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Most pressure vessels will be designed using Design by Formula (DBF) according to ASME VIII Boiler & Pressure Vessel Code or EN 13445. However, not all loads and geometries can be considered with these standard design rules. For example think of cyclic thermal loading, where the metal temperature distribution needs to be calculated, or the design of a nozzle with gussets or a nozzle close to a discontinuity in the shell geometry.
At DRG we regularly perform Finite Element Analyses (FEA) and assessments according to ASME VIII-2 Part 5 or EN 13445-3. For these analyses we use the software packages ANSYS, CREO simulate and FEPipe. Our knowledge in these areas also feeds through to our training courses in FEA software and pressure vessel design codes.
Cyclic load assessment
The most common use of FEA for pressure vessel design is for a cyclic loading assessment. Such an analysis is required if the vessel does not conform to the fatigue screening criteria in ASME VIII-2 Part 5.5 or EN 13445-3 5.4. Cyclic loading can lead to the accumulation of micro strain, crack initiation and crack growth. A crack will typically reach macroscopic dimensions and cause failure after a high number of cycles (typically in the order of thousands, but there is no fixed limit).
On the other hand there is cyclic failure due to a limited number of cycles. This type of failure results from crack growth due to the build up of plastic strain (ratcheting).
Not all geometries are covered by a standard design rule, think of the closure of a hairpin heat exchanger or a rectangular flange connection. One option is to expand the DBF approach to cover these geometries in a conservative manner. However, this most likely results in more material usage and the requirement to justify to the client or notified body why the method is conservative. Using FEA can be useful here, providing the possibility to optimize and a straightforward way to demonstrate code conformance.
When analyzing components under high temperatures and stresses, the understanding of possible creep deformations is of crucial importance. Creep is the tendency of a solid material to move slowly or deform permanently under the influence of stresses well below the yield strength. It is a time-dependent deformation which does not occur suddenly under the application of stress. Rather, it is the accumulation of strain as a result of long-term stresses.
When a component deforms plastically, the stress in the component is redistributed. This behavior is not captured with a linear elastic material model. For some geometries the results of the stress assessment may be more optimistic when a plastic material model is used.
Steps in an FEA assessment
Step 1: Thermal loading
What is the temperature distribution within the vessel? Do significant local thermal gradients occur or are there large differences between components? Determining the (transient) heat transfer boundary conditions, and thereby the actual temperature distribution is a key part of most FEA analyses. Here we take care to ensure a conservative but credible case, which is either based on flow calculations with CFD, analytical formulas or HTRI results.
Step 2: Calculate the stresses
The calculated temperature distribution is used as a boundary condition in the FEA model, together with the other loadings such as pressure and nozzle loads. With an elastic material model the calculated stresses need to be categorized, it needs to be considered which load is primary (or weight driven) or secondary (displacement limited). It is important to consider which loads should be combined, for instance what is the range for the startup/shut down, or the operating cycle, or does the pressure load always act simultaneously with the thermal loading.
Step 3: Results and recommendations for the client
The results from a DRG analysis will always be documented in a detailed technical report. This will include all of the boundary conditions, details of the model setup and the analysis approach, and will be suitable for a rigorous review by a notified body. The report will also make sure that the results are explained to the client in a concise manner to build up to conclusions and practical recommendations.