Coefficient of Thermal Expansion Over Large Temperature Range 1

[dozer]

I'm not a pipe stress engineer by trade but I like to understand what other disciplines do. I do have a mechanical engineering degree and a strong background in stress analysis. Just a little background for reference. Anyway, I asked one of my associates to run a simple straight length of pipe with a temperature change so I could understand what it is using for the coefficient of thermal expansion. The test case was stainless steel pipe installed at 70 deg F then cooled down to -320 deg F. For those who are curious, these are actually real world numbers for cryogenic processes. I found that even though CAESAR recognizes that the coefficient of thermal expansion (COTE) is a function of temperature (it has a table of COTE at various temperatures) it actually uses the value at the design temperature to do the calculation. For stainless at -320 F the COTE is 8.16E-6 in/in-F. At 70 F it is 9.11 in/in-F. To see how much the pipe shrinks going from +70 to -320 I would have thought it would be more correct to use the average COTE between these two temperatures but CAESAR used the lower value. Granted it's only about a 5% difference, but that doesn't seem right to me. Is this a bug in CAESAR or is this just the way it is done in the piping world?

 

[racookpe1978]

What is the more conservative approach? If the pipe temperature stabilizes with flow at -320 degrees, then after only a few minutes at -320, the entire pipe length change "stabilizes" at its length with the coefficient of expansion based on the final temperature.

Not a middle temperature that is quickly passed as the pipe continues to cool towards its final temperature. Assume maybe that at that intermediate temperature the total pipe length change is -1.00 inch with a coefficient of 8.8E-6/degree. If the pipe continues to cool down to -320, then the total change that must be accommodated is far greater than -1.0 inch. So you must design for the greater change in length regardless.

Assume though that the pipe coefficient is larger at the starting temperature of 70 degrees nominal. That temperature definitely sets the original (rest) position of the supports and anchors, and it sets the changes over any small temperature change (due to weather perhaps) when the temperature cycles around room temperature; but as the pipe cools towards -320, its final length depends only on the entire change from 70 to -320.

And that is the change in length that was actually measured at the final -320 temperature and written into the "book".

 

[Gator]

A former colleague who's done stress analysis for cold boxes says:

"B31.3 Table C3 gives you the mean coefficient between 70°F and the indicated temperature. The thermal expansion should be calculated with this value which is 8.16E-6 in/in/°F for -320°F. I’m not sure what CAESAR’s doing."

 

[dozer]

Gator, thanks, that answers my question. CAESAR is using the mean COTE when going from 70 deg F like the table you pointed me to, so it is doing it correctly. I should know better than to question a program that old but I'm from Missouri so you gotta show me. I just assumed (you know what assuming does) that the table in CAESAR was the actual COTE at temperature, not the mean. It all makes sense now.

Did you notice that for austenitic stainless steel it changed fairly significantly from 2012 to 2014? What happened? Did physics change during then? From 70 F to -325 F, type 304 used to shrink 3.85 inches. Now it only shrinks 3.6 inches. There's something weird going on in the universe.

Racookpe1978, I didn't really get what you were saying but thanks for the reply.