Journal of Applied Mathematics

Volume 2016 (2016), Article ID 5238737, 19 pages

http://dx.doi.org/10.1155/2016/5238737

## Numerical Simulation of Bubble Coalescence and Break-Up in Multinozzle Jet Ejector

^{1}Centre for Industrial Mathematics and Department of Applied Mathematics, Faculty of Technology and Engineering, The M. S. University of Baroda, Vadodara, Gujarat 390001, India^{2}Centre of Computational Engineering and Integrated Design (CEID), Lappeenranta University of Technology, P.O. Box 20, 53851 Lappeenranta, Finland^{3}Department of Chemistry, Lappeenranta University of Technology, P.O. Box 20, 53851 Lappeenranta, Finland^{4}Department of Mathematics and Physics, Lappeenranta University of Technology, P.O. Box 20, 53851 Lappeenranta, Finland^{5}Department of Chemical Engineering, Faculty of Technology and Engineering, The M. S. University of Baroda, Vadodara, Gujarat 390001, India

Received 26 October 2015; Accepted 22 December 2015

Academic Editor: Guan H. Yeoh

Copyright © 2016 Dhanesh Patel et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Designing the jet ejector optimally is a challenging task and has a great impact on industrial applications. Three different sets of nozzles (namely, 1, 3, and 5) inside the jet ejector are compared in this study by using numerical simulations. More precisely, dynamics of bubble coalescence and breakup in the multinozzle jet ejectors are studied by means of Computational Fluid Dynamics (CFD). The population balance approach is used for the gas phase such that different bubble size groups are included in CFD and the number densities of each of them are predicted in CFD simulations. Here, commercial CFD software* ANSYS Fluent 14.0* is used. The realizable - turbulence model is used in CFD code in three-dimensional computational domains. It is clear that Reynolds-Averaged Navier-Stokes (RANS) models have their limitations, but on the other hand, turbulence modeling is not the key issue in this study and we can assume that the RANS models can predict turbulence of the carrying phase accurately enough. In order to validate our numerical predictions, results of one, three, and five nozzles are compared to laboratory experiments data for Cl_{2}-NaOH system. Predicted gas volume fractions, bubble size distributions, and resulting number densities of the different bubble size groups as well as the interfacial area concentrations are in good agreement with experimental results.

#### 1. Introduction

There are number of industrial processes in which two-phase flows, that is, gas-liquid mixture, in a jet ejector are encountered. Hence, reactions occurring in gas-liquid systems are of great importance in the chemical as well as in the process industry. Mass transfers in dispersions are directly related to the mass transfer coefficients as well as the interfacial area. The jet ejector is one kind of a venturi scrubber and it is widely used for conducting gas-liquid reactions in practical applications in industry such as pollution control and waste water treatment. Due to their simple construction, low operating cost, high energy efficiency, and good mass transfer characteristics, the jet ejectors have many advantages when used as the gas-liquid contactors. The experimental observations show that dispersed bubbles towards the bottom of the jet ejector cause highly nonuniform volume distribution in the jet ejector. The gas volume fraction, the interfacial area, and the Sauter mean bubble diameter are the three important parameters that characterize the internal flow structure of gas-liquid flows in the jet ejector [1]. The interfacial transport of mass and momentum are proportional to the interfacial area and the driving forces. This is an important parameter required for a two-fluid model formulation [1]. The mean bubble diameter serves as a link between the gas volume fraction and the interfacial area concentration [1]. An accurate knowledge of local distributions of these three parameters is of great importance to eventual understanding and modeling of the interfacial transfer processes [1, 2]. Depending on the gas flow rate, two main flow regimes are observed in the jet ejector, namely, the homogeneous bubbly flow regime and the heterogeneous (churn-turbulent flow) regime [3]. The homogeneous regime is encountered at relatively low gas velocities and characterized by a narrow bubble size distribution and radially uniform gas holdup and it is the most desirable one for practical applications, because it offers a large contact area [2–4].

The bubble size distribution and gas holdup in gas-liquid dispersions depend extensively on the jet ejector geometry, operating conditions, and the physicochemical properties of the two phases. The design of the jet ejector has primarily been carried out by means of empirical or semiempirical correlations based mainly on experimental data. The scale-up of the jet ejector is still poorly understood due to the complexity of flow patterns and their unknown behavior under different sets of design parameters such as area ratio, projection ratio, nozzle diameter, length of free jet, throat, diffuser, convergence angle, divergence angle, and physical properties of the liquid. As a whole, the phenomenon depends strongly on the jet ejector geometry and fluid dynamics involved. It is important to note that the similar kind of study has been developed for bubble column reactor by [3].

The method to gain more knowledge and detailed physical understanding of the hydrodynamics in the jet ejector is Computational Fluid Dynamics (CFD). CFD can be regarded as an effective tool to clarify the importance of physical effects (e.g., gravity, surface tension) on flow by adding or removing them. An increasing number of papers deal with CFD applications of bubble columns [3, 5–7]. To analyze the flow pattern of the jet ejector both in steady and transient state conditions employing CFD, the majority of researchers use either two- or three-dimensional models, when numerical simulations are usually compared to experimental data. As most of the early CFD studies consider monodispersed bubble size distributions ignoring break-up and coalescence mechanisms, their validity is limited [3].

During the last two decades, significant developments have been done in the modeling of two-phase flow processes because of the introduction of the two-fluid models [1]. In the two-fluid models, the interfacial transfer terms are related to the interfacial area concentration and the degree of turbulence near the interfaces [1]. Since the interfacial area concentration represents the key parameter that links the interaction of the phases, significant attention has been paid towards developing a better understanding of the coalescence and breakage effects due to interactions among bubbles and between bubbles and turbulent eddies for gas-liquid bubbly flows [1, 2, 7–11]. The population balance method is a well-known method for tracking the size distribution of the dispersed phase and accounting for the breakage and coalescence dynamics in bubbly flows [1, 12–22]. The population balance method was also used by Hämäläinen et al. [23] and Hämäläinen [24] in paper industry for papermaking suspension flow.

In gas-liquid two-phase systems, bubble break-up and coalescence can greatly influence their overall performance by altering the interfacial area available for the mass transfer between the phases [3]. Therefore, in order to develop reliable predictive tools for designing the jet ejectors, it is essential to obtain some insight into the prevailing phenomena through simulation models based on the bubble formation and distraction mechanisms, that is, bubble coalescence and break-up [3, 12, 15, 25–28], incorporated into CFD simulation making it possible to calculate hydrodynamic variables such as liquid velocity, gas holdup, and bubble size distributions.

In this work, an attempt has been made to demonstrate the possibility of combining the population balance models with Computational Fluid Dynamics (CFD) for the case of a gas-liquid bubbly flow in the jet ejector. In all these processes gas holdup, , and bubble size distribution are important design parameters, since they define the gas-liquid interfacial area available for interfacial area mass transfer (), which is given bywhere is the mean Sauter diameter of the bubble size distribution [3]. The MUSIG model implemented in* ANSYS Fluent 14.0*, which accounts for the nonuniform bubble size distribution in a gas-liquid flow [1, 2, 6, 16, 29], is used in this paper. Gas volume fraction, bubble size distribution, number density of bubbles, gas and liquid pressure variation, interfacial area concentration, and gas and liquid velocity variation in jet ejector are predicated. The flow pattern development has been studied at the free jet end, and at the throat end, and at the end of the ejector in detail. In addition, numerical predictions are compared with experiments and the predicated gas interfacial area is in a good agreement with experimental results.

#### 2. Jet Ejector

A large choice of gas-liquid contactors, for example, the falling film column, spray column, packed column, plate column, bubble column, mechanically agitated contactors, spray towers, and venturi scrubbers, are available for understanding the mass transfer process. Among these, the venturi scrubber is a wet type design for gas-liquid contactors. In venturi type of scrubber(i)liquid is a medium to absorb objectionable gases and particulates from industrial gaseous waste streams;(ii)a high velocity section of fluid jet is utilized to bring the liquid and gas into intimate contact with each other.

Venturi scrubbers fall into two categories [30, 31].

In the first category, it uses mechanical blower to draw a high velocity gas stream through the system. The liquid was originally at rest but once the gas accelerates, it splits into droplets. Particulates and gases are then confined into the comparatively slower moving droplets. This type is called a “high energy venturi scrubber” (HEVS). The scrubbing liquid can be introduced in two ways:(i)If the liquid is introduced through nozzles which is usually at the throat it is known as Pearce-Anthony venturi scrubber.(ii)In this case liquid is introduced as a film which is usually known as the wetted approach type.

Secondly, a mechanical pump or compressor is used to generate a high velocity to the liquid/fluid jet. This liquid/fluid jet creates suction and gas is entrained into it by transfer of momentum. This type of the venturi scrubber is called an ejector venturi scrubber or “jet ejector.”

The jet ejectors have some advantages over other types of contactors which are mentioned as follows [31, 32]:(i)Lower initial capital cost.(ii)Simple construction and being compact.(iii)Easy installation and operation.(iv)No moving parts, so little chances of mechanical failure and hence highly reliable.(v)Being able to deal with wet, hot, and corrosive gases and thick, aggressive, and inflammable particles.(vi)Ability to separate gaseous pollutant and fine particulate matter simultaneously.(vii)Being able to handle large gas flow rates.(viii)High heat and mass transfer rates and interfacial area.

However, it is not energy efficient equipment as a fluid moving device. But it has been reported that it has high efficiency as a gas-liquid contacting device [33–36].

The jet ejectors are especially effective in chemical and biochemical industries for gas purification and for collaborating gas-liquid reactions like chlorination, oxidation, hydrogenation, and hydroformulation processes. Jet ejectors use high kinetic energy of the operating fluid jet to promote break-up and distribution of the suction fluid into small droplets/bubbles and to pull the gas through the system and push through the connected outlet.

A typical gas-liquid jet ejector is displayed in Figure 1. It consists of a converging section, a throat section, and a diffuser/divergent section. The gas is accelerated to atomize the scrubbing liquid in the convergent section to reach a higher velocity in the throat. Throat is used for interaction of liquid and gases. In the diffuser/divergent section the gas is slowing down allowing some recovery of pressure [37, 38].