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Numerical investigation of the mixing process in a Twin Cam Mixer: Influence of triangular cam height-base ratio and eccentricity

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Abstract

The twin cam mixer (TCM), as a general-purpose mixer, shares many attributes in common with 3D industrial mixers, like the internal mixer. We investigated the mixing process in a 2D TCM with two identical isosceles triangular cams rotating at 0.5 rpm. A 2D numerical model coupled with the species transport model was employed to study the influence of cam height-base ratio and eccentricity qualitatively and quantitatively, and both were found to have a significant effect on the mixing behavior of the mixer. Furthermore, a dimensionless parameter, named the modified pressurization coefficient, is put forward to quantify the geometry of the mixer. The logarithmic relationship between the modified pressurization coefficient and the mixing quality was discovered and expected to provide new ideas for establishing the relationship between the geometric parameters of a mixer and its mixing performance.

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Abbreviations

a:

distance between the centers of the cavity cylinders [m]

A:

total area of the whole computational domain

Aj :

area of jth cell [m2]

Ak :

area of kth cell in the computational domain of the left cavity cylinder [m2]

At :

total area of the left domain [m2]

b:

base of the cams [m]

c:

tip width of cam [m]

d:

diameters of the cavity cylinders [m]

Dm :

mass diffusion coefficient [m2/s]

e:

ratio of E to the radius of the cavity cylinder

E:

distance between the center of the cavity cylinder and the centroid of the cam at the same side [m]

f1j :

mass fraction of Liquid 1 in jth cell

f1k :

mass fraction of Liquid 1 in kth cell of the left domain

f2 :

mass fraction of Liquid 2

favg :

mean mass fraction of Liquid 1 in whole computational domain

fi :

mass fraction of the species i

flavg :

mean mass fraction of Liquid 1 in the left cavity cylinder

F :

source term [N/m3]

h:

height of the cams [m]

h0 :

minimum clearances between the rotor and the cavity wall [m]

h1, h2, h3 :

clearance between the three tips and cavity wall [m]

H0 :

maximum clearances between the rotor and the cavity wall [m]

H1, H2 H3 :

maximum clearance between the cavity wall and three leading faces [m]

l 0 :

initial length of the interface [m]

l t :

interfacial length between the two fluids at time t [m]

m:

total number of cells in the left domain

n:

total number of cells in computational domain

N:

revolutions of the cam

p:

fluid pressure [Pa]

Pcl :

centroid of the left cam

Pcr :

centroid of the right cam

Pr :

sampling point located at (0, 52 mm)

Prl :

center of left cavity cylinder

Prr :

center of left cavity cylinder

r:

cam height-base ratio

S:

pressurization coefficient

Scam :

cam area [m2]

Sm :

modified pressurization coefficient

t:

time [s]

Δt:

time step [s]

u:

magnitude of velocity [m/s]

u :

velocity vector [m/s]

Δx:

mesh size [m]

α :

mixing quality

β :

length stretch

θ :

leading face angle

ρ :

fluid density [kg/m3]

σ 2 :

variance of mass fraction distribution

σ 2max :

the maximum variance

τ :

viscous stress tensor

References

  1. G. Grosso, M. A. Hulsen, A. S. Fard, A. Overend and P. D. Anderson, AIChE J., 64, 1034 (2018).

    Article  CAS  Google Scholar 

  2. R. Wójtowicz and J. Talaga, Chem. Eng. Commun., 203, 161 (2016).

    Article  Google Scholar 

  3. R. Wójtowicz, Chem. Eng. Sci., 172, 622 (2017).

    Article  Google Scholar 

  4. Y. Li, J. Si, M. Arowo, Z. Liu, B. Sun, Y. Song, G. Chu and L. Shao, Chem. Eng. Process. — Process Intensification, 148, 107801 (2020).

    Article  CAS  Google Scholar 

  5. M. Robinson and P. W. Cleary, AIChE J., 57, 581 (2011).

    Article  CAS  Google Scholar 

  6. T. Avalosse and M. J. Crochet, AIChE J., 43, 577 (1997).

    Article  CAS  Google Scholar 

  7. F. Bertrand, F. Thibault, L. Delamare and P. A. Tanguy, Comput. Chem. Eng., 27, 491 (2003).

    Article  CAS  Google Scholar 

  8. M. Robinson, P. Cleary and J. Monaghan, AIChE J., 54, 1987 (2008).

    Article  CAS  Google Scholar 

  9. A. Eitzlmayr, G. Koscher and J. Khinast, Comput. Phys. Commun., 185, 2436 (2014).

    Article  CAS  Google Scholar 

  10. J. Liu, F. Li, L. Zhang and H. Yang, J. Appl. Polym. Sci., 132, 42496 (2015).

    Google Scholar 

  11. T. Chen, Y. Hao, X. Chen, H. Zhao, J. Sha, Y. Ma and L. Xie, J. Appl. Polym. Sci., 135, 46623 (2018).

    Article  Google Scholar 

  12. Y. Nakayama, T. Kajiwara and T. Masaki, AIChE J., 62, 2563 (2016).

    Article  CAS  Google Scholar 

  13. S. A. Salahudeen, R. H. Elleithy, O. AlOthman and S. M. AlZahrani, Chem. Eng. Sci., 66, 2502 (2011).

    Article  CAS  Google Scholar 

  14. J. Luo, B. Xu, H. Yu, Y. Du and Y. Feng, Fiber. Polym., 16, 95 (2015).

    Article  CAS  Google Scholar 

  15. B. Xu, Y. Liu, H. Yu, L. Turng and C. Liu, Macromol. Theor. Simul., 27, 1800021 (2018).

    Article  Google Scholar 

  16. H. H. Yang and I. Manas-Zloczower, Polym. Eng. Sci., 32, 1411 (1992).

    Article  CAS  Google Scholar 

  17. X. Zhang, L. Feng, W. Chen and G. Hu, Polym. Eng. Sci., 49, 1772 (2009).

    Article  CAS  Google Scholar 

  18. A. S. Fard and P. D. Anderson, Comput. Fluids, 87, 79 (2013).

    Article  Google Scholar 

  19. T. Ishikawa, F. Nagano, T. Kajiwara and K. Funatsu, Int. Polym. Proc., 21, 354 (2006).

    Article  CAS  Google Scholar 

  20. Y. Nakayama, E. Takeda, T. Shigeishi, H. Tomiyama and T. Kajiwara, Chem. Eng. Sci., 66, 103 (2011).

    Article  CAS  Google Scholar 

  21. Y. Nakayama, H. Takemitsu, T. Kajiwara, K. Kimura, T. Takeuchi and H. Tomiyama, AIChE J., 64, 1424 (2018).

    Article  CAS  Google Scholar 

  22. O. S. Carneiro, G. Caldeira and J. A. Covas, J. Mater. Process. Tech., 92, 309 (1999).

    Article  Google Scholar 

  23. X. Zhang, Z. Xu, L. Feng, X. Song and G. Hu, Polym. Eng. Sci., 46, 510 (2006).

    Article  CAS  Google Scholar 

  24. X. Zhang, L. Feng, S. Hoppe and G. Hu, Polym. Eng. Sci., 48, 19 (2008).

    Article  Google Scholar 

  25. G. Shearer and C. Tzoganakis, Polym. Eng. Sci., 39, 1584 (1999).

    Article  CAS  Google Scholar 

  26. G. Shearer and C. Tzoganakis, Polym. Eng. Sci., 40, 1095 (2000).

    Article  CAS  Google Scholar 

  27. G. Shearer and C. Tzoganakis, Adv. Polym. Technol.: J. Polym. Process. Inst., 20, 169 (2001).

    Article  CAS  Google Scholar 

  28. G. Shearer and C. Tzoganakis, Polym. Eng. Sci., 41, 2206 (2001).

    Article  CAS  Google Scholar 

  29. X. Zhan, Z. Sun, Y. He, B. Shen, T. Shi and X. Li, Can. J. Chem. Eng., 97, 1931 (2019).

    Article  CAS  Google Scholar 

  30. F. Huang, D. Wang, Z. Li, Z. Gao and J. J. Derksen, Chem. Eng. J., 362, 229 (2019).

    Article  CAS  Google Scholar 

  31. C. Park, K. Lee, S. Hong, J. Lee, S. Cho and I. Moon, Powder Technol., 355, 309 (2019).

    Article  CAS  Google Scholar 

  32. M. Mansour, Z. Liu, G. Janiga, K. D. P. Nigam, K. Sundmacher, D. Thévenin and K. Zähringer, Chem. Eng. Sci., 172, 250 (2017).

    Article  CAS  Google Scholar 

  33. R. K. Connelly and J. L. Kokini, Adv. Polym. Technol., 22, 22 (2003).

    Article  CAS  Google Scholar 

  34. R. K. Connelly and J. L. Kokini, J. Non-Newton. Fluid, 123, 1 (2004).

    Article  CAS  Google Scholar 

  35. R. K. Connelly and J. L. Kokini, J. Food Eng., 79, 956 (2007).

    Article  Google Scholar 

  36. Q. He, J. Huang, X. Shi, X. Wang and C. Bi, Comput. Math. Appl., 73, 109 (2017).

    Article  Google Scholar 

  37. J. Cheng and I. Manas-Zloczower, Polym. Eng. Sci., 29, 701 (1989).

    Article  CAS  Google Scholar 

  38. R. B. Bird, R. C. Armstrong and O. Hassager, Dynamics of polymeric liquids, Wiley, New York (1987).

    Google Scholar 

  39. P. Dhakal, S. R. Das, H. Poudyal and A. J. Chandy, J. Appl. Polym. Sci., 134, 44250 (2017).

    Article  Google Scholar 

  40. ANSYS, ANSYS Fluent User’s guide, release 19.0 (2017).

  41. U. Fatima, M. Shakaib and I. Memon, Chem. Pap., 74, 1267 (2020).

    Article  CAS  Google Scholar 

  42. P. Vatankhah and A. Shamloo, Anal. Chim. Acta, 1022, 96 (2018).

    Article  CAS  PubMed  Google Scholar 

  43. J. M. Ottino, The kinematics of mixing stretching, chaos, and transport, Cambridge University Press, New York (1989).

    Google Scholar 

  44. S. Smale, B. Am. Math. Soc., 73, 747 (1967).

    Article  Google Scholar 

  45. I. Manas-Zloczower and Z. Tadmor, Mixing and compounding-theory and practice, Hanser, Cincinnati (2009).

    Book  Google Scholar 

Download references

Acknowledgements

This project is supported by National Natural Science Foundation of China (Grant Nos. 51975226 and 51605179).

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Correspondence to Xiaobin Zhan.

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He, Y., Li, X., Long, J. et al. Numerical investigation of the mixing process in a Twin Cam Mixer: Influence of triangular cam height-base ratio and eccentricity. Korean J. Chem. Eng. 38, 552–564 (2021). https://doi.org/10.1007/s11814-020-0715-y

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  • DOI: https://doi.org/10.1007/s11814-020-0715-y

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