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Transient Arc Discharge in Guided Copper Rails
Introduction
Unwanted arcing can have serious adverse effects on electrical and electronic equipment and systems. To improve the understanding and prediction of arc dynamics, it is crucial to conduct multiphysics simulations of transient arc processes. This model features a 3D simulation of transient arc discharge movement in guided copper rails, utilizing the Arc Discharge multiphysics interface based on a magnetohydrodynamics formulation. The simulated arc voltage and arc velocity show good agreement with experimental results.
Model Definition
Experiments
The experimental data are provided by associate professor Hengxin He from Huazhong University of Science and Technology (HUST). The experimental setup is shown in Figure 1, where an electric arc is generated and move along a copper rail. A thin wire connecting the upper and lower rail is installed to ignite the arc discharge. The measured voltage and current are recorded in the file data0400.txt. The arc root displacement is computed from the high-speed images and the data is stored in the file data0400x.txt.
Figure 1: Experimental setup.
Simulation
The Arc Discharge multiphysics interface is used to simulate the transient arc. To save computation time, a symmetry plan is assumed such that only half of the domain is modeled. The magnetohydrodynamics (MHD) model solved is given as
where the first equation is Ampère’s Law and the second is the current conservation equation. They are reformulated by the A–V formulation and solved by the Magnetic and Electric Fields interface. The third is the mass conservation equation and the forth is the momentum conservation equation. They are solved with the Laminar Flow interface. The last equation is the energy conservation equation solved by the Heat Transfer in Fluid interface. The coupling between electromagnetics and fluid flow is defined by the Magnetohydrodynamics multiphysics coupling feature. The coupling between electromagnetics and heat transfer is defined by the Equilibrium Discharge Heat Source multiphysics coupling feature.
Results and Discussion
Figure 2 shows the temperature distribution of the electric arc developed at t = 4 ms, where the arc reaches a maximum temperature of 20 kK.
Figure 3 and Figure 4 compare the simulated arc voltage and displacement, respectively, with experimental results. Overall, the simulated results are in good agreement with those from experiments.
Figure 2: LTE arc temperature.
Figure 3: Comparison of the simulated and measured arc voltages.
Figure 4: Comparison of the simulated and measured arc displacements.
Application Library path: Electric_Discharge_Module/Arc_Discharges/transient_arc_3d
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  3D.
2
In the Select Physics tree, select Electric Discharge > Arc Discharge.
3
Click Add.
4
Click  Study.
5
In the Select Study tree, select General Studies > Stationary.
6
Click  Done.
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
In the table, enter the following settings:
Name
Expression
Value
Description
L
200[mm]
0.2 m
Copper rail length
L_wire
20[mm]
0.02 m
Ignition wire position
r0
10[mm]
0.01 m
Electrode radius
gap
10[mm]
0.01 m
Rail gap
d0
5[mm]
0.005 m
Insulator thickness
ts_ms
0.4
0.4
Simulation start time in ms
t
ts_ms[ms]
4E-4 s
Time
Interpolation 1 (int1)
1
In the Home toolbar, click  Functions and choose Global > Interpolation.
2
In the Settings window for Interpolation, locate the Definition section.
3
In the Function name text field, type ic.
4
Click  Load from File.
5
Browse to the model’s Application Libraries folder and double-click the file ic400.txt.
6
Locate the Interpolation and Extrapolation section. From the Interpolation list, choose Piecewise cubic.
7
From the Extrapolation list, choose Linear.
8
Locate the Units section. In the Function table, enter the following settings:
Function
Unit
ic
A
9
In the Argument table, enter the following settings:
Argument
Unit
t
ms
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.
Work Plane 1 (wp1)
1
In the Geometry toolbar, click  Work Plane.
2
In the Settings window for Work Plane, locate the Plane Definition section.
3
From the Plane list, choose yz-plane.
Work Plane 1 (wp1) > Plane Geometry
In the Model Builder window, click Plane Geometry.
Work Plane 1 (wp1) > Rectangle 1 (r1)
1
In the Work Plane toolbar, click  Rectangle.
2
In the Settings window for Rectangle, locate the Size and Shape section.
3
In the Width text field, type r0*3.
4
In the Height text field, type (r0+d0+gap/2).
5
Locate the Position section. In the yw text field, type -(r0+d0+gap/2).
6
Click to expand the Layers section. In the table, enter the following settings:
Layer name
Thickness (mm)
Layer 1
d0
Work Plane 1 (wp1) > Circle 1 (c1)
1
In the Work Plane toolbar, click  Circle.
2
In the Settings window for Circle, locate the Size and Shape section.
3
In the Radius text field, type r0.
4
In the Sector angle text field, type 90.
5
Locate the Position section. In the yw text field, type -(r0+gap/2).
Work Plane 1 (wp1) > Mirror 1 (mir1)
1
In the Work Plane toolbar, click  Transforms and choose Mirror.
2
Click in the Graphics window and then press Ctrl+A to select both objects.
3
In the Settings window for Mirror, locate the Normal Vector to Line of Reflection section.
4
In the xw text field, type 0.
5
In the yw text field, type 1.
6
In the Work Plane toolbar, click  Build All.
7
In the Model Builder window, click Mirror 1 (mir1).
8
Locate the Input section. Select the Keep input objects checkbox.
9
In the Work Plane toolbar, click  Build All.
10
Click the  Zoom Extents button in the Graphics toolbar.
Extrude 1 (ext1)
1
In the Model Builder window, right-click Geometry 1 and choose Extrude.
2
In the Settings window for Extrude, locate the Distances section.
3
In the table, enter the following settings:
Distances (mm)
L
4
Click  Build All Objects.
5
Click the  Go to Default View button in the Graphics toolbar.
Work Plane 2 (wp2)
1
In the Geometry toolbar, click  Work Plane.
2
In the Settings window for Work Plane, locate the Plane Definition section.
3
From the Plane list, choose zx-plane.
Work Plane 2 (wp2) > Plane Geometry
In the Model Builder window, click Plane Geometry.
Work Plane 2 (wp2) > Circle 1 (c1)
1
In the Work Plane toolbar, click  Circle.
2
In the Settings window for Circle, locate the Size and Shape section.
3
In the Radius text field, type 1[m].
4
In the Sector angle text field, type 180.
5
Click to expand the Layers section. In the table, enter the following settings:
Layer name
Thickness (mm)
Layer 1
0.2[m]
Revolve 1 (rev1)
1
In the Model Builder window, right-click Geometry 1 and choose Revolve.
2
In the Settings window for Revolve, locate the Revolution Angles section.
3
Click the Angles button.
4
In the End angle text field, type 90.
5
Locate the Revolution Axis section. Find the Direction of revolution axis subsection. In the xw text field, type 1.
6
In the yw text field, type 0.
7
Click  Build All Objects.
Form Union (fin)
1
In the Geometry toolbar, click  Build All.
2
Click the  Go to Default View button in the Graphics toolbar.
Definitions
Infinite Element Domain 1 (ie1)
1
In the Model Builder window, expand the Component 1 (comp1) > Definitions node.
2
Right-click Definitions and choose Infinite Element Domain.
3
Select Domains 1 and 9 only.
4
In the Settings window for Infinite Element Domain, locate the Geometry section.
5
From the Type list, choose Spherical.
Hide for Physics 1
1
In the Model Builder window, right-click View 1 and choose Hide for Physics.
2
Select Domains 1, 2, and 9 only.
Define a terminal boundary for the input current. Note that the input current should be half of the total current because the model only solves for half of the geometry, assuming symmetry.
Magnetic and Electric Fields (mef)
Magnetic Insulation 1
In the Model Builder window, under Component 1 (comp1) > Magnetic and Electric Fields (mef) click Magnetic Insulation 1.
Boundary Terminal 1
1
In the Physics toolbar, click  Attributes and choose Boundary Terminal.
2
Click the  Go to Default View button in the Graphics toolbar.
3
Select Boundary 19 only.
4
In the Settings window for Boundary Terminal, locate the Terminal section.
5
In the I0 text field, type ic(t)/2.
Magnetic Insulation 1
In the Model Builder window, click Magnetic Insulation 1.
Electric Insulation 1
1
In the Physics toolbar, click  Attributes and choose Electric Insulation.
2
Select Boundaries 1, 3, 4, 7, 13, 16, 22, 26, and 29 only.
Perfect Magnetic Conductor 1
1
In the Physics toolbar, click  Boundaries and choose Perfect Magnetic Conductor.
2
Select Boundaries 2, 5, 8, 11, 14, 17, 20, 23, and 27 only.
3
In the Settings window for Perfect Magnetic Conductor, locate the Boundary Selection section.
4
Click  Create Selection.
5
In the Create Selection dialog, type Symmetry for EM in the Selection name text field.
6
Click OK.
Heat Transfer in Fluids (ht)
1
In the Model Builder window, under Component 1 (comp1) click Heat Transfer in Fluids (ht).
2
Select Domains 5 and 6 only.
Outflow 1
1
In the Physics toolbar, click  Boundaries and choose Outflow.
2
Select Boundaries 13, 16, 33, 34, 39, and 40 only.
3
In the Settings window for Outflow, locate the Boundary Selection section.
4
Click  Create Selection.
5
In the Create Selection dialog, type Outflow in the Selection name text field.
6
Click OK.
Symmetry 1
1
In the Physics toolbar, click  Boundaries and choose Symmetry.
2
Select Boundaries 14 and 17 only.
3
In the Settings window for Symmetry, locate the Boundary Selection section.
4
Click  Create Selection.
5
In the Create Selection dialog, type Symmetry for Heat and Flow in the Selection name text field.
6
Click OK.
Definitions
Variables 1
1
In the Model Builder window, under Component 1 (comp1) right-click Definitions and choose Variables.
2
In the Settings window for Variables, locate the Variables section.
3
In the table, enter the following settings:
Name
Expression
Unit
Description
T0
15e3[K]*exp(-((x-L_wire)/1.5[mm])^2-((y-0[mm])/1[mm])^2)+293.15[K]
K
Initial temperature
Heat Transfer in Fluids (ht)
Initial Values 1
1
In the Model Builder window, under Component 1 (comp1) > Heat Transfer in Fluids (ht) click Initial Values 1.
2
In the Settings window for Initial Values, locate the Initial Values section.
3
In the T text field, type T0.
Heat Flux 1
1
In the Physics toolbar, click  Boundaries and choose Heat Flux.
2
Select Boundaries 15, 21, 30, and 31 only.
3
In the Settings window for Heat Flux, locate the Boundary Selection section.
4
Click  Create Selection.
5
In the Create Selection dialog, type Wall in the Selection name text field.
6
Click OK.
7
In the Settings window for Heat Flux, locate the Heat Flux section.
8
From the Flux type list, choose Convective heat flux.
9
In the h text field, type 600.
Laminar Flow (spf)
1
In the Model Builder window, under Component 1 (comp1) click Laminar Flow (spf).
2
Select Domains 5 and 6 only.
Outlet 1
1
In the Physics toolbar, click  Boundaries and choose Outlet.
2
In the Settings window for Outlet, locate the Boundary Selection section.
3
From the Selection list, choose Outflow.
Symmetry 1
1
In the Physics toolbar, click  Boundaries and choose Symmetry.
2
In the Settings window for Symmetry, locate the Boundary Selection section.
3
From the Selection list, choose Symmetry for Heat and Flow.
Materials
Copper Rail
1
In the Model Builder window, under Component 1 (comp1) right-click Materials and choose Blank Material.
2
Select Domains 4 and 7 only.
3
In the Settings window for Material, type Copper Rail in the Label text field.
4
Locate the Material Contents section. In the table, enter the following settings:
Property
Variable
Value
Unit
Property group
Relative permeability
mur_iso ; murii = mur_iso, murij = 0
1
1
Basic
Electric conductivity
sigma_iso ; sigmaii = sigma_iso, sigmaij = 0
1e7[S/m]
S/m
Basic
Relative permittivity
epsilonr_iso ; epsilonrii = epsilonr_iso, epsilonrij = 0
1
1
Basic
Insulator
1
Right-click Materials and choose Blank Material.
2
Select Domains 3 and 8 only.
3
In the Settings window for Material, type Insulator in the Label text field.
4
Locate the Material Contents section. In the table, enter the following settings:
Property
Variable
Value
Unit
Property group
Relative permeability
mur_iso ; murii = mur_iso, murij = 0
1
1
Basic
Electric conductivity
sigma_iso ; sigmaii = sigma_iso, sigmaij = 0
1e-3
S/m
Basic
Relative permittivity
epsilonr_iso ; epsilonrii = epsilonr_iso, epsilonrij = 0
1
1
Basic
Add Material
1
In the Materials toolbar, click  Add Material to open the Add Material window.
2
Go to the Add Material window.
3
In the tree, select Equilibrium Discharge > Air (1[atm]).
4
Right-click and choose Add to Component 1 (comp1).
5
In the Materials toolbar, click  Add Material to close the Add Material window.
Materials
Air (1[atm]) (mat3)
Select Domains 1, 2, 5, 6, and 9 only.
Mesh 1
1
In the Model Builder window, under Component 1 (comp1) click Mesh 1.
2
In the Settings window for Mesh, locate the Physics-Controlled Mesh section.
3
In the table, clear the Use checkboxes for Geometric Analysis, Detail Size, Magnetic and Electric Fields (mef), Heat Transfer in Fluids (ht), Laminar Flow (spf), Equilibrium Discharge Heat Source 1 (phs1), and Magnetohydrodynamics 1 (mhd1).
4
Click  Build All.
5
Locate the Sequence Type section. From the list, choose User-controlled mesh.
Free Tetrahedral 1
1
In the Model Builder window, under Component 1 (comp1) > Mesh 1 click Free Tetrahedral 1.
2
In the Settings window for Free Tetrahedral, locate the Domain Selection section.
3
From the Geometric entity level list, choose Domain.
4
Click  Clear Selection.
5
Click  Paste Selection.
6
In the Paste Selection dialog, type 2-8 in the Selection text field.
7
Click OK.
Size 1
1
Right-click Free Tetrahedral 1 and choose Size.
A coarse mesh was used here to save computation time. It is always good to refine the mesh later to ensure that the results do not change significantly.
2
In the Settings window for Size, locate the Geometric Entity Selection section.
3
From the Geometric entity level list, choose Edge.
4
Select Edges 15 and 21 only.
5
Locate the Element Size section. Click the Custom button.
6
Locate the Element Size Parameters section.
7
Select the Maximum element size checkbox. In the associated text field, type 0.6.
Size 2
1
Right-click Free Tetrahedral 1 and choose Size.
2
In the Settings window for Size, locate the Geometric Entity Selection section.
3
From the Geometric entity level list, choose Boundary.
4
Select Boundaries 14 and 17 only.
5
Locate the Element Size section. Click the Custom button.
6
Locate the Element Size Parameters section.
7
Select the Maximum element size checkbox. In the associated text field, type 0.9.
Size 3
1
Right-click Free Tetrahedral 1 and choose Size.
2
Select Domains 5 and 6 only.
3
In the Settings window for Size, locate the Element Size section.
4
Click the Custom button.
5
Locate the Element Size Parameters section.
6
Select the Maximum element size checkbox. In the associated text field, type 10.
7
Select the Maximum element growth rate checkbox. In the associated text field, type 1.15.
Swept 1
1
In the Mesh toolbar, click  Swept.
2
In the Settings window for Swept, locate the Domain Selection section.
3
From the Geometric entity level list, choose Domain.
4
Click  Paste Selection.
5
In the Paste Selection dialog, type 1,9 in the Selection text field.
6
Click OK.
Distribution 1
1
Right-click Swept 1 and choose Distribution.
2
In the Settings window for Distribution, locate the Distribution section.
3
In the Number of elements text field, type 3.
4
Click  Build All.
5
Click the  Go to Default View button in the Graphics toolbar.
Study 1
Step 1: Stationary
1
In the Model Builder window, under Study 1 click Step 1: Stationary.
2
In the Settings window for Stationary, locate the Physics and Variables Selection section.
3
In the Solve for column of the table, under Component 1 (comp1), clear the checkboxes for Heat Transfer in Fluids (ht) and Laminar Flow (spf).
4
In the Solve for column of the table, under Component 1 (comp1) > Multiphysics, clear the checkboxes for Equilibrium Discharge Heat Source 1 (phs1) and Magnetohydrodynamics 1 (mhd1).
Step 2: Time Dependent
1
In the Study toolbar, click  Time Dependent.
2
In the Settings window for Time Dependent, locate the Study Settings section.
3
From the Time unit list, choose ms.
4
In the Output times text field, type range(ts_ms,0.2,4).
Solution 1 (sol1)
1
In the Study toolbar, click  Show Default Solver.
In order to save computational memory, an iterative solver is used here.
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 > Iterative 1 node.
4
In the Model Builder window, expand the Study 1 > Solver Configurations > Solution 1 (sol1) > Time-Dependent Solver 1 > Segregated 1 node, then click Study 1 > Solver Configurations > Solution 1 (sol1) > Time-Dependent Solver 1.
5
In the Settings window for Time-Dependent Solver, click to expand the Time Stepping section.
6
Select the Initial step checkbox. In the associated text field, type 0.1[us].
7
From the Maximum step constraint list, choose Constant.
8
In the Maximum step text field, type 2[us].
9
In the Model Builder window, under Study 1 > Solver Configurations > Solution 1 (sol1) > Time-Dependent Solver 1 click Segregated 1.
10
In the Settings window for Segregated, locate the General section.
11
In the Tolerance factor text field, type 1.
12
In the Model Builder window, under Study 1 > Solver Configurations > Solution 1 (sol1) > Time-Dependent Solver 1 > Segregated 1 right-click Velocity u, Pressure p and choose Delete.
13
In the Model Builder window, under Study 1 > Solver Configurations > Solution 1 (sol1) > Time-Dependent Solver 1 > Segregated 1 click Temperature.
14
In the Settings window for Segregated Step, type Fluid & Heat in the Label text field.
15
Locate the General section. Under Variables, click  Add.
16
In the Add dialog, in the Variables list, choose Pressure (comp1.p) and Velocity Field (comp1.u).
17
Click OK.
18
In the Settings window for Segregated Step, locate the General section.
19
From the Linear solver list, choose AMG, fluid flow variables (spf).
20
Click to expand the Method and Termination section. In the Model Builder window, under Study 1 > Solver Configurations > Solution 1 (sol1) > Time-Dependent Solver 1 > Segregated 1 click Magnetic and Electric Fields.
21
In the Settings window for Segregated Step, locate the Method and Termination section.
22
From the Jacobian update list, choose Once per time step.
23
In the Model Builder window, under Study 1 > Solver Configurations > Solution 1 (sol1) right-click Time-Dependent Solver 1 and choose Iterative.
24
Expand the Study 1 > Solver Configurations > Solution 1 (sol1) > Time-Dependent Solver 1 > Iterative 2 node.
25
Right-click Study 1 > Solver Configurations > Solution 1 (sol1) > Time-Dependent Solver 1 > Iterative 2 and choose Multigrid.
26
In the Settings window for Multigrid, locate the General section.
27
From the Solver list, choose Algebraic multigrid.
28
Click to expand the Hybridization section. From the Use as list, choose Multi preconditioner.
29
In the Preconditioner variables list, choose Pressure (comp1.p), Temperature (comp1.T), Velocity Field (comp1.u), Electric Potential (comp1.V), and Terminal Voltage (comp1.mef.mi1.term1.V0_ode).
30
Under Preconditioner variables, click  Delete.
31
Right-click Iterative 2 and choose Direct Preconditioner.
32
In the Settings window for Direct Preconditioner, locate the General section.
33
From the Solver list, choose PARDISO.
34
Click to expand the Hybridization section. In the Preconditioner variables list, choose Magnetic Vector Potential (comp1.A), Pressure (comp1.p), Temperature (comp1.T), and Velocity Field (comp1.u).
35
Under Preconditioner variables, click  Delete.
36
In the Model Builder window, under Study 1 > Solver Configurations > Solution 1 (sol1) > Time-Dependent Solver 1 > Segregated 1 click Magnetic and Electric Fields.
37
In the Settings window for Segregated Step, locate the General section.
38
From the Linear solver list, choose Iterative 2.
39
In the Study toolbar, click  Compute.
Results
Streamline Multislice 1
1
In the Model Builder window, expand the Results > Magnetic Flux Density (mef) node.
2
Right-click Streamline Multislice 1 and choose Delete.
Temperature (ht)
1
In the Model Builder window, under Results click Temperature (ht).
2
In the Settings window for 3D Plot Group, locate the Color Legend section.
3
Select the Show maximum and minimum values checkbox.
4
Locate the Plot Settings section. Clear the Plot dataset edges checkbox.
5
In the Temperature (ht) toolbar, click  Plot.
6
Click the  Zoom Extents button in the Graphics toolbar.
Table 1
1
In the Results toolbar, click  Table.
2
In the Settings window for Table, locate the Data section.
3
Click  Import.
4
Browse to the model’s Application Libraries folder and double-click the file data0400.txt.
Table 2
1
In the Results toolbar, click  Table.
2
In the Settings window for Table, locate the Data section.
3
Click  Import.
4
Browse to the model’s Application Libraries folder and double-click the file data0400x.txt.
Current and Voltage
1
In the Results toolbar, click  1D Plot Group.
2
In the Settings window for 1D Plot Group, type Current and Voltage in the Label text field.
3
Locate the Plot Settings section. Select the Two y-axes checkbox.
Table Graph 1
1
Right-click Current and Voltage and choose Table Graph.
2
In the Settings window for Table Graph, locate the Data section.
3
From the Plot columns list, choose Manual.
4
In the Columns list box, select I (A).
5
Click to expand the Legends section. Select the Show legends checkbox.
6
In the Current and Voltage toolbar, click  Plot.
7
From the Legends list, choose Manual.
8
In the table, enter the following settings:
Legends
I (A), experiments
Table Graph 2
1
Right-click Table Graph 1 and choose Duplicate.
2
In the Settings window for Table Graph, locate the Data section.
3
In the Columns list box, select V (V).
4
Locate the y-Axis section. Select the Plot on secondary y-axis checkbox.
5
Locate the Legends section. In the table, enter the following settings:
Legends
V (V), experiments
Global 1
1
In the Model Builder window, right-click Current and Voltage and choose Global.
2
In the Settings window for Global, locate the Data section.
3
From the Dataset list, choose Study 1/Solution 1 (sol1).
4
Locate the y-Axis Data section. In the table, enter the following settings:
Expression
Unit
Description
comp1.mef.I0_1*2
A
 
5
Click to expand the Coloring and Style section. Find the Line markers subsection. From the Marker list, choose Cycle.
6
From the Positioning list, choose Interpolated.
Global 2
1
Right-click Global 1 and choose Duplicate.
2
In the Settings window for Global, locate the y-Axis Data section.
3
In the table, enter the following settings:
Expression
Unit
Description
comp1.mef.V0_1
V
Terminal voltage
4
Locate the y-Axis section. Select the Plot on secondary y-axis checkbox.
Current and Voltage
1
In the Model Builder window, click Current and Voltage.
2
In the Settings window for 1D Plot Group, locate the Plot Settings section.
3
Select the x-axis label checkbox. In the associated text field, type Time, ms.
4
Select the y-axis label checkbox. In the associated text field, type Current, A.
5
Select the Secondary y-axis label checkbox. In the associated text field, type Voltage, V.
6
Locate the Axis section. Select the Manual axis limits checkbox.
7
In the x minimum text field, type 0.
8
In the x maximum text field, type 4.
9
In the y minimum text field, type 0.
10
In the y maximum text field, type 900.
11
In the Secondary y minimum text field, type 0.
12
In the Secondary y maximum text field, type 90.
13
In the Current and Voltage toolbar, click  Plot.
Definitions
Maximum 1 (maxop1)
1
In the Definitions toolbar, click  Nonlocal Couplings and choose Maximum.
2
In the Settings window for Maximum, locate the Source Selection section.
3
From the Geometric entity level list, choose Edge.
4
Select Edge 21 only.
Maximum 2 (maxop2)
1
In the Definitions toolbar, click  Nonlocal Couplings and choose Maximum.
2
In the Settings window for Maximum, locate the Source Selection section.
3
From the Geometric entity level list, choose Edge.
4
Select Edge 15 only.
Variables 1
1
In the Model Builder window, click Variables 1.
2
In the Settings window for Variables, locate the Variables section.
3
In the table, enter the following settings:
Name
Expression
Unit
Description
disp_a
maxop1(x*(T==maxop1(T)))-L_wire
m
Simulated arc displacement (anode)
disp_c
maxop2(x*(T==maxop2(T)))-L_wire
m
Simulated arc displacement (cathode)
Study 1
In the Study toolbar, click  Update Solution.
Results
Arc Root Displacement
1
In the Results toolbar, click  1D Plot Group.
2
In the Settings window for 1D Plot Group, type Arc Root Displacement in the Label text field.
Table Graph 1
1
Right-click Arc Root Displacement and choose Table Graph.
2
In the Settings window for Table Graph, locate the Data section.
3
From the Table list, choose Table 2.
4
Locate the Legends section. Select the Show legends checkbox.
5
In the Arc Root Displacement toolbar, click  Plot.
6
From the Legends list, choose Manual.
7
In the table, enter the following settings:
Legends
Experiments (anode)
Experiments (cathode)
Global 1
1
In the Model Builder window, right-click Arc Root Displacement and choose Global.
2
In the Settings window for Global, locate the y-Axis Data section.
3
In the table, enter the following settings:
Expression
Unit
Description
comp1.disp_a
mm
Simulated arc displacement (anode)
comp1.disp_c
mm
Simulated arc displacement (cathode)
4
Locate the Coloring and Style section. Find the Line markers subsection. From the Marker list, choose Cycle.
5
From the Positioning list, choose Interpolated.
Arc Root Displacement
1
In the Model Builder window, click Arc Root Displacement.
2
In the Settings window for 1D Plot Group, locate the Legend section.
3
From the Position list, choose Lower right.
4
Locate the Plot Settings section.
5
Select the x-axis label checkbox. In the associated text field, type Time, ms.
6
Select the y-axis label checkbox. In the associated text field, type Arc root displacement, mm.
7
Locate the Axis section. Select the Manual axis limits checkbox.
8
In the x minimum text field, type 0.
9
In the x maximum text field, type 4.
10
In the y minimum text field, type -10.
11
In the y maximum text field, type 180.
12
Locate the Legend section. From the Position list, choose Upper left.
13
In the Arc Root Displacement toolbar, click  Plot.