(145g) CFD analysis of shear rate distribution and the Metzner-Otto constant with different concentrations of shear-thinning fluid in a stirred vessel

Background: In the chemical industries, different kinds of impellers are frequently employed for the mixing of pseudo- plastic fluids to resolve inadequate mixing. Power consumption and mixing time plays an important role in the evaluation of mixing quality. For accurate determination of power consumption and shear rate; Metzner-Otto concept (Metzner and Otto 1957) is used widely to optimize the mixing process for non-Newtonian shear-thinning fluids. By using Computational Fluid Dynamics (CFD) software it is possible to compute the shear rate distribution in a stirred tank.

Method and Materials: In this study, power consumption and average shear rate were investigated with Newtonian and different concentrations of non-Newtonian shear-thinning fluid in the stirred tank vessel stirred by six-blade paddle impeller, to understand the effect of rheological parameters of non-Newtonian shear-thinning fluid on Metzner-Otto constant using multi-purpose CFD software. For stirring liquid starch syrup (η = 6.7 Pa‧s) and polyglycerin (η = 26.7 Pa‧s) were used as Newtonian fluids, and an aqueous solution of hydroxyethyl cellulose (HEC) was used as pseudoplastic fluid. HEC concentration varied from 1.75 wt.% to 3 wt.%. Rheometer (ONRH–1) and Carreau model were used to calculate the rheological parameters of the different concentrations of HEC, and the flow behavior index n was in the range of 0.62 – 0.48.

Experimental results: The results obtained from previous study (Jain and Misumi 2024) suggest that power number decreased linearly with increasing Reynold number in the laminar flow regime, and using the Metzner–Otto method, all power curves for the shear-thinning fluids coincide with those of the Newtonian fluids. Double power needs to rotate the double-stage impeller (2S) as compared to single-stage impeller (1S). Further, Metzner-Otto constant Ks,exp was found to be dependent on power index n for non-Newtonian highly shear-thinning fluids for 1S and Ks,exp value is same for 1S and 2S.

CFD analysis: To check the applicability of the experimental results i.e. to understand the dependence of Ks on n for single-stage impeller, power dissipation and shear rate distribution was analyzed by using multi-purpose CFD software. For the CFD analysis, a similar geometry of the experimental stirred tank with different impellers was constructed. To validate the CFD, power results of CFD were compared with the experimental power results. Direct numerical simulation (DNS) results were in excellent agreement with the experimental results of power consumption for both Newtonian and non- Newtonian shear-thinning fluids. Local shear rate distribution for Newtonian and shear-thinning fluids was analyzed at different impeller speeds. From the local shear rate distribution, it is evident that local shear rate changes with change in the shear-thinning behavior of non-Newtonian shear-thinning fluids at the same impeller speed and this could be the reason of the dependence of Ks on n. DNS results of double-stage impeller (2S) shows that power dissipation is double for 2S as compared to 1S. With the help of MATLAB, volumetric flow region was calculated for 1S and 2S at different shear rates and found out that volumetric flow region is double for 2S as compared to 1S at the same average shear rate. As the average shear rate is same for 1S and 2S, Ks is also same for 1S and 2S.

References:

1. Metzner, A. B., & Otto, R. E. (1957). AIChE Journal, 3(1), 3-10.
2. Jain, M., and R. Misumi. (2024). Journal of Chemical Engineering of Japan, 57 (1): 2387459.

Acknowledgment:

This study was financially supported by the JSPS KAKENHI (Grant No. 22K04799).