Internal Heads thermal expansion

[PVchemEng]

If I have an internal head welded on a cylindrical shell and it works at a temperature higher than the design temperature of the cylindrical shell, how can I take into account for the stresses generated by the thermal expansion of the internal head?

Does exist any formula to take into account for the stresses due to the thermal expansion of the internal head or is necessary to make a FEM analysis?

 

[corus]

You could assume that the internal head imposes a fixed radial displacement (from the differential thermal expansion) on the cylinder with a rotational restraint. This will give you an idea of the nominal stresses in the cylinder wall. You'd also need to calculate the stresses at the junction of the head and cylinder, which would need FEM, alas.

corus

 

[prex]

The most important part is to correctly calculate the temperature distribution. If you simplistically assumed the whole internal head, including its skirt, at a different temperature than the shell, you would get unacceptable stresses for a relatively limited temperature difference.
To calculate the temperature distribution, if you have no test data, probably FEM is the only way to go. And of course also the stresses would be determined with the same model.
However it all depends on where is and how is shaped the thermal source. For a similar (simpler) problem , the thermal stress in a vessel skirt due to the longitudinal gradient, I've used in the past a simplified approach by formula.

prex

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