Calculation of Metzner Constant for Double Helical Ribbon Impeller by Computational Fluid Dynamic Method

Abstract

Abstract: Using the multiple reference frames(MRF)impeller method,the three-dimensional non-Newtonian flow field generated by a double helical ribbon(DHR)impeller has been simulated.The velocity field calculated by the numerical simulation was similar to the previous studies and the power constant agreed well with the experimental data.Three computational fluid dynamic(CFD)methods,labeled I,Ⅱ and Ⅲ,were used to compute the Metzner constant ks.The results showed that the calculated value from the slop method(method I)was consistent with the experimental data.Method II,which took the maximal circumference-average shear rate around the impeller as the effective shear rate to compute ks,also showed good agreement with the experiment.However,both methods suffer from the complexity of calculation procedures.A new method(method Ⅲ)was devised in this paper to use the area-weighted average viscosity around the impeller as the effective viscosity for calculating ks.Method Ⅲshowed both good accuracy and ease of use.

Key words: computational fluid dynamic, double helical ribbon impeller, non-Newtonian fluid, Metzner constant

摘要： Using the multiple reference frames(MRF)impeller method,the three-dimensional non-Newtonian flow field generated by a double helical ribbon(DHR)impeller has been simulated.The velocity field calculated by the numerical simulation was similar to the previous studies and the power constant agreed well with the experimental data.Three computational fluid dynamic(CFD)methods,labeled I,Ⅱ and Ⅲ,were used to compute the Metzner constant ks.The results showed that the calculated value from the slop method(method I)was consistent with the experimental data.Method II,which took the maximal circumference-average shear rate around the impeller as the effective shear rate to compute ks,also showed good agreement with the experiment.However,both methods suffer from the complexity of calculation procedures.A new method(method Ⅲ)was devised in this paper to use the area-weighted average viscosity around the impeller as the effective viscosity for calculating ks.Method Ⅲshowed both good accuracy and ease of use.

关键词: computational fluid dynamic, double helical ribbon impeller, non-Newtonian fluid, Metzner constant

ZHANG Minge, ZHANG Lühong, JIANG Bin, YIN Yuguo, LI Xingang. Calculation of Metzner Constant for Double Helical Ribbon Impeller by Computational Fluid Dynamic Method[J]. Chin.J.Chem.Eng., 2008, 16(5): 686-692.

张敏革, 张吕鸿, 姜斌, 尹玉国, 李鑫钢. Calculation of Metzner Constant for Double Helical Ribbon Impeller by Computational Fluid Dynamic Method[J]. Chinese Journal of Chemical Engineering, 2008, 16(5): 686-692.

References

1 Ryan, D.F., Janssen, L.P.B.M., van Dierendonck, L.L., “Circulation time prediction in the scale-up of polymerization reactors with helical ribbon agitators”, Chem. Eng. Sci., 43 (8), 1961-1966 (1988).

2 Kumaresan, T., Joshi, J.B., “Effect of impeller design on the flow pattern and mixing in stirred tanks”, Chem. Eng. J., 115 (3), 173-193 (2006).

3 Shervin, C.R., Raughley, D.A., Romaszewski, R.A., “Flow visualization scaleup studies for the mixing of viscoelastic fluids”, Chem. Eng. Sci., 46 (11), 2867-2873 (1991).

4 Delaplace, G., Leuliet, J.C., Relandeau, V., “Circulation and mixing times for helical ribbon impellers. Review and Experiments”, Exp. Fluids, 28 (2), 170-182 (2000).

5 Niedzielska, A., Kuncewicz, C., “Heat transfer and power consumption for ribbon impellers. Mixing efficiency”, Chem. Eng. Sci., 60 (8/9), 2439-2448 (2005).

6 Carreau, P.J., Chhabra, R.P., Cheng, J., “Effect of rhecological properties on power consumption with helical ribbon agitators”, AIChE J., 39 (9), 1421-1430 (1993).

7 Yap, C.Y., Patterson, W.I., Carreau, P.J., “Mixing with helical ribbon agitators (III) Non-Newtonian fluids”, AIChE J., 25 (3), 516-521 (1979).

8 Brito-De La Fuente, E., Choplin, L., Tanguy, P.A., “Mixing with helical ribbon impellers:Effect of highly shear thinning behavior and impeller geometry”, Chem. Eng. Res. Des., 75, 45-52 (1997).

9 Novak, V., Rieger, F., “Homogenization with helical screw agitators”, Trans. Inst. Chem. Eng., 47 (10), 335-340 (1969).

10 Rieger, F., Novak, V., “Power consumption of agitators in highly viscous non-Newtonian liquids”, Trans. Inst. Chem. Eng., 51, 105-111 (1973).

11 Metzner, A.B., Otto, R.E., “Agitation of non-Newtonian fluids”, AIChE J., 3 (1), 3-10 (1957).

12 Sestak, J., Zitny, R., Houska, M., “Anchoragitated systems:Power input correlation for pseudoplastic and thixotropic fluids in equilibrium”, AIChE J., 32 (1), 155-158 (1986).

13 Tanguy, P.A., Lacroix, R., Bertrand, F., Choplin, L., Brito de la Fuente, E., “Finite element analysis of viscous mixing with a helical ribbon-screw impeller”, AIChE J., 38 (6), 939-944 (1992).

14 Castell-Perez, M.E., Steffe, J.F., “Evaluating shear rates for power law fluids in mixer viscometry”, J. Text. Stud., 21, 439-453 (1990).

15 Thakur, R.K., Vial, C., Djelveh, G., Labbafi, M., “Mixing of complex fluids with flat-bladed impellers:Effect of impeller geometry and highly shear-thinning behavior”, Chem. Eng. process., 43 (10), 1211-1222 (2004).

16 Wang, Z., Mao, Z.S., Yang, C., Shen, X.Q., “Computational fluid dynamics approach to the effect of mixing and draft tube on the pre-cipitation of barium sulfate in a continuous stirred tank”, Chin. J. Chem. Eng., 14 (6), 713-722 (2006).

17 Zhang, Y.H., Yang, C., Mao, Z.S., “Large eddy simulation of liquid flow in a stirred tank with improved innerouter iteration algorithm”, Chin. J. Chem. Eng., 14 (3), 321-329 (2006).

18 Cui, B., Zhu, Z., Zhang, J., Chen, Y., “The flow simulation and experimental study of low-specific-speed high-speed complex centrifugal impellers”, Chin. J. Chem. Eng., 14 (4), 435-441 (2006).

19 Min, J., Gao, Z.M., “Large eddy simulations of mixing time in a stirred tank”, Chin. J. Chem. Eng., 14 (1), 1-7 (2006).

20 Shekhar, S.M., Jayanti, S., “Mixing of pseudoplastic fluids using helical ribbon impellers”, AIChE J., 49 (11), 2768-2772 (2003).

21 Jiang, S., Fan, W., Zhu, C., Ma, Y., Li, H., “Bubble formation in non-Newtonian fluids using laser image measurement system”, Chin. J. Chem. Eng., 15 (4), 611-615 (2007).

22 Iranshahi, A., Heniche, M., Bertrand, F., Tanguy, P.A., “Numerical investigation of the mixing efficiency of the Ekato Paravisc impeller”, Chem. Eng. Sci., 61 (8), 2609-2617 (2006).

23 Xu, T., Zhu, Q., Chen, X., Li, W., “Equivalent cake filtration model”, Chin. J. Chem. Eng., 16 (2), 214-217 (2008).

24 Kelly, W., Gigas, B., “Using CFD to predict the behavior of power law fluids near axial-flow impellers operating in the transitional flow regime”, Chem. Eng. Sci., 58 (10), 2141-2152 (2003).

25 Deglon, D.A., Meyer, C.J., “CFD modelling of stirred tanks:Numerical considerations”, Minerals Eng., 19 (10), 1059-1068 (2006).

26 Lane, G.L., Schwarz, M.P., Evans, G.M., “Comparison of CFD methods for modelling of stirred tanks”, In:Proceedings of the 10th Europ. Conf. on Mixing, Delft, the Netherlands, 273-280 (2000).

27 Bourne, J.R., Butler, H., “An analysis of the flow produced by helical ribbon impellers”, Trans Inst. Chem. Eng., 47, 11-17 (1969).

28 Yao, W., Mishima, M., Takahashi, K., “Numerical investigation on dispersive mixing characteristics of MAXBLEND and double heli-cal ribbons”, Chem. Eng. J., 84, 565-571 (2001).

29 Delaplace, G., Guerin, R., Leuliet, J.C., Chhabra, R.P., “An analytical model for the prediction of power consumption for shearthinning fluids with helical ribbon and helical screw ribbon impellers”, Chem. Eng. Sci., 61 (10), 3250-3259 (2006).

30 Wang, J.J., Feng, L.F., Gu, X.P., Wang, K., Hu, C.H., “Power consumption of innerouter helical ribbon impellers in viscous Newtonian and non-Newtonian fluids”, Chem. Eng. Sci., 55 (12), 2339-2342 (2000).

31 Montante, G., Mostek, M., Jahoda, M., Magelli, F., “CFD simulations and experimental validation of homogenisation curves and mixing time in stirred Newtonian and pseudoplastic liquids”, Chem. Eng. Sci., 60 (8/9), 2427-2437 (2005).

[1]	Lijuan Zhao, Zhe Tan, Xiaoguang Zhang, Qijun Zhang, Wei Wang, Qiang Deng, Jie Ma, De'an Pan. Research on process modeling and simulation of spent lead paste desulfurization enhanced reactor [J]. Chinese Journal of Chemical Engineering, 2023, 60(8): 293-303.
[2]	Chengang Yang, Huaizhi Han, Quan Zhu, Xiangyuan Li. Cracking and buoyancy effect on hydrocarbon endothermic and heat transfer characteristics in rectangular mini-channel [J]. Chinese Journal of Chemical Engineering, 2023, 56(4): 242-254.
[3]	Shuangfei Zhao, Yingying Nie, Wenyan Zhang, Runze Hu, Lianzhu Sheng, Wei He, Ning Zhu, Yuguang Li, Dong Ji, Kai Guo. Microfluidic field strategy for enhancement and scale up of liquid–liquid homogeneous chemical processes by optimization of 3D spiral baffle structure [J]. Chinese Journal of Chemical Engineering, 2023, 56(4): 255-265.
[4]	Qi Han, Xin-Yuan Zhang, Hai-Bo Wu, Xian-Tai Zhou, Hong-Bing Ji. Different efficiency toward the biomimetic aerobic oxidation of benzyl alcohol in microchannel and bubble column reactors: Hydrodynamic characteristics and gas–liquid mass transfer [J]. Chinese Journal of Chemical Engineering, 2023, 55(3): 84-92.
[5]	Songsong Wang, Hong Li, Changyuan Tao, Renlong Liu, Yundong Wang, Zuohua Liu. Study on cavern evolution and performance of three mixers in agitation of yield-pseudoplastic fluids [J]. Chinese Journal of Chemical Engineering, 2023, 55(3): 111-122.
[6]	Yongbo Zhou, Yang Jin, Jun Li, Qinyan Wang, Ming Chen. Numerical study on the hydrodynamics behavior of a central insert microchannel [J]. Chinese Journal of Chemical Engineering, 2023, 53(1): 361-373.
[7]	Tianpeng LiZhou, Jiajia Luo, Tiefeng Wang. Enhancement of acetylene and ethylene yields in partially decoupled oxidation of ethane by changing the composition of heat carrier [J]. Chinese Journal of Chemical Engineering, 2022, 47(7): 71-78.
[8]	Zewen Chen, Yongjun Wu, Jian Wang, Peicheng Luo. Study on the solid–liquid suspension behavior in a tank stirred by the long-short blades impeller [J]. Chinese Journal of Chemical Engineering, 2022, 47(7): 79-88.
[9]	Liying Chen, Junheng Guo, Wenpeng Li, Shuchun Zhao, Wei Li, Jinli Zhang. A numerical study of mixing intensification for highly viscous fluids in multistage rotor–stator mixers [J]. Chinese Journal of Chemical Engineering, 2022, 47(7): 218-230.
[10]	Yaqi Ren, Shuqian Xia. Synthesis and mechanism analysis of a new oil soluble viscosity reducer for flow improvement of Chenping heavy oil [J]. Chinese Journal of Chemical Engineering, 2022, 45(5): 58-67.
[11]	Zijun Li, Shubo Wang, Sai Yao, Xueke Wang, Weiwei Li, Tong Zhu, Xiaofeng Xie. Experimental and numerical study on improvement performance by wave parallel flow field in a proton exchange membrane fuel cell [J]. Chinese Journal of Chemical Engineering, 2022, 45(5): 90-102.
[12]	Yongjun Wu, Pan You, Peicheng Luo. Effect of pitched short blades on the flow characteristics in a stirred tank with long-short blades impeller [J]. Chinese Journal of Chemical Engineering, 2022, 45(5): 143-152.
[13]	Ning Liu, Xingping Liu, Fumin Wang, Feng Xin, Mingshuai Sun, Yi Zhai, Xubin Zhang. CFD simulation study of the effect of baffles on the fluidized bed for hydrogenation of silicon tetrachloride [J]. Chinese Journal of Chemical Engineering, 2022, 45(5): 219-228.
[14]	Narjes Hemati Alam, Eslam Kashi, Razieh Habibpour. Computational fluid dynamics simulation of gas dispersion in complex facilities using Kit Fox field experiments: Validation and statistical evaluation [J]. Chinese Journal of Chemical Engineering, 2022, 44(4): 412-423.
[15]	Huina Wang, Xiaoxia Duan, Xin Feng, Zai-Sha Mao, Chao Yang. Effect of impeller type and scale-up on spatial distribution of shear rate in a stirred tank [J]. Chinese Journal of Chemical Engineering, 2022, 42(2): 351-363.