MOM 6.2.10

15.14.1.1. Benchmark Description

This document shows several examples for studying the thickness of a radome by using the parametric simulations. In particular, we are interested in studying the behavior of a radome with three layers, where the external ones are identical but the middle one has a different material and its thickness depends on the parameter t. This idea is shown in the bi-dimensional example of the figure below.

Layers

Figure 1: Parametric radome design.

 

It has been analyzed by using several radome shapes and also different excitation methods.

 

15.14.1.2. Setting-up common parameters

The table below resumes the common parameters taken into account in the following examples:

 

Data

Definition

Values

Frequency

Simulation frequency

5 GHz

Material 1

Dielectric constant of Material 1

4 - 0.08·j

Material 2

Dielectric constant of Material 2

1.1 - 0.0055·j

Thickness

Constant thickness of material 1

0.25 mm

t

Parametric thickness of material 2

3 , 3.5 , 4, 4.5, 5 mm

Units

Units for working in newFasant

Millimeters

 

Now, we set-up the parameters of this table within a project that will be copied and renamed for all the configurations shown.

 

1.      Create a new MOM project. To do that, click on New Project button and select the MOM module.

 

MoM Module

 

Figure 2: Choose the MOM module.

2. Set the units. Click on the current units and select Millimeters to make easier working with the thickness.

Units

Figure 3: Set units to Milimeters unit.

 

3. Set the frequency. Click on Simulation – Parameters menu and then the Simulation panel is open on right side of screen. Set the frequency to 5 GHz and click on Save button before closing the panel.

Simulation Parameters

Figure 4: Set the frequency to 5 GHz.

4. Define the materials. Click on Materials – Add menu and then the Add Material panel is open on right side of screen. Set the Name and Color of the materials to be defined, keep the default Material Definition option, that is Material defined by geometry, and then click on Set Parameters button to specify the dielectric values of each material (click on OK button within the Geometry Material window to confirm the dielectric constant assigned). Remember clicking on Save button after defining every material

 Define Material

Figure 5: Material 1 definition.

Define Material

Figure 6: Material 2 definition.

5. Define the parameters. Click on Geometry – Parameters – Define Parameters, and then the Define Parameters panel is open on right side of screen. Unless it is not necessary to add the thickness of the Material 1 as a parameter because it has a fixed value, we will define its parameter to create the geometry also as a full parametric model. To assign a fixed value to a parameter, the value must be inserted between “{ }” characters. The interesting parameter is the thickness of the Material 2, which we have named t, and it must be ranging between 3 and 5 millimeters. To assign a range of values to a parameter, the initial and end values are inserted between “[ ]” characters and separated by spaces, and then the number of samples must be specified. Remember click on Save button before closing this panel.

Define Parameters

Figure 7: Parameters definition.

6. Save the project. Click on File – Save As… menu and specify where you want to save this project, which will be used as base project for the next example. We have named it as baseProject.nfp. Then, for every example we will copy and rename this base project and only will have to set-up the antenna and the radome.

7. Solver parameters. Click on Solver – Parameters menu to open the Solver panel on right side. The only parameter to be modified in this document may be the Preconditioner one that may be enabled or disabled for speeding-up the solver convergence. Click on Advanced Options button to open the Solver Advanced Options window, then select the Preconditioner tab and enable or disable the option Enable Precontioner as desired.

Preconditioner Solver Options

 Figure 8: Preconditioner Solver options

15.14.1.3. Feeding with a circular horn

Create a copy of baseProject.nfp project and rename it as baseProjectHorn.nfp. Then open it with newFASANT by clicking on File – Open menu or clicking twice on the project icon.

Insert a conical horn by using the existing primitives. To do that, click on Source – Primitive Antenna – Horns – Conical Horn menu and then the Conical Horn panel is open on right side of screen. 

Conical Horn

Figure 9: Conical Horn menu.

The radomes will be placed on the origin of coordinates to make easier its geometrical definition, so the horn is created 10 centimeters below it on the Z axis. Keep the most of parameters in the Conical Horn panel by default except the Z-Position that must be set to -100. Click on Add button to insert the horn before closing the panel.

Conical Horn

Figure 10: Conical Horn definition.

Save the current project, as it will be used again as base project in the following subsections.

 

 

15.14.1.3.1. Square radome

Create a copy of baseProjectHorn.nfp project and rename it as Horn_Square.nfp. Then open it with newFASANT by clicking on File – Open menu or clicking twice on the project icon.

The radome considered in this section is a square of 50 centimeters of side with the base centered at the origin of coordinates.

 

15.14.1.3.1.1. Geometric design

Four square planes will be generated to model the radome as a thin layer approximation. It may be achieved by using the plane command, which requires the first corner (the lower one), the width (X size) and the depth (Y size). The table below shows the parameters to be used for every plane:

Plane

X (mm)

Y (mm)

Z (mm)

width (mm)

Depth (mm)

1

-250

-250

0

500

500

2

-250

-250

thickness

500

500

3

-250

-250

thickness+t

500

500

4

-250

-250

(2*thickness)+t

500

500

Command Line Planes Definition

Figure 11: Command line planes definition.

tree

 

Figure 12: List of geometric entities in the tree.

After creating the four planes, in the tree we can see that they have been added in order as Objects, and each one has a different name

 

15.14.1.3.1.2. Radome definition

Having defined the geometric model, the radome must be created and assigned. To do that, click on Source – Radome – Define Radome menu and the Radome panel is open on right side of screen. 

In the Radome panel, no radomes are created so click on Add Radome button to insert a new radome. Then, the table of interfaces of the selected radome (1) is loaded below. As we have shown in Figure 1, the radome is made of 4 interfaces that define the 3 layers, so click on New Interface button twice to get the 4 interfaces. 

Each plane must be assigned to every radome interface in the same order than specified in Figure 1. Remember that the normal vectors of every interface must be pointing to the next one. To assign a plane to an interface, select the geometrical object from the tree or in the Geometry panel, then select the corresponding row in the Interfaces table, and click on Set Objects button. Then, assign the Material to its interface, which is defined to the current layer.

The material (or layers) is considered between one interface and its next one, so the last interface does not required a material.

Remember clicking on Save button to confirm the radome definition.

Radome definition

Figure 13: Radome definition.

The next figure shows the final design of the radome with the horn, with the Material Shaded view. In this representation, we verify that the layers of the radome have the correct materials.

Shaded View

Figure 14: Shaded view with materials of the final design

15.14.1.3.1.3. Mesh and run

The only parameters modified in the meshing process are the number of Processors and the Multilevel Meshing Mode (click on Advanced Settings to open the Meshing Advanced Parameters window), which has been disabled. Click on OK and Mesh buttons to confirm the changes and mesh.

The five parametric steps are meshed by requiring about 4 GB of RAM memory and 10 seconds per step.

Click on Calculate – Execute menu and launch the simulation with 8 processors by clicking on Execute button.

The five parametric steps are simulated by requiring about 4 GB of RAM memory and 5 minutes per step.

Meshing parameters

Figure 15: Meshing parameters

15.14.1.3.1.4. Computational specifications

Step

1

2

3

4

5

Number of unknowns

43165

43165

43165

43165

43165

Required RAM (GB)

4.5

4.5

4.5

4.5

4.5

Without Preconditioner

Number of iterations

100

91

92

82

79

Simulation Time

(min : ss)

5 : 34

5 : 07

5 : 12

4 : 57

5 : 03

With Preconditioner

 

Number of iterations

23

24

23

22

22

Simulation Time

(min : ss)

3 : 42

3 : 39

3 : 36

3 : 40

3 : 31

15.14.1.3.1.5. Results
Radiation Pattern
  • Step 1
  • Step 2
  • Step 3
  • Step 4
  • Step 5
Current Density
  • Step 1
  • Step 2
  • Step 3
  • Step 4
  • Step 5
 
 
 

Step

1

2

3

4

5

Insertion Losses

(dB)

-0.006747

-0.028946

-0.000466

0.005269

0.007828

Radiated Power – Antenna (RPA)

(Watts)

0.00263137

Radiated Power with radome

(RPR)

(Watts)

0.00246143

0.0024529

0.00246828

0.00245143

0.00246245

RPA/RPR (dB)

0.579888591

0.61004152

0.5557499

0.61524845

0.57628996

 
Cut Phi0 Theta0
Figure 16: Cut Phi = 0 comparison - radome steps and isolated antenna
 
15.14.1.3.2. Semi spherical radome

Create a copy of baseProjectHorn.nfp project and rename it as Horn_SemiSphere.nfp. Then open it with newFASANT by clicking on File – Open menu or clicking twice on the project icon.

The radome considered in this section is a semisphere of 25 centimeters of radius with the base centered at the top of the horn.

 

15.14.1.3.2.1. Geometric design

Four semispheres will be generated to model the radome as a thin layer approximation. It may be achieved by using the sphere command, which requires both the center and the radius. The table below shows the parameters to be used for every sphere:

Sphere

X (mm)

Y (mm)

Z (mm)

Radius (mm)

1

0

0

-100

250

2

0

0

-100

250+thickness

3

0

0

-100

250+ thickness+t

4

0

0

-100

250+(2*thickness)+t

Note that the sphere command creates the full closed sphere and we need just the upper semisphere. Then, after creating each sphere, we use the explode command to separate it in several surfaces, then remove the lower semisphere with the delete command, and finally we use the group command on the upper remaining surfaces to have one object for every semisphere.

Commands Spheres

Figure 17: Command line semispheres definition.

After creating the four semispheres, in the tree we can see that they have been added in order as Objects, and each one has a different name. 

Figure 18: List of geometric entities in the tree.

15.14.1.3.2.2. Radome definition

Having defined the geometric model, the radome must be created and assigned. To do that, click on Source – Radome – Define Radome menu and the Radome panel is open on right side of screen. 

In the Radome panel, no radomes are created so click on Add Radome button to insert a new radome. Then, the table of interfaces of the selected radome (1) is loaded below. As we have shown in Figure 1, the radome is made of 4 interfaces that define the 3 layers, so click on New Interface button twice to get the 4 interfaces. 

Each semisphere must be assigned to every radome interface in the same order than specified in Figure 1. Remember that the normal vectors of every interface must be pointing to the next one. To assign a semisphere to an interface, select the geometrical object from the tree or in the Geometry panel, then select the corresponding row in the Interfaces table, and click on Set Objects button. Then, assign the Material to its interface, which is defined to the current layer.

The material (or layers) is considered between one interface and its next one, so the last interface does not required a material.

Remember clicking on Save button to confirm the radome definition.

Figure 19: Radome definition.

The next figure shows the final design of the radome with the horn, with the Material Shaded view. In this representation, we verify that the layers of the radome have the correct materials.

Figure 20: Shaded view with materials of the final design.

15.14.1.3.2.3. Mesh and run

The only parameter modified in the meshing process is the number of Processors, which is set to 8. Specify the number of processors and click on Mesh buttons to confirm the changes and mesh.

The five parametric steps are meshed by requiring about 4 GB of RAM memory and 10 seconds per step.

Click on Calculate – Execute menu and launch the simulation with 8 processors by clicking on Execute button.

The five parametric steps are simulated by requiring about 4.5 GB of RAM memory and 10 seconds per step.

 

15.14.1.3.2.4. Computational specifications

Step

1

2

3

4

5

Number of unknowns

68816

68818

68834

68906

68906

Required RAM (GB)

4.5

4.5

4.5

4.5

4.5

Without Preconditioner

Number of iterations

337

331

295

248

245

Simulation Time

(min : ss)

26 : 25

25 : 46

21 : 30

19 : 31

18 : 33

With Preconditioner

 

Number of iterations

30

27

27

29

20

Simulation Time

(min : ss)

7 : 49

7 : 29

7 : 20

7 : 09

6 : 37

15.14.1.3.2.5. Results
Radiation Pattern
  • Step 1
  • Step 2
  • Step 3
  • Step 4
  • Step 5
 
Current Density
  • Step 1
  • Step 2
  • Step 3
  • Step 4
  • Step 5
 
 

Step

1

2

3

4

5

Insertion Losses

(dB)

0.01443

0.049481

0.053826

0.033855

-0.017957

Radiated Power – Antenna (RPA)

(Watts)

0.00263137

Radiated Power with radome

(RPR)

(Watts)

0.00254001

0.00253671

0.002516

0.00247856

0.002511

RPA/RPR (dB)

0.306929852

0.31822196

0.38942565

0.51964965

0.40670413

 
Figure 21: Cut Phi = 0 comparison - radome steps and isolated antenna
 
 
 
15.14.1.3.3. Custom nose-airplane shape radome

Create a copy of baseProjectHorn.nfp project and rename it as Horn_Nose.nfp. Then open it with newFASANT by clicking on File – Open menu or clicking twice on the project icon.

The radome considered in this section is modified ogive which resembles to the noise of an airplane. We have created its geometry by using the userFunctions utility included in newFASANT tools that allow the user to create geometries with its own Java programmed functions.

The geometry shape may be defined in two parts according to the next parameters and functions:

Parameter

a

b

c

d

e

Value

0.5

2

1.2

1.4

a*1000

 

Figure 22: Positive Y-axis half geometry definition.

Figure 23: Negative Y-axis half geometry definition.

 

These functions may be used to interpolate a surface defined by its u and v parametric coordinates and using the surfaceFunction command. We recommend using it to build the same geometry. 

Anyway, the next content may be copied to a text file to be imported as a newFASANT script, for example, “nose_radome.nfp”. 

 

#

#   newFASANT script file to generate a Nose-Airplane shape, in milimeters

#

#required parameters

set a {0.5}

set b {2.0}

set c {1.2}

set d {1.400}

set e = 1000.0*a

#first half nose (Y-axis positive)

surfaceFunction -n id2a4dc855 -p \ #command start with main parameters

 0.0 1.0 19 \ # $u definition

 0.0 1.0 11 \ # $v definition

 "$x=a*cos(Math.PI*$v/2.0)*cos(Math.PI*$u)-Math.pow($v/b,2)" \ # x definition

 "$y=a*cos(Math.PI*$v/2.0)*sin(Math.PI*$u)/c" \ # y definition

 "$z=d*$v" \ #z definition

#second half nose (Y-axis negative)

surfaceFunction -n id5a4dc856 -p \ #command start with main parameters

 0.0 1.0 19 \ # $u definition

 0.0 1.0 11 \ # $v definition

 "$x=a*cos(Math.PI*$v/2.0)*cos(Math.PI*$u)-Math.pow($v/b,2)" \ # x definition

 "$y=-a*cos(Math.PI*$v/2.0)*sin(Math.PI*$u)/c" \ # y definition

 "$z=d*$v" #z definition

#set the second half normal vectors pointing to -Y

invertNormals -s id5a4dc856

#group the two halfs in the same object

group -s id2a4dc855 id5a4dc856 -n id31a94b3d

#scale the objects from meters to millimetres

scale -s id31a94b3d -p 1000.0

 

This script contains several commands:

• The first section defines the required values for creating the geometry.

• The second section generates two surfaces according to the formulas given previously.

• The last section processes the normal vectors orientation, group the surfaces in an only object and scale it from meters to millimeters.

 

 

 

15.14.1.3.3.1. Geometric design

Four nose surfaces are generated to model the radome as a thin layer approximation. To do that, click on Tools – Script – Load menu and load the “nose_radome.nfp” script that provides the internal layer of the radome. Not that the script is ready for loading it in millimetres because of its last command.

As it is not a canonical shape, we can approximate the next interfaces by scaling the original one. Use three times the command duplicate to create three additional copies of the generated shape.

The selected dimension as reference is the X-one, which has a distance to the origin of 500 millimetre, given by the e parameter (it is the a parameter, in meters, scaled to millimetres). As we need that the reference dimensions varies according to the thickness and t parameters, the scale factor is computed as the desired size divided by the original one.

Use the scale command to scale the three copies of the nose shape, each one by the corresponding factor:

Plane

Scale factor

2

(e+thickness)/e

3

(e+thickness+t)/e

4

(e+(2*thickness)+t)/e

Figure 25: Command line semispheres definition.

After creating the four noses, note that the base is centred at the origin of coordinates, so they must be moved to the horn. 

Use the move command to move the four noses from 0 0 0 to 0 0 -100 point.

Figure 26: List of geometric entities in the tree

 

15.14.1.3.3.2. Radome definition

Having defined the geometric model, the radome must be created and assigned. To do that, click on Source – Radome – Define Radome menu and the Radome panel is open on right side of screen. 

In the Radome panel, no radomes are created so click on Add Radome button to insert a new radome. Then, the table of interfaces of the selected radome (1) is loaded below. As we have shown in Figure 1, the radome is made of 4 interfaces that define the 3 layers, so click on New Interface button twice to get the 4 interfaces. 

Each nose must be assigned to every radome interface in the same order than specified in Figure 1. Remember that the normal vectors of every interface must be pointing to the next one. To assign a nose to an interface, select the geometrical object from the tree or in the Geometry panel, then select the corresponding row in the Interfaces table, and click on Set Objects button. Then, assign the Material to its interface, which is defined to the current layer.

The material (or layers) is considered between one interface and its next one, so the last interface does not required a material.

Remember clicking on Save button to confirm the radome definition.

Figure 27: Radome definition.

The next figure shows the final design of the radome with the horn, with the Material Lines view. In this representation, we verify that the layers of the radome have the correct materials.

Figure 28: Lines view with materials of the final design.

15.14.1.3.3.3. Mesh and run

Note that it is an electrically large case, so we have run it in a workstation

The only parameter modified in the meshing process is the number of Processors, which is set to 16. Specify the number of processors and click on Mesh buttons to confirm the changes and mesh.

The five parametric steps are meshed by requiring about 7 GB of RAM memory and 1 minute per step.

Click on Calculate – Execute menu and launch the simulation with 16 processors by clicking on Execute button.

The five parametric steps are simulated by requiring about 4.5 GB of RAM memory and 10 seconds per step.

 

15.14.1.3.3.4. Computational specifications

Step

1

2

3

4

5

Number of unknowns

454,780

454,983

455,342

455,780

456,010

Required RAM (GB)

10

10

10

10

10

With Preconditioner

 

Number of iterations

28

28

30

29

29

Simulation Time

(min : ss)

31 : 36

30 : 15

29 : 53

31 : 23

30 : 40

15.14.1.3.3.5. Results
Radiation Pattern
 
  • Step 1
  • Step 2
  • Step 3
  • Step 4
  • Step 5


Current Density
  • Step 1
  • Step 2
  • Step 3
  • Step 4
  • Step 5
 
 
 
 

Step

1

2

3

4

5

Insertion Losses

(dB)

-0.15372

-0.14825

-0.1358

-0.13691

-0.13398

Radiated Power – Antenna (RPA)

(Watts)

0.00263137

Radiated Power with radome

(RPR)

(Watts)

0.00220632

0.0020827

0.00217986

0.00215892

0.00213711

RPA/RPR (dB)

1.530268344

2.03110404

1.63506634

1.71890739

1.80710085

 
Figure 29: Cut Phi = 0 comparison - radome steps and isolated antenna.

15.14.2. Example 2: Radome with FSS

This document shows an example to create a radome with FSS. The table below resumes the parameters taken into account in the following example:

 

Data Definition Values
Frequency Simulation Frequency 10 GHz
Material Teflon Er = 1.9
Thickness Radome thickness 4 mm
FSS Radome FSS Cross

 

Create a new MOM project. To do that, click on New Project button and select the MOM module.

 MoM Module

Figure 1: Choose the MOM module.

 

Set the frequency. Click on Simulation –> Parameters menu and then the Simulation panel is open on right side of screen. Set the frequency to 10 GHz and click on Save button before closing the panel.

 

Figure 2: Simulation Parameters

 

Set the feeding. Click on Source -> Primitive Antennas -> Horn -> Pyramidal Horn menu and click on Add with default parameters. Note: The default parameters of the horn are calculated automatically for the simulation frequency.

Figure 3: Set up a Pyramidal Horn

 

 Set the Radome Geometry. To create the radome geometry folow this steps:

1. Change Y axis of Reference Plane to Z axis. Click on View -> Reference Plane and set Y-axis to (0.0, 0.0, 1.0) and then click on Update button.

2. Draw an arc with the following parameters. Click on Geometry -> Curve -> Arc.

Figure 4: Change Reference plane and draw an arc

3. Draw another arc with the following parameters. The thickness between the two arcs is 4mm.

Figure 5: Second arc with 4mm of thickness

4. Click on Reset button of the Reference Plane panel.

5. Revolve arcs. Click on Geometry -> Surface -> Revolve and select the two arcs. For a better meshing create the surfaces with 90 degrees of revolution.

Figure 6: Revolve arcs

 

Set the FSS. To create a conformed FSS on the radome surface folow this steps:

1. Draw the FSS Element. Click on Source -> Radome -> FSS Primitives -> Crosses -> Cross and click on Save button with default parameters. The FSS Element must be on XY plane and centered on (0.0, 0.0, 0.0).

Figure 7: FSS Element

2. Select the upper surfaces of the radome and click on Edit -> Geometric Operations -> Arrays -> Array On Surface.

Figure 8: Set up a conformed FSS on Radome Surface

3. Group radome interfaces. Select the upper and lower surfaces of the radome and group them separately.

Figure 9: Group Radome Interfaces

 4. Remove the crosses that are not closed and the FSS Element. Select crosses and click on Edit -> Explode and then select the individual cross and click on Edit -> Delete.

Figure 10: Remove FSS Element and individual crosses.

5. Group the crosses again. Crosses can be selected by clicking on the tree surfaces folder. Click on Edit -> Group.

6. It is possible to give a thickness to the crosses. In this case select the crosses and click on Geometry -> Solid -> Extrude Normal. Set the thickness to 1mm.

Figure 11: Set a thickness to the crosses

7. Group the crosses with their thickness and rename the objects as you can see in the following image.

Figure 12: Geometry at this point

 

Configure Radome Parameters. To finish defining the radome follow the next steps:

1. Click on Source -> Radome -> Define Radome menu and add a radome.

Figure 13: New Radome

2. Select the object of Interface 1 (lower) and the first row in Radome panel and then click on Set Objects button. Repeat the process with the object of Interface 2.

Figure 14: Add Interface Object

3. Selects the FSS object and the second interface in Radome Panel. Click on Set FSS Elements button.

Figure 15: Set up a FSS in the Radome

4. Select the material 'Teflon' on Interface 1. Click on Save button of Radome panel. Note: The material of interface 1 corresponds to the material between the two interfaces.

Figure 16: Select the material

 

Meshing Geometry. Click on Meshing -> Create Mesh and set planar and curved divisions to 20. Click on Mesh button.

Figure 17: Meshing panel

 

Start Simulation. Click on Calculate -> Execute.

Figure 18: Simulation

 

Results

Radiation Pattern:

 

Currents:

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