Bimetallic Strip in Airflow

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Bimetallic Strip in Airflow

This is a conceptual example, illustrating how to couple fluid-structure interaction, heat transfer, and thermal expansion.

A bimetallic strip in an air channel is heated so that it bends. After some time, an airflow with an inlet temperature that varies with time is introduced. As a result, there are changes in deformation caused by both the fluid pressure and the convective cooling. The computed structural deformations are compared for three different cases:

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No imposed airflow through the channel.

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Convective cooling with an airflow at room temperature.

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Hot airflows through the channel.

Model Definition

The bimetallic strip geometry consists of two 10 mm x 0.5 cm strips made of copper (lower part) and iron (upper part) materials. The bimetallic strip is placed inside a 70 cm x 10 cm air channel.

Figure 1: Model geometry.

The strip displacements are fixed at the left (upstream) extremity. A 50 W heat source with a uniform distribution is applied to the structure. When the strip is heated, the copper expands more than the iron due to the difference in thermal expansion coefficients. This causes the strip to bend upward.

At the air channel inlet (on the left), the velocity varies with time. Initially there is no flow. After 3000 seconds the inlet velocity is smoothly ramped up to 0.2 m/s.

The inlet temperature is initially set to room temperature (293.15 K). After 5000 seconds it is ramped up to 593.15 K.

Results and Discussion

Figure 2 shows the vertical displacement at the tip of the bimetallic strip as function of time.

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From 0 to 3000 seconds, the tip displacement keeps increasing as there is only a very weak cooling caused by self convection.

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Between 3000 and 5000 seconds, there is a decay is the tip displacement as a forced convective cooling is introduced. A steady-state solution is observed, where the tip displacement is about 2 mm.

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Between 5000 and 7000 seconds, the air is heated, and the tip displacement increases again. A new steady-state is reached, at which there is a balance between the heat generated in the strip and the heat dissipated by convection.

Figure 2: Vertical strip tip displacement.

Figure 3 shows the temperature distribution in the channel when there is no imposed airflow.

Figure 3: Velocity (surface) and temperature (contour) in the channel at 3000 s.

Figure 4 shows the temperature distribution in the channel with an airflow cooling the strip. The temperature is significantly decreased and so is the strip tip displacement. The velocity profile in the channel is almost symmetric as the strip has only a small deformation.

Figure 4: Velocity (surface) and temperature (contour) in the channel at 5000 s.

Figure 5 shows the temperature distribution and the velocity profile in the channel with hot airflow at the final time step. Now the cooling effect is significantly decreased as the air is warm. The strip deformation clearly changes the flow pattern, and most of the air is passing below the structure.

Figure 5: Velocity (surface) and temperature (contour) in the channel at 7000 s.

Modeling in COMSOL Multiphysics

COMSOL Multiphysics offers the possibility to easily set up this type of combined multiphysics analysis. In the model wizard, you can choose the Fluid-Solid Interaction, Conjugate Heat Transfer multiphysics interface and you will automatically get the multiphysics coupling between the fluid flow, the structural deformation and the heat distribution.

CFD_Module/Fluid-Structure_Interaction/bimetallic_strip_fsi

Modeling Instructions

From the menu, choose .

In the window, click

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In the window, click

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In the tree, select .

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In the tree, select .

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Global Definitions

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In the window, under click .

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In the window for , locate the section.

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In the table, enter the following settings:


Name	Expression	Value	Description
lc	0.7[m]	0.7 m	Length of channel
hc	0.1[m]	0.1 m	Height of channel
ls	0.1[m]	0.1 m	Length of spring
hs	1[mm]	0.001 m	Height of spring

Rectangle 1 (r1)

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In the toolbar, click

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In the window for , locate the section.

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In the text field, type ls.

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In the text field, type hs.

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Locate the section. In the text field, type -hs/2.

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Click to expand the section. In the table, enter the following settings:


Layer name	Thickness (m)
Layer 1	hs/2

Rectangle 2 (r2)

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In the window for , locate the section.

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In the text field, type lc.

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In the text field, type hc.

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In the text field, type -hc/2.

Form Union (fin)

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In the toolbar, click

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button in the toolbar.

Laminar Flow (spf)

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In the window, under click .

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Select Domain 1 only.

Solid Mechanics (solid)

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In the window, under click .

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Select Domains 2 and 3 only.

Heat Transfer in Solids and Fluids (ht)

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In the window, under click .

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Select Domain 1 only.

Deforming Domain 1

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In the window, under click .

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Select Domain 1 only.

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In the toolbar, click

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Go to the window.

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In the tree, select .

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In the toolbar, click

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In the window for , locate the section.

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In the dialog box, type 2 in the text field.

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In the dialog box, type 3 in the text field.

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In the toolbar, click

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In the window for , type Vinlet in the text field.

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Locate the section. In the text field, type 3050.

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In the text field, type 0.2.

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Click to expand the section. In the text field, type 100.

Laminar Flow (spf)

In the window, under click .

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In the toolbar, click

and choose .

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In the window for , locate the section.

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From the list, choose .

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Locate the section. In the Uav text field, type Vinlet(t).

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Select Boundary 1 only.

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In the toolbar, click

and choose .

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Select Boundary 11 only.

Solid Mechanics (solid)

In the window, under click .

Fixed Constraint 1

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and choose .

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In the dialog box, type 4 6 in the text field.

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In the toolbar, click

and choose .

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In the window for , type Tinlet in the text field.

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Locate the section. In the text field, type 5050.

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In the text field, type 293.15.

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In the text field, type 593.15.

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Locate the section. In the text field, type 100.

Heat Transfer in Solids and Fluids (ht)

In the window, under click .

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In the toolbar, click

and choose .

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Select Boundary 1 only.

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In the window for , locate the section.

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In the Tustr text field, type Tinlet(t).

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In the toolbar, click

and choose .

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Select Boundary 11 only.

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and choose .

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In the window for , locate the section.

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In the dialog box, type 2 3 in the text field.

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In the Q0 text field, type 50[W]/(ls*hs*ht.dz).

Thermal Expansion 1 (te1)

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In the window for , locate the section.

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In the dialog box, type 2 3 in the text field.

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In the window, under right-click and choose .

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From the list, choose .

Corner Refinement 1

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Select Domains 2 and 3 only.

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button in the toolbar.

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In the window for , locate the section.

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In the window for , locate the section.

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In the text field, type 100.

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Step 1: Time Dependent

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In the text field, type range(0,1e2,7e3).

Solution 1 (sol1)

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From the list, choose .

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In the text field, type 0.1.

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In the window, click .

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In the text field, type 1e-2.

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In the text field, type 600.

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In the toolbar, click

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button in the toolbar.

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button in the toolbar.

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button in the toolbar.

Temperature (ht)

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button in the toolbar.

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In the window for , click in the upper-right corner of the section. From the menu, choose .

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In the toolbar, click

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Isothermal Contours (ht)

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From the list, choose .

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Locate the section. From the list, choose .

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button in the toolbar.

Vertical Strip Displacement

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In the toolbar, click

and choose .

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In the window for , type Vertical Strip Displacement in the text field.

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Right-click and choose .

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In the window for , locate the section.

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In the dialog box, type 7 in the text field.

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In the window for , click in the upper-right corner of the section. From the menu, choose .

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Click to expand the section. In the text field, type 2.

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In the toolbar, click

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