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Thermal deflection of the inside of a pressure vessel.

Thermal deflection of the inside of a pressure vessel.

Thermal deflection of the inside of a pressure vessel.

(OP)
I have a motor incased in a pressure vessel.
Inside the casing the motor atmosphere is rated to 80°C. The outside atmosphere can be towards -2°C.
I assume that the outside temperature of the casing is higher than -2° but lower than 80°C so I would get a temperature gradient over the casing wall thickness.

The motor has various pressure compartments for driving cooling flows over the motor that require seal between the motor and the casing.
I would like to know the clearance between the motor and the casing for all temperature scenarios.
I can do this with FEA but it is a cumbersome process so an analytical approach would be preferred.
I have found temperature gradient dependent formulas in Roark’s formulas for the stress in the casing wall but I can’t find any analytical formulas for the diametrical change on the inside (or outside) diameter.

RE: Thermal deflection of the inside of a pressure vessel.

Change in diameter due to temperature gradient across thickness is what I guess you want to calculate.
Thermal expansion of cylinder diameter=diameter*temperature difference*coefficient of expansion.
The formula remains same for any thermal expansion, diametrical or longitudinal.

RE: Thermal deflection of the inside of a pressure vessel.

(OP)
Thank you nrp99,
If the tempratur was uniform over the thickness i would agree. In my problem the outside dia would constrain the inside dia so im not sure its the right solution in this case.

RE: Thermal deflection of the inside of a pressure vessel.

I guess expansion will be linearly varying from the outside diameter(-2oC) to inside diameter(80oC). So you can calculate the inside diameter expansion and outside diameter expansion separately and your expansion of in between diameters will be along line connecting these two expansion values.

RE: Thermal deflection of the inside of a pressure vessel.

The post is really asking "what happens when the ID wants to expand and be bigger than the OD wants to allow, and how do you calculate that?"

RE: Thermal deflection of the inside of a pressure vessel.

1gibson

In my humble opinion, answer is straight forward. The outer diameter will not allow the inner diameter to expand. Still the expansion will be linear as I already stated in earlier post. The inner fibers will get compressed in between contraction of outer fiber and expansion of inner fiber. Net amount of expansion/contraction will depend on the exact values of the OD expansion and ID contraction.

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