mean temperature of shell material 1

[orch]

We have a vessel that is heated with steam in an atmospheric jacket.

The steam is thus at atmospheric pressure. The bulk water inside the vessel is at approx 35C and static. How can I calculate the mean temperature of the material of the vessel shell (in this case stainless steel).

I recognise that any condensate will create a barrier on the steam side and that the water in contact on the inside would have a hot layer close to the vessel wall.

We are concerned that thermal expansion on the vessel could cause issues and I need a mean material temperature in order to undertake some stress calculations.

Any advice much appreciated!

 

[boddah]

Where is the tank situated and what is the ambient temp?

 

[mjpetrag]

I would assume a constant wall temperature (temp of steam) for the inner jacket's wall and use that as a worst case scenario for thermal expansion. Really simple calculation, but it's a start. What sort of wall thickness are you looking at?

-Mike

 

[orch]

Thanks for the quick replies.

The tank is indoors and the ambient is 25 - 30C.

Wall thickness 3mm

Taking the temperature of steam seemed a good starting point, but that is also true of the outer jacket skin too, so the jacket and vessel shell would expand together = no problem.

We have experienced cracking at the vessel / jacket weld though, and believe that the inner vessel is not expanding equally with the jacket.

I have taken some measurements of the jacket skin externally (80C max) and can assume that the surface of the jacket in steam contact is at almost 100C (after an allowance for an air film), But I am struggling to find a method to calculate the mean inner wall temperature to calculate the relative expansion of the vessel.

Graham

 

[chicopee]

Because the conductive coefficient of metal is linear within certain temperature ranges, the mean temperature of the metal would be appx. 1/2*(Tsi+Tso),whereby Tsi,Tso are the wall surface temperatures on the inside and outside of the shell. Statement "Appx." because I don't know if vessel is rectangular or cylindrical.

 

[corus]

Consider the worst case for your calculation, say with the jacket at 100C and the outer vessel at a constant 80C. At only 3mm thick the temperature gradient is likely to be very small anyway. If, with a mean temperure difference of a maximum 20C, the stresses at the weld aren't sufficiently large then you'll know the problem lies elsewhere.

corus

 

[orch]

Thanks again.

We know the worst case scenario is sufficient to cause stress points. For info the assmbly (horizontal cylinder) is 6 metres long.

I have been given an analysis by an unknown "expert" who has suggested that with steam at a nominal 105C will give a temperature on the jacket wall of over 100C (reasonable as it is then insulated). The expert has sugested that the vessel wall in contact with the water at 30C will have a mean temperature of 92C (this 8C difference is not enough to cause stress issues).

My feeling is that this calculation is incorrect but I have no way to demonstrate why.

My gut feeling is based on the assumption that the water is able to dissipate the heat quicker than the steam can add it, so the skin temperature should not be above the mid temperature between the two (i.e steam 105, water 30, mean temperature max <62C. This equates to a 40C difference between jacket and vessel. This is probably enough to cause our stress issues.

Is it a case of knowing the U value for steam to st/st transfer, similar for water to st/st, then ariving at a temperature where the delta T's and U values cause the two energy transfers balance? i.e a state of equilibrium?

This would be reasonably easy to calculate but I do not want to argue a point based on flawed logic.

Regards Graham

 

[mjpetrag]

The thermal expansion of the inner jacket (assuming a temperature of 92 deg C and 6 m length) is about 0.175". Thermal expansion of the outer tank shell (assuming a temperature of 100 def C and 6 m length) is about 0.20".

But the expansion on the inner jacket is going to be sloped toward the side closest to the steam and drop off closest to the water.

How full is this tank going to be with water?

-Mike

 

[prex]

If I understand you correctly, you have condensing steam in the jacket, and you collect the condensate, right?
That condition makes a very good arrangement for heat transfer, I would expect a heat exchange coefficient well in excess of 1000 W/m²°C. Water side the exchange is much worse, as the water is not flowing: I would expect a heat exchange coefficient with an order of magnitude of 100 W/m²°C. These numbers are just gut feeling and could be calculated much more precisely, but, at least to me, that would require quite a long time.
If I'm correct, it seems that your expert is well to the point.

prex

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[corus]

If the expert ha said 92C and you have measured 80C max, then surely that puts doubt into the expert's calculation given that the vessel wall is thin, or have I missed something there. Even if the expert is correct then you have 80C outside and a mean temperature of 92C suggests that you would have bending stresses in the wall, which would have to be added to the differential thermal expansion of the jacket and vessel, which in themselves will apply bending at the weld.

corus

 

[orch]

Interesting thoughts, thank you.

For clarification the jacket is outside of the vessel. The 92C mean temp calculated is the wall between the steam and the water.

The measured 80C figure was on the outside of the jacket (which is the outer skin excluding the insulation and cladding.)

We all expected the measured 80C figures to be closer to 100, and this added to my concerns that the calculations were flawed.

Prex, thank you for the post, You seem to have hit the nail on the head suggesting that the steam condensing is much better at heat transfer than the water is at taking the heat "away", as this would agree with the figures that were previously calculated.

In the course of this discussion, I have realised that the calculations etc are based on the availabilty of sufficient steam, The fact the jacket only reaches 80C suggests to me that there is simply not enough steam to raise the equilibrium point to it's maximum.

This would make Prex's (and our "experts") calculations valid, but explain the findings from the field. I now just need to work out what is actually happening....

 

[athomas236]

The above calculations seemed to consider steady state operation. Have you considered what happens when steam is admitted after the vessel has been out of service. In such a case the jacket temperature could, in theory, be that of the steam whereas the vessel wall temperature could still be that of the internal water.

Actual case will be more complicated but the simple explanation given just to emphasise the possibilities.

Regards,

athomas236