Mathematical model nitrogen cooling 2

[mechchem]

I am trying to solve a problem on a shroud that covers vacuum chamber. It isn't in contact with the chamber but they are separated by teflon blocks. A shroud is a metal enclosure which has pipes on it's surface through which heating or cooling materials flow.

Liquid Nitrogen is used to achieve cooling and heating is acheived by heating rods stuck to the shroud's outer body. The LN2 pipes are spot welded every 6 inches to the stainless steel body of the shroud. So that is the only physical contact between the pipes carrying LN2 and the body below.

I want to calculate the cooling rate with liquid nitrogen, and time to achieve 90 Kelvin (come up with a model). So I need to figure out the flow of LN2 (liquid nitrogen) into the tubing, and correlate that to the cooling.

I don't quite know where to start, what sort of assumptions will go into making the model. I would appreciate any help/hints that you can give of how to go about solving this problem and coming up with a model.

All dimensions of the shroud are known, the material densities are also known. The shroud is black from inside so we dont need to consider heat exchange in there since it will be a black body. The outside of the shroud is polished and will reflect the ambient temperature. LN2 will be flowing in the pipe and the pipe is welded to the body only at distance of 6 inches each. So the ways in which heat gets transferred to the body of the shroud and to the vacuum chamber inside will need to be taken into account.

 

[prex]

It is not an easy problem, if you want to go with an approach by formula (as I would do anyway). The alternative is to build a 3D FEM model.
For the first approach these are starting considerations.
First point is to define which part of the internal surface of the tubing is effective in exchanging with LN2, as it is evident that only the parts of the tubing closest to the spot welds are fully effective. Assuming the exchange is circumferentially uniform (not really true but hopefully not too wrong), you would look for an equivalent length that could be defined using the formulae for fins of uniform section. The main parameters for this result are the thickness (and of course material) of the tubing and the exchange coefficient with LN2.
Second point is to model the flow of heat from the spot weld into the shroud. Taking the surface of the shroud divided by the number of welds you can define an area of shroud associated with each weld. Now imagine this area to be a circle with the weld at the center: you could take the half radius as a distance and the section through thickness of the shroud at mid radius as the area through which heat flows: this will give you a rough heat resistance associated with the heat flow in the shroud.
Third point is that one of the two resistances analyzed above will be higher than the other one. If the higher (presumably the resistance on tube inner surface) is also much higher, then you can go on by neglecting the lower resistance. The problem becomes unidimensional and may be solved quite easily.
Hope the above discussion will help you in deciding if you can go on by yourself with a by formula approach.

prex

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[mechchem]

I kept the window open after posting a reply since I expected quality and fast replies from the brothers/sisters on this forum. Thanks for the reply prex, you contributed in very good points. Maybe others can pitch in with something too. Thanks for your time.

 

[mechchem]

Hey Prex, if you can expand on two points please.

1. "formulae for fins of uniform section". What are those?
2. "Now imagine this area to be a circle with the weld at the center: you could take the half radius as a distance and the section through thickness of the shroud at mid radius as the area through which heat flows: this will give you a rough heat resistance associated with the heat flow in the shroud."

IF I understood this correct, u mean to say that the spot area can be added up and it can be assumed to be a O-ring around the shroud welded at the centre of the shroud. Right?
What do you mean to say by: take the half radius as a distance?

 

[IRstuff]

A picture or drawing would help. Is this something that already works? I'm having difficulty imagining what all the condensation from moisture in the air is doing on the shroud. Nitrogen has pretty poor thermal conductivity, so how are you going to get 90 K on a surface that's exposed to air?

I'm likewise unclear why you would heat or cool a vacuum chamber shroud, since the thermal conductivity is essentially nil. Why wouldn't you just heat or cool the sample in the chamber directly? The inefficiency of controlling the shroud to control the sample has got to be ferocious.

TTFN

FAQ731-376

 

[mechchem]

Hey guys! I am REALLY SORRY for the confusion. There is a thermal vacuum chamber. The shroud goes IN the thermal vacuum chamber so it won't be exposed to air. However the pipes won't be touching the inside surface of the vacuum chamber since there are about 12 teflon blocks (3 each at 0 deg, 90 deg, 180 deg, 270 deg) which separate the shroud from the thermal vacuum chamber.
So the only heat transfer would be by radiation and conduction and no convection. The inner surface of the shroud is black. The outer surface is high quality polished. So emissivity would be need to be taken into account.
Yea now it makes more sense and 90K should be achieved since it will be inside the thermal chamber and not exposed to air.
See attached JPEG picture. I couldn't make it 3D.
So how should I proceed now? And is there a way to make a note in the first post that please read this one too before brainstorming so that others who read that don't get confused.

 

[IRstuff]

One thing to do to reduce confusion is to not start another thread on the same subject. ;-)

OK, so this is now a relatively straightforward heat balance problem. You have coolant coming in, and heat coming in from the inside as well as the outside, to differing degrees because of the emissivity differences, plus heat coming through the teflon blocks.

To the first order, you can lump all the stuff together, and see how much heat is coming in, and whether there's enough LN2 flow to stay liquid.

The second is more challenging, which would be to create a distributed lumped model of the LN2 lines which stay close to 77K, and the place on the shroud that's in the middle, between the LN2 lines. You might treat the geometry as if everything was circular as a start. So, a series of annuli, with heat coming in from radiation, and conducted to the next outermost annulus, until the outermost annulus is attached to the LN2 pipe. Add in some fraction of the total heatload from the teflon blocks, and you should have some sort of answer.



TTFN

FAQ731-376

 

[mechchem]

Thanks.

 

[prex]

mechchem, what have you done so far to start clearing out your problem?
Determining the heat exchange coefficient for various LN2 flows is something you need to know the first. Then, from the heat capacity of the shroud and assuming that the heat transfer is effective over the whole tubing length, you'll get a lower limit of the required time. I guess this would be a useful piece of information to start with (and if you have problems arriving there, I can't see how you will reach your goal).
See thread391-200151 concerning the fins (or bars) of uniform section.

prex

http://www.xcalcs.com

: Online engineering calculations

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: Air bearing pads

 

[chicopee]

Wouldn't it be easier to use thermocouples and record temperatures including ambient under different N2 flow rates for this particular case. Any initial equations ( until tweeked) will be at least 50% off.

 

[kstifle]

mechchem,

We did similar work about 17 years ago when I worked for the SSC (Superconducting Super Collider). You can search for SSC cryogenics and find information on how we modeled the LN2 heat shield.