Cyclone
Solidsgas separation according to Muschelknautz
Constant geometric parameters
Operational parameters
Geometric parameters
Velocities
Mass separation between main and secondary streams
Separation at wall due to exceeding the loading limit in main stream
Separation in the internal vortex of main stream
Separation at wall due to exceeding the loading limit in secondary stream
Separation at vortex finder of secondary stream
Overall separation
Note
Notations:
Symbol 
Units 
Type 
Description 

[] 
Relative width of cyclone gas entry 

[°] 
UP 
Angle of attack of blades in axial gas entry 

[°] 
UP 
Spiral angle in spiral gas entry 

[] 
UP 
Wall friction coefficient of pure gas 

[] 
Wall friction coefficient of solidscontaining gas 

[kg/kg] 
Solids loading at inlet 

[kg/kg] 
Threshold for solids loading in main stream 

[kg/kg] 
Threshold for solids loading in secondary stream 

[] 
UP 
Separation efficiency adjustment factor 

[] 
Overall separation efficiency in main stream 

[] 
Separation efficiency due to exceeding of solids loading limit in main stream (from main stream to solids output) 

[] 
Separation efficiency in internal vortex (from internal vortex to solids output) 

[] 
Overall separation efficiency in secondary stream 

[] 
Separation efficiency due to exceeding of solids loading limit in secondary stream (from secondary stream to solids output) 

[] 
Separation efficiency at vortex finder (from vortex finder to solids output) 

[] 
Total separation efficiency of cyclone 

[Pa s] 
MDB 
Dynamic viscosity of gas at inlet 

[kg/m^{3}] 
MDB 
Gas density at inlet 

[kg/m^{3}] 
MDB 
Solids density at inlet 

[m] 
Height of blades channel in axial gas entry 

[m^{2}] 
Lateral area of the conical part 

[m^{2}] 
Lateral area of the top half of conical part 

[m^{2}] 
Lateral area of the cylindrical part 

[m^{2}] 
Average wall area considered for the first revolution after entry 

[m^{2}] 
Lateral area of vortex finder 

[m^{2}] 
Sedimentation area 

[m^{2}] 
Frictional area of the spiral in spiral gas entry 

[m^{2}] 
Area of upper wall 

[m^{2}] 
Total wall friction area 

[m] 
UP/ 
Width of gas entry/blade channel 

[m] 
SP 
Particle diameter 

[m] 
SP 
Particle size median 

[m] 
UP 
Thickness of blades in axial gas entry 

[m] 
UP 
Diameter of particles exit 

[m] 
UP 
Diameter of vortex finder 

[m] 
UP 
Outer diameter of cyclone 

[m] 
Cut size of separation on the first revolution due to exceeding the loading limit 

[m] 
Cut size of separation in internal vortex of main stream 

[m] 
Cut size of separation at vortex finder in secondary stream 

[] 
UP 
Coefficient for grid efficiency curve calculation according to Muschelknautz 

[m] 
Height of the cone part of cyclone 

[m] 
Effective height of the cone part of cyclone 

[m] 
UP 
Height of the cylindrical part of cyclone 

[m] 
UP 
Height of gas entry 

[m] 
UP 
Height (depth) of vortex finder 

[m] 
Height of separation zone 

[m] 
UP 
Total height of cyclone 

[] 
Exponent for solids loading threshold in main stream 

[] 
UP 
Constant for solids loading threshold in main stream 

[kg/s] 
SP 
Gas mass flow at inlet 

[kg/s] 
SP 
Solids mass flow at inlet 

[kg/s] 
Solids mass flow at solids outlet 

[kg/s] 
Gas mass flow at solids outlet 

[kg/s] 
Solids mass flow at gas outlet 

[kg/s] 
Gas mass flow at gas outlet 

[] 
Parameter for calculating secondary stream 

[#] 
UP 
Number of blades in axial gas entry 

[m] 
Mean radius of the conical part 

[m] 
UP 
Core radius of blades in axial gas entry 

[m] 
Radius of the middle gas streamline at gas entry 

[m] 
Mean radius of the gas streamline at gas entry 

[m] 
Radius of the particles exit 

[m] 
Effective radius of the particles exit 

[m] 
Radius of vortex finder 

[m] 
Outer radius of cyclone 

[m] 
Reference mean radius 

[] 
Mass fraction of particles with size at inlet 

[m/s] 
Tangential velocity at mean cone radius 

[m/s] 
Tangential velocity at gas streamline radius at gas entry 

[m/s] 
Tangential velocity at vortex finder 

[m/s] 
Tangential velocity at outer cyclone radius 

[m/s] 
Inlet velocity in the middle gas streamline at gas entry 

[m^{3}/s] 
Gas volume flow at inlet 

[m^{3}/s] 
Gas volume flow of secondary stream 

[m/s] 
Sinking speed at which 50% of particles are sedimented at wall 

[] 
Fraction of material going to main stream 

[m^{2}/s] 
Mean centrifugal acceleration along streamline 
UP: Userdefined model parameters
MDB: Value from materials database
SP: Value from the input stream
Note
Model parameters:
Name 
Symbol 
Units 
Description 
Values 

d_o 
[m] 
Outer diameter of cyclone 
≥0.01 

h_tot 
[m] 
Total height of cyclone 
≥0.01 

h_cyl 
[m] 
Height of the cylindrical part of cyclone 
≥0.01 

d_f 
[m] 
Diameter of vortex finder 
≥0.01 

h_f 
[m] 
Height (depth) of vortex finder 
≥0.01 

d_exit 
[m] 
Diameter of particle exit 
≥0.01 

Entry shape 
Gas entry shape 
Rectangular slot/Full spiral/Half spiral/Axial 

b_e 
[m] 
Width of gas entry 
≥0.01 

h_e 
[m] 
Height of gas entry 
≥0.01 

epsilon 
[°] 
Spiral angle in spiral gas entry 
[0…360] 

N_b 
[#] 
Number of blades in axial gas entry 
≥1 

d_b 
[m] 
Thickness of blades in axial gas entry 
≥0 

r_core 
[m] 
Core radius of blades in axial entry 
≥0 

Blade shape 
Blades shapes in axial gas entry 
Simple straight/Curved/Curved and twisted 

delta 
[°] 
Angle of attack of blades in axial gas entry 
[15…30] 

lambda_0 
[] 
Wall friction coefficient of pure gas 
≥0 

D 
[] 
Coefficient for grid efficiency curve calculation according to Muschelknautz 
[2…4] 

K_main 
[] 
Constant for solids loading threshold in main stream 
[0.02…0.03] 

eta_adj 
[] 
Separation efficiency adjustment factor 
[0…1] 

Plot 
Whether to generate plots 
YES/NO 
See also
Muschelknautz, U. (2019). L3.4 Zyklone zum Abscheiden fester Partikel aus Gasen. In: Stephan, P., Kabelac, S., Kind, M., Mewes, D., Schaber, K., Wetzel, T. (eds) VDIWärmeatlas. Springer Reference Technik. Springer Vieweg, Berlin, Heidelberg. https://doi.org/10.1007/9783662529898_91
A demostration file at
Example Flowsheets/Units/Cyclone Muschelknautz.dlfw
.