Pulse Tube Cryocooler - Part 1

foreign I'm going to expand on my previous experiment with a resonant linear motor to build a linear compressor which I'll use as the pressure Source in an attempt to build a pulse tube cooler a pulse tube is a device used for refrigeration down to extremely low temperatures in extreme cases multi-stage pulse tube coolers can drive a cold tip down to a few degrees above absolute zero this temperature range is required for things like Quantum Computing and various scientific instruments such as superconducting magnetometers for my own purposes I'd simply like to liquefy nitrogen which happens at a much higher but still extremely cold temperature of 77 Kelvin or negative 196 degrees C a pulse tube isn't necessarily as efficient as a sterling cycle cooler but it has the huge advantage that it has no moving Parts in the cold end in the case of a sterling cooler a displacer piston moves back and forth in the cold end but a pulse tube replaces this part with a carefully tuned pneumatic circuit that involves a long tube and a buffer tank which act like an inductor and a capacitor in an electrical circuit to create a phase shift between pressure and gas flow similar to how an LC circuit creates a phase shift between voltage and current for starters let's imagine a piston and a cylinder where everything is at ambient temperature now suppose the Piston compresses the air inside the cylinder when the air is compressed it heats up let's look at this on a pressure versus volume graph we start at 0.1 and those gray lines are lines of constant temperature or isotherms when the air is compressed volume goes down and pressure goes up the temperature goes up too so 0.2 is up and to the left of 0.1 and also on a different isothermal line on the graph if we leave the piston in place for some time and let the heat from compression dissipate will return to ambient temperature but now still at a higher pressure and lower volume than we started with this is 0.3 now suppose we do the opposite and suddenly expand the air in the cylinder this will cause a drop in temperature now point four is below ambient temperature and the cylinder will start absorbing heat from its surroundings causing a cooling effect here's what the cycle would look like on a temperature versus time graph from point three to four we're creating a temperature drop but we're also heating from point one to two so there's no net cooling effect we're going to have to change the system a little bit to make it useful let's add a second cylinder and another piston this is called a displacer the displacer is a loose fitting piston that doesn't compress or expand the air it's just there to take up space and by moving back and forth it can shuttle the air from one spot to another now when I compress the air I can dissipate the heat on one side of this place or cylinder move the displacer and then cool the air on the other side and practice the hot end here would have a big heatsink on it and the cold end would be insulated against the outside world if we return to the temperature graph our hot in temperature over time would look like this and the cold end temperature would progressively get colder and colder down to a certain limit this is pretty much how a sterling cycle cooler works now there are some practical limitations to the setup for one the heat transfer to the outside world is far from perfect and the compression ratio usually isn't all that high with commercial Sterling cooler devices maybe in the neighborhood of 1.5 to 3. let's take an example case where the compression ratio is 1.5 if you assume everything is isentropic the minimum temperature you'll end up with is about 268 Kelvin which is just a few degrees below zero C something doesn't add up here these devices can go well below liquid nitrogen temperature but that's all the way down at 77 Kelvin even if we pushed up the compression ratio to say three or four it wouldn't get anywhere near that temperature so what's going on here well to make this thing get really really cold we need one more component which is called a regenerator a regenerator is a heat exchanger but it doesn't transfer heat to or from the outside world it's an internal heat exchanger to understand why we need this let's return to our pressure versus volume graph this process shows a perfect case that assumes heat is perfectly transferred but in reality it'll probably be more like this because the hot end won't dissipate 100 of its heat in one cycle which means the cold end won't get as cold as we wanted plus the cold end won't transfer all of its cooling power to the load in one cycle to resolve this we'll dump that leftover heat from the hot end into the regenerator which is like a big thermal sponge made from a really dense Matrix of material that has a ton of surface area to transfer heat almost instantaneously and hold on to it now the regenerator has pre-cooled the air before the expansion and cooling phase so now we've got high pressure air that's been pre-cooled by the regenerator down to ambient temperature and we can expand and cool it absorbing energy from the cold load like I said before we won't get perfect heat transfer from the cold load so as the displacer Piston moves back the cold air rushes back up through the regenerator cooling the bottom portion of it to a little bit below ambient temperature from the leftover cooling power that didn't get transferred to the load a well-designed regenerator will recycle almost all of the unused thermal energy in one cycle and the temperature of the cold end will become progressively colder even below the minimum temperature that would result from isentropic expansion the concept of regenerative cooling is also used in Continuous Flow devices like a joule Thompson cooling cycle where high pressure ambient temperature air is expanded and the cold expanded air is used to pre-cool the incoming air below ambient temperature which then expands to an even lower temperature causing a sort of snowballing effect that can drop the temperature far below what the expansion valve alone can accomplish regenerators can be made from lots of different materials but what they'll all have in common is an extremely high internal surface area a high specific heat capacity and somewhat counter-intuitively a low thermal conductivity this is because you want to drop off the thermal energy right at the surface and leave it there until the next cycle meaning there's going to be a temperature gradient across the regenerator if it's thermally conductive the temperature gradient will disappear and the whole thing is pretty much useless because of this fact some pretty weird materials can be found in cryo cooler regenerators like cotton fiber or certain types of plastic you also want a really low flow resistance in the regenerator however this particular parameter is in competition with the surface area parameter because more surface area means more heat transfer but it also means more losses from viscous effects especially in situations where you have very tiny gaps like plates or wires that are spaced a few fractions of a millimeter apart there's usually a sweet spot in any particular design where you want to balance between not causing too much flow resistance but at the same time having enough surface area to get extremely fast heat transfer okay so that's how a sterling cooler works in a nutshell now here's a pulse tube just like before we've got a compressor heat exchanger regenerator and a cold end but we've also got a few more bits to the right of the cold end although none of them are moving Parts the tube to the right of the cold end is called pulse tube and it replaces the displacer Piston from the Sterling cycle with a so-called gas piston that forms a thermal barrier between the ends of the tube like before the compressor pressurizes the gas and heats it heat is removed by the hot heat exchanger and the regenerator and flows into the cold end at ambient temperature however when the air on the right side of the pulse tube is pressurized it heats up from compression even though the incoming gas is at ambient temperature which is why it needs a hot heat exchanger on the right side of the pulse tube this pressure causes the gas in the right side of the tube to accelerate through the needle valve and into the buffer tank now the compressor moves back and starts expanding the gas but the displacer gas is still moving to the right from its momentum so a net cooling effect occurs before the displacer gas can make it back to the other side of the pulse tube if this is the compressor movement and thus pressure this is what the movement of the displacer gas would look like in the pulse tube the combination of the so-called inertance tube and buffer tank creates a phase shift that causes gas flow to lag behind pressure by around 60 to 90 degrees which is about the same phase shift as a displacer piston would have in a sterling cycle cooler the needle valve inertens tube and buffer tank form the pneumatic equivalent of a resistor inductor capacitor or RLC circuit the needle valve creates a flow resistance the inertens tube effectively works like an inductor by causing a lag between gas flow and pressure due to gas momentum and the buffer tank acts like a big capacitor the sinusoidal motion of the compressor piston is analogous to the sinusoidal ac voltage waveform all right that's enough Theory let's try to actually build it I'll start with the linear compressor I printed some new pla Springs which have a smaller diameter than the ones in my previous video because if this works I want it to fit inside a four inch PVC tube so that the whole assembly can be pressurized I'm also going to add this feedback coil which will create a voltage from a little magnet stub on the end of the spring assembly so that down the road I can keep the mass spring assembly at its resonant frequency and phase by switching the coils based on zero Crossing events on the feedback voltage here's what the output of the feedback coil looks like on the scope when I flick the magnet on the spring so I've got the motor coils in this design there's two coils in a push-pull configuration and the big n52 magnet is in the rest position halfway between them the coils are wound with a thousand turns of 26 gauge wire and have about 50 ohms of resistance when they're cold big magnet is clamped between two clamshell housings that are screwed to the spring stacks on either end I designed it this way because there wasn't enough clearance between the magnet and the walls to fit axial screws this little Mount flange screws to the front of the spring stack which will attach to the compressor piston for first test I used a 200 millimeter long glass tube this is far from optimal but it would allow me to look inside to see what's going on when the cooler is running the tube is glued to a 3D printed adapter to an aluminum cylinder that the Piston goes back and forth inside of it didn't have a perfect seal but it held pressure for a second or two when it was pushed on which I guess is a decent starting point here's a look at the readout from the pressure sensor when it's hooked up to the cylinder foreign [Music] before I assemble everything I'm going to cram in some stainless steel sponge as a regenerator this is again far from optimal but it's good for a first go now let's put everything together and see if it works [Music] foreign [Music] looks pretty good so far the first test I'm going to do is check to make sure the coils move the piston back and forth when they're energized next I built an h-bridge circuit to drive the coils this has a range of around 15 to 80 Hertz that I can sweep through with a potentiometer knob foreign there's a ton of vibration and no noticeable temperature change at least on the outside wall of the tube before I do anything else I think I need some balance to do this I added another stack of Springs which were mounted on standoffs at the back of the motor and attached a little bit of Mass to them when the vibrations from the motor match the resonant frequency of the mass spring system of the balancer it almost completely cancels out vibration because it's pretty much 180 degrees out of phase with the motor vibration in an ideal case the mass of the balancer is tuned just right so that it resonates at the same frequency as the motor Springs and minimum vibration occurs at the point of maximum power this thing is really cool when I start up the motor it's practically shaking itself to Pieces but as I sweep through the driver frequency the vibration almost entirely disappears when I hit that balancer frequency I mounted an accelerometer on the motor so that we can see the effect on a plot the vibration Peaks and then drops to a much lower value at the same time that I start to see maximum travel out of the passive balancer I got about a six degree temperature difference in the tube but this was really from the cylinder getting hotter than Ambien not the cold end going below ambient I think with the current setup I'm just heating the tube from compression so I need to try a longer tube to get more of the phase shift effect I removed the glass and put on a new adapter with a coupling for a one inch PVC pipe I added these grates in the coupler to keep the regenerator mesh in place although in retrospect that probably wasn't necessary because I packed it in so tight foreign again and this time with a much longer pipe of about eight feet but it only got a temperature difference of 4.2 degrees and once again that was above ambient not below I suspected that part of the problem might have to do with the fact that the Piston had a pretty bad seal and leaked a ton of air I already spent a bunch of time fine tuning it to get a good fit against the cylinder wall so I didn't think I'd be able to make it any better instead I changed to an accordion piston which I printed out of TPU this piston had a much wider bore which meant it should displace more air with the relatively Short Stroke of my linear motor next I added a balancer with a much larger Mass to try and get its resonant frequency closer to the motor's frequency which seemed to work pretty well [Music] foreign against the Piston I can really feel the compression and suction the TPU actually forms a really good seal with no pores that leak air out I also figured part of my problem might be the fact that I have a really low compression ratio which means the compression heating is pretty low so there's not a very large temperature difference to transfer heat out of the system to help solve that problem I took some two millimeter copper tubing and cut it up into straight pipes that I clustered together between the compressor piston and the regenerator this will exponentially increase the surface area to volume ratio and help dissipate heat from the relatively small temperature difference in the hot end [Music] this time I added a valve inertens tube and buffer volume so that everything was set up like an actual pulse tube cooler however when I ran it there was basically no temperature difference even after making several adjustments to the valve position what I did find though was that when I manually pushed the compressor piston even at a low frequency I did manage to drop the temperature a few degrees below ambient this makes me think that the pulse tube is set up correctly but my linear motor is probably too weak to create a reasonable pressure ratio so I'm not really seeing any measurable effect from it the next part of this project I'll probably have to build a stronger compressor using a brushless motor and an air cylinder on a crankshaft because getting to a higher compression ratio seems to be really important there's actually another type of pulse tube that uses a completely separate compressor and only has to open and close valves to create pressure oscillations that could be a big Advantage because it would allow me to use a commercial air compressor which is a lot more powerful than what I can build with a small motor there's also a lot of fine tuning that's required with the valve and nurtens tube and buffer volume this is no different than tuning a resonant AC circuit where the resistance inductance and capacitance all need to be carefully adjusted to get a particular phase and current I found these formulas in some research papers on pulse tubes that relate inductance and capacitance to inertance and compliance so these will be useful in designing future iterations I've provided links to some white papers in the description if you're interested in learning more I'm also simultaneously experimenting with other cryo cooler construction methods while I was working on this video I was also designing and building an alpha type Sterling cooler and a Gifford Mac Mahon type cooler which uses only a displacer piston and valves connected to a commercial compressor these projects have been consuming a lot of time and research effort so if there's a long gap between my video uploads don't worry I haven't quit YouTube it's just taken me a lot of time to get this right I hope you found this interesting and stay tuned for the next part of this series thanks for watching

Channel: Hyperspace Pirate

Views: 445,802

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Id: GjRoThMyNGA

Length: 18min 16sec (1096 seconds)

Published: Wed Dec 07 2022