ASME Standards
This has led ASME to create codes that pressure vessels and boilers must meet to ensure safety. Adrian Jensen, Sr. Staff Mechanical Engineer at Predictive Engineering, tends to work with ASME Section VIII, Division 2 pressure vessels. He notes that these tanks are becoming more popular in the engineering analysis world as they are well suited to be idealized and optimized using simulation.
Table 1: ASME Section VIII Pressure Vessel Classification.| Loading Conditions | Materials |
|---|---|
| Internal or external pressure load > 15 psig | Usually Stainless Steel (ductile) |
| Hydrostatic pressure (fluid dead weight) | Fatigue Properties |
| Thermal loads (local/general, cooling jackets, hot/cold fluid) | Allowable Stresses set by σy |
| Seismic loads (even if standard geometry aka Div. 1) | Other metals (rare) |
Jensen explains, “What makes a pressure vessel Div. 2 versus Div. 1 is non-standard geometry. If you are just making a propane tank without extremely angled nozzles or sharp transitions, you can do the code calculations by hand. But with complicated geometry or complicated loading you need to follow the Div. 2 guidelines and analyze it within a program.”
He continues “Maybe you don’t have a complicated vessel, maybe you don’t need optimization. You are still going to need an advanced analysis program. You are going to need to use FEA to certify this vessel for seismic analysis.” So it seems that regardless of your design, simulation can play an important role in getting your ASME certification.
Table 2: The modeling and post processing needed for ASME Pressure Vessels| Stress Output | Post-Processing Tool |
|---|---|
| Stress Intensity | ASME Stress Intensity Calculator |
| Plate Membrane Stress | ASME Stress Intensity Calculator |
| Solid Membrane Stress | Femap Stress Linearization Tool |
Nozzle Weld and Femap’s API
Figure 1: Nozzle Weld.
Jensen used Femap and API (Application programming interface) to create an optimized pressure vessel. To do so you will need a high quality mesh, accurate loads and efficient pre- and post- processing tools. “We put a lot of work into the building of the geometry and the creation of the mesh. That allows these special stress evaluations to be easier down the road,” says Jensen.
Figure 1 depicts the cross section through a nozzle or other shell penetration. It is modeled with plate elements; however, the true structure will have additional thickness at the weld.
“Per ASME guidelines, the first stress evaluation point we look at is at the toe of the weld,” explains Jensen. He cautions that “we don’t recover stresses at the mid-plane intersection. That singularity is going to give you artificially high stresses.” Femap makes it so you can move away from these discontinuities. Users can place the nodes where they are needed to study stresses accurately.
“By default we get top and bottom stresses for plate elements. But (for ASME) we also have to look at stress at the mid-plane, the membrane of the elements. Fortunately, these output vectors are easy to calculate using an API. I commonly use the stress intensity calculator under Femap’s custom tools,” says Jensen.
When learning to program in Femap’s API Jensen suggests it is best to search the directory and look at the code of similar programs. You can learn how the programs work and see what parts are useful to your code. You can then mix and match them together as needed or come up with your own.
API Speeds Up the Filling of a Tank
Figure 2: Pressure vessel fills with liquid oxygen.
One complicated simulation to produce is a transient thermal analysis of a pressure vessel, i.e. filling the tank. Assuming the tank starts at room temperature, and it is filling with liquid oxygen at the bottom, there will be two simultaneous transient thermal conditions.
The first transient thermal condition is that the temperature profiles will change with time. There will be a temperature gradient through the thickness. The next transient thermal condition is that the fluid level will be changing, which is complicated by the fact that the fluid boils on contact with the tank wall. This “makes an extremely high heat transfer coefficient where the delta T isn’t quite as great. But as we drop below that boiling, we get the non-boiling region we have a lower heat transfer coefficient with a slightly higher delta T,” says Jensen.
“To solve this,” explains Jensen, “we had one function for the heat transfer coefficient and one function for the temperature that work as a “switch” for the boundary conditions as the liquid moves up the vessel.”
George Laird, Principal Mechanical Engineer at Predictive Engineering says, “The vessel, at room temperature, is hit at the bottom with fluid at negative 355 ͦF so you get these huge contractions and tensile stresses.”
To perform this analysis traditionally, Laird explains, you would map a temperature profile on the load and perform the thermal stress using NASTRAN. Unfortunately, this is only one time step. You will have to repeat the process for each time step.
That’s why Laird and Jensen came up with a different solution. “We broke this down into 90 steps over the 15 minutes (fill time) so the API maps the loads on the inside of the vessel and the transient thermal analysis generates 90 result cases with full temperature profiles. Then, as you have only one constraint set in NASTRAN, you don’t have to run it 90 times. Just run the stiffness matrix once, slap the loads on it, and you’re done in 5 minutes,” boasts Laird.
Fatigue Analysis
Figure 3: Fatigue Essentials analysis of a pressure vessel.
Fatigue Essentials is a program Laird and his mechanical engineering colleagues produced to help guide engineers through the often tedious process of calculating fatigue. Laird’s partner Brian Reiling, Principal Engineer at Endeavor Analysis, adds that “The intent of Fatigue Essentials isn’t to simplify the analysis … it’s to simplify the process of getting to the answer. And to create a flow to guide the user to do the right things to hopefully get to the right answer … This all could be done in a spreadsheet, but I don’t think Excel is a great user interface for solving complex problems. So we’ve tried to put this in a user friendly package that guides the user through it and minimized the risk of mistakes … What’s behind the scenes of the package is what most of the aerospace companies do for fatigue analysis so it’s not a watered down answer.”
Jensen adds that “originally when doing fatigue analysis with a pressure vessels, we create load combinations: dead weight with fluid, dead weight with pressure, dead weight with fluid and pressure, etc. We would then have to pick one hotspot and pick stresses from each of these combinations and find which permutation has the biggest stress range. Even with all the API and spreadsheets we had, I’d need about 90 minutes of solitude or I would lose my spot. That is where Fatigue Essentials comes in. It is a tool to keep you on track.”
Fatigue Essentials provides an intuitive interface to manage complex analysis such as the aforementioned ASME Div. 2 example. For these problems, traditional hand calculations become too cumbersome to manage.
Despite the fact that Laird has just released Fatigue Essentials on the market, he suggests you “Avoid software sales people. Do your own work, software isn’t going to solve your problems. How to solve a problems means understanding the physics behind it. And be able to do first order approximations via hand calculations, sketches, or intuition. If you have to rely on software out of the gate to solve your problems then it probably means the problem is over your head and you don’t know what you are doing … If you don’t have the right training you just get the wrong answer faster.” Sounds like sage advice from one engineer to another.
For more on Fatigue Essentials follow Predictive Engineering.