中文 English

Open topic with navigation

You are here: Optimization Module and Tutorial > Optimization of 2D Shape Tutorial > Setting up the model > Building the Mesh

Building the Mesh

This section describes the step-by-step procedure to prepare the mesh for the optimization model.

The Template Mesher is used to create the initial mesh and then it is deformed through Volume Remesh. Volume is re-meshed based on the shape of the 2D profile through expressions.

Annulus mesh
  1. Select Template Mesh/Surface in the Mesh Panel.
  2. Select Shape as Annulus and and enter the following parameters to create the exact domain.
  3. Enter following parameters below to create the exact domain:

    • 1st Point: 0, 0, 0.01 m

    • Pie Angle (0-360): 180 deg

    • Inner Radius: 0.05 m

    • Outer Radius: 1 m

    • No. of Grid in 1st Dir.: 1

    • No. of Grid in 2nd Dir.: 120

    • No. of Grid in 3rd Dir.: 180

    • Grid Distribution: Nonuniform

    • Size Distribution in 2nd Dir.: Cluster toward Reference Point

    • Power in 2nd Dir.: 1.5

  4. Click Build Annulus Mesh. A new mesh Annulus is created under Built Meshes and Volumes in the Geometric Entities Panel.

  5. Select annulus under Volumes in the Geometric Entities Panel (see, Figure 9.19).

  6. Select Transform Geometry or Grid in the Mesh Panel.
  7. Select Rotate from the Operation drop-down list in the Properties Panel.
  8. Enter Direction as 0,0,-1 and Angle as 90 deg, click Rotate.

 

 

  

Figure 9.18 - Annulus mesh settings

 

Figure 9.19 - Rotating Volume

 

´ Note: The mesh can be edited/replaced by selecting it under Built Meshes, and modify the mesh parameters in the Properties Panel. Click Create Mesh to reflect the changes.

 

The mesh created for the external flow domain around the 2D shape is shown below:

Figure 9.20 - Original mesh

Figure 9.21 - After Rotation

Figure 9.22 - Mesh zoomed view

 

Mesh Deformation

This section explains the procedure to remesh the volume based on the shape of the 2-D profile through expressions. The initial mesh is a half annulus with an inner radius r as shown in Figure 9.21. The mesh is clustered with finer near cells near the inner circle. This mesh is now deformed based on the inner profile shape.

 

To know more about how Mesh Deformation works, click Description drop-down list.

ClosedDescription

For any mesh point, consider a vector that starts from the center of the original mesh circle, passing through the original location of the point, and finally hitting the outer circle. This vector intercepts with the original inner circle, as well as the corresponding ellipse as shown in Figure 9.23. The new node will still lay on the same vector, except at a different distance from the outer circle. The distances satisfy the following relation.

 

9.16

 

Figure 9.23 - Mesh deformation calculation

 

Algorithm finding intersection

For a point with coordinates (, ), the radial vector starts from origin go through the current point can be defined in a parametric form:

9.17

9.18

 

where is a parameter, and

9.19

 

Substitute equation 9.17 and equation 9.18 into equation 9.5 to get a quadratic equation solving for :

9.20

 

Where,

9.21

 

The radius at the intersection with the ellipse is obtained by solving equation 9.20 and using only the positive values of the solution. Now, the new radius for each mesh point and their corresponding coordinates can be obtained using equation 9.16. An example of deformed mesh obtained using the new coordinates according to the shape of a non-circular 2-D profile is shown in Figure 9.24.

 

Figure 9.24 - Typical deformed mesh

 

 

 

 Copyright © 2023 Simerics Inc.,