How do I create thermal connections for axisymmetric models with bolts and nuts?

This article explains how to accurately model thermal contacts with bolts and nuts in turbomachinery models.

Introduction

You can model heat paths between 2D axisymmetric and plane stress elements using the Edge-to-Edge Gluing/Contact or Surface-to-Surface Gluing/Contact simulation objects. Surface-to-Surface Contact/Gluing can be used between 2D and 3D elements, for example the face of a plane stress to the face of a 3d body. Use these simulation objects in the coupled thermal-structural analysis to apply both structural and thermal couplings between two regions without creating a separate simulation object for each coupling. You activate the thermal coupling when selecting the Activate Thermal Coupling check box.When you create thermal couplings, select a smaller surface as a primary region.

Modeling thermal contacts of the bolt and flange

To model the thermal coupling between the flange and bolt, you must define one edge and one face coupling in the 2D model. Note that the flange is meshed using axisymmetric elements and plane stress elements with associated hole thickness. Bolt and nut are meshed with plane stress elements.

Edge coupling between the flange and bolt head
The contact area is the minimum thickness between the involved elements.

The area of the bolt head is defined as:

The flange area is defined as:

The area of the flange meshed with axisymmetric element is defined as:

The area of the flange meshed with plane stress elements is defined as:

Where:
  • is the external radius of the bolt.
  • is the internal radius of the bolt.
  • is the radius of the plane stress elements with associated hole thickness.
  • is the number of hole or bolt instances.
  • and are the maximum and minimum radius from the axis of rotation of the first part of the flange.
  • and are the maximum and minimum radius from the axis of rotation of the second part of the flange.
Face coupling between the flange meshed with plane stress elements and bolt shank
For the plane stress elements of type hole and bolt, the thermal solver considers the coupling area as the surface area of a cylinder. The convective area is the overlapping area of the primary selection.

When the flange (plane stress) is the primary selection:

When the bolt shank is the primary selection:

Modeling thermal contacts of the nut and flange

To model the thermal coupling between the flange and nut, you must define one edge and one face coupling in the 2D model:

Edge coupling between the nut and flange
Face coupling between the nut and flange

The coupling area is the overlapping area of the primary selection between the nut meshed with plane stress elements, and flange meshed with plane stress elements defined with associated hole thickness.

Modeling thermal contacts of the nut and bolt shank

For the nut meshed with plane stress elements defined with field or expression, the thermal solver considers the coupling area as the surface area of a plane.

When the nut face is a primary selection:

When the bolt shank face is a primary selection:

Where:
  • is the length of the nut.
  • is the width of the nut.
  • is the number of nut instances.
  • is the radius of the bolt shank.

Algorithm for 2D elements edges selection

For 2D elements with the thickness, the thermal solver computes the coupling area by:

  1. Extracting the thickness per element.
  2. Comparing the connected elements and identifying the smallest overlap thickness.
  3. Multiplying by overlap length (if the overlap area option is selected) to obtain the overlap area on the edge of each primary element.
  4. Summing all the areas.

Calculating convective area on the internal edge

When modeling the thermal connection between the flange, which meshed with plane stress elements and bolt head, or the nut, there is an internal edge.

To compute the coupling area, the thermal solver:

  1. Extracts the thickness on left side () and right side () of each element of the internal edge.

  2. Associates the thickness to each ( ) element's length .

  3. Finds the internal line area as:
  4. Computes the sum of convective areas as min ()

You should pay attention when modeling the thermal coupling between the flange (plane stress) and nut, where the thickness of one of the regions is defined as an expression or field.

The following example shows the thickness distribution on the flange and nut edges. The internal edge of the flange (1) exhibits decreasing thickness towards the centerline, while the nut's thickness (2) is modeled as being proportional to its radius.

As a result, the convective area in this thermal coupling is affected by both the nut and the flange edges. Representing the nut in a 2D format may result in loss of thickness distribution information, which may lead to inaccuracies in the convective coupling. Therefore, it is recommended to use the area correction factor when defining the heat transfer coefficient as an expression. To find the correction factor, use the BC data summary in HTML or in table format to acquire information about the computed convective area.

Use the PLOT BC SUMMARY advanced parameter in the solution to generate the HTML file that displays graphs of thermal properties of thermal couplings included in the solution.

The following example shows comparison of convective areas for the 3D and 2D models with nut and bolt thermal coupling.

You can also use the DISPLAY BC SUMMARY TABLES advanced parameter that describes the data stored for each thermal coupling in the model. For more information, see How can I understand and diagnose my thermal model results and setup?

Comparing 2D and 3D results

To validate the 2D model representation, compare temperature results with the 3D model. This step helps ensure that the 2D model accurately represents the behavior of the bolts and nuts within acceptable tolerances.

Additional recommendations

When you select the Only Connect Overlapping Elements check box for thermal coupling:

  • It is recommended to divide faces so that coupled edges/faces are fully overlapping. If the faces/edges do not fully overlap, then an overlap factor needs to be applied to the coupling areas.
  • Note that the area correction will not be done by the solver for the elements that are not used in the coupling, therefore the primary area correction may not be as expected. In the following bolt shank and nut example, if the two surfaces (surface 1 and surface 2) are selected as a primary area, the solver will correct the areas based on the curvature only for the connected elements that it detects in the thermal coupling, i.e., the surface 1. The thermal solver considers surface 1 as a cylindrical area and surface 2 as a plane area.