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### Cooling gas by expansion

Posted: Thu May 31, 2018 3:38 pm UTC
So I have a compressed gas in a tank.

1)

I release it through a nozzle into an infinite vacuum, like say, space.

Does the gas cool to absolute zero due to infinite expansion, or is there some limit to cooling?

Does the mean-free-path have anything to do with this?

2)

Same question but this time the nozzle extracts work from the gas by producing thrust with a bell nozzle.

***

The context here is producing IR-stealth-in-space by active cooling the entire ship with liquid hydrogen, then venting the hot (potentially very hot, say 1000K) hydrogen through an expansion nozzle which expands and cools therefore emmitting no significant IR radiation above background. Clever geometry is used to avoid anyone outside "seeing" the gas before it cools. Im not interested in the geometry right now.

I am coming at this from a position of scepticism, I find it hard to believe that 1000K gas can be used to propel a spaceship with a zero (or very close to zero) temperature exhaust.

Real-life example: footage of apollo stages/interstages being flambeed during stage seperation.

### Re: Cooling gas by expansion

Posted: Thu May 31, 2018 3:54 pm UTC
Temperature as a concept doesn't work too well in a gas with zero pressure. You should be able to cool the ship though. Aerosol cans will lose heat while spraying into open air, and I don't think the ambient pressure is making a strong contribution. Can't make a strong argument/reference for that of the top of my head, though. Here's a wiki article for you, though.
https://en.wikipedia.org/wiki/Venturi_effect

As a propellant, hot Hydrogen actually ideal, in the sense of propellant efficiency (for thermal rockets; electromagnetic thrusters are quite different). Monatomic H is the best, but generally not practical.

Stealth in space is hard, but it depends a lot on how strict your requirements are. You speak of an "IR background". Where is that coming from?
http://www.projectrho.com/public_html/r ... h_In_Space

You might be able to maintain a temperature gradient such that you have a cooler face towards the adversary, and a hotter one behind, but that takes energy (the generation of which is going to make its own waste heat that must be gottten rid of!) to maintain, and you will have a lot of trouble keeping the cool side cold enough to blend in with open space at 3K.

You say you can use clever geometry to prevent observation. You can't seal off all 4pi steradians, though. The exhaust has to go somewhere. You will be detectable if sufficiently surrounded.

Combining stealth and propulsion is a bad idea anyway. They aren't, in general, going to be directing thrust in the same direction. Correcting one is going to defeat the other. You will find situations where they can be balanced effectively to be very unusual.

It gets easier if you dispense with all that useless meat that has to be kept warm, though. This also makes your craft a lot smaller/lighter, requires less fuel, has way fewer ways to break down, and more maneuverable!

Space is a severely intuition-defeating environment.

### Re: Cooling gas by expansion

Posted: Thu May 31, 2018 5:09 pm UTC
thoughtfully wrote:Temperature as a concept doesn't work too well in a gas with zero pressure. You should be able to cool the ship though. Aerosol cans will lose heat while spraying into open air, and I don't think the ambient pressure is making a strong contribution. Can't make a strong argument/reference for that of the top of my head, though. Here's a wiki article for you, though.
https://en.wikipedia.org/wiki/Venturi_effect

As a propellant, hot Hydrogen actually ideal, in the sense of propellant efficiency (for thermal rockets; electromagnetic thrusters are quite different). Monatomic H is the best, but generally not practical.

Stealth in space is hard, but it depends a lot on how strict your requirements are. You speak of an "IR background". Where is that coming from?
http://www.projectrho.com/public_html/r ... h_In_Space

You might be able to maintain a temperature gradient such that you have a cooler face towards the adversary, and a hotter one behind, but that takes energy (the generation of which is going to make its own waste heat that must be gottten rid of!) to maintain, and you will have a lot of trouble keeping the cool side cold enough to blend in with open space at 3K.

You say you can use clever geometry to prevent observation. You can't seal off all 4pi steradians, though. The exhaust has to go somewhere. You will be detectable if sufficiently surrounded.

It gets easier if you dispense with all that useless meat that has to be kept warm, though. This also makes your craft a lot smaller/lighter, requires less fuel, has way fewer ways to break down, and more maneuverable!

Space is a severely intuition-defeating environment.

"Background" meaning cosmic microwave background.

And the concept of "temperature" in terms of emission of black body radiation.

Naturally Im aware that some cooling can be done, but can an exhaust plume be made "invisible" (as in within a handful of Kelvin of absolute zero) in terms of IR emission?

I know that an expanding gas cools adiabatically, but once the molecules are past a certain distance, surely further expansion has little effect on the energy content of each molecule, thus allowing them to radiate it as normal?

The geometry thing is another matter, Im sceptical of that too, but honestly, if the low-observable exhaust is possible, it would be a massive boon for stealth in space, fancy geometry or not.

Of course when I say "stealth" or "low observable" I dont mean "zero-point-zero Kelvins", but there is a detection threshold of todays cutting edge IR observatories, so if you can get within a handful of Kelvins of the CMBR, it would be very difficult to spot you at range.

Yes I klnow there are other complications in bringing the whole skin of the vehicle to the temperature of your coolant, and many other intricacies, but if the thermodynamics doesnt work at this key point, there no point in worrying about all of that.

Im "au-fait" with all the standard wisdom prject-rho-wise, and all the usual arguments against. But lately have come across a couple of time this concept including active cooling which - as explained - produces a very difficult to observe ship. But there are a few key concepts that I am sceptical of. The entire heat load of the ship being magicked out of existant through its own exhaust being the main one.

I think this is the concept, though I first heard of it on the KSP fora:

http://toughsf.blogspot.com/2016/10/the ... eship.html

Again, I dont want to muddy the waters talking about waste heat from heat pumps, various thermodynamic inefficiencies, angles of observation etc, just want to know if the cold exhaust thing is valid or not.

### Re: Cooling gas by expansion

Posted: Thu May 31, 2018 5:39 pm UTC
That's a very interesting post by somebody who has a lot of knowledge on the subject (likely more than me). I didn't check the details, but overall it seems like it could work as described. Describing all black-body emissions as "IR" is confusing, but it's a common enough mistake. It's enormous, though. Occlusion is going to be an issue. Getting out of the way of threats will be difficult. It also relies on the Sun for its propulsion. Engineering is about trade-offs, though. Like I said, it depends on the requirements.

### Re: Cooling gas by expansion

Posted: Thu May 31, 2018 6:49 pm UTC
thoughtfully wrote:Describing all black-body emissions as "IR" is confusing, but it's a common enough mistake.

Well we aren't going to be looking for these things with radio telescopes, but I see your point

Wait, or are we?

Probably a discussion for another thread.

### Re: Cooling gas by expansion

Posted: Fri Jun 01, 2018 3:44 pm UTC
Does this concept have any bearing on the subject?

https://en.wikipedia.org/wiki/Free_expansion

Here it states that free expansion into a vacuum is isothermal, no temperature change.

However it also states that no work must be done by the expansion - although the "work" they refer to is pushing against an external pressure, would the reaction force from the gas escaping count as this "work"?

Would it, in reality, be a combination of adiabatic and isothermal expansion? So we could expect a drop in the temperature of the exhaust but perhaps not all the way to absolute zero?

Im still interested in whether or not "mean free path" is an important factor.

### Re: Cooling gas by expansion

Posted: Fri Jun 01, 2018 5:25 pm UTC
would the reaction force from the gas escaping count as this "work"?

Yes. That's exactly what the laval nozzle does, it turns the heat of the gas into work. Not just the reaction force, also the kinetic energy of the jet. Attach the nozzle to the fixed world, and it's basically a machine to turn the random heat movement of the molecules into a single linear movement. I don't there's a simple fundamental thermodynamic limit to that - on paper, you can expand all the way to infinity and zero K.

In practice, there will be friction losses. For regular shoet rockets, it's in the 1% range. That could build up to much more for a super long nozzle, I guess. That 1% friction heating on a 2000K gas would already play havoc if your end goal is sub-20k.

And the free path will mean that gas flow won't be a coherent jet after some point. I am not quite sure what happens then, but I bet that the quasi-1D nozzle equation is not valid anymore.

I plugged in a temperature decrease in the nozzle for hydrogen from 1 ATM and 2000K, down to 20K and to 2K. That gives me mean free path of about 0.1 respectively 1 meter. The limit must be there somewhere.

### Re: Cooling gas by expansion

Posted: Sun Jul 01, 2018 4:09 am UTC
There's several basic issues with the hydrogen steamer. Rocket exhaust expansion is isentropic. You need an expansion ratio of about 230000 for the exhaust to reach 20 K, not the author's estimated 45000. The serpentine nozzle is also far from an ideal de Laval nozzle, and you'd have thermal signatures from internal shocks and scatter within the exhaust. And if you did get the exhaust to be that cold, it wouldn't stay cold after it hit sunlight. It'd heat up, ionize, and make a big glowing arrow pointing at your "stealth" ship.

The author also assumes without justification that Vantablack can be made to be almost totally absorbent from visible light down through radio, and assumes that it and the tanks its on have no thermal resistance and won't heat up significantly compared to the hydrogen in the tanks. Incident lidar or radar pulses would produce thermal pulses, and might even damage the Vantablack (camera flashes have been known to ignite single-walled nanotubes here on Earth). Then there's the giant but magically invisible zone plate used to focus the sunlight...

There still isn't any stealth in space.

### Re: Cooling gas by expansion

Posted: Sun Jul 01, 2018 4:47 am UTC
Reionization is an insoluble problem with this approach to stealth as far as I can see. Instead of a rocket, you now have a comet.

### Re: Cooling gas by expansion

Posted: Fri Jul 06, 2018 10:03 pm UTC
p1t1o wrote:So I have a compressed gas in a tank.

1)

I release it through a nozzle into an infinite vacuum, like say, space.

Does the gas cool to absolute zero due to infinite expansion, or is there some limit to cooling?

Does the mean-free-path have anything to do with this?

Yes, it cools with no limit, and the mean free path would have bearing on the intermediate temperatures.

This is because after a reasonable span of time there won't be any more collisions (assume a small enough amount of gas that they will have escape velocity). After that point, the speed and position just get better and better correlated with time. In the limit of a long time passing, it becomes perfect. And then it's functionally zero kelvin - you have gases which are moving in some direction and speed, entirely based on where they are.

The mean free path determines how long it takes to get to that condition.

### Re: Cooling gas by expansion

Posted: Sun Jul 08, 2018 11:26 pm UTC
If the absolute temperature of a gas is proportional to the average particle kinetic energy, then how can a moving particle (regardless of whether it will ever collide again or not) represent zero kelvin? I don't get why the mean free path is such a big deal.

### Re: Cooling gas by expansion

Posted: Sun Jul 08, 2018 11:58 pm UTC
Moving relative to what? A single particle "gas cloud" would have all particles stationary relative to the cloud.

### Re: Cooling gas by expansion

Posted: Mon Jul 09, 2018 1:30 am UTC
Thesh wrote:Moving relative to what? A single particle "gas cloud" would have all particles stationary relative to the cloud.

An interesting point. So what you're saying is that EK is only meaningful if speed is measured with respect to the COM of a gas cloud within which some collisions might still occur? That seems a bit arbitrary. The mean free path might be light years, but a moving particle can still contribute EK to whatever and whenever it interacts. That potential exists as long as there are collections of particles elsewhere.

I would say assign the particle an EK based on its speed relative to the CMB. I have no idea how to calculate that temperature, but it would certainly be above absolute zero.

It would be cool (no pun intended) if that temperature came out to 2.6 kelvin.

### Re: Cooling gas by expansion

Posted: Mon Jul 09, 2018 2:52 am UTC
Cross-compare with the likes of…
https://physics.stackexchange.com/quest ... e-universe
…maybe?

(I tend to think along the lines of the quote in the latter that "the CMB does not define some special frame of reference. Simply an identifiable one." I'd have to seriously think more about the follow-up comments to that before I changed my mind significantly.)

### Re: Cooling gas by expansion

Posted: Mon Jul 09, 2018 3:33 am UTC
Heimhenge wrote:
It would be cool (no pun intended) if that temperature came out to 2.6 kelvin.

There's nothing special about the CMBR temperature; it's just how cool the CMBR happens to be at our current time. It was hotter in the past, it'll be cooler in the future.

### Re: Cooling gas by expansion

Posted: Sun Jul 15, 2018 6:09 pm UTC
If you are writing a story and want stealthy propulsion you should check out this thread. The idea is really straight forward and simple. Thrust is generated the exact same way as a chemical rocket, but the atoms are replaced with neutrinos. All that is required [I think] is a nuclear generator and a fantasy material that reflects neutrinos.

### Re: Cooling gas by expansion

Posted: Mon Jul 16, 2018 2:06 am UTC
Sterile neutrinos would be the stealthiest possible exhaust. But there is no known way even to convert a significant amount of energy into regular neutrino radiation. Anyway, that's pretty far off topic.

### Re: Cooling gas by expansion

Posted: Mon Jul 16, 2018 8:19 am UTC
Actually I dont want stealth, Im trying to falsify the hypothesis that the "hydrogen steamer" space-stealth design can work.

Because if it does everything it says on the tin, its pretty damn stealthy. And if it stands up to all the questions I can think to put to it, then I can consider it a legitimate answer to the stealth-in-space question.

Have to say, so far, whilst there are myriad complications which make its stealth perhaps less perfect than whoever came up with the idea would have liked, its about the stealthiest design I have come across.

Whether its stealth is sufficient to be of tactical use is a whole other - much harder - question, for a much longer thread.