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Inductively Coupled Plasma (ICP) Torch
Introduction
Thermal plasmas have nowadays a large range of industrial applications including cutting, welding, spraying, waste destruction, and surface treatment. Thermal plasmas are assumed to be under partial to complete local thermodynamic equilibrium (LTE) conditions. Under LTE, the plasma can be considered a conductive fluid mixture and therefore, be modeled using the magnetohydrodynamics (MHD) equations. This model shows how to use the Equilibrium Discharges, Out-of-Plane Currents interface (available in 2D and 2D axisymmetric) to simulate the plasma generated in an inductively coupled plasma torch.
Figure 1 displays the geometry of the to-be-modeled inductive plasma torch.
Figure 1: Geometry of an inductively coupled plasma torch. The torch is composed of three concentric quartz tubes in which gas are injected from the bottom and exit from the top the torch. In this model, a fixed power of 11 kW is transferred to the plasma by a three-turn coil operating at 3MHz.
Note: This application requires the Plasma Module and AC/DC Module.
Model Definition
This model is based on the work presented in Ref. 1 and uses the following assumptions:
•
The plasma torch is modeled by a fully axisymmetric configuration.
•
The current inside the plasma is dominated by the induced current which is out-of-plane, that is, in the azimuth direction.
•
The coil consists of parallel current carrying rings with a circle cross section, 6 mm in diameter. This implies neglecting the axial component of the coil current.
•
Steady state, laminar pure argon plasma flow at atmospheric pressure.
•
Optically thin plasma under local thermodynamic equilibrium (LTE) conditions.
Figure 2 shows the geometry of the model.
Figure 2: Schematic of the ICP torch. Flow enters from the base (v1, v2 and v3) and leaves out the top. The dimensions of the different part of the model are given in the Modeling Instructions section.
In this model excitation is provided to a three turns coil at 3 MHz. The gas flowing in the sheath tube (plasma confinement tube) is then ionized by Joule heating.
The model is solved using a frequency-stationary study in combination with a single turn coil feature which set a fixed power to the system (11 kW). By fixing the power, the current and electric potential can vary in the coil as the plasma electrical conductivity builds up.
In this model the three different gas stream velocities (v1 for the carrier tube, v2 for the central tube and v3 for the sheath tube) are composed of pure argon. The temperature-dependent physical properties of argon are loaded from the material library under Equilibrium Discharge. Note that the temperature range of the physical properties span from 500 K to 25,000K. Note also that a minimum electrical conductivity of 1 S/m is used for numerical stability reasons.
If the initial temperature is too low chances are that the solution found corresponds to a flat profile of the minimum electrical conductivity (the default is 1 S/m). This is obviously a solution without interest and in fact it is the easiest solution to obtain. To avoid this start at an higher temperature closer to the experimental value as it is done in the present example. Always make sure to plot the conductivity to see if it is set to the minimum electrical conductivity.
Results and Discussion
Figure 3 and Figure 4, respectively, shows the plasma temperature distribution and velocity magnitude of the argon plasma. The temperature peaks near the coils to a value of 10,000 K. The plasma conductivity increases with the temperature and it has a maximum in the regions of maximum temperature as shown in Figure 5 where the electrical conductivity of the plasma is plotted. Figure 6 displays the magnetic flux norm. Note that the electrical conductivity of the plasma screens the magnetic flux as a consequence of the skin effect.
Figure 3: Surface plot of the LTE plasma temperature.
Figure 4: Plot of the velocity magnitude.
Figure 5: Plot of the plasma electrical conductivity.
Figure 6: Norm of the magnetic flux. Note the effect of the resistivity on the penetration of the field (skin effect).
Reference
1. S. Xue, P. Proulx, and M.I. Boulos, “Extended-field electromagnetic model for inductively coupled plasma,” J. Phys. D. 34, 1897, 2001.
Application Library path: Plasma_Module/Equilibrium_Discharges/icp_torch
Modeling Instructions
From the File menu, choose New.
New
In the New window, click  Model Wizard.
Model Wizard
1
In the Model Wizard window, click  2D Axisymmetric.
2
In the Select Physics tree, select Plasma>Equilibrium Discharges>Equilibrium Discharges, Out-of-Plane Currents.
3
Click Add.
4
Click  Study.
5
In the Select Study tree, select Preset Studies for Selected Multiphysics>Frequency-Stationary.
6
Click  Done.
Root
Select the mm units.
Geometry 1
1
In the Model Builder window, under Component 1 (comp1) click Geometry 1.
2
In the Settings window for Geometry, locate the Units section.
3
From the Length unit list, choose mm.
Global Definitions
Parameters 1
1
In the Model Builder window, under Global Definitions click Parameters 1.
2
In the Settings window for Parameters, locate the Parameters section.
3
Click  Load from File.
4
Browse to the model’s Application Libraries folder and double-click the file icp_torch_parameters.txt.
Define the computational domain.
Geometry 1
Rectangle 1 (r1)
1
In the Geometry toolbar, click  Rectangle.
2
In the Settings window for Rectangle, locate the Size and Shape section.
3
In the Width text field, type r_3.
4
In the Height text field, type L_3.
Define the carrier tube.
Rectangle 2 (r2)
1
In the Geometry toolbar, click  Rectangle.
2
In the Settings window for Rectangle, locate the Size and Shape section.
3
In the Width text field, type d_1.
4
In the Height text field, type L_0.
5
Locate the Position section. In the r text field, type r_1.
Define the central tube.
Rectangle 3 (r3)
1
In the Geometry toolbar, click  Rectangle.
2
In the Settings window for Rectangle, locate the Size and Shape section.
3
In the Width text field, type d_2.
4
In the Height text field, type L_0.
5
Locate the Position section. In the r text field, type r_2.
Define the tube.
Rectangle 4 (r4)
1
In the Geometry toolbar, click  Rectangle.
2
In the Settings window for Rectangle, locate the Size and Shape section.
3
In the Width text field, type d_3.
4
In the Height text field, type L_3.
5
Locate the Position section. In the r text field, type r_0.
Define the coils.
Circle 1 (c1)
1
In the Geometry toolbar, click  Circle.
2
In the Settings window for Circle, locate the Size and Shape section.
3
In the Radius text field, type d_c/2.
4
Locate the Position section. In the r text field, type r_c.
5
In the z text field, type L_1.
Circle 2 (c2)
1
In the Geometry toolbar, click  Circle.
2
In the Settings window for Circle, locate the Size and Shape section.
3
In the Radius text field, type d_c/2.
4
Locate the Position section. In the r text field, type r_c.
5
In the z text field, type (L_1+L_2)/2.
Circle 3 (c3)
1
In the Geometry toolbar, click  Circle.
2
In the Settings window for Circle, locate the Size and Shape section.
3
In the Radius text field, type d_c/2.
4
Locate the Position section. In the r text field, type r_c.
5
In the z text field, type L_2.
6
Click  Build All Objects.
Define the different domain type for easy selection.
Definitions
Air
1
In the Definitions toolbar, click  Explicit.
2
In the Settings window for Explicit, type Air in the Label text field.
3
Select Domain 5 only.
Plasma
1
In the Definitions toolbar, click  Explicit.
2
In the Settings window for Explicit, type Plasma in the Label text field.
3
Select Domain 1 only.
Quartz
1
In the Definitions toolbar, click  Explicit.
2
In the Settings window for Explicit, type Quartz in the Label text field.
3
Select Domains 2–4 only.
Coils
1
In the Definitions toolbar, click  Explicit.
2
In the Settings window for Explicit, type Coils in the Label text field.
3
Select Domains 6–8 only.
Add the different materials used in the model using the material library.
Add Material
1
In the Home toolbar, click  Add Material to open the Add Material window.
2
Go to the Add Material window.
3
In the tree, select Built-in>Air.
4
Click Add to Component in the window toolbar.
5
In the tree, select AC/DC>Copper.
6
Click Add to Component in the window toolbar.
7
In the tree, select AC/DC>Quartz.
8
Click Add to Component in the window toolbar.
9
In the tree, select Equilibrium Discharge>Argon.
10
Click Add to Component in the window toolbar.
11
In the Home toolbar, click  Add Material to close the Add Material window.
Materials
Air (mat1)
1
In the Model Builder window, under Component 1 (comp1)>Materials click Air (mat1).
2
In the Settings window for Material, locate the Geometric Entity Selection section.
3
From the Selection list, choose Air.
Copper (mat2)
1
In the Model Builder window, click Copper (mat2).
2
In the Settings window for Material, locate the Geometric Entity Selection section.
3
From the Selection list, choose Coils.
Quartz (mat3)
1
In the Model Builder window, click Quartz (mat3).
2
In the Settings window for Material, locate the Geometric Entity Selection section.
3
From the Selection list, choose Quartz.
Argon (mat4)
1
In the Model Builder window, click Argon (mat4).
2
In the Settings window for Material, locate the Geometric Entity Selection section.
3
From the Selection list, choose Plasma.
Adjust the selection and features of each physics composing the model.
The magnetic field interface is used over the whole computational domain. The Single conductor Coil feature is used here to transfer the excitation power to the plasma.
Magnetic Fields (mf)
1
In the Model Builder window, under Component 1 (comp1) click Magnetic Fields (mf).
2
In the Settings window for Magnetic Fields, click to expand the Discretization section.
3
From the Magnetic vector potential list, choose Linear.
Coil 1
1
In the Physics toolbar, click  Domains and choose Coil.
2
In the Settings window for Coil, locate the Domain Selection section.
3
From the Selection list, choose Coils.
4
Locate the Coil section. Select the Coil group check box.
5
From the Coil excitation list, choose Power.
6
In the Pcoil text field, type Pext.
The heat transfer in the air is neglected in this model.
Heat Transfer in Fluids (ht)
1
In the Model Builder window, under Component 1 (comp1) click Heat Transfer in Fluids (ht).
2
Select Domains 1 and 4 only.
Solid 1
1
In the Physics toolbar, click  Domains and choose Solid.
2
Select Domain 4 only.
Initial Values 1
It is important to start with an high temperature.
1
In the Model Builder window, click Initial Values 1.
2
In the Settings window for Initial Values, locate the Initial Values section.
3
In the T text field, type 6000.
Add a heat transfer in solids feature for the solid part of the heat transfer model (tubes and coils).
Temperature 1
1
In the Physics toolbar, click  Boundaries and choose Temperature.
2
Select Boundaries 2, 8, 13, 15, and 17 only.
3
In the Settings window for Temperature, locate the Temperature section.
4
In the T0 text field, type T0.
Outflow 1
1
In the Physics toolbar, click  Boundaries and choose Outflow.
2
Click the  Zoom Extents button in the Graphics toolbar.
3
Select Boundary 3 only.
The single phase flow is only applied to the plasma region.
Laminar Flow (spf)
Since the density variation is not small, the flow cannot be regarded as incompressible. Therefore set the flow to be weakly compressible.
1
In the Model Builder window, under Component 1 (comp1) click Laminar Flow (spf).
2
In the Settings window for Laminar Flow, locate the Physical Model section.
3
From the Compressibility list, choose Weakly compressible flow.
4
Locate the Domain Selection section. From the Selection list, choose Plasma.
5
Click to expand the Equation section. From the Equation form list, choose Stationary.
Inlet 1
1
In the Physics toolbar, click  Boundaries and choose Inlet.
Add the inlets with their proper velocities.
2
Select Boundary 2 only.
3
In the Settings window for Inlet, locate the Velocity section.
4
In the U0 text field, type v1.
Inlet 2
1
In the Physics toolbar, click  Boundaries and choose Inlet.
2
Select Boundary 8 only.
3
In the Settings window for Inlet, locate the Velocity section.
4
In the U0 text field, type v2.
Inlet 3
1
In the Physics toolbar, click  Boundaries and choose Inlet.
2
Select Boundary 13 only.
3
In the Settings window for Inlet, locate the Velocity section.
4
In the U0 text field, type v3.
Outlet 1
1
In the Physics toolbar, click  Boundaries and choose Outlet.
2
Select Boundary 3 only.
3
In the Settings window for Outlet, locate the Pressure Conditions section.
4
Clear the Suppress backflow check box.
Mesh 1
Size
In the Model Builder window, under Component 1 (comp1) right-click Mesh 1 and choose Edit Physics-Induced Sequence.
Size 1
1
In the Settings window for Size, locate the Element Size section.
2
From the Predefined list, choose Extra fine.
Edge 1
1
In the Mesh toolbar, click  Edge.
2
Drag and drop below Size.
3
Select Boundaries 2, 8, and 13 only.
Size 1
1
Right-click Edge 1 and choose Size.
2
In the Settings window for Size, locate the Element Size section.
3
Click the Custom button.
4
Click to collapse the Element Size Parameters section. Click to expand the Element Size Parameters section.
5
Select the Maximum element size check box. In the associated text field, type 0.5.
Size 2
1
In the Model Builder window, under Component 1 (comp1)>Mesh 1 click Size 2.
2
In the Settings window for Size, locate the Element Size section.
3
From the Predefined list, choose Extra fine.
Boundary Layers 2
1
In the Mesh toolbar, click  Boundary Layers.
2
Right-click Boundary Layers 2 and choose Move Up.
3
In the Settings window for Boundary Layers, locate the Domain Selection section.
4
From the Geometric entity level list, choose Domain.
5
Select Domains 6–8 only.
Boundary Layer Properties
1
In the Model Builder window, click Boundary Layer Properties.
2
Select Boundaries 21–32 only.
3
In the Settings window for Boundary Layer Properties, locate the Layers section.
4
In the Number of layers text field, type 4.
5
From the Thickness specification list, choose First layer.
6
In the Thickness text field, type 8[um].
7
Click  Build All.
For this case it is better to solve the equation fully coupled. Some settings in the solver need to be changed to increase stability.
Study 1
Step 1: Frequency-Stationary
1
In the Model Builder window, under Study 1 click Step 1: Frequency-Stationary.
2
In the Settings window for Frequency-Stationary, locate the Study Settings section.
3
In the Frequency text field, type f0.
Solution 1 (sol1)
1
In the Study toolbar, click  Show Default Solver.
2
In the Model Builder window, expand the Solution 1 (sol1) node.
3
In the Model Builder window, expand the Study 1>Solver Configurations>Solution 1 (sol1)>Stationary Solver 1 node.
4
Right-click Study 1>Solver Configurations>Solution 1 (sol1)>Stationary Solver 1 and choose Fully Coupled.
5
In the Settings window for Fully Coupled, click to expand the Method and Termination section.
6
In the Initial damping factor text field, type 1e-4.
7
In the Minimum damping factor text field, type 1.0E-6.
8
In the Restriction for step-size update text field, type 1.2.
9
In the Recovery damping factor text field, type 0.1.
10
In the Maximum number of iterations text field, type 200.
11
In the Study toolbar, click  Compute.
Results
Temperature, 2D
1
In the Home toolbar, click  Add Plot Group and choose 2D Plot Group.
2
In the Settings window for 2D Plot Group, type Temperature, 2D in the Label text field.
Surface 1
1
Right-click Temperature, 2D and choose Surface.
2
In the Settings window for Surface, locate the Expression section.
3
In the Expression text field, type T.
4
In the Temperature, 2D toolbar, click  Plot.
Temperature, 2D
In the Model Builder window, right-click Temperature, 2D and choose Move Up.
Conductivity
1
In the Home toolbar, click  Add Plot Group and choose 2D Plot Group.
2
In the Settings window for 2D Plot Group, type Conductivity in the Label text field.
Surface 1
1
Right-click Conductivity and choose Surface.
2
In the Settings window for Surface, locate the Expression section.
3
In the Expression text field, type mf.sigmarr.
Selection 1
1
Right-click Surface 1 and choose Selection.
2
Select Domain 1 only.
3
In the Conductivity toolbar, click  Plot.
Conductivity
In the Model Builder window, under Results right-click Conductivity and choose Move Up.