(546e) Improvement of Mixing Characteristics of an Atypical Unbaffled Vessel with Unsteady Rotation Speed Impeller

Mixing of liquids is a key unit operation across diverse industrial processes, frequently employing standard mixed vessels with four wall baffles and a central impeller. However, in some industries, such as biotechnology and pharmaceuticals, this mixing-efficient configuration is not preferred because the presence of built-ins or shaft seals contradicts the increased requirements on equipment cleanability and sterility. A common alternative solution that addresses these requirements is an unbaffled stirred bioreactor with an off-center, magnetically driven impeller [1]. The eccentrical agitator position mitigates the central vortex formation. Nevertheless, since magnetic propulsion requires the impellers to be placed at the vessel bottom, the maximum agitator size is limited due to the vessel bottom curvature. This vessel configuration has not been extensively studied, which results in a lack of fundamental understanding and characterization. Moreover, while the standard baffled vessels ensure rapid batch homogenization, these unconventional stirred bioreactors are prone to the development of a poorly mixed segregated region, prolonging homogenization times, particularly with higher liquid levels [2]. The segregated zone may pose risks to microorganisms, especially during aerobic processes. Our objective is to enhance mixing while preserving the benefits of unbaffled setups with magnetically driven impellers.

Introduction

The literature survey yielded a promising approach leveraging variation in agitator rotational speed or direction - dynamic mixing protocol (DMP) - implemented by Yao et al. to destabilize segregated regions and thereby enhance laminar mixing of viscous liquids [3]. The application of forward-reverse mixing to enhance turbulent flow in unbaffled vessels was investigated in pioneer studies by [4, 5]. Although they did not report a comparison of mixing times in the unbaffled vessels, they observed suppression of tangential liquid rotation and central vortex formation. Studies also address an increase in the power number to values similar to or slightly higher than those in the fully baffled configuration, which indicates an increase in peak shear stresses and the risk of batch degradation. We assume that this increase in unbaffled vessels with a central impeller is associated with the transition of the flow to the turbulent regime, while in the configuration of interest, the stirrer already operates in the turbulent region at a constant speed mixing [2].

We present a novel and comprehensive study combining experimental and validated CFD data to demonstrate the DMP potential to enhance mixing in unbaffled vessels with magnetically driven impellers. The study focuses on the effect of DMP on peak shear stresses that directly affect cultured microorganisms or shear-sensitive products. We analyzed the impact of DMP on segregated region destabilization and overall mixing time in a pilot-scale, unbaffled bioreactor with an off-centered impeller. The CFD methodology used in this work was validated using experimental data on mixing power and mixing times. Thus, it can serve as a standalone framework for further study and design of these systems.

Experimental setup and methodology

The experiments were carried out in a cylindrical pilot-plant vessel with a diameter of T=390 mm, using tap water at two different liquid levels (H=440 mm and 600 mm). The tank was operated in an unbaffled arrangement with low clearance (C=10 mm) and an eccentrically mounted impeller, mimicking a bioreactor with a magnetically driven impeller. Two Rushton turbines with D=60 mm and 100 mm diameters were used. The shaft torque was measured using a Burster 8645 torque meter (±2.5 Nm, accuracy <1% F.S.). The experimental setup is depicted in Fig. 1.

The primary rotational speeds (N_P) corresponding to power inputs P_P of 10 W/m³ and 100 W/m³ were used for both impellers and liquid levels. DMP with rotational speeds alternating between N_P and various secondary speeds N_S was employed. The protocol consists of phases of constant speeds N_P and N_S with a linear acceleration/deceleration between the phases. The duration of the constant-speed phase (5-20s) was optimized for any N_P/N_S combination; the acceleration/deceleration phase lasted 3 s in the cases of constant rotation direction and 6 s in the cases of changing rotation direction. The mixing characteristics were measured using the decolorization method based on the iodine-starch-sodium thiosulfate system. To measure the standard mixing time θ, the color tracer was injected near the impeller. To evaluate the segregated zone stability, the tracer was injected directly into the segregated zone, and the time Ï„ required to vortex decolorization was measured. Each measurement was performed at least three times under given conditions.

Numerical flow and tracer transport simulations were performed using a modified transient flow solver in the OpenFOAM^© environment. The computational domain matched the true geometry of the pilot-plant vessel filled up to H=600 mm. The mesh consisted mostly of hexahedral elements, locally refined close to the impeller, walls, and inside the MRF region. The k-ω SST DES model for turbulence modeling was employed. The impeller rotation was modeled using the MRF approach. First, a converged steady-state flow simulation was obtained using k-ω SST turbulence model, which was used as an initial condition for the following 60-s transient flow simulation with the impeller rotating according to the desired DMP protocol. Then, the initial concentration of a tracer was prescribed to a small volume inside the vessel positioned either close to the impeller or inside the vortex near the water surface, and the simulation continued for an additional 60 seconds. The tracer dispersion dynamics was evaluated as the development of the coefficient of variance (CoV) of the tracer concentration.

Results and discussion

To investigate the impact of DMP on impeller power characteristics, the torque M was measured for a 100mm impeller operating in the following ways: (i) a constant speed of 5.9 s^-1, (ii) periodically stopping the impeller and (iii) periodically reversing impeller. Concurrently, numerical simulations of these three cases were also evaluated. When operating at a constant speed, the specific power input P/V remains at 100±8 W/m³. With the DMP, neither stopping the impeller nor reversing the impeller caused a significant increase in the peak torque compared to the continuously running impeller. The results of the experiments and simulations are illustrated in Fig. 2. Evidently, employing the DMP does not substantially elevate the impeller power number and peak shear stress. The results also show that the numerical simulation has captured the experimental power characteristics well.

Contrary to the small effect of DMP on impeller power characteristics, its employment has a significant impact on the segregated zone stability. As illustrated in Fig. 3, the segregated zone is most stable in the case of constant mixing (r_P =1). However, even a minor change in rotation speed results in a relatively sharp decrease in the time Ï„ required to decolorize the segregated zone. The best results were achieved with the rotation direction fully reversed (r_P =-1), resulting in the prevention of central vortex formation. Under these conditions, the decolorization times almost matched the mixing time.

As for the standard mixing times θ, the DMP impact differs depending on the liquid level height. At H=440 mm, θ remains almost independent of the DMP used. The small observed increase in θ with the impeller periodically stopping corresponds to a 50% lower total dissipated power. At H=600 mm, disrupting the segregated zone stability using DMP also results in a noticeable decrease in θ in most cases. In the cases where a slight increase in θ is shown, the cause lies in the different speed change frequencies optimal either for the segregated zone destabilization or the entire vessel homogenization. As experimentally proven, it is possible to find the speed change frequency at which θ and τ are both reduced significantly.

Tracer spreading was also simulated using CFD for the same cases as for the torque evolution (i-iii); the results are shown in Fig. 4. Apparently, the experimentally determined values of θ agree very well with the simulation time required for CoV to decrease below 0.05 (which, in the literature, is usually identified as the standard mixing time θ₉₅). Simultaneously, the simulated trends in the Ï„ evolution correspond to those measured.

Conclusions and implications

This study presents the benefits of the dynamic mixing protocol for the mixing characteristics of a bioreactor stirred with a magnetically driven impeller. The experimental and numerical results indicate that DMP breaks down the segregated vortex zone and significantly facilitates its blending with the liquid bulk without elevated shear stress imposed by the impeller. Moreover, a lower total energy consumption is required compared to a constant-speed operation. In most cases, the DMP does not increase the measured standard mixing time and, conversely, improves it at higher liquid levels. The results, coupled with the relative simplicity of DMP, imply the potential of DMP to be used in a wide range of mixing processes across the biotechnology and pharmaceutical industries.

References

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[2] Gebouský, O.; Idžakovičová, K.; Haidl, J.; Chem.Eng.Sci. 2023, 276, 118801.

[3] Yao, W. G.; Sato, H.; Takashi, K.; Koyama, K.; Chem.Eng.Sci. 1998, 53, 3031–3040.

[4] Woziwodski, S.; Chem.Eng.Technol. 2011, 34, 767–774.

[5] Yoshida, M.; Shigeyama, M.; Hiura, T.; Yamagiwa, K.; Ohkawa, A.; Tezura, S.; Asia-Pac.J.Chem.Eng. 2007, 2, 659–664.