Abstract
Separation efficiency of flat- and domed-roof cyclones was investigated in a polypropylene (PP) production process at 20 bar and 80 °C, using computational fluid dynamics (CFD) coupled with the Reynolds stress model for gas turbulence and a discrete random walk model for particles. The geometry of the domed-roof cyclone was based on a high-efficiency Stairmand cyclone and the ASME standard for high-pressure vessels. The meshing strategy and CFD model validation of the cyclones were performed systematically. At an inlet velocity of 20 m/s and atmospheric pressure, the fractional separation efficiency of the domed-roof cyclone was 1.5% higher than that of the flat-roof cyclone in an air-CaCO3 system for particle sizes ranging from 0.1 to 100 µm. Under the high-pressure operating conditions of the domed-roof cyclone, the diameter (De) of the vortex finder was selected as 40% of the cyclone barrel diameter (D), maintaining its high separation efficiency and moderate pressure drop. The optimized domed-roof cyclone achieved an 8.4% higher mean fractional separation efficiency and a 6.4% lower pressure drop compared to a standard flat-roof cyclone for PP particles from 1 to 40 µm. The CFD result provides a useful guide for designing a high-efficiency domed-roof cyclone at high pressures.
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Abbreviations
- a:
-
speed of sound [m/s]
- cf :
-
skin friction coefficient
- d:
-
the normal distance to the wall [m]
- dp :
-
particle diameter [m, µm]
- D:
-
cyclone barrel diameter [m]
- De :
-
vortex finder diameter [m]
- D T,ij :
-
turbulence diffusion [m2/s]
- DL,ij :
-
molecular diffusion [m2/s]
- DP :
-
particle diffusivity [m2/s]
- Eu:
-
Euler number
- \(\overrightarrow {\rm{g}} \) :
-
gravity vector [9.81m/s2]
- k:
-
turbulence kinetic energy [m2/s2]
- L:
-
hydraulic diameter [m]
- Le :
-
eddy length scale [m]
- mp :
-
particle mass [kg]
- ms :
-
particle feed rate [kg/h]
- np :
-
numberof points
- nfrac :
-
fractional separation efficiency [%]
- ntot :
-
total separation efficiency [%]
- Np :
-
number of particle sizes
- N cell :
-
number of cells
- N mesh :
-
total number of meshes
- P:
-
pressure [Pa]
- Pout :
-
pressure outlet [Pa]
- \(\overline {\rm{P}} \) :
-
mean pressure [Pa]
- Pij :
-
stress production term
- ΔP:
-
pressure drop [Pa]
- r:
-
radial direction coordinate [m]
- R:
-
cyclone radius [m]
- Re:
-
Reynolds number
- t:
-
time [s]
- Δt:
-
pseudo time step for each cell in the domain [s]
- TL :
-
Lagrangian integral time [s]
- tcross :
-
particle eddy crossing time [s]
- \(\overrightarrow {\rm{u}} \) :
-
fluid velocity vector [m/s]
- \({\overrightarrow {\rm{u}} _p}\) :
-
particle velocity vector [m/s]
- \({\overline {\rm{u}} _i}\) :
-
mean velocity [m/s]
- u ′i :
-
fluctuation velocity of number i component [m/s]
- \(\overline {{\rm{u}}_i^\prime {\rm{u}}_j^\prime } \) :
-
Reynolds stress tensor
- ua :
-
axial velocity [m/s]
- uin :
-
inlet velocity [m/s]
- ut :
-
tangential velocity [m/s]
- uτ :
-
friction velocity [m/s]
- u∥ u⊥ :
-
gravitational vector
- V:
-
volume of computational domain [m3]
- X50 :
-
cut-off diameter [m, µm]
- xi :
-
mass fraction of particle size
- y+ :
-
dimensionless wall distance
- yp :
-
distance from the wall to the first cell [m]
- z:
-
axial direction coordinate [m]
- α :
-
asymptotic range of convergence solution
- δ 99 :
-
minimum fluid boundary thickness [m]
- δ X :
-
average grid size [m]
- η :
-
separation efficiency [%]
- η 10 :
-
fractional separation efficiency for dp=10 µm [%]
- ε :
-
turbulence dissipation rate [m2/s3]
- ε ij :
-
dissipation rate tensor
- ζ :
-
Gaussian normally distributed random number
- ε :
-
gas kinematic viscosity [Pa·s]
- ε t :
-
turbulent kinetic viscosity [Pa·s]
- φ ij :
-
pressure strain term
- ϕ :
-
physical quantities of data
- ρ :
-
density of gas [kg/m3]
- ρ p :
-
density of particle [kg/m3]
- τ :
-
residence time [s]
- τ r :
-
particle relaxation time [s]
- τ e :
-
characteristic lifetime of the eddies [s]
- τ w :
-
wall shear stress [Pa]
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Acknowledgements
This research was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF), funded by the Ministry of Education (grant numbers: 2021M3I3 A1084950 and 2021R1A2C1011618). The authors also appreciate the editing contributions of Ms. Hannah Y. Cha.
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Bui, H.T.H., Ngo, S.I. & Lim, YI. Separation efficiency of flat- and domed-roof cyclones in high-pressure polypropylene production using computational fluid dynamics. Korean J. Chem. Eng. 40, 2419–2433 (2023). https://doi.org/10.1007/s11814-023-1507-y
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DOI: https://doi.org/10.1007/s11814-023-1507-y