Module: Surface Integrals ()

Description:

This module performs calculation of integrals or sums on 3d unstructured grid boundaries, on 2d unstructured grids, on 2d unstructured surfaces and on triangulated Surfaces. The computation might involve unstructured scalar or vector fields.

The results of the computation are written in a spreadsheet. The spreadsheet displays the name of the data, the name of the surface(s) on which the integral is computed, the nature of the integral computed and its numerical value. If the data is transient, the time step is displayed, and if a physical time is associated with the time step, it is displayed too. Depending on the option chosen, information about surfaces may be displayed.

Press the Apply button to start the computation.

Connections:

Data [required]
An Unstructured Model or an unstructured scalar or vector Unstructured Model Field.

• If the data is a 3D unstructured model, surface integrals can be computed on the boundaries of the model.
• If the data is a 3D unstructured field, field integrals can be computed on the boundaries of the 3d model the field is connected to and on any surface that intersects at least partly the 3d model.
• If the data is a 2D unstructured model, surface integrals can be computed on this 2D unstructured surface.
• If the data is a 2D unstructured field, field integrals can be computed on the 2D unstructured surface the field is connected to.

Density [optional]
An unstructured Unstructured Model Field scalar field containing density values.
This port is only displayed when density is required for the selected computation, for example mass flow rate.
If the data is an unstructured model, tries to retrieve a density connected to this model. If the data is an unstructured scalar or vector field, tries to retrieve a density connected to the same model as the data field. If one and only one density field is found, it is suggested by default.

Velocity [optional]
A 3D unstructured Unstructured Model Field vector field containing velocity vectors.
This port is only displayed when velocity is required for the selected computation, for example volumetric flow rate.
If the data is an unstructured model, tries to retrieve a velocity connected to this model. If the data is an unstructured scalar or vector field, tries to retrieve a velocity connected to the same model as the data field. If one and only one velocity field is found, it is suggested by default.

Ports:

Surface integral

This port is displayed when the data is an unstructured model. The following quantities can be computed:

• total area
  
  

  where is the number of faces and is the area of face f.

• volumetric flow rate This is the volume of fluid that passes through a given surface per unit time.
  
  

  where is the velocity, the velocity at the center of face f and is the normal area vector of face f.

• mass flow rate This is the mass of fluid that passes through a given surface per unit time.
  
  

  where and are the velocity and the density, and are their value at the center of face f and is the normal area vector of face f.

Field integral

This port is displayed when the data is an unstructured scalar or vector field (denoted by here). The following quantities can be computed:

• surface integral
  
  

  where is the value of at face f and is the area of face f.

• flow rate
  
  where and are the values of and of the density at face f and is the normal area vector of face f.
• area-weighted average
  
  where is the value of the field at face f and is the area of face f.
• mass-weighted average
  
  where , and are the values of the field , of the density and of the velocity at face f and is the normal area vector of face f.
• minimum
• maximum
• sum
  
  where is the value of the field at face f.
• mean
  
  where is the value of the field at face f.
• standard deviation
  
  where is the value of the field at face f and is the mean value of .

Notes:

• If the field is a vector field, the results will be given component per component, except for minimum and maximum which will be equal to the vector's magnitude scalar field minimum and maximum.
• If data is bound per node, an interpolation is performed to get the values at face centers.
• Integrals can be computed on boundaries only if data are stored at the boundary faces' center.
• It is normal to get a different result by integrating a data set on boundaries and on a surface created through the Boundary View module. Actually in the first case, a weighted sum of values stored at the center of the faces of a boundary surface is computed. In the second case, a weighted sum of values probed at face centers of a triangulated surface is computed.

Spreadsheet

The computation results are written in the tables of a spreadsheet. Choose append table to append the current table, or new table to open a new table.

Table

If the box is checked, a new table will be opened everytime the integral type changes. The new tables will be named after the integral names.

Info

Check this box to display in the tables the following information:

• Translate port value of Cross Sections,
• Isovalue port value of Isosurfaces,
• Id of boundaries.

Information are displayed if and only if all surfaces selected are of the same type and this type is one of the three mentioned before.
This port is disabled in global computation mode (see next port description).

Compute

This port is displayed when the data is a 3D unstructured model or field. Choose globally to get one result corresponding to the global surface composed of all the boundaries and surfaces selected in Boundaries and Surfaces ports.
Choose per surface to compute the result on each selected boundary and surface.

Boundaries

This port is displayed when the data is a 3D unstructured model or field.
Select the grid boundaries where the computation should be done.
A boundary has a name and an Id. Both are displayed in the port. In the resulting table, a boundary of Id i will be displayed under the name Bnd i.

Boundary types

This port is displayed when the data is a 3D unstructured model or field at the same time as the Boundaries port.
Select the type of boundaries where the computation should be done. This effectively selects/deselects all boundaries of specific type in the Boundaries port.

Surfaces

This port is displayed when the data is a 3D unstructured field. All the unstructured surfaces and display modules that compute a surface are listed in this port. If no such surface or module exist, then the port is hidden. Notice the Parametric Surface macro button in the upper side of the Project View: use this module to create arbitrary parametric surfaces in 2D and 3D.
Select the surfaces where the computation should be done. The data will be probed on the selected surface(s) cell centers in order to compute the chosen integrals.

Tip: this port can be convenient for example to compute integrals on several parallel cuts of a 3d model. Create a Cross Section, connect it to an Animate Ports module. Select the Cross Section in the Surfaces port, set the computation mode of the Surface Integrals module to auto-refresh. Launch the animation: the current table is appended at every step of the animation with the value of the integral on each successive cut.