Computational fluid dynamics to evaluate recirculation vessel mixing in TFF

Real-time mixing experiments in the 5 L ReadyCircuit™ 2D bag

The experiment was conducted using the ÄKTA readyflux™ tangential flow filtration system, where a 5 L bag was connected to a ¼” tube flow kit and routed through the pump for recirculation, as shown in Figure 3. The pump flow rates were set to 1 and 2.5 standard liters per minute (slpm).

A water-starch solution was prepared, which turns blue upon the addition of iodine, forming a starch-iodine complex. Sodium thiosulfate solution was also prepared for decolorization, and a stock solution was made following Dechema guidelines. The starch solution was mixed with a potassium iodide-iodine solution to form the blue starch-iodine complex, which was then pumped into the 5 L bag. Sodium thiosulfate solution was injected through the sample port, and the stopwatch was started immediately. The experiment continued until the solution turned colorless, indicating complete decolorization of the starch-iodine complex. When no blue residue remained in the bag the experiment was stopped, and the time recorded on the stopwatch was noted as the mixing time for each flow rate (1 slpm and 2.5 slpm). The mixing experiment was recorded using video to analyze the mixing time.

Fig 3. Experimental setup.

CFD setup and simulations of 5 L ReadyCircuit™ 2D bag

Geometry and mesh

The 3D model of the 2D bag was created by accurately measuring the shape of the bag filled with 5 L of liquid. The fluid flow domain was constructed, which included the bag, tube, tracer injection port, and pump as shown in Figure 4. A polyhedral mesh was created using Fluent mesh, as illustrated in Figure 5.

Fig 4. Fluid domain of ReadyCircuit™ 5 L bag and tubes.

Fig 5. The meshed fluid domain of ReadyCircuit™ 5 L bag and tubes in the CFD model.

Material properties

Medium

The fluid (starch solution) present in the bag and tubes is referred to as medium and has the following physical properties:

• Density = 1000.17 kg/m³
• Viscosity = 1 cP

Tracer

The substance (sodium thiosulphate) that is introduced into the system for the purpose of mixing is referred to as tracer and has the following physical properties:

• Density = 1024.8 kg/m³
• Viscosity = 1 cP

CFD setup, probe map and mixing time estimation

CFD simulations of the 5 L ReadyCircuit™ 2D bag were performed using the ANSYS Fluent 2024R1 simulation software. The k-omega shear stress transport (SST) viscous model was employed to solve the flow dynamics, and the pump was modeled as momentum source to simulate the pump behavior. A transient simulation was performed until the velocity and flow was stabilized. Once the flow and velocity stabilized, the species transport model was activated, and 25 mL of tracer was introduced from the inlet for a duration of 2 s to simulate the actual experiment. The mixing analysis was carried out until the concentration of all the virtual probes reached 95% homogeneity.

Twenty virtual probes were added at the center plane of the bag and tubes to monitor the tracer concentration as shown in Figure 6. In the CFD analysis the concentration of tracer was captured at these virtual probes over time as shown in Figure 7. For each probe, the time required to reach 95% homogeneity is calculated and it is termed as T95 mixing time for the given probe.

Fig 6. Location of virtual probes in 5 L ReadyCircuit™ 2D bag and tubes.

Fig 7. Tracer concentration captured over time and estimation of slowest T95 mixing time for all probes.

CFD simulations of Xcellerex™ XDUO 50 mixer

The Xcellerex™ XDUO 50 mixer with the custom wedge solution has been specifically developed for efficient low volume mixing and it allows uniform mixing in small-scale applications. Figure 8 shows the 3D model of the Xcellerex™ XDUO 50 mixer with the custom wedge solution.

Fig 8. 3D model of Xcellerex™ XDUO 50 mixer with the custom wedge solution placed inside the mixer to enable low volume mixing.

Geometry and mesh

The fluid domain containing the tank and impellor zones was extracted from the 3D model for both configurations, with and without the wedge, across maximum and minimum working volumes as shown in Figure 9. The total volume of the tank was divided into two zones, the impellor zone and the tank zone. A polyhedral mesh was created using ANSYS Fluent software, as illustrated in Figure 10. A finer element size was employed for meshing near the impellor faces, where most flow gradients occur. Multiple reference frame (MRF) approach was utilized to model the impellor rotation.

Fig 9. Fluid domains of Xcellerex™ XDUO 50 mixer showing different fill volumes with and without the custom wedge solution.

Fig 10.Meshed fluid domain showing the refined elements near the low-profile impellor region along with the cross-section view of the domain.

Geometry and mesh

Medium

The fluid present in the tank is referred to as medium and below are its physical properties.

• Density = 998.2 kg/m³
• Viscosity = 1 cP

Tracer

The substance that is introduced into the system for the purpose of mixing is referred to as tracer and below are its physical properties.

• Density = 998.2 kg/m³
• Viscosity = 1 cP

CFD model and equations

CFD simulations of the mixer were performed using the ANSYS Fluent 2024R1 simulation software. Single-phase analysis was utilized to determine the power density values, while a multispecies model was employed to determine the mixing time. Equations used were:

• Power (P,Watt)= 2πNT
• Power number,(Np)= P/(ρN^3 D^5 )
• Power input= P/V

N = Impellor speed in rps
T = Torque in Nm
D = Impellor diameter in m
ρ = Density of media in kg/m³
V = Working volume of the fluid in the vessel in m³

Operating conditions

The mixing analysis of the Xcellerex™ XDUO 50 mixer were performed for maximum and minimum fill volumes with and without the custom wedge solution at a nominal power density of 16.5 W/m3. The resulting operating conditions are shown in Table 1.

Table 1. Operating conditions used for CFD mixing analysis with the Xcellerex™ XDUO 50 models, using the low-profile impellor

Probe map and mixing time estimation

Virtual probes were added to monitor the tracer concentration as shown in Figure 11 and 12. The virtual probes were placed at three levels throughout the tank, covering both its width and height at top (T), middle (M), and bottom (B). Among these, T1 and B2 represent the location of physical probes that were used in the actual experiments.

For minimum fill volumes, we used one level of probes, which is sufficient to capture the mixing time as it covered the entire fluid domain. The concentration of tracer was captured at these virtual probes over time using CFD as shown in Figure 13. The T95 lines represent 95% homogeneity. For each probe, the time required to reach 95% homogeneity was calculated, and it is termed as T95 mixing time for the given probe.

Fig 11. Location of virtual probes shown on the three vertical cross-section planes of Xcellerex™ XDUO 50 without the custom wedge solution.

Fig 12. Location of virtual probes shown on the cross-section planes of Xcellerex™ XDUO 50 system, 8.5 L without the custom wedge solution.

Fig 13. Location of virtual probes shown on the three vertical cross-section planes of Xcellerex™ XDUO 50 system, 50 L with the custom wedge solution.

Fig 14. Location of virtual probes shown on cross-section planes of Xcellerex™ XDUO 50 system, 5.2 L with the custom wedge solution.

Fig 15. Tracer concentration over time and estimation of the slowest T95 mixing time for all probes.

The video recording of the mixing experiment was analyzed and snapshots of the bag every 5 s was captured as shown in Figure 16 and 17. At a flow rate of 1 slpm the blue liquid changed to colorless between 45 and 50 s, indicating that homogeneity had been achieved. The same color change was observed in quicker time (20 to 25 s) utilizing a flow rate of 2.5 slpm, confirming that a higher flow rate enables faster mixing within the 2D bag.

Fig 16. Snapshots of the mixing time experiment at 1 slpm. The time stamp shows the time taken for the solution to turn completely colorless.

Fig 17. Snapshots of the mixing time experiment at 2.5 slpm. The time stamp shows the time taken for the solution to turn completely colorless.

The mixing time simulations were performed for the 5 L ReadyCircuit™ 2D bag at pump flow rates of 1 slpm and 2.5 slpm. Figure 18 shows the average T95 mixing time and slowest mixing time for each pump flow rate tested. Higher flow rates result in faster mixing times, enhancing overall circulation within the mixing vessel, allowing fluid to be transported more efficiently throughout the entire volume. This improved circulation reduces the time required to achieve homogeneity. Additionally, higher flow rates increase turbulence within the mixing vessel, which promotes the rapid dispersion of tracer, leading to faster homogenization of the mixture. Table 2 in the appendix shows the T95 mixing time for different probe locations.

Fig 18. Graphical representation of Average T95 mixing time and slowest mixing time for pump flow rates of 1 slpm and 2.5 slpm.

Velocity contour and velocity vector

Figure 19 shows the velocity contour and velocity vectors of 5 L ReadyCircuit™ 2D bag at a pump flow rate of 1 slpm and 2.5 slpm. For better visualization, the velocity is limited to 0.1 m/s in the contour plots. It can be observed that the fluid velocity in the bag increases with the increase in the pump flow rate. The velocity vectors illustrate recirculation inside the bag at both the pump flow rates which is responsible for mixing inside the 2D bag.

Fig 19. Velocity contour and velocity vector in 5 L ReadyCircuit™ 2D bag at different pump flow rates.

Comparison of CFD mixing simulation prediction with the real-time experiment

The mixing time values predicted by the CFD analysis were compared against the actual experiments and the results are shown in Figure 18. The values predicted by CFD closely match the experimental results for the tested pump flow rates of 1 slpm and 2 slpm, validating the accuracy of the CFD model and the assumptions made during the simulations.

Fig 20. CFD predicted mixing time vs real-time experiment.

Single-phase CFD simulations

We conducted single-phase simulations for the operating conditions given in Table 1 to estimate the power number and impellor speed (Table 3) corresponding to the required P/V at each working volume in the mixer.

Mixing analysis CFD simulations

We performed the mixing time simulations for all the configurations given in Table 2 at the impellor speeds determined through single-phase simulations. Through the CFD analysis, the average and slowest T95 mixing time was estimated. Figure 19 presents the slowest T95 mixing time with and without the custom wedge solution in the mixer. All the fill volumes achieved 95% homogeneity within 18 s at the power density of 16.5 W/m³, demonstrating the overall efficiency of the mixer system. The results of mixing analysis are shown in Table 4.

Fig 21. Column chart showing the slowest T95 mixing times and the locations of the regions with the slowest mixing for maximum and minimum fill volumes with and without the custom wedge solution in the mixer.

Velocity contour

The velocity contour of maximum and minimum working volume at 16.5 W/m³ is shown in Figure 22. For better visualization, the velocity is limited to 0.5 m/s in all contour plots. The regions immediately surrounding the impellor exhibit significantly higher velocity values indicative of intense mixing as a direct result of impellor agitation. As the distance from the impellor increases, the velocity values tend to decrease gradually. This is a natural consequence of the dissipation of kinetic energy as the fluid moves away from the impellor.

Note that in this CFD study, the minimum working volume is defined as the volume of media 15mm above the minimum mixing volume. The minimum mixing volume is the volume where the impeller is completely submerged by the media.

Fig 22. Velocity contours at mid plane for maximum and minimum working volume at 16.5 W/m³.

Table 2. CFD simulation mixing time of 5 L ReadyCircuit™ 2D bag at different probe locations

Table 3. Results of single-phase analysis for Xcellerex™ XDUO 50 mixer (estimation of the power number and impellor speed)

Table 4. Results of CFD mixing analysis for Xcellerex™ XDUO 50 mixer (estimation of T₉₅ mixing time)