Thermal stress on a thick pipe

[fredkfchan]

I have a problem about thermal stress on a thick pipe, can anyone can give me a hand to sort it out.

The dimension of the pipe:
Outside diameter = 325mm
Inside diameter = 350mm
Wall thickness = 150mm

Physical properties
Outer surface temperature = 576 degreeC
Inner surface temperature = 350 degreeC

The temperature of the inner pipe changed by time, it will cool down for 2 degreeC per min.

I have calculated the maximum stress (circumferential stress) by using the equation from the “Roark” Temperature Stress 15.6, 16, st = [DT aE / (2(1-n) loge (c/b))] [1- (2c2/(c2 – b2))(loge c/b)]. However, I would like to change the inner surface temperature from constant to variable. By changing the criteria of the temperature, can I still using this equation. Can anyone can give me any suggestions to calculate that.

“Roark” Temperature Stress, 15.6, 17, that is an equation for temperature of outer surface raised at the uniform rate, st = [Eam / (8A(1-n)] [3b2 - c2 - (4c4/(c2 – b2))(loge c/b)], however my situation is inner surface temperature drop. Can I use that?

Can I use the 15.6, 16 equation by changing the DT to produce a set of stress values, then using these points to plot a graph?

 

[davefitz]

first of all, the dimensions you stated are not consistent with each other.

If the operating data you stated are accurately known and verified, then it should be straightforward to solve the problem using either a canned finite element program , or it is simple enough to solve using fourier series exact solution of the 1 dimensional harmonic linear DE. To solve the transient heat transfer diff. equation, you would need to know the metal heat capacity, thermal conductivity, initial conditions, and heat transfer coefificnet at the ID and OD.

After you solve for the metal temperature distribution vs time, you can then calcuate the linear elastic thermal stress vs time. You can directly plug into the formula you had stated in your post ( should be checked against the published solutions by Timoshenko)or this can also be obtained from a finite element model directly.

If the total time period for the linear ramp in temperature exceeds about 2s^2/a ( s= wall thick, a= thermal diffuss.) , then you can use the german boiler code approximation that the thermal stress at the ID is ...

q,t=SCF*B*E*S^2*PHI(u)*V/(1-mu)/a
q,t= ID thermal stress
SCF= inside stress conc factor
B=linear thermal diff exp coef
E=Young's mod
S= wall thick
mu= poisons ratio
a= thermal diffus
u= Ro/Ri
PHI(u)={(u2-1)(3u2-1)-4u4*Ln(u)}/{8(u2-a)(u-1)^2}
u2=u^2, u4=u^4

 

[prex]

Though the dimensions of your pipe are unclear, I guess that the additional thermal stress due to a gradient that increases only by 1% in a minute would be negligible. You can calculate that for a changing outer temperature and compare to the steady state stress for the final gradient to confirm my guess.
Roark's formulae don't give you the transient thermal stress (also called the skin effect), but again for that transient this should be by far negligible.

prex

http://www.xcalcs.com

Online tools for structural design

 

[turboengineer]

I'd really need to know the pressures, internal as well as external, as well as the correct pipe dimensions, before I could be of much help other than to say that thermalally induced stresses can kill you if you aren;t careful, so the best rule of thumb is to use the thinnest wall that you can get away from unless the wall thickness has some specific intent towards form, fit or function.

Tim

 

[fredkfchan]

Dear all,

Sorry about my poor typing error, the correct parameters of the pipe are
Outer diameter of the pipe is 650 mm,
Inner diameter of the pipe 350 mm,
The wall thickness of the pipe = 150 mm,
The temperature of the outside surface is 570 degree C
The temperature of the inner surface is 350 degree C
Operating pressure is 272 bar g
The material of the pipe is a Low and intermediate alloy steel A335 P91, 9Cr 1MoV

Thanks so much for your kindly help.

Best regards,

Frederick Chan

 

[davefitz]

That is a monster of a pipe- 150 mm thick F91 !!

While I have not calculated the stresses, from inspection a 226C temperature ID to OD difference will result in enormous thermal stresses and fatigue damage . The damage should be computed using a modern design code tailored to piping components, such as TRD 301 annex 1 ( german boiler code) or EN 12952-3 annex B( EU PED).

Other issues:
a) a 150 MM thick wall F91 will imply that reduced metallurgical properties should be used,as specifed by ASME code
b) this thick a F91 component should utilize a weld technique that minimizes interpass reheating /overtempering of the HAZ- see Japanese papers on very narrow groove welding by IHI.
c) stress concentrations at welds or structural discontinuities msut be investigated to ensure that they will not be a source of failure.