A stress analysis was conducted on a tubular heat condenser utilizing finite element analysis (FEA). This condenser configuration includes a rotational asymmetric tube bundle secured between two tube sheets within a shell structure.
Analysis
During operation, significant thermal gradients are anticipated across and along the tube sheets, posing risks of thermal fatigue. To address this, a comprehensive stress analysis using the FEA method was performed, encompassing primary and thermal loads. The analysis employed Pro Mechanica software, utilizing 3D brick elements to provide detailed insights into the stresses and temperatures within the shell and tube sheet sections.
To streamline the FEA model, symmetry conditions were applied, and heat dissipation to the ambient air was accounted for by establishing an equivalent film coefficient for the cylindrical components of the shell and channel.
Four critical load cases were identified, aligning with ASME Section VIII Div. 2 standards, to evaluate stresses within key areas of the condenser: tube sheet, tube sheet-to-shell junction, tube sheet-to-channel junction, and tube-to-tube-sheet welds.

Results
The primary stress assessment revealed that the highest stresses and displacements occur at the junction between the unperforated part of the tube sheet and the cylindrical shell. Linearization of stresses in this region confirmed compliance with allowable limits stipulated by the code. Maximum average bending stresses concentrated at the center of the tube sheet also fell within acceptable limits.
Secondary stress values were most pronounced under normal operating conditions but remained within 90% of allowable stress limits. Additionally, maximum weld stresses consistently stayed well below specified allowable limits across all load cases.
Conclusions
In conclusion, the stress analysis confirms that all stress levels are within acceptable limits, necessitating no geometric modifications. Furthermore, a shakedown assessment indicated that the condenser is capable of enduring at least 7,000 operational cycles without structural concerns.