Pipe with temperature diff at the wall 1

[CostasV]

Hello everyone,

We have a 50 mm diameter, API 5L Gr B, not thermally insulated, 2 m long, pipe with about 5mm wall thickness. The pipe is positioned straight vertical (free of constraints in the long direction) with the upper end open at the atmosphere, and the bottom end is welded a valve which is connected to a similar pipe which is used to blow down transmission gas pipelines operating at about 50 to 60 bar.

During blow down, because of the sudden drop of pressure, there is a sudden drop of temperature (a rule of thumb says 0.5 deg C per 1 bar) of about 25 to 30 deg C. We confirm it by noticing the ice that is build on the external wall due to atmospheric humitidy.

The phenomenon is impressive. It also happens at the moment when nothing is allowed to go wrong (gas released, man being beside the valve , etc)

I would like to find out if the temperature drop has any major effects to the pipe strength and if yes is there a limited number of cycle (temp drops) that the pipe can undergo.

I have tried thermal analysis, using JL Analyser 8.0 from AutoFEA Engineering Software Technology Inc. and came up with the result that maximum Von Mises stress due to ambient temperature difference (inside/outside of 100 deg F, convection film coeff in BTU/in^2/s/F inside=80 and outside=1) is 10 times the maximum Von Mises stress due to inside pressure of 40 bar.

The questions :
1. Is there a formula (not numerical analysis) of calculating the maximum stress on the pipe wall caused by inside/outside wall temperature differences.
2. Has anyone faced similar situation, and what to do.

Thank you in advance.
Costas

 

[davefitz]

Yes, there is a formula. It can be found in the Timoshenko textbooks, or in the german boiler code TRD 301 annex 1.

One other issue is the cooling may bring the pipe wall temperature below the ductile brittle transition temperature- you may wish to check that issue also.

At the inner wall ,the tangential ( circumferential)thermal stress is:

stress= E*B*(To-Ti)/(1-v)/2
E=Youngs mod
B=coef thermal expansion
(To-Ti)= wall temp diff
V= poison's ratio

assumes thermal stress conc factor for pipe = 1.0

 

[prex]

What you should compare the pressure + thermal stress with is the yield minimum stress of pipe material: as long as the resulting stress intensity (Tresca stress) is lower than two times the yield stress, the pipe will sustain an infinite number of cycles.
More dangerous is the brittle transition recalled by davefitz: API 5L is a welded pipe and is certainly not the best choice for those operating conditions.

prex

http://www.xcalcs.com

Online tools for structural design

 

[CostasV]

Hi davefitz,

thank you for your reply. This formula is very interesting. It has no length dimensions, so it independent from any size data. It only has to be applied on cylindrical bodies. It involves the basic material properties. And the only external condition is the ÄÔ, which can be relatively easily measured.

Unfortunately, I don’t have Timoshenko’s book, which, from a quick search I have done in the web, seem to be a “Bible”. I will try to read it, if I can find it in any bookstore (I live in Greece).

And now I will come to the subject. As you said the stress (in the Timoshenko folmula) is tangential in direction (circumferential). Is it the same direction with the stress caused by internal pressure (neglecting the axial stress caused by the end cap effect)? I suppose it is.
I have done some quick calculations and the result are:

assuming for steel, E=200 GPa, B=4.45e-06 (deg C)-1, v=0.32

1. for ÄÔ=50 deg C , thermal stress=32 MPa (=4700 psi) which is 14% of the yield strength

2. for Äp=65 bar (=940 psi), D=50mm and t=5mm, hoop stress=32.5 MPa that is about the same with the previous thermal stress

Of course the distribution of the stress in the radial direction is different between these two examples. In the pressure example it is almost constant, while in the temp. example it goes maximum, minimum, maximum.

Now the question: Regarding only the theoretical models (and neglecting any end effect), combining these two conditions (imposing Äp and ÄÔ together as in the previous examples) will result in having a total stress equal to the sum (which for the inner wall be 64.5=32+32.5 MPa). And if instead of ÄT=50 deg C, we impose -50 deg C, can we say that (for the inner side) the total stress will be about 0? Do you confirm?

Thanks again.
Costas

 

[hacksaw]

It is not clear that you'll actually get a 100 oF delta T across the pipe wall at the conditions stated.

typically you'll see pipe wall delta's of less than 5 deg or so. it will be close to the fluid temperature with most of the drop occuring at the outside wall.

with icing the delta T will even be less.

I'd be more concerned with the issue of ductile-brittle transitions raised in the other responses