Flow in a Hydrocyclone

Cyclones are used in a variety of applications ranging from the mining industry to vacuum cleaners (Ref. 1). In the pulp and paper industry, hydrocyclones are used for contaminant removal, pulp thickening, and fiber fractionation. Most cyclones do not contain any moving parts, and the flow is hence entirely driven by the applied pressure drops between the inlet(s) and the two outlets. The forward stream in the process is referred to as the accept flow, whereas the discarded stream is referred to as the reject flow. Depending on the application, the accept outlet could either be the overflow located at the base of the cone, near the inlet(s), or the underflow near the apex of the cone. The former configuration is used for removal of heavy (compared to the carrier fluid) contaminants, whereas the latter is used for removal of light contaminants and in thickening processes. In fractionation processes the definition of accept and reject is more or less a matter of convenience since both streams are applied forward in the system.

Model Definition

The model geometry used in this application is shown in Figure 1.

Figure 1: Model geometry showing the inlets, overflow (here the accept outlet), and underflow (the reject outlet).

Two circular inlets are tangentially attached to the annular inlet chamber, which is separated from the overflow by a wall called the “vortex finder”. This design creates a strong swirl in the incoming flow. From the annular inlet chamber, the flow enters a conical chamber where the separation takes place. The conical shape preserves the angular momentum and stabilizes the vortex core — the central region of the swirl motion characterized by solid-body rotation. A portion of the flow is effluxed through the underflow near the apex of the conical separation chamber, and the rest exits through the overflow.

The flow in a hydrocyclone is characterized by a very strong swirl, which makes it difficult to simulate using an isotropic turbulence model. It is imperative that the swirl flow is accurately captured in order to assess the separation efficiency for various particles. The streamlines essentially follow the azimuthal direction whereas mixing of momentum by turbulent fluctuations takes place in the radial direction, which also happens to be the wall-normal direction in the major part of the hydrocyclone. This makes the v2-f turbulence model a good candidate for the prevailing flow conditions.

Stationary operating conditions corresponding to those of heavy contaminant removal are studied in this application. The flowing medium is pure water at 20ºC. The hydrocyclone is assumed to be pressurized and is hence operating without an air core. Initial values were chosen as zero velocity, zero pressure, and default values for the turbulence variables. No-slip conditions with automatic wall treatment were applied on all walls. At the two inlets the velocity is set to 5 m/s, and the turbulence conditions to isotropic with an intensity of 5% and a length scale of 0.07 times the inlet diameter are default settings. 5% of the flow exits through the underflow where a uniform velocity profile is specified. A constant pressure condition is applied at the overflow. The outlet conditions can be improved by attaching outlet chambers at both ends.

Results and Discussion

Figure 2 shows the streamlines for the swirling flow in the hydrocyclone.

Figure 2: Streamlines for the overflow (burgundy) and underflow (teal).

The streamlines describe the typical flow field encountered in hydrocyclone applications. From the inlet chamber, the flow is diverted toward the underflow. In this case, 95% of the incoming flow is reversed and exits through the overflow. This is illustrated by the burgundy streamlines in the core. The remainder (teal) stays closer to the wall and exits through the underflow.

The pressure drop and in-plane streamlines on two orthogonal cut planes through the hydrocyclone are displayed in Figure 3.

Figure 3: Pressure drop and in-plane streamlines in the xz- and yz-planes.

The two jets mix in the inlet chamber, resulting in azimuthal pressure variations on the vortex core. For certain hydrocyclone designs, this may cause the vortex core to destabilize resulting in poor separation performance. The optimal number and design of the inlet pipes, and the design of the inlet chamber, is an active research field. The pressure drop between the inlets and outlets is of the order 100 kPa. Figure 4 shows a contour surface displaying a vertical (stable) vortex core. The swirl flow in the hydrocyclone can be divided into an outer region, described by a semi-free vortex, and an inner region of solid body rotation.

Figure 4: Contour surface of the vortex core.

The graph in Figure 5 shows the azimuthal velocity component as a function of the radius at a vertical position 10 cm below the vortex finder. An inner core of solid-body rotation is clearly distinguishable from the outer semi-free vortex.

Figure 5: Azimuthal (swirl) velocity versus radius 10 cm below the vortex finder.

Notes About the COMSOL Implementation

The mesh is deliberately made coarse to reduce the computational time for this tutorial model. If the maximum size of the elements is reduced by thirty percent, the maximum swirl velocity in Figure 5 reaches 12 m/s.

Reference

1. D.Bradley, “The Hydrocyclone, 1st Edition, International Series of Monographs in Chemical Engineering,” Pergamon, 1965.

CFD_Module/Single-Phase_Flow/hydrocyclone

Modeling Instructions

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New

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Model Wizard

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In the tree, select .

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Global Definitions

Parameters 1

In the window, under click .

In the window for , locate the section.

In the table, enter the following settings:


Name	Expression	Value	Description
u_in	5[m/s]	5 m/s	Inlet velocity
r_in	0.0725[m]	0.0725 m	Inlet radius
r_out	0.07[m]	0.07 m	Reject radius
R_f	0.05	0.05	Reject volume fraction
u_out	R_f2(r_in/r_out)^2*u_in	0.53635 m/s	Reject velocity

Geometry 1

Work Plane 1 (wp1)

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In the window for , locate the section.

From the list, choose .

Work Plane 1 (wp1)>Plane Geometry

In the window, click .

Work Plane 1 (wp1)>Polygon 1 (pol1)

In the toolbar, click

In the window for , locate the section.

In the table, enter the following settings:


xw (m)	yw (m)
0.4	1
0.4	0.8
r_out	-1
0	-1
0	1.2
0.15	1.2
0.15	0.7
0.18	0.7
0.25	1
0.4	1

Click

Revolve 1 (rev1)

In the window, right-click and choose .

In the window for , locate the section.

Clear the check box.

Cylinder 1 (cyl1)

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In the window for , locate the section.

In the text field, type r_in.

In the text field, type 0.5.

Locate the section. In the text field, type 0.3215.

In the text field, type -0.5.

In the text field, type 0.9.

Locate the section. From the list, choose .

Cylinder 2 (cyl2)

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In the window for , locate the section.

In the text field, type r_in.

In the text field, type 0.5.

Locate the section. In the text field, type -0.3215.

In the text field, type 0.9.

Locate the section. From the list, choose .

In the toolbar, click

Form Composite Domains 1 (cmd1)

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and choose .

Use the virtual operation to remove the interior boundaries of the hydrocyclone. This reduces the amount of elements and thereby the memory consumption and computing time for this model.

On the object , select Domains 1–5 only.

In the window for , click

Add Material

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to open the window.

Go to the window.

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to close the window.

Turbulent Flow, v2-f (spf)

Inlet 1

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Select Boundaries 9 and 40 only, corresponding to the two inlets.

In the window for , locate the section.

In the U0 text field, type u_in.

The fully developed flow condition could be used as well to give a computed flow field for the inlet parameters. However, by doing so, the computing time would increase slightly. Thus, an analytic expression is used for the inlet parameters.

Outlet 1

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and choose .

Select Boundaries 20, 21, 29, and 30 only, corresponding to the reject outlet.

In the window for , locate the section.

From the list, choose .

Locate the section. In the U0 text field, type u_out.

Outlet 2

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Select Boundaries 18, 19, 28, and 31 only.

In the window for , locate the section.

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Mesh 1

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From the list, choose .

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Add Component

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Mesh 2

Import 1

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Click .

Browse to the model’s Application Libraries folder and double-click the file hydrocyclone_mesh.mphbin.

Click .

Mesh 1

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Copy 1

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Study 1

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Results

First, create datasets needed to produce Figure 2, Figure 3 and Figure 5.

Surface 2

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and choose .

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Click

In the dialog box, type 2, 4-17, 22-27, 32-42 in the text field.

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Edge 3D 1

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In the dialog box, type 1 2 4 5 7 9 10 11 12 13 14 16 17 18 19 21 23 24 25 27 28 29 31 32 34 35 36 37 38 39 40 41 42 43 45 47 49 55 58 59 61 63 65 66 72 73 74 75 78 80 81 82 in the text field.

Click .

Cut Plane 1

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