(728c) Scale-up between Tanks in Agitation of Newtonin and Non-Newtonian Fluids

Scale-up between tanks is an essential technique for the design of these industrial units. Majority of the equations available in the literature for scaling up in terms of power consumption were obtained in bench-top tanks. The present study aimed at graphical relations of scale-up based on three tanks, with a volume of 10, 50 and 750 liters, in the agitation of Newtonian and non-Newtonian liquids with an axial impeller with 4 blades inclined at 45 ° and a Rushton turbine. The results indicated a good adjustment of the experimental data with the models proposed for scale-up, which had an R² greater than 0.91.

2. INTRODUCTION

Tanks with mechanical impellers are equipment used for stirring and mixing liquids in various operations, such as reactors, extractors, heat exchangers, distillers, flotators and storage units. Determination of power consumption is essential for engine sizing, depending on the type of mechanical impeller, the geometry of the tank and the rheological properties of the agitation. Traditionally, the power consumed is determined from the power number as a function of the Reynolds and Froude numbers (Labik et. Al. 2018). Most industrial tanks have a volume close to 500 liters, which makes the use of the correlations proposed in experimental works and by numerical solution unreliable. Basically, the scale-up equations are obtained in the power-to-volume (P/V) between two tanks, depending on the number of Reynolds (Re) and the number of Froude (Fr), with i for the smallest tank and j for the largest tank (Equation 1).

The difficulty of Equation 1 is found with the use of non-Newtonian liquids, because in this case, there is a variation of the apparent viscosity as the rotation of the mechanical impeller is changed. For example, in the tank with the lowest volume, the flow becomes laminar and in the tank with the largest volume, it may be that the flow is in the transition region. In this situation, the best option is to scale-up through the same geometric similarity between the tank and the internals (Kresta et. Al., 2016). Therefore, an equality parameter between the tanks is chosen, such as the same number as Reynolds (Triveni et. Al., 2008). The present study aimed to present graphical relations for the scale-up between three tanks in the stirring of Newtonian and non-Newtonian liquids with the use of a Rushton turbine and an axial impeller with 4 blades inclined at 45 °.

3. MATERIAL AND METHOD

Figure 1 shows a schematic of the experimental unit used in the present article.

Acrylic tanks with volumes of 10 l, 50 l and 750 l were used, each one equipped with a Rushton turbine and an axial impeller with 4 blades inclined at 45 °. As Newtonian liquids, sucrose solution diluted 50% in water. The non-Newtonian liquid used was an aqueous solution of carboxymethylcellulose (CMC) with a mass concentration of 0.5%. The rheology of the CMC solution was analyzed on a Brookfield rheometer model DV-III, and the solution has a pseudoplastic behavior (adjusted by the power law). Each liquid was subjected to 10 rotations (N) in the range of 100 rpm to 1000 rpm depending on the volume of the tank (V) and the type of mechanical impeller, with each impeller having a diameter (Da) equal to 1/3 of the internal diameter of the tank (Dt). The tests were conducted in duplicate, totaling 360 experiments in the experimental unit. The electric motor of each of the tanks was placed on a swing on bearings, where a metallic arm was attached. At each rotation, the force (F) generated at three points on the arm (Bf) was measured using a dynamometer, so that the power (P) was calculated using Equation 2 (Rosa et. Al., 2020).

4. RESULTS AND DISCUSSION

With the results obtained in the experiments, the power consumed in all cases was calculated. The Reynolds numbers were calculated from the Metzner and Otto (1957) concept, which verified a linear relationship between the shear rate by the rotation of the mechanical impeller. In Figure 2, the results were plotted with the axial impeller with 4 blades inclined at 45 °. The ratio shown on the abscissa axis for x-axis was obtained from the ratio of the Reynolds number as a function of tanks with different volumes. The Dtj / Dti factor was placed in order to take into account the effect of the diameter of the tanks used in the study in the scale-up.

Similarly, in Figure 3, the results with the Rushton turbine are shown. It is noteworthy that the exponents of Equation 1 (disregarding the number of Froude because the tanks have Baffless) were obtained by a non-linear regression performed by combining 900 points (power and Reynolds number) by mechanical impeller. It was observed in Figure 2 and in Figure 3 an excellent adjustment of the experimental data to the model obtained. It is noted that in both cases, the scale-up relationships were initiated from the origin, which corroborates with works presented in the current literature.

5. CONCLUSION

The scale-up prediction models are valid for tanks with volumes between 10 l and 750 l, with the same geometric similarity, for stirring Newtonian liquids and non-Newtonian liquids with rheological index n between 0.79 and 1.0.

6. REFERENCE

KRESTA SM, ETCHELLS III AW, DICKEY DS, ATIEMO-UBENG VA, Advances in industrial mixing: A Companion to the Handbook of industrial mixing. New Jersey: Wiley, 2016.

LABIK L, PETRICRÍCEK R, MOUCHA T, BRUCATO A, CAPUTO G, GRISAFI F, SCARGIALI F, Scale-up and viscosity effects on gas-liquid mass transfer rates in unbaffled stirred tanks. Chemical Engineering Research and Design, v. 132, p.584-592, 2018.

METZNER AB, OTTO RE, Agitation of non-Newtonian Fluids. AIChE J, v. 3, p. 3-10, 1957.

ROSA VS, TORNEIROS DLM, MARANHÃO HWA, MORAES MS, TAQUEDA MES, PAIVA JL, SANTOS AR, MORAES JÚNIOR D, Heat transfer and power consumption of Newtonian and non-Newtonian liquids in stirred tanks with vertical tube baffles. Applied Thermal Engineering, v.176, article 115355, 2020.

TRIVENI B, VISHWANADHAM B, VENKATESHWAR S, Studies on heat transfer to Newtonian and non-Newtonian fluids in agitated vessel. Heat and Mass Transfer, v.44, p.1281-1288, 2008.