# Intense Vortex Motion in a Two-Phase Bioreactor

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

_{g}= 1150 kg/m

^{3}and kinematic viscosity ν

_{g}= 15 mm

^{2}/s. The methods of particle image velocimetry and adaptive track visualization allow one to observe and measure the vortex motion of the culture medium. In this work, the vortex flow investigation was performed in a practical bioreactor at the operation regimes. Our research determines not only the optimal flow structure, but also the optimal activator rotation speed, which is especially important in the opaque biological culture. The main result is that, similar to the case of two rotating immiscible liquids, a strongly swirling jet is formed near the axis, and the entire flow acquires the pattern of a miniature gas–liquid tornado. The aerating gas interacts with the liquid only through the free surface, without any mixing. This intensifies the interphase mass transfer due to the high-speed motion of the aerating gas.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Experimental Setup

_{g}= 1150 kg/m

^{3}; kinematic viscosity ν

_{g}= 15 mm

^{2}/s). In the reactor, mixing of the cell suspension was carried out by creating a quasi-stationary rotational motion generated by a swirling gas flow. The tornado-like swirling gas flow was generated by an impeller (activator) above the surface of the culture medium (Figure 1b). The aerating gas interacted with the cell suspension only through the free surface of the latter, without mixing with it. As a result, the interfacial mass transfer was intensified due to the high velocity of the aeration gas, and the suspension was mixed evenly, without stagnant zones.

_{g}= 150 mm) and, by continuously adding the working model medium, to the maximal filling of 80% (h

_{g}= 240 mm).

^{3}; diameter, ~10 μm) were employed as seeding light-scattering particles for both flow visualization and PIV measurements. The air flow was seeded by a fog generator. Measurements were performed in a horizontal section in the vicinity of the interface, at a distance of 2 mm in air and liquid and near the bottom of the reactor vessel, as well as in a vertical section passing through the axis of the cylinder. The light cross-section was formed by a laser sheet of the PIV measuring system [14], and the image was recorded by a camera through the transparent glass bottom and sidewall of the bioreactor.

#### 2.2. The CFD Approach

_{l}+ (1 − α)ρ

_{a}; subscripts ‘l’ and ‘a’ represent the liquid and gas phases, respectively. F is the source term due to surface tension, which is modeled using the Continuum Surface Force (CSF) method. s = μ(∇U + ∇U

^{T}− 2/3(∇∙U))I is the viscous stress tensor; I is the identity tensor; and μ = αμ

_{l}+ (1 − α)μ

_{a}is the dynamic viscosity.

_{g}= 1150 kg/m

^{3}for glycerol and ρ

_{a}= 1.2 kg/m

^{3}for air. The kinematic viscosities are ν

_{g}= 15 mm

^{2}/s for glycerol and ν

_{a}= 18 mm

^{2}/s for air; the surface tension is σ = 0.05 N/m.

_{0}= 101,325 Pa. The gravity was considered here, where g = 9.8 m/s

^{2}.

## 3. Results

#### 3.1. Experimental

_{tgm}) depending on the velocity of the activator (Ω) at h = 0.5 and 0.8. These values serve to determine the characteristic Re

_{g}. In this case, the Reynolds number for the liquid is defined as Re

_{g}= V

_{tgm}R/ν

_{g}, where V

_{tgm}is the maximum value of the tangential component of the velocity, R is the radius of the reactor vessel, and ν is the kinematic viscosity of the working fluid. The use of a 2.3 MP sensor Sony IMX174 with 10 Hz framing and a delay of up to 100 ms allowed us to significantly improve quality of the recorded images, and the preliminary subtraction of the background image reduced the noise level. Figure 4 shows examples of converging and diverging helical motion of the working fluid under the interface (Figure 4a) and in the vicinity of the bottom (Figure 4b), which illustrates the circulating meridional movement of the working fluid generated by an intense air vortex in the bioreactor.

_{tg}and radial V

_{r}velocity components in the horizontal section in the vicinity of the interface in air and the model liquid at low and high rotation speeds of the activator Ω = 90, 180, 360, 540, and 720 rpm. Further, for convenience, the heights of reactor filling with the working fluid h

_{g}= 210 mm and 340 mm are presented in dimensionless quantities h = H/h

_{g}= 0.5 and h = H/h

_{g}= 0.8, respectively.

_{g}> 10 cCt. When working with low-viscosity media (e.g., when cultivating microalgae in which the solution viscosity is close to that of water), full meridional circulation, according to Table 1 and the results of work [25], will already be achieved at the value of the activator rotation Ω > 180 rpm.

#### 3.2. Numerical Data

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

D | diameter of the reactor vessel |

F | source term due to surface tension |

g | gravitational acceleration |

H | height of the reactor vessel |

h_{g} | height of model fluid |

h= h_{g}/H | dimensionless height of model fluid |

I | identity tensor |

p | pressure |

p_{0} | initial pressure above the free surface |

R | radius of the reactor vessel |

Re = V_{tgm}R/ν_{g} | the Reynolds number |

s = μ(∇U + ∇U^{T} − 2/3(∇∙U))I | viscous stress tensor |

U | absolute velocity |

V_{ax} | axial component of velocity |

V_{r} | radial component of velocity |

V_{tg} | tangential component of velocity |

V_{tgm} | the maximum value of the tangential component of velocity |

Subscripts | |

a | air |

g | aqueous glycerol solution |

l | liquid |

r | radial component |

R | rotary |

S | stationary |

tg | tangential component |

m | maximum value |

Greek | |

μ = αμL + (1 − α)μ_{a} | dynamic viscosity |

ρ = αρ_{l} + (1 − α)ρ_{a} | density |

ρ_{a} | density of air |

ρ_{g} | density of aqueous glycerol solution |

ν_{a} | kinematic viscosity of air |

ν_{g} | kinematic viscosity of aqueous glycerol solution |

Ω | rotation speed of activator |

σ | surface tension |

Acronym | |

CFD | Computational Fluid Dynamics modeling |

CSF | Continuum Surface Force method |

DNS | Direct Numerical Simulations |

FVM | Finite Volume Method |

MRF | Multiple Reference Frame method |

NS | Navier–Stokes |

PIV | Particle Image Velocimetry |

VOF | Volume of Fluid method |

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**Figure 1.**(

**a**) A gas–liquid bioreactor: a photo of the test bench; (

**b**) an impeller (activator) generating vortex motion in the bioreactor.

**Figure 4.**Visualization of the motion of the model fluid: (

**a**) the flow diverging from the axis below the interface and (

**b**) the flow converging to the axis near the bottom at Ω = 900 rpm, h

_{g}= 0.5h.

**Figure 5.**The streamlines reconstructed from the vector fields obtained in a horizontal section near the interface ((

**left**)—in air; (

**right**)—in the working model fluid).

**Figure 6.**The tangential velocity profiles at Ω = 90 rpm: (

**a**) h = 0.5; (

**b**) h = 0.8; and (

**c**,

**d**) the radial and tangential velocities at Ω = 720 rpm and h = 0.5, respectively.

**Figure 7.**Tangential velocity profiles in air (

**a**) at h = 0.5, (

**b**) at h = 0.8, and in glycerin (

**c**) at h = 0.5 and (

**d**) at h = 0.8.

**Figure 8.**The radial velocity profiles in air (

**a**) at h = 0.5, (

**b**) at h = 0.8, and in glycerol (

**c**) at h = 0.5 and (

**d**) at h = 0.8.

**Figure 10.**Comparison between the numerical and experimental (

**a**) radial and (

**b**) tangential profiles above the air–water interface at Ω = 180, 360, 720, and 900 rpm.

**Figure 11.**The velocity fields and streamlines in the vertical cross-section: Ω = 180 rpm (

**top**), Ω = 540 rpm (

**middle**), and Ω = 900 rpm (

**bottom**).

**Table 1.**The maximum values of the tangential velocity under the interface and the Reynolds number in the liquid, depending on the rotation of the activator.

Ω, rpm | V_{tgm}, mm/s | Re | |
---|---|---|---|

h = 0.5 | 180 | 7.7 | 48.8 |

360 | 18.1 | 114.6 | |

540 | 29.2 | 184.9 | |

720 | 36 | 228 | |

900 | 46.8 | 296.5 | |

h = 0.8 | 180 | 9.7 | 61.3 |

360 | 18.5 | 117.4 | |

540 | 32.4 | 205.5 | |

720 | 52.5 | 332.7 | |

900 | 77.1 | 488.6 |

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**MDPI and ACS Style**

Sharifullin, B.R.; Skripkin, S.G.; Naumov, I.V.; Zuo, Z.; Li, B.; Shtern, V.N. Intense Vortex Motion in a Two-Phase Bioreactor. *Water* **2023**, *15*, 94.
https://doi.org/10.3390/w15010094

**AMA Style**

Sharifullin BR, Skripkin SG, Naumov IV, Zuo Z, Li B, Shtern VN. Intense Vortex Motion in a Two-Phase Bioreactor. *Water*. 2023; 15(1):94.
https://doi.org/10.3390/w15010094

**Chicago/Turabian Style**

Sharifullin, Bulat R., Sergey G. Skripkin, Igor V. Naumov, Zhigang Zuo, Bo Li, and Vladimir N. Shtern. 2023. "Intense Vortex Motion in a Two-Phase Bioreactor" *Water* 15, no. 1: 94.
https://doi.org/10.3390/w15010094