Do CAESAR II formulas for thermal bowing and output results match with FEA?
Short Answer: There can be significant differences between the results of CAESAR II and FEA.Explanation:
The main differences arise due to the distinct assumptions and modeling methodologies used by each approach:
- CAESAR II is a 1-D beam-based stress analysis software, relying on simple 1-D beam elements and Euler-Bernoulli beam theorems. It provides a general 1-dimensional stress state of the piping.
- FEA calculates the 3-D (or 2-D with shell elements) stress state of the piping, capturing detailed variations in stress through the wall thickness and over the cross-section. It also considers 3D heat transfer effects and thermal gradients more accurately.
Key Advantages of FEA Over CAESAR II:
- Handles non-linear thermal gradients across the cross-section.
- Models angled or side-to-side thermal gradients.
- Accommodates realistic boundary conditions and materials with temperature-dependent properties.
- Simulates non-linear effects like plasticity or creep and local stress concentrations due to discontinuities or ovalization.
- Analyzes complex geometries such as elbows, tees, and supports.
In simple cases (e.g., a straight pipe with a uniform thermal gradient), results from CAESAR II and FEA should align. However, as complexity increases, the differences become more pronounced due to the constraints and assumptions of CAESAR II.
Modeling Thermal Bowing on Riser Piping
Thermal Bowing Tolerance in CAESAR II:
CAESAR II applies thermal bowing calculations to horizontal elements with a pitch below a certain threshold. The maximum parameter value is 5.0, but this is a known bug in the software. Selecting this value can reset the thermal bowing tolerance to 0 or a default value. The actual maximum value for thermal bowing pitch is 0.001, which means riser piping cannot be analyzed for thermal bowing using CAESAR II’s default method.Alternative Methods for Analyzing Thermal Bowing on Risers:
- Manual Calculation:
- Calculate bending moments for each node manually.
- Apply these moments to the system using a script or macro.
- This mimics CAESAR II’s method but requires you to include force/moment terms in the load case manually.
- FEA Analysis:
- Use FEA to analyze riser piping, which allows for more complex geometries, boundary conditions, and temperature-dependent effects. FEA is not constrained by CAESAR II’s horizontal piping limitations.
Example of Thermal Bowing in a Riser:
In one case, our team analyzed a flange failure caused by thermal bowing. A small riser with a 45-degree bend and a flange experienced rapid cooling on one side due to cooling fluid dripping down the riser. This caused a thermal gradient across the elbow, leading to large bending moments on the flange, which ultimately caused leakage. FEA analysis confirmed the thermal gradient across the elbow, and thermal imaging by the client validated these findings.While thermal bowing on risers is rare, it should not be disregarded in situations where thermal gradients are possible.
Calculating Metal Temperature of Uninsulated Piping from Thermal Bowing
Use Heat Transfer Calculations: The VDI Heat Atlas offers reliable methods for calculating thermal data based on conduction, convection, and radiation.
For simple geometries (e.g., a 1-D linear thermal gradient), a hand calculation may suffice. However, for complex systems, you may need to use an FEA model to simulate thermal transients and obtain the required temperature data.
Additional Questions from the Webinar
- When specifying temperature differences in CAESAR II, will all pipes be analyzed for bowing? Yes, CAESAR II will analyze all horizontal pipes below your specified horizontal tolerance criteria. Multiple bowing temperatures cannot be modeled in a single instance.
- Can we specify multiple delta-Ts for thermal bowing? Unfortunately, no. All lines under the horizontal tolerance will receive the same delta-T. Manual calculations using an Excel sheet and a Python script can be employed to model thermal bowing.
- Can CAESAR II add a length tolerance for short runs? Currently, there is no length tolerance input available. You can create a workaround by adjusting the pitch of the element to exceed the horizontal tolerance.
- Does CAESAR II consider additional bending moments from thermal bowing in flange leakage checks? Yes, CAESAR II does take these additional bending moments into account.
- Should negative vertical displacements due to vessel weight be conveyed to piping? Yes, even with vertical supports, the vessel’s weight will deform the structural steel, leading to vertical displacement that should be communicated to the relevant parties.
