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Numerical investigation of cone angle effect on the flow field and separation efficiency of deoiling hydrocyclones

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In this study, the effect of cone angle on the flow field and separation efficiency of deoiling hydrocyclones is investigated taking advantage of large eddy simulation. The dynamic Smagorinsky is employed to determine the residual stress tensor of the continuous phase. The method of Lagrangian particle tracking with an optimized search algorithm (closest cell) is applied to evaluate the separation efficiency of deoiling hydrocyclone. Simulations are performed on a 35-mm deoiling hydrocyclone with the three different cone angles of 6, 10 and 20 degree. The numerical results revealed that the changes in the cone angle would affect the velocity and pressure distribution inside hydrocyclone, and lead to changes in the separation efficiency. However, the large cone angle increases the tangential velocity and pressure gradient inside the hydrocyclone, but reduces the separation efficiency. The reasons behind the decrease in the separation efficiency are the flow structure and reduction of oil droplets residence time in hydrocyclones with large cone angles.

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C D :

Drag coefficient (–)

C S :

Smagorinsky constant (–)

D :

Hydrocyclone diameter (m)

d :

Droplet diameter (m)

F D :

Drag force (kg/m2 s2)

F P :

Pressure gradient force (kg/m2 s2)

F V :

Virtual mass force (kg/m2 s2)

k :

Density ratio (k = ρ d /ρ f ) (–)

p :

Static pressure (kg/ms2)

Q i :

Inlet volume flow rate (m3/h)

R :

Flow split (Qoverflow/Qinlet) (%)

Re :

Reynolds number (–)

L ij :

\( L_{\rm ij}={\mathop{\overline{\hbox{u}_{\rm i}\hbox{u}_{\rm j}}}\limits^{\frown}}- {\mathop{\overline{\hbox{u}_{\rm i}}}\limits^{\frown}}\, {\mathop{\overline{\hbox{u}_{\rm j}}}\limits^{\frown}} \) (m2/s2)

M ij :

\( \hbox{M}_{\rm ij} = \left[\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\frown$}} \over \Updelta } ^{2} \left| \mathop{{\overline{\hbox{S}}}}\limits^{\frown{}} \right|\mathop{{\overline{\hbox{S}_{\rm ij}}}}\limits^{\frown{}} -\Updelta^2 \mathop{{\left|\overline{\hbox{S}}\right|} \overline{\hbox{S}}_{\rm ij}}\limits^{\frown{}}\right]\) (m2/s2)


Pressure differential ratio (–)

S ij :

Strain tensor (1/s)

U d :

Droplet velocity (m/s)

V d :

Droplet diameter (m3)

X d :

Droplet coordinate (m)

Z :

Axial distance from the top wall (mm)


Cone angle (deg)


Viscosity (kg/ms)


Kinematic viscosity (m2/s2)


Density (kg/m3)


Stress tensor (N/m2)


Filter width (m)




Fluid phase (water)

i, j, k, l:

Coordination index


Time fluctuation quantity

\( \bar{} \) :

Filtered quantity

\( \frown{{}} \) :

Test filtered quantity


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Correspondence to Reza Maddahian.

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Saidi, M., Maddahian, R. & Farhanieh, B. Numerical investigation of cone angle effect on the flow field and separation efficiency of deoiling hydrocyclones. Heat Mass Transfer 49, 247–260 (2013). https://doi.org/10.1007/s00231-012-1085-8

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  • Large Eddy Simulation
  • Separation Efficiency
  • Tangential Velocity
  • Cone Angle
  • Recirculation Zone