Question

Expansion bellows are provided in the shell and tube heat exchangers in order to

• A. Increase the surface area
• B. Relieve stresses caused by thermal expansion
• C. Increase the turbulence
• D. Reduce the pressure drop

Hint:

Structural guidelines for heat exchangers: - Fixed Tubesheet Exchangers: Low cost, but require an expansion bellow on the shell if the temperature differential between tube and shell exceeds roughly \(50^\circ\text{C}\). - Floating Head Exchangers: Alternative design where one tubesheet is left free to move axially, completely avoiding thermal expansion stresses without needing shell bellows.

Answer 1

The Correct Option is B

Concept: In a shell-and-tube heat exchanger, two fluids flow at different temperatures: one through the internal tube bundle and the other through the surrounding outer shell structure. As the heat exchanger operates, these components absorb or reject heat, causing their temperatures to change. According to linear thermal expansion principles, the change in length (\(\Delta L\)) of a structural component depends on its material properties and temperature change: \[ \Delta L = \alpha \cdot L \cdot \Delta T \] Where:

• = Coefficient of linear thermal expansion.

• \(L\) = Original length of the component.

• \(\Delta T\) = Change in temperature relative to the initial state.
Let us analyze the structural behavior under these conditions:

Step 1: Evaluating the source of thermal stresses.
Because the shell and the tubes are made of different materials or operate at different temperatures, they expand by different amounts (\(\Delta L_{\text{shell}} \neq \Delta L_{\text{tubes}}\)). In a fixed tubesheet heat exchanger, both ends of the tubes are rigidly welded to the shell. This rigid constraint prevents free expansion, generating high thermal stresses within the assembly: \[ \sigma_{\text{thermal}} = E \cdot \epsilon_{\text{thermal}} = E \cdot \frac{\Delta L_{\text{constrained}}}{L} \] These large stresses can cause mechanical failures, such as buckling of the tubes, cracking of the tubesheet welds, or structural distortion of the outer shell.

Step 2: Analyzing the function of expansion bellows.
To mitigate this issue, designers incorporate a flexible component known as an expansion bellow (or expansion joint) into the outer shell structure. Bellows consist of a series of thin, corrugated metal rings that can compress or extend axially under low forces.

Step 3: Determining the structural benefit.
The inclusion of expansion bellows alters the system behavior:

• The flexible corrugations absorb the differential thermal expansion (\(\Delta L_{\text{shell}} - \Delta L_{\text{tubes}}\)) by deforming elastically.

• This flexibility allows the shell to change length slightly, reducing structural constraints and safely relieving internal thermal stresses.
Therefore, expansion bellows are used primarily to relieve stresses caused by thermal expansion, matching Option (2).