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

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

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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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Keywords

  • Twin Cam Mixer
  • Mixing Process
  • 2D Numerical Model
  • Species Transport
  • Pressurization Coefficient