Heat loss through stainless steel tubing

Please redirect me to the appropriate forum if I have posted in the wrong place...
This stuff is FAR over my head, and I need somebody with some real knowledge of thermodynamics and heat flow...
I own a scuba dive shop and of course we compress air to very high pressure, on the order of 300 BAR.
Common knowledge is that as air is compressed, the water being incompressible condenses out.
In out compressors which are multistage (3 or 4 is normal) we have separators to remove the water from the airstream between each stage.
Of course we must make this air VERY pure, pretty darn close to laboratory pure on a large scale, thousands of liters a day.
There are a number of principle contaminants that we have to deal with in our filtration systems.
In general however, the more water we get out, the better the air will be, as we are removing the oil from the compressor, another contaminant in the process.
We typically try for dew points around minus 50 to 60 *C, or more, so this is pretty dry air !
Of course the cooler the air stream, the more water that will condense out, the better the air and the longer the life of the filter system...(Not inexpensive).
So....I have taken the air stream which is passing through a stainless steel coil, (035 wall thickness) 1/4 inch outside diameter, 12 meters long and put it in an in water bath at 0*. The air is moving through this tube at 265 liters or more a minute, so it is going pretty fast. The temperature on the surface of the coil, before it enters the ice water is about 39*C.
The temperature of the surface of the coil after immersion 20 cm above the ice water is about 5*c. By the time the air has traveled about 1 meter to the separator the surface of the coil is now at about 30* C. Now, knocking the air temp down by 10*C will nearly double the life of my filters, but...since the coil surface temperature rises so quickly, and I would be thrilled to have the air inside it at 3 or 4* when it enters the separation chamber, my question is...do I have enough coil in the ice water ? I think I am not loosing any where near the amount of heat that is possible with this method. If I can get the air stream down to 4* I will increase my filter life by about five times !
Thoughts ? questions for clarification ?
Thanks very much for any or all ideas...

haruspex
Homework Helper
Gold Member
If I'm calculating correctly, each molecule of air spends about a twentieth of a second in the tube. So yes, you're going to need a much longer tube.

Hello:
Thanks very much for confirming my suspicions....
I did write a much more detailed follow up question including links to some images but for some reason it has not posted.
I clearly get the idea, and will be knocking my head to try and come up with another solution. There are commercial chillers on the market, but they serve another and additional purpose, which is to cool the air steam going into the third stage head as well as remove moisture, thus keeping the third stage compression chamber cool....and they are expensive in capital letters, and anything that complicated is bound to break and require a six week wait for parts to my little tiny island in the south china sea.

One further question to throw at the barn door, any idea of how many meters I WOULD need in the ice water to cool the air stream more effectively ? Of course if it a linear progression, we are talking about a whole lot..and we are looking at diminishing returns...
If by chance it is some sort of exponential function and I just need to hit the magic number, it may well be worth it.
Intuition tells me it will be a linear function, but as I know nothing about this and you quite apparently do can you revisit this for a moment.
Thanks very much for your time !

haruspex
Homework Helper
Gold Member
Unfortunately it is diminishing returns. The rate of transfer of heat is proportional to the temperature difference, so the closer the air gets to 0C the slower the transfer. Indeed, it will be a negative exponential. Based on your observations, looks like the length in metres you'd need to get the temperature down to T*C would be 46*ln(39/T).
Btw, since water is densest at 4*C, it would be best for the pipe to go to the bottom of the vat first then wind its way up. That way the air 'contacts' the coldest water last.

Hi Haruspex.
Thanks again for you quick reply...
Well I can say, I did get one part right on intuition, I DID indeed send the hottest air straight to the bottom of the vat ! I tried to add some photos but need ten posts, but if not in html maybe it will work if you look here.. H???://dl.dropbox.com/u/61531697/coil%20and%20compressor.rar
I did also have some feeling that there would be the greatest heat loss at the greatest differential in temperature...and it would be an exponential function to continue to remove the heat as it approached the temperature of the vat.
I did a test run with a 5 meter coil, and was most disappointed with the results, so I then went to the 12 meter coil.
Since this high pressure stainless steel tubing is almost impossible to get here, and there in significant benefit, as mention I have already doubled the filter life with the 10*c drop, I am willing to give it one more go, as I can reuse the tubing on another project, how about a 10 mm tube ? This would increase the internal diameter by at least double, but this could be a double edged sword, it could reduce the velocity, but it could also keep some or most of the hot molecules away from the cold walls of the tubing..
Any thoughts on this one ?
Or since you quite obviously know more about thermodynamics then me, do you have an idea for a system that would work ?
Thanks again for your help. This is not so much a matter of saving money, but getting things I need here on an island with a population of 2,500.... 350 Km from the mainland, there is no butter in the market, and I have to special order diet coke and bring it in by ship.
There is well and truly nothing here, no over night mail...fastest from the U.S. or Europe is 8 days and then I have to fly to the customs office on the mainland..This place is seriously remote !
Thanks again for your help !
Best regards
Larry

haruspex
Homework Helper
Gold Member
I think a wider tube will help, but assessing that is as much a question of fluid flow as of thermodynamics. You need the flow to be turbulent. Maybe helped by inserting something near the start of the pipe.. a bit like a fan blade?
From what I read, the viscosity of air depends mainly on temperature, not pressure. At the temps in question, Kinematic Viscosity η should be about 1.6 10^-5 m^2/s. The Reynolds number is
Re = 4Q/(π.D.η)
where Q is the volumetric flow rate, D the diameter.
Q = 265 L/min = 0.0044 m^3/s
So Re = 300/D (D in metres)
For turbulence need Re > 4000, so it looks like this won't be an issue. OTOH, I'm just figuring this out as I go along from articles on the web (I'm a pure mathematician/software writer by training), so don't mistake me for an expert.
Assuming you get turbulence, so good mixing, the gain from a larger pipe should be as the cube of the diameter. Doubling the diameter quadruples the time the air spends in the pipe and doubles the area of contact. This should give the same effect as a pipe 8 times as long.

Hi Haruspex...
Thanks again for your help !
Seems like my intuitions are confirmed by your mathematics ! I was considering putting something in the airstream to increase turbulence, this would break up any boundary layer on the tubing,and allow more more of the warm air to come into contact with the S.S. But if you saw the machine shop I do this stuff in. First you would be shocked, second you would call O.S.H.A. and third you would say it cannot be done in those conditions...with that in mind, I am more then a little scared of putting anything in the airstream that can become dislodged and swallowed by the compressor !

I think I will go hunting for some 10 mm tubing !
Eight times the length equivalent, if we are not getting anywhere with that, then this is indeed an exercise in futility !
If anything comes of this, provided I can find the tubing.....I will let you know.
Thanks again for your time and help with this !
Best regards
Larry