deformation to develop proper drag and lift force models (Grace et al., 1976, Bozzano and Dente, 2001, Tomiyama et al., 2002, Ziegenhein and Lucas, 2017). The mixing, mass, and heat transfer in these flows also depend on the shape, size, and flow behavior of the bubbles. Further, the bubble coalescence and breakup also affect the bubble morphological and flow behavior and must be studied for a better understanding of the gas–liquid flows. A comprehensive numerical model that simulates the gas–liquid flows in a wide range of operating conditions is still not available. Developing such a model requires detailed information on the morphological and flow behavior of bubbles. The understanding of dense bubbly flow behavior, particularly low Morton number flows $(~O({10}^{-11}\left)\right)$, is also limited and needs further exploration. In this regard, the air–water plumes are studied in the current work at relatively high bubble Reynolds number (${10}^3-5\times {10}^4$), and Eotvos number ($10-{10}^3$), which has not gained much attention in the past. The plume dynamics were captured using a high-speed camera, and individual bubbles were tracked from successive images by developing an algorithm based on Particle Tracking Velocity (PTV) techniques. Various properties, like the bubble diameter, aspect ratio, velocity, and number flux, as well as the bubble coalescence and splitting, are quantified using this algorithm. The distribution of these properties in the plume at different inflow rates is analyzed. The variation of these properties along the axial direction of the plume is also investigated. The measured bubble aspect ratio was compared with the data available in the literature, and an empirical correlation is also proposed for the same, in terms of dimensionless parameters defined at the bubble-scale. This novel correlation accurately describes the bubble shape and covers a broader range than the existing correlations in the literature.