International Journal of Chemical Engineering

Volume 2018, Article ID 5254087, 12 pages

https://doi.org/10.1155/2018/5254087

## Numerical Simulation of Gas-Liquid Flow in a Bubble Column by Intermittent Aeration in Newtonian Liquid/Non-Newtonian Liquid

Southwest Jiaotong University, School of Civil Engineering, Cheng du, China

Correspondence should be addressed to Yang Shunsheng; moc.621@esnaes

Received 25 June 2018; Accepted 13 September 2018; Published 6 November 2018

Academic Editor: Doraiswami Ramkrishna

Copyright © 2018 Zheng Xipeng 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

The dynamic behaviors of gas-liquid two-phase flow were simulated in a lab-scale intermittent bubble column by Euler-Euler two-fluid model coupled with the PBM (population balance model) using two different liquid phases, i.e., Newtonian fluid (water)/non-Newtonian fluid (activated sludge). When non-Newtonian fluid was used during intermittent aeration, some interesting results were obtained. Two symmetric vortexes existed in the time-averaged flow field; the vertical time-averaged velocity of the liquid phase decreased with increasing anaerobic time; the average gas holdup distribution was like a trapezoid with long upper side and short lower side and affected by the dynamic viscosity of the liquid phase. Compared with non-Newtonian fluid, the use of Newtonian fluid as the liquid phase led to a more complicated time-averaged flow field structure and vertical time-averaged velocity distribution, higher average gas holdup, and the asymmetric column-shaped gas holdup distribution with increasing anaerobic time. For different liquid phases, the instantaneous flow field, instantaneous vertical velocity, and instantaneous gas holdup distribution all periodically changed with anaerobic time; however, different from Newtonian liquid phase, non-Newtonian liquid phase had no periodic oscillating instantaneous horizontal velocity.

#### 1. Introduction

As an aeration reactor, the bubble column is widely used for study on wastewater treatment because of its low price, easy transport, and high mass transfer characteristics [1–4]. The bubble column is mainly researched by experiment and numerical simulation [5, 6]. Numerical simulation is extensively used for study on bubble column due to its good economics and ability to obtain the information in the entire bubble column, such as velocity distribution, gas phase distribution, and turbulence energy. Ali et al. [7, 8] used experiments and numerical simulation method for numerical simulation of a rectangular bubble column. For numerical simulation, they considered the effects of different drag models, simulation methods, and model dimensions on the simulation results. The results showed that different drag models did not significantly influence the predicted velocity, and Euler-Euler approach had better simulation results than Euler–Lagrangian approach. Wang et al. [9] used CFD-PBM for simulation of the bubble column, and their results showed that this model was effective for prediction of bubble size distribution, interfacial area, gas-liquid mass transfer rate, etc., in the bubble column. Gupta and Roy [10] used the PBM for numerical simulation of a rectangular bubble column by considering bubble breakage and coalescence, analysis of different breakage and coalescence equations, and the effects of lift force and virtual mass force on the flow field and gas content in the bubble column.

Pure water in Newtonian fluids is always used as the liquid phase in the above simulations in bubble columns, but few researchers are studying the activated sludge (non-Newtonian fluid). It should be noted that the liquid phase is activated sludge when the bubble column is used as a sewage treatment facility. Activated sludge is not transparent, so it is very difficult to efficiently test the flow field in the bubble column by particle image velocimetry (PIV) and laser Doppler velocimetry (LDV) and to obtain the flow regime and flow characteristics in the bubble column. Fan et al. [11] used polystyrene spheres instead of activated sludge to experimentally study the lab-scale oxidation ditch by PDA (particle dynamic analyser) but did not take the activated sludge as non-Newtonian fluid into account [12, 13]. For the rheological behavior of a liquid, transparent Newtonian fluids, such as aqueous solution of sodium carboxymethyl cellulose (CMC) or Xanthan solution, always were experimentally used as the liquid phase [14–16]. Passos et al. [17] additionally used the nonionic surface active agent Triton X-100 to modify the surface tension of the non-Newtonian solutions and found that the diameter of the bubbles decreased. Dapelo et al. [18] used CMC as a liquid for numerical simulation of the anaerobic digestion unit based on the Euler–Lagrangian approach and found that the relative simplicity of the viscosity model did not affect the results of the simulations. Bandyopadhyay and Das [19] used the non-Newtonian pseudoplastic power law model to simulate the flow through elbows under non-Newtonian liquid and obtained an ideal result. Wu [20] performed the gas-liquid numerical simulation of an anaerobic digester and considered the effect of non-Newtonian liquid. His results showed that the low Reynolds number *k*-*ε* model was better than other turbulence models, and the gas-liquid mixing efficiency depended on the mixing mechanism and pumping cycle, but he used the drag force model for Newtonian fluid. There was a difference in drag force equation between Newtonian and non-Newtonian fluids [21], so the simulation results would be evaluated.

However, most liquid phases for numerical simulation of gas-liquid two-phase flow in a bubble column are Newtonian fluids, and there is a rare literature on dynamic behaviors of gas-liquid two-phase flow of Newtonian/non-Newtonian liquid phase in an intermittent aerating bubble column. Thus, Euler-Euler two-fluid model coupled with PBM (EEPBM) was used in this paper for numerical simulation of gas-liquid two-phase flow in a lab-scale bubble column and analysis of dynamic behaviors of the fluids in a bubble column, such as gas holdup distribution, liquid-phase flow field, and liquid phase velocity field, based on the comparison with the experiment [22] and verification of the mathematical model. The drag force equation and intermittent aeration control of the non-Newtonian fluids were simulated by UDF (user-defined program). The research results provide references and guides for optimized design of the intermittent aerating bubble column for wastewater treatment.

#### 2. Mathematical Model

An Euler-Euler two-fluid model (EE) was used to simulate gas-liquid two-phase flow, and PBM was considered to simulate the bubble coalescence and breakage. During the simulations, the gas-liquid interphase heat transfer was ignored, and the two phases were considered for the incompressible fluids. We adopted the assumptions that the mixture of the activated sludge and water was a single-phase liquid [23].

##### 2.1. Euler-Euler Two-Fluid Model

Mass conservation equation:

Momentum conservation equation:where is the volume fraction; is the density, kg/m^{3}; is the shear stress, Pa, determined from Equation (8); is the pressure, Pa; is the acceleration of gravity, 9.8 m/s^{2}; is the phase division, with being the gas phase and *l* being the liquid phase; *F* is the two-phase interphase force, the drag and lift forces were considered in this paper [10]. The two-phase interphase force is calculated as follows:

The drag force and the lift force were taken into account in this work. The lift force is calculated as follows:where is the lift coefficient, 0.5 [24].

Drag force can be determined as follows:where is the bubble diameter. The drag force coefficient model can be expressed as follows considering the effects of the rheological properties on non-Newtonian fluids [25]:

Since Newtonian and non-Newtonian fluids exhibit different flow behaviors, the definition of Reynolds number for Newtonian fluids is invalid for non-Newtonian fluids [26]. Thus, the Reynolds number of spherical bubbles of non-Newtonian fluids is calculated as follows [27]:where *K* is the viscosity coefficient, kg/(m·sn), 0.0741 and *n* is the rheological index, 0.49. The formula for calculating the drag force between gas and liquid in Newton’s liquid phase is shown in reference [28].

Turbulent effects were modeled by the RNG *k*- model. This turbulence model was usually applied to predict the liquid flow pattern and gas holdup at low superficial gas velocity due to its simplest algorithm and lower computational cost [5, 29].

##### 2.2. Population Balance Model

In order to study the bubble breakup and coalescence phenomena in the bubble column, the population balance model can be applied to calculate the bubble size distribution. According to the researchers’ studies [30, 31], the population balance equation can be expressed as follows:where is the bubble size distribution function; *B*^{+}, *B*^{−}, *C*^{+}, and *C*^{−} are the birth due to coalescence, death due to aggregation, birth due to breakage, and death due to breakage, respectively; and *u*_{i} is the average velocity of the *i*th bubble group, m/s. The discrete method was used to solve [32] Equation (8). The simulations of the breakup phenomena were performed using the Luo and Svendsen [31] model. The model proposed by Luo [33] I was used for the modeling of the coalescence processes. The coalescence and breakage model described in this paper has been used to study the numerical simulation of a bubble column [5, 10, 22]. The number of cases, *i* = 1 to 10, represents the 10 groups of bubbles [22].

#### 3. Modeling and Calculation

##### 3.1. Physical Model and Grid

Ali et al. [7] found that 2-D and 3-D models for bubble columns had the same predicted velocity, and 2-D model could reflect the gas-liquid two-phase flow behaviors in the bubble column. Thus, a 2-D model was created, as shown in Figure 1(a), with length = 0.45 m and width = 0.2 m. The gas inlet is modeled as a rectangle area with the length of 0.018 m at the bottom of the domain in the center, representing the experimental sparger setup. As shown in Table 1 and Figure 1(c), we modeled fourteen different cases according to the distance from the gas inlet center to the bottom center of the bubble column as well as the liquid properties. In the simulation, the air density was set to 1.29 kg/m^{3}, water density 1000 kg/m^{3}, viscosity 0.001787 Pa∗s, and gas-liquid surface tension 0.072 N/m.