The main aim of this research, writes University of Limerick chemical and biochemical engineering student Úna Real, is to investigate the possible advantages of using an angle-mounted Rushton impeller in a mixing tank.
Mixing is a main process step in many research areas and industries. The main objective of mixing is to achieve homogeneity in a tank efficiently in terms of time and power consumption. There are a wide range of different mixing tank configurations possible.
Options include tank diameter or height along with the number and design of impellers or baffles. The main aim of this research is to investigate possible advantages of using an angle-mounted Rushton impeller in a mixing tank.
This study was carried out with the use of numerical simulations to predict the complex and challenging fluid mechanic phenomena that are encountered in mixing tanks. Computational Fluid Dynamics (CFD) software ANSYS Student 2019 R2 was used as it can gain exhaustive information about the mixing characteristics that are present in a mixing tank.
In this study, the efficiency of a straight entering Rushton impeller was compared to two different angle-mounted Rushton impellers (20° and 40°) implemented in a lab-scale mixing tank with four baffles equally spaced around the tank.
A comparison was made for mixing efficiency in relation to mixing profile, power required for agitation and mixing time. The geometry of the three different mixing tank configurations are shown in Figure 1.
Figure 1: Straight mounted Rushton impeller (top left); 20° angle-mounted Rushton impeller (top right); 40° angle-mounted Rushton impeller (base)
A grid independence study was carried out initially to find the optimum grid resolution. Two different grids investigated are displayed in Figure 2. Five inflation layers were enforced on external walls of the tank to ensure that the boundary layer was resolved correctly and different impeller wall sizing, MRF body sizing and tank sizing was enforced.
Figure 2: Coarse grid (left); fine grid (right)
The mixing time for all three impeller configurations was predicted by placing a sphere of tracer (tracer concentration of 1 at time=0) was placed in all three tanks and a time dependent simulation was run. Mixing time was defined as the time taken for the fluid in the tank to report a mass fraction of tracer that was within 2% of the final solution mass fraction of tracer.
The predicted flow pattern in each mixing tank is displayed using vectors (Figure 3). A radial flow pattern was observed when using a straight Rushton impeller as expected.
When using an angle-mounted impeller, the stream of fluid that is pushed out in-line with the impeller blade hits the tank wall at an angle and therefore doesn’t split into equal proportions up and down the tank.
This results in there being a large predominant circular flow created the whole way around the tank propelled by the larger off-stream. The disadvantage of this is that there are recirculation zones created by the smaller split stream coming off the impeller that is pushed against the predominant flow direction in the tank.
Figure 3: Predicted flow patterns in a mixing tank (top left: straight Rushton impeller, top right: 20° angle mounted Rushton impeller, base: 40° angle mounted Rushton impeller)
The predicted power required for agitation was investigated using two different methods; τ based method and ɛ based method. It was found that grid resolution impacts the τ based power number prediction whereas both grid resolution and discretisation scheme used impacts the ɛ based power number prediction.
The same trend was found when predicting power number in a mixing tank with an angle mounted impeller. Therefore, it is possible to more accurately predict the power number in a mixing tank using a high order discretisation scheme and fine grid.
This was supported by the Turbulence Dissipation Rate (TDR) values measured in the tank where is was detected that TDR is underpredicted when first order discretisation is used.
The power number predictions for the three different impeller configurations were calculated and are compiled in Table 1. It was found that the power required for mixing decreases when the impeller is positioned at an angle in the tank and the power required keeps decreasing as the angle is increased based on both τ based and ɛ based predictions.
This is potentially due to the flow in the tank generating a flow pattern similar to axial flow. This theory is also supported by the mixing profile in the tank.
The lower power number prediction shows that there is a smaller power input required to mix the contents of the tank due to less resistance to mixing encountered. Angle mounted impellers may therefore be important and useful in industry when trying to decrease power consumption.
Table 1: Power number predictions in mixing tank using a fine mesh and second order discretisation
Based on comparison to experimentally determined correlations used to calculate the mixing time in a tank, the mixing times found in this study were overpredicted. It was found that a high grid resolution and discretisation scheme is necessary in order to accurately predict the mixing time in a vessel.
This can be seen in the graphs below (Figure 4) where the mixing time is approximately halved when a fine grid and second order discretisation is used.
The position of tracer in the tank only caused a slight change in the predicted mixing time however a change in the mixing profile was observed (Figure 5). When the tracer position was tested at both the top and base of the tank using the 20° angle mounted impeller, there is more chaos seen in the mixing profile when the tracer is placed at the base of the tank.
A possible cause for this behaviour is that the impeller is placed at 1/3 tank height in this simulation and is therefore closer to the base of the tank than the top of the tank.
A possible recommendation is to increases the impeller clearance when using an angle mounted impeller in order to impose the same degree of chaos both above and below the impeller.
Figure 4: Mixing profile for 20° angle mounted Rushton impeller (left: coarse mesh and first order upwind discretization, right: fine mesh and second order discretisation)
Figure 5: Mixing profile for 20° angle mounted Rushton impeller (left: tracer at top of tank, right: tracer at base of tank)
I have shown that with the use of a fine grid and high order discretisation scheme, the turbulent flow in a mixing tank can be accurately predicted in terms of flow pattern, power number and mixing time.
When an angle mounted Rushton impeller is used in a mixing tank there is less power required for mixing compared to a straight entering Rushton impeller.
The issue with an angle mounted Rushton impeller is that there are recirculation zones created in the tank, therefore it is important to investigate these zones further before selecting an inlet position in the mixing tank to ensure efficient mixing of the inlet stream with the rest of the tank.
The power number in a mixing tank can be accurately predicted using the τ based and the ɛ based method given the right conditions are imposed in the model.
Power number predictions based on τ are possible with a moderate grid and the use of a low order discretisation scheme, however to get accurate predictions based on ɛ, a fine grid and high order discretisation scheme must be implemented.
The mixing time in a mixing tank is overpredicted when the k-ɛ turbulence model is used and it is recommended that the LES or DNS turbulence model is used to increase the accuracy of these predictions.
There was no significant difference in mixing time observed when using a straight Rushton impeller compared to an angle mounted Rushton impeller however the mixing profiles are different due to different flow patterns created in the tank.
Author: Úna Real, chemical and biochemical engineering, University of Limerick