(256c) Comparison of FLOW Patterns and Pumping between Newtonian and Pseudoplastic Fluids Produced By PBT Impeller in Laminar Regime

In the present work, a numerical investigation of the pumping capacity was carried out using CFD simulation tools for a PBT impeller in a laminar regime with a Newtonian fluid and a pseudoplastic fluid. It was found that in the case of the Newtonian fluid when increasing the Reynolds number, two circulation loops are formed, however in the pseudoplastic fluid, a single circulation loop is maintained in a higher N_Re range, this is related to a number of smaller total pumping for this fluid.

Introduction

The mixing of fluids with a high viscosity is a common operation in several processes of pharmaceutical, biotechnology and food industries. In many cases it is common to find fluids with a non-Newtonian behavior, such as slurries, culture broths or foods prepared with gums. Usually the rheological behavior tends to be pseudoplastic. In high viscous fluid mixing it is common to use proximity impellers, however in processes where the viscosity can change during the process they are inefficient [1]. An alternative is the use of turbine type impellers which can be found operating in the laminar regime due to high fluid viscosity or because turbulence can cause damage to the process material [2].

Although there are numerous studies of the turbine type impellers in the laminar regime, the study of the pitched blade turbines (PBTs) in this regime is scarce, although it is widely used in the industry in flow-sensitive processes. On the other hand, the impact of the rheology of the work fluid on the hydrodynamic parameters has also been scarcely studied for this type of impeller, for them in this work it was carried out In this paper, a numerical study based on Computational Fluid Dynamics tools (CFD) was carried out to know the impact of the rheology of the fluid on the pumping number and the flow pattern.

Methodology

The system analyzed consists of a cylindrical tank with a curved bottom, the dimensionless geometric relationships corresponding to the distance from the bottom of the tank to the center of the impeller (C), the height of liquid at rest (Z) and the diameter of the impeller that we used were: C/T=0.3848, Z/T=1 and D/T=0.3848, respectively. As impeller a turbine with 4 blades pitched at 45° was used.

The non-Newtonian fluid (pseudoplastic), considered was a 2.0% by weight aqueous solution of food grade carboxymethylcellulose (CMC) and food grade glycerol as a Newtonian fluid. The properties of these fluids were measured by Márquez-Baños et al. [3]. The density (ρ) and viscosity (µ) of the Newtonian fluid at 10 ºC were 1281 kg/m³ and µ=3.2 Pa·s, respectively. The density of the pseudoplastic fluid at 23°C was 998 kg/m³, and its rheology was adjusted to a power law model, that is,

μ_a(γ) = m(γ)ⁿ (1)

The parameters set in the shear rate range of 0.67 s^-1 <<760 s^-1 were m=22.4 Pa·sⁿ and n=0.357, which gives R²=0.994 in this range.

The Reynolds number of the impeller for a Newtonian fluid is given by:

N_Re = ρND²/μ (2)

The apparent Reynolds number was calculated by applying the concept of Metzner and Otto [4], where it is proposed that the average shear rate around the impeller is proportional to the agitation speed, that is:

γ_av = K_sN (3)

Where Ks is known as the Metzner and Otto constant, for the PBT impeller it has been reported with a value of 8.56 [3, 5]. Inserting the equations (1) and (2) in ec. (3) to obtain a modified impeller Reynolds number (apparent)

N_rea = ρN^2-nD²/(K_s^n-1m) (4)

The highest N_Re evaluated in this study was around 20 and therefore, laminar model was used for modelling the fluid flow through the mixing tank.

Steady state numerical solutions of the Navier-Stokes equations were implemented in Ansys-Fluent® 17.1 by using a single rotating reference frame in the whole fluid domain. As a solution method, the pressure-velocity coupled algorithm was employed. For momentum and pressure discretization, the QUICK and PRESTO! schemes were used, respectively. For gradient approximation a least squares cell-based method was used. All simulations were stopped when the values of all residuals were below 10^-5. The computational mesh used in this study was validated and its independence analysis can be consulted in [3]

On the other hand, the impeller pumping capacity was calculated by the normal flow to the impeller discharge plane, either radial or axial. As the impeller PB4 in laminar flow conditions is a mixed flow impeller, the radial pumping capacity, Q_r is determined by calculating the projected flow through a cylinder of equal diameter and height to those of the impeller. In the case of axial pumping capacity, Q_z must calculate the flow through the area that sweeps the impeller.

Results

In Figure 1, flow patterns are presented in the form of streamlines and velocity vectors for Newtonian (μ=3.2 Pa∙s) and pseudoplastic (m=22.4, n=0.357) fluids. The flow patterns are shown in a cut plane in the middle of the blades, in these images the current lines show the recirculation zones, while the velocity vectors the flow direction.

In the case of the Newtonian fluid it can be noted that at low N_Re a circulation loop is generated at the upper tip of the vane and another elongated loop below the impeller, it can also be noted that the discharge of the flow tends to be in the axial direction and that the separation line between the circulation loops is inclined towards the bottom of the tank. On the other hand at N_Re greater than 5.1, the discharge of the flow begins to become radial, contracting lower circulation loop and the separation line between the circulation loops tends to become horizontal as in the case of radial impellers in laminar regime like the Rushton turbine, however the circulation ties remain asymmetrical.

As for the non-Newtonian fluid, it can be distinguished that at low N_Re a single circulation loop is generated whose center is close to the edge of the vane in the middle plane of the impeller and the discharge of the flow is predominantly axial. From an N_Re greater than 6.38, a circulation loop begins to be generated at the bottom of the impeller which is maintained below the impeller by increasing the N_Re with the separation line between the inclined circulation loops in the range of N_Re analyzed.

Figure 2 shows the curves of the pumping number as a function of the Reynolds number, in this figure it can be distinguished that the radial firefighter in both fluids increases exponentially as the N_Re increases, being always greater in the case of the Newtonian fluid. As soon as it can be noted that the axial pumping is reduced in both fluids, however for the Newtonian fluid this drop is greater, this can be attributed to the formation of the circulation loops with preferably radial flow. Finally, the total pumping is greater in the Newtonian fluid in the N_Re ranges analyzed.

Conclusions

The rheology of the working fluid has an important impact on the flow pattern of the PBT impeller operating in the laminar regime, these changes in the flow pattern cause the pump to have a smaller radial component and the total pump to be reduced. As a future work, the effect of flow thinning index on this hydrodynamic parameter is explored.

References

[1] Letellier, B., Xuereb, C., Swaels, P., Hobbes, P., & Bertrand, J. (2002). Scale-up in laminar and transient regimes of a multi-stage stirrer, a CFD approach. Chemical Engineering Science, 57(21), 4617-4632.

[2] Sossa-Echeverria, J., & Taghipour, F. (2015). Computational simulation of mixing flow of shear thinning non-Newtonian fluids with various impellers in a stirred tank. Chemical Engineering and Processing: Process Intensification, 93, 66-78.

[3] Márquez-Baños, V. E., Aarón, D., Valencia-López, J. J., López-Yáñez, A., & Ramírez-Muñoz, J. (2019). Shear rate and direct numerical calculation of the Metzner-Otto constant for a pitched blade turbine. Journal of food engineering, 257, 10-18.

[4] Metzner, A. B., & Otto, R. E. (1957). Agitation of non‐Newtonian fluids. AIChE Journal, 3(1), 3-10.

[5] Kelly, W., & Gigas, B. (2003). Using CFD to predict the behavior of power law fluids near axial-flow impellers operating in the transitional flow regime. Chemical Engineering Science, 58(10), 2141-2152.