Numerical and experimental modelization of the two-phase mixing in a small scale stirred vessel
Graphical abstract
Introduction
Stirred tanks are widely used in the chemical and petrochemical industries for different types of processes. Frequently these stirred tanks include one or more baffles in order to avoid the formation of a vortex in the free surface. The turbulent flow generated by the interaction of the impeller blades and the other elements present in the tank (like the baffles) is certainly complex, and its topology depends on the shape and size of the different components in the tank.
Different experimental studies have been performed for this type of systems. The influence of the gas flow rate on the structure of the trailing vortices formed behind the blades of a Rushton turbine was studied with Particle Image Velocimetry (PIV) measurements in a baffled stirred vessel with a flat bottom [1]. Gas accumulation behind the impeller blades was shown in the PIV results. The locations of those gas cavities were coinciding with the location of trailing vortices in one-phase liquid flows. A two-camera PIV technique was used on a laboratory scale stirred tank equipped with a Rushton turbine to obtain turbulence data of the flow and angle resolved velocity [2]. Both single phase and two-phase flows were studied. In the two-phase flow, it was observed that the radial velocity of the liquid jet and its trailing vortices were diminished by the presence of the gas. Gas cavities surrounding the back of the impeller blades were also observed in the visualizations. Digital image analysis was coupled with a shadowgraphy-based technique to investigate, for unbaffled tanks, the shape of the free surface vortex [3]. Tank filling level and impeller clearance from the vessel bottom were varied to determine how they influenced the shape of the vortex. A correlation was proposed describing the vortex shape. The oxygen transfer in an unbaffled vessel used as a biochemical reactor for animal cell growth was studied in [4]. The experimental results showed that this kind of bioreactors could provide enough mass transfer for animal cell growth, being that way a valid alternative to sparged reactors.
Several researchers have carried out numerical simulations of gas–liquid stirred vessels over the years using different numerical techniques. Some authors have performed Large Eddy Simulations (LES) [5]. In that computational approach, the large scales of the flow are solved, while the smaller scales are modeled. Although not as computationally expensive as performing Direct Numerical Simulations (DNS), where all the flow scales are solved, it is still an expensive method. A key feature in LES is the choice of the SubGrid Scale model (SGS), since the accuracy of the results on the smaller scales will depend on it. LES with an implicit SGS model was performed to study a gas–liquid Rushton stirred reactor [6]. To solve the multiphase flow, a combination of Volume of Solid (VOS) and Lagrangian Particle Tracking (LPT) was used [7]. Air was entered at the bottom of the reactor and, under the assumption of bubbly flow the bubbles were tracked in the three-dimensional time-dependent flow field generated by LES. Another study using LES can be found at [8], although in that work there was a single-phase flow. The Smagorinsky SGS model [9] was used in the simulations, performed with the commercial software CFX. As an example of the computational cost of LES, the authors needed 33 days to solve the flow field for the time corresponding to 22 impeller revolutions at 200 rpm, using a 3 GHz processor.
Given the high computational cost of LES, the Reynolds Averaged Navier-Stokes (RANS) approach [5] has become more popular. In this approach, only the average field is solved and turbulence is modeled. A widely used turbulence model is the two-equation k − ϵ model [10], which uses the kinetic turbulent energy (k) and its dissipation rate (ϵ) to compute the turbulent viscosity. The works from other authors using RANS reported here all except one use the k − ϵ model. A gas–liquid stirred tank using CFX and the Sliding Grid (SG) technique [11] was simulated [12]. In the Eulerian–Eulerian multiphase model [13], both phases shared the same values of k and ϵ. The authors found that including lift and virtual mass forces does not change the results. The SG technique was also used in the study of an aerated Rushton impeller [2]. The authors report that the drag force is the most important one in these systems, and that the bubble induced turbulence should be taken into account, thus making the effective viscosity the sum of the molecular, turbulent and bubble induced turbulent viscosities. The free surface of a Continuous Stirred Tank Reactor (CSTR) was studied at [14]. The authors also employed the SG technique, but this time using the Star CD software and the VOF model [15], instead of the Eulerian–Eulerian multiphase model. The range of rotation rates was between 70 and 280 rpm. The authors reported that macromixing is bad in low velocity regions found at the curved bottom, slightly downstream the baffles and near the free surface, although the one at the curved bottom may be destroyed by gas bubbles. The vortex shape in a partially baffled agitated vessel, with a Eulerian–Eulerian multiphase model and using the Multiple Reference Frame (MRF) technique [16], where a region of the computational domain, placed around the impeller, rotates with the same velocity that the impeller and the rest of the domain is static was studied in [17]. The authors found that extracting an isosurface of liquid volume fraction of 0.9 from the numerical simulations matched experimental data better than the classical value of 0.5. The MRF technique was also used to study the two-phase flow mass transfer in a stirred reactor [18], where Computational Fluid Dynamics (CFD) was coupled with Population Balance Method (PBM). The mass transfer prediction was compared with experimental data, showing reasonable agreement. The MRF technique was also used to study the micromixing of viscous systems with competitive parallel reactions in a stirred-tank reactor [19], but the Reynolds Stress Model (RSM) was used to account for the effects of turbulence. They found that micromixing was improved when the agitation speed was high and the fluid viscosity low. A stirred vessel using a Rushton turbine was studied in [20]. The computational software FLUENT [21] was used with a Eulerian–Eulerian multiphase model, and the Snapshot method [22] was implemented through User Defined Functions (UDF). This method consists in adding a mass source term to the equations solved to model impeller motion. The author reports that there is an accumulation of gas behind the impeller blades, and that the hydrodynamics cannot be determined with a steady state approach.
The aim of the present work is to analyze the two-phase mixing processes that occur in a small-scale batch reactor. A sketch of the stirred tank reactor is shown in Fig. 1, corresponding to the unbaffled (Fig. 1a and c) and baffled (Fig. 1b and d) configurations. The liquid and gas phases are in contact and, due to rotation, the free surface of the liquid changes its shape and gas bubbles are formed around the axis and blades and move within the liquid. The main objective is to determine the mass transfer rates for the different gas components (hydrogen (H2) and carbon monoxide (CO)) within the liquid phase and whether it is a limiting step in the process or not. A numerical simulation approach was used in this study. Previous to the simulations some flow information was needed. For this reason the work has an initial stage that implies an experimental part. All relevant information about how bubbles inside the liquid phase are formed, the amount and their sizes were extracted from these experiments and used in the numerical simulations, performed with the commercial CFD software FLUENT. However, the actual operating conditions of the reactor could not be reproduced in the laboratory, given that the experimental analysis of the flow requires a transparent vessel to allow the visualization of the fluid within the reactor. Therefore, a dimensional analysis was performed in order to be as close as possible to reality. Table 1 shows the comparison between the actual operating conditions and the laboratory conditions. Bubble size depends strongly on the Weber number, and as it can be seen, Weber numbers are similar in both laboratory and actual conditions. The difference in Reynolds numbers is larger, but it is due to the difference in physical properties, since the rotation rates are the same in both cases. As it will be seen and discussed later, those differences are believed to not impact significantly the size of the bubbles. However, they add a degree of uncertainty. The numerical simulations were performed in a two-step process. First, the dynamic field for each case was obtained, and then, bubbles were released from the free surface and tracked numerically to compute the particle Reynolds number (Rep). The values of Rep were used to estimate the mass transfer rates of the gas components (H2 and CO) within the liquid phase through conventional mass transfer correlations.
Section snippets
Experimental study
The main objective of this part of the work was to estimate the amount and the mean diameter of the gas bubbles that appear in the liquid phase at different rotation rates in order to feed the numerical simulations. The experiments were also useful for the understanding of the flow behavior inside the reactor for different rotation rates. The information obtained from the experimental work was used as input data for the numerical simulations of the reactor and to validate the results.
Numerical simulations
The numerical part of the study is presented in this section. First, the physical, mathematical and numerical models are presented. Results for both the dynamic fields and the mass transfer rates are discussed after that.
Conclusions
The flow in the reactor model has been visualized and characterized at rotation rates up to 2000 rpm. The reactor with and without baffle has been considered. It has been determined experimentally that the amount of bubbles inside the reactor increases with the rotation rate, while the bubble size decreases. Typical bubble diameters range from 0.2 mm to 0.7 mm. The mean measured bubble diameter was compared with that predicted by correlations found in the literature for similar reactors, and the
Acknowledgements
This work has been funded by Total Raffinage Chimie under contract IPA-3964. S.V., M.M., J.P. and A.V. acknowledge the support of the Spanish Ministerio de Economía y Competitividad under projects CTQ2013-46799-C2-1-P and DPI2016-75791-C2-1-P.
References (28)
- et al.
Chem. Eng. Res. Des.
(2001) - et al.
Comput. Fluids
(2008) - et al.
Chem. Eng. Sci.
(2005) - et al.
Chem. Eng. Res. Des.
(2007) - et al.
Chem. Eng. Sci.
(2001) - et al.
J. Comput. Phys.
(1981) - et al.
Chem. Eng. Sci.
(2007) - et al.
Chem. Eng. Sci.
(2011) - et al.
Chem. Eng. Sci.
(2012) Chem. Eng. Sci.
(1997)
Chem. Eng. Process.
Can. J. Chem. Eng.
Chem. Eng. Trans.
Chem. Eng. Trans.
Cited by (3)
Process optimization in a stirred tank bioreactor based on CFD-Taguchi method: A case study
2019, Journal of Cleaner ProductionCitation Excerpt :Unstructured meshes were generated in ICEM CFD 18.1, and they were converted to polyhedral meshes in Fluent 18.1. Multiple reference frame (MRF), as a steady-state method, was adopted to solve the problems with rotating impellers (Varela et al., 2018). Pressure-based solver with coupled algorithm was chosen for improvement of rate of solution convergence.
- 1
These authors contributed equally.