Cyclic stress and api 579

[NovaStark]

Problem is described as follows, I have a pressure vessel which basically consists of a hollow cylindrical body with two hemispherical shells attached to both ends. Within the vessel, there is a gas flowing from top to bottom. Over a period of one week, the vessel was subjected to changes in both temperatures and pressures (inlet and outlet). I need to get how the stresses varied within the vessel (due to pressure and temp). Which happen to be through thermal stress and stress due to pressure in a "cyclic manner".


Both hemispheres and cylinders are thin, so at each time interval hence change in pressure I can calculate hoop stress using

σ=PD/2t.

However the thermal stress becomes a bit confusing as I am not sure how to model it/solve it.

I am simplifying the situation by ignoring the convective element of the fluid flowing and concentrating on conduction.

The heat equation is as follows

I can simplify my situation by converting the problem to 1-D such that my temperature function T will just be of t and r i.e. T = T(r,t).

My main issue is determining how to get ∂T/∂t.

Plotting my data collection against time doesn't really fit any equation trendline and just looks a bit erratic.

or do I assume T(r,t)=X(r)Y(t) and solve the PDE using separation of variables which if I remember correctly will eventually give me a Fourier Series which might complicate my situation. Is there any way to make this easier to do by hand rather than an FEA simulation?


Following API 579 (FFS), in order to even see if I need to do all of the above, it says I need to make a load histogram, but I find that the instructions within it are a bit confusing to me. Does anyone have an example of a load histogram or an example of how to make it from a set of data points?

 

[TGS4]

A couple of comments:
- the highest pressure stresses will be at the discontinuity between the shell and the hemi-heads. This location also has a weld, so you will need to account for that, as well (structural stress method or FSRF).
- even though you think that you only have a shell and heads, you will also have at least two nozzles. Those could also be regions of high pressure discontinuity stresses. These transitions can also be rather thick, depending on size and pressure, so any thermal stresses due to thermal transients.
- the assumption of infinite heat transfer rate (assumed temperature vs convective heat transfer) is a very poor assumption and can result in temperature profiles in significant error (and not necessarily conservative errors, either).
- considering that the highest thermal stresses are at transitions between thick and thin (owing to the different heat up rates from the different thermal masses), although it is nice that you want to try an ODE (or PDE) approach, the real problem is vastly more complicated.

All that aside - if you do go through with this approach, may I suggest that you seriously consider publishing the results - the ASME PVP Conference is an ideal venue.

Sorry that this doesn't answer you question about histograms. You may find some good guidance for load histograms in ASME PTB-1. The methods in 579 are identical to those in Section VIII, Division 2.

 

[NovaStark]

Thanks for the reply TGS4.

The main reason I wanted to do it by hand was due to the fact that I don't have any FEA software available, so by hand was my only method. I wanted to start with what might be the easiest place which would be the shells and welds.

If it is too complex to do by hand (in your experience), then FEA would be a better approach just a bit time consuming for me as I'd need to learn to use the software first.

 

[Engdoitbetter]

As far as I remember, you can use separation of variables, but I don't remember exactly how to get to the Fourier Series.

Anyway, pay attention to the coefficients since this method is useful if you can achieve ODEs with constant coefficients, otherwise this might prove a bit harder than usual.

Regards,

Stefano

 

[NovaStark]

Based on how the heat equations are, I think my problem will become much harder!

I should also mention that if I myself don't do the FEA, I will have to pay a designer to do it so the simplified hand calculation may be required to justify cost to seek external help.

 

[davefitz]

The problem is well covered in the european norm EN 12952-3 section 13, this is a standard problem in boilers. This EN method borrows from the older german boiler code TRD 301 annex 1.

A similar solution is published by Timoshenko

"Nobody expects the Spanish Inquisition! "

 

[NovaStark]

The problem is well covered in the european norm EN 12952-3 section 13, this is a standard problem in boilers. This EN method borrows from the older german boiler code TRD 301 annex 1.

A similar solution is published by Timoshenko

Do you know where I can get a link to any of those (or some preview)? Preferably whichever is in English? (I don't have access to any EN or German codes.

 

[davefitz]

The least costly version is the "draft BS EN 12952-3", about $40 USD.

"Nobody expects the Spanish Inquisition! "