 So, welcome to the 29th lecture on cryogenic engineering. In the last lecture we were talking about sterling cryocoolers. In fact, we touched upon various aspects of design of sterling cryocooler and we found that for an optimum design of sterling cryocooler a compromise between the operating and the design parameters may be sought. So, you got to compromise between the dimensions and various operating parameters like pressure, frequency etcetera. So, we had studied Schmitt's analysis and we found that based on Schmitt's analysis the variation of Q e divided by P max into V t which we called as Q max and W t upon P max into V t which called as W max for a few non-dimensional numbers was presented. So, we understood how this parameter Q max and W max vary with respect to various parameters. A combined effect of parameters on performance of system as a whole was given by walkers optimization chart and we saw how this charts look and how do we use this charts for initial design of sterling cryocooler. Also, we understood that in order to account for the various losses and to make the analysis more realistic we took some Q e design value that is cooling effect required for designing aspect and that we took as 3 times Q e required. So, actually required Q e suppose 1000 watts we designed the cryocooler for around 3000 watt or 3 kilowatt. This was basically to take into consideration the account of various losses because we did not go in the details of calculation of each of the losses alright. So, this is the kind of a factor of safety which is used to design a sterling cryocooler using walkers design chart. In the earlier lecture a tutorial problem was solved on sterling cryocooler design using the walkers optimization chart and when we say design we basically intend to calculate the diameter of the piston, the stroke of the piston diameter of the displacer and the stroke of the displacer which in turn decide various others diameters of which we did not go in the details of those dimension calculations. For a given Q e design the dimensions of the piston and expander displacer are very large the system is designed for 2 cylinders or more. So, for a given cooling capacity if you found that the diameters are coming very large then we can conclude that this is not possible using 1 cylinder, but we may have to go for 2 cylinders or even if then the diameter comes very large then we have to go for 4 cylinder like that. And therefore, a 4 cylinder machine can you know generate lot of cooling effect than a single cylinder machine basically like any other automobile also if you want to compare this with. So, that is what we had talked about during the last lecture on sterling cryocooler and extending this topic further on cryocoolers here in this particular lecture we will talk about Gifford-MacBohon or GM cryocooler ok. So, we will talk about also we will try to compare the GM cryocooler with sterling cryocooler and this comparison is very important for you to understand. Then we will see how this GM cryocooler works I have got some schematics. So, that we can as understand how GM cycle or GM cryocooler works then the various important aspect related to regenerator especially the regenerators at low temperature wall mechanism how do they function I will explain that and let us lastly we have some commercial applications of GM cryocooler just to explain a few of them. So, in the earlier lecture we have seen the classification of cryogenic refrigeration and from here we can find out where the GM cryocooler lies. So, GM cryocooler lies somewhere over here. We found that for a close cycle version we have got a dynamic in dynamic we have got a regenerative and recuperative heat exchanger and under regenerative you have got a walls and no wall walls and wall less system. The sterling cooler comes under the wall less category the working of a wall less close cycle regenerative type sterling cryocooler that is what we had discussed. That means, during the last lecture we concentrated on this type and in this lecture now we are talking about this. That means, a regenerative cryocooler with walls and that is of GM cooler. So, on the other hand the wall system under the regenerative type is the geofford macphoon cryocooler on which we are going to talk in this lecture. So, how does this look like schematic of a GM cryocooler looks like this we had talked about this earlier. So, you got a piston here which is oscillating the piston will generate high pressure and low pressure. That means, here with this walls which are in built in the system or the no return wall here the high pressure and the low pressure side gets divided this was not. So, in a sterling cycle if you try to compare each and every place of GM cooler it is very good to understand from this that the output from the compressor was only 1 and not 2 here. So, in this case we have got two outputs one is a high pressure and one is a low pressure. After the gas gets compressed the high pressure here heat is removed at this point and then it has got a wall mechanism. A Gifford macphoon cryocooler was basically invented by W. E. Gifford and H. O. McMohan where the first to present the idea of introduction of wall in the year 1950 as old as 60 years around. This wall mechanism now this is a wall mechanism which basically exists between the compressor and the expander. If I call this region as expander and this as compressor the wall exists between these two. This wall mechanism is used to generate the pressure variation or the pressure pulse. So, the high pressure wall gets open for some time and therefore, the expander is subjected to high pressure the gas comes in the expander and after some time the high pressure wall gets closed and the low pressure wall opens thereby having expansion of the gas over here and you get lowering of temperature. This is what we will see in the GM cycle. This working cycle was later called as Gifford macphoon cycle or shortly GM cycle. The sequential opening and closing of these walls generate the required pressure variation or the pressure pulse. Now, all depends on the opening and closing of this wall. In earlier case what we had was sinusoidal pressure variation for sterling cycle. Now, here we can have any waveform for a pressure pulse and that can be incorporated that can be produced by this rotary wall. The opening and closing of this wall will determine what kind of wave do you want to go straight up, step for some time, come down to low pressure, step for some time. So, in short you can have basically a very close to kind of a trapezoidal wave in this case and everything depends on the design of this rotary wall. And therefore, this rotary wall plays a very important role. Normally in a GM you will not have sinusoidal variation of the pressure pulse, but you will possibly have a kind of a trapezoidal wave in this case. Also, the timing of the walls, the opening and the closing of this wall is in the relation with the position of the displacer and this is very vital for optimum operation. So, when does my high pressure wall opens, according to that the displacer motion should basically get influenced by. So, when this wall open where should this displacer be, when low pressure wall open where should this displacer be and therefore, the movement of this displacer is going to be in accordance with the rotary wall motion and we will see that in a GM cycle when I explain to that after couple of minutes. So, here I have to worry about a rotary wall opening and according to this the displacer should move up and down this is very important. Therefore, in a GM system there is relation between the pressure pulse generated by the wall mechanism and the expander of the displacer motion is what I just talked about. Different variations in the wall design of a GM pullers are possible. Some of these systems how does this wall work, what kind of wall this is basically. So, we can have various versions of this lot of manufacturers use different kinds of walls and most of the details cannot be made public. Some of the systems may have one wall each on the high and the low pressure side. So, you can have a wall on this side, you can have a wall on this side and this wall opens and close. Also, some of the system may have puppet walls like in IC engine you got a puppet wall, spring loaded wall and therefore, such walls also could be used if one wants to it will have different you know losses, loss mechanisms something like that. Some of them can have even solenoid walls. So, you can have a pneumatic control, you can have electrical control over there in the opening and closing diagrams of this particular walls. Mostly however, in commercially available corridors they use something called as rotary wall. That means there is a motor which drives this wall and this motor goes on rotating continuously and during the revolution of this motor at some point in time the high pressure wall opens and at some point in time it gets close and low pressure wall opens. So, normally a rotary wall is open is working there to control and regulate the flow of the working fluid all right. So, normally it will be a rotary wall and once I say rotary wall it will have a motor to give a rotary motion. So, you can see here if I want to compare a sterling cycle cryocooler and a GM cycle cryocooler. So, you can see both the units together both the schematics over here directly it reveals that there is no wall here there is a wall here all right. I have shown this connection that means the piston and the displacer has a fixed phase difference that is what we have talked about in the sterling cycle cryocoolers. So, this displacer motion is having some relationship with the piston motion on the compressor while that is not so in a GM cryocooler the displacer motion is in relationship with the opening and closing of this rotary wall here that means it is not bothered about what is happening on this side as long as I get a pressure pulse on this side after the rotary wall we should be in the relation with the displacer motion which is going up and down this is very critical all right. So, this rotary wall normally works at very low frequency as compared to that of sterling cycle. Now, one again one more aspect is because they are in going in a phase difference with each other the frequency of this piston is going to the frequency of the displacer all right while it is not so over here the frequency of the rotary wall opening and closing is going to be the same which is driving the frequency of the displacer motion this is very important. This displacer has nothing to do with the frequency of the piston all right these are very important aspect if I want to compare sterling cryocooler with a GM cryocooler. So, here you can see because this works at a low frequency you can see that the ceiling works very fine while a ceiling will be absent in kind of a sterling cooler because it moves very fast this ceiling is kind of a rubbing ceiling across in the cylinder and therefore, at low frequency this ceiling could remain perfect while at high frequency this ceiling will never remain perfect because it is a rubbing ceiling. And therefore, in sterling cycle we do not have seal problems while in GM cryocooler or GM cycle sometimes you have ceiling problems but this is therefore is very important because if this seal does not function then the gas at low temperature can go to the gas at higher temperature or the gas at higher temperature can cross this seal and come to the gas at low temperature and therefore, it will kill the cooling effect in this case. So, at low frequencies the rubbing seal between the displacer and the cylinder is perfect it is designed in such a way that this remains perfect the walls facilitates production of any kind of pressure wave as per the requirement system. So, here we had a sinusoidal motion sterling cooler we had a sinusoidal pressure and I just talked earlier with the usage of such a rotary wall I can have any kind of pressure wave which I feel as optimum for giving me low temperature in a GM cooler. So, rotary wall could be designed in such a way that I can have a pressure pulse which you know takes so much time to go up to high pressure I can retain it at high pressure at whatever time I want in a cycle come down to low pressure and retain it at low pressure at for whatever time I want. So, I can play with the waveform that will be generated using this rotary wall in a GM cooler. Sterling cryocooler is a high frequency machine this is what I talked about this is a high frequency machine and also the frequency of the piston is equal to the frequency of the displacer while GM cooler it is a low frequency machine alright because we talked about having this seal if this seal start moving at a very high frequency then this rubbing seal will not function properly and therefore, displacer works at a very low frequency of let us say 1 to 2 hertz and that should be the again the frequency of the rotary wall. So, opening and closing of a rotary wall should also this frequency should be the same as what of a GM displacer in a GM cycle cryocooler. Although presence of walls deteriorates the system performance always whenever the walls come into picture you going to have essentially lot of pressure drop across this wall the opening and closing of this wall will have a lot of pressure drop and therefore, the system normally is an inefficient system as compared to that of sterling cooler this is very important aspect. So, a system COP or a GM cooler efficiency will be quite less as compared to sterling cooler, but then it is possible to reach much lower temperature using a GM cooler as compared to sterling cycle machine alright. So, a 2 stage GM cooler can give me around 4 Kelvin temperature while a 2 stage sterling cycle may give me around 20 Kelvin temperature that is the difference between these 2 systems a high frequency machine and a low frequency machine. So, if I were to compare these 2 systems I would like to show with a simple schematic over here and we can see that this is a sterling cycle machine where you got a electrical input and this electrical input is AC form that means, the voltage is fluctuating or this piston is going up and down and ultimately what I get output from this machine also is a PV work output which is also the pressure is oscillating. So, ultimately for any input which goes to the expander is going in the form of a alternative AC oscillating circuit basically alternating current kind of a thing basically. So, input is also alternating while output also is alternating and there is no conversion from AC to DC or alternating current let us say to a direct current for example. So, my input frequency around 20 to 140 Hertz and the output also will be of the same frequency 20 to 150 Hertz at whatever frequency the piston is oscillating and therefore, in such a system where there is no change of AC to DC mode for example, your efficiencies are pretty high and this efficiency we can say as high as 85 percent. We can assume 15 percent to be mechanical losses in a system because of friction etcetera. If I were to compare this with the gm cryocooler you can understand I am giving oscillating input over here, but then I have got a DC here I have got a HP line I have got a LP line high pressure line and low pressure line which we can compare with a DC direct current now there is no oscillations in this case. That means, whatever input has come to this piston it has got from converted from AC to DC over here. After rotary wall what I get again is like what I get here in sterling cooler oscillating PV mode that means, oscillating pressure which goes to expander. That means, I am converting this DC again to AC that means, there are two variations happening two mode changes are happening AC to DC and DC to AC again. So, this is what I am going to show here AC to DC and DC to AC again and if I assume that my conversion frequency from AC to DC is around 50 percent and again from DC to AC is 50 percent. So, whatever is available is only 25 percent. So, if I give 100 watts input at this point only 25 watts are available to go to the expander while in this case if I give 100 watts around 85 watts of PV power will go to the expander and that is the difference between these two cycles. A sterling cycle therefore, is more efficient because there is no transfer of modes from AC to DC or DC to AC it is all AC to AC while in this case of GM cooler you convert first the oscillating motion to oscillating pressures to steady pressures no changes and again you convert the steady pressures to oscillating pressures if we assumed the efficiency to be 50 percent for each conversion what you get ultimately is only 25 watts if I supply 100 watts here. That means, it shows the inefficiency of a system is very high the inherent efficiency of a GM cycle is very very low in this case. So, I just want to compare in short a sterling cycle with a Gifford-Macmon cycle. I have explained all these things a sterling cycle is a high frequency machine of around 20 to 150 hertz while a Gifford-Macmon is 1 to 5 hertz now low frequency machine. You got a direct connection a compressor is directly connected to expander without having a wall while you got a wall connection between the compressor and expander which is what we talked about. Now, when you have got a compressor directly connected to expander I cannot use any lubricant in the sterling cycle compressor and therefore, it use lubrication free compressor which is what we call as dry compressor. In Gifford-Macmon cryocooler you have got a lubrication compressor which therefore, there will be oil compressor and one has to take care of this oil one has to separate this oil from the compressed gas this oil should not go to the expander otherwise oil will get frozen. So, you got a kind of filtering mechanism in a helium compressor that you use normally in a GM cryocooler. Because of the efficient system you got a very high COP in this case for example, I can get 10 watts of power cooling effect at 80 Kelvin for power input of around 350 watts while in a Gifford-Macmon cryocooler I get low COP I can get only 100 watts of cooling effect at 80 Kelvin for a power input of around 4 kilowatt plus chilled water whatever power goes for chilling water. So, I say around 1 or 2 kilowatts additional. So, I get only 100 watts of cooling effect by giving almost 5 to 6 kilowatt power input in a GM cycle machine that means it shows that the COP is particularly less in this case as compared to that of sterling. The pressure ratios are low in this case which is a disadvantage in sterling coolers because they are directly connected compressor to expander I get low pressure ratio while because I got a wall I got higher pressure ratios in case of a GM cryocooler and because the system works again at low frequency. Normally, I will get around 20 Kelvin using 2 stages in sterling cryocooler while I can reach up to 4 Kelvin using 2 stages in a Gifford-Macmon cryocooler again going to the fact that I am basically having a wall unit but I am do not forget that to get this 4 key cooler I am going to give a lot of power input to the compressor I am going to give 5 to 6 kilowatts over here. So, normally in a sterling cooler I will have a low power cryocoolers and it could be very compact while in GM cooler I will get high power compressor and it will be bulky basically. Normally, in sterling cycle cryocooler because they use dry compressor this facilitates to go for miniaturization and it is again because there are no walls in a system. So, miniaturization is possible due to fewer moving parts in this case because of the absence of walls in this case mostly while miniaturization is not possible normally in a GM cryocooler due to the presence of wall and therefore less efficiency in this case. Mostly sterling coolers are preferable for space applications because they can be miniaturized and they are most reliable as there are no walls in the system and the efficiencies or the COP of the system is pretty high while here mostly the GM coolers are land based applications only because of the inefficiencies involved because the reliability are questionable sometimes because the servicing requirement that is required for a lubricated compressor. So, now let us see how the GM cryocooler works. So, let us see the working of a GM cryocooler and what I am showing here is a cylinder which is housing the GM displacer and this GM displacer houses the regenerator. So, you have got a seal between the cylinder and the displacer which is moving and the displacer is kind of hollow and in this we have got a regenerator material sitting over here and this displacer will move up and down in this thing and there are walls high pressure and the low pressure wall which open and close which generates the pressure wave. So, consider a displacer housing the regenerator at a bottom dead center BDC. So, displacer is at the bottom most portion and there is some gas which is actually the clearance volume the lowest volume that is possible in this cylinder. So, the displacer is at a BDC position as shown in this figure and there are two volumes V 1 and V 2 V 1 is below the displacer V 2 is above the displacer. So, cold space is going to be at V 1 we are going to create cold at this point. So, cold space V 1 and the warm space V 2 are as shown over here. Similarly, what we have is a high pressure wall LP HP and LP in this schematic both the high pressure wall and low pressure wall are in close condition. So, if I have got these two parallel lines shown they are opposing the flow and therefore, the high pressure gas is going to come from this side and this is right now in a close condition also this is shown to be in close condition right now and the seals are provided between the displacer and the cylinder as shown over here and this will not allow the gas from V 2 to go to V 1 or from V 1 to V 2. I would like to show now what is how the pressure V pressure versus volume diagram changes with this motion of displacer and we are talking about this volume V 1. So, at present we have got a V minimum this and the gas let us say at low pressure is there at V 1. So, corresponding situation of the cold space V 1 when plotted on a PV diagram is as shown in the adjacent figure as shown over here. So, now you can see that I have made the high pressure gas open I have made the HP wall open with the opening of this HP wall the high pressure gas fills V 1 and V 2. So, high pressure gas will come from this side and it will go through the displacer the regenerator and everything will be now filled up with high pressure gas. So, the gas is filled up with V 1 and V 2 spaces at constant volume and therefore, the V 1 pressure will suddenly go from LP to HP all right it was initially assumed to get LP it will go to HP and therefore, the volume as V minimum only after some time the displacer will move on this side the displacer moves back on right side and therefore, it will let the gas in the regenerator and the V 2 everything to move in V 1. What is therefore, therefore, going to happen to V 1 the V 1 volume will increase from V minimum to V maximum and during this time the high pressure gas is going to come from this side to this side because of the motion of displacer and therefore, the HP remains the same the gas entirely remains at high pressure except that the V 1 volume in the V 1 increases from V minimum to V maximum at constant pressure. The displacer moves back to the right side it displaces the gas from V 2 there is some gas which is stored in the regenerator also is goes to V 1 at constant pressure because the gas entirely is there at HP because only HP is open right now. After that what happens the HP valve will get open will get closed and LP valve will open. So, suddenly the high pressure gas in V 1 and even in V 2 and in the regenerator suddenly will get exposed from high pressure to low pressure. So, what you can see now the cold space V 1 in this case has increased from this to this while the warm space V 2 has decreased. Now, the third thing is LP has opened HP has remained in a closed condition the LP valve opens and now the HP valve is closed and LP valve is open this leads to an expansion of the gas. So, suddenly what was at high pressure suddenly gets exposed to the low pressure therefore, what will happen the temperature will come down alright the gas temperature here at V 1 will suddenly come down this expansion produces the cold and now with the motion of this displacer later as the displacer will move to the left the displacer moves back reducing the cold space volume. So, now when the displacer moves from this side to this side it goes to the minimum position it will displace all the gas from here to come out on this side the gas will go to the LP and the cycle will continue. So, we have come from first increase the pressure HP opens LP is closed HP opens the pressure increases for V 1 then displacer moves therefore, the V minimum goes to V maximum constant pressure line here and then suddenly LP opens HP remains closed expansion happens this is the period when we get low temperature generated at this point and when the displacer moves to the left side the gas will go out the volume of the gas reduces from V max to V minimum and the cycle continues. This cycle continues to produce lower and lower temperature and at particular temperature it will get studied down depending on the kind of regenerative action you will have. So, as soon as the regenerator cannot take more heat it cannot store more heat the lowest temperature will be there and initially you will have unsteady state that means the temperature will go on lowering and at a particular temperature when the regenerator material gets saturated the lowest temperature can be achieved. This is how the GM cooler works very important that if I want to reach lower and lower temperature I cannot attain this lower temperature in one stage, but I do multi-staging. So, GM cooler is always known for it two stage machine because it produces 10 Kelvin or 4 Kelvin temperature. So, normally a single stage GM cryocooler produces a refrigeration effect of around 12 watts at 80 Kelvin for a power input of around 1.2 kilowatt these are some commercial figures available. So, I give 1.2 kilowatt input to the compressor what I get in effect is cooling effect of around 12 watts at 80 Kelvin and then I will go for if I want to come down below 80 Kelvin or below low temperature I will go for multi-stage or two stage machine. So, this is the kind of a two stage machine you can see here and this is where you see the high pressure and low pressure gases coming from and they got a wall housed over here. This is the cylinder which houses a displacer which goes up and down this is the first stage and the second stage. This is a typical cold head a GM cold head the compressor is going to be away from this place, but the high pressure line of the compressor will get attached to the high pressure port or wall here and the low pressure will come and it will get attached to the low pressure all over here. So, in order to reach much lower temperature for example, to go to 10 Kelvin or 2.2 Kelvin right of this order 10 Kelvin 4.2 Kelvin multi-staging is done in this system. So, I will get 10 Kelvin or 4.2 Kelvin at this second stage while the first stage could be around 40 to 50 Kelvin depending on the sizing of this particular cryocooler commercially available two stage GM cryocoolers are capable of reaching temperatures lower than 4.2 Kelvin. In fact, the lowest temperature that could be reached could be around 2.4 to 2.5 Kelvin, but you need some cooling effect at 4.2 Kelvin. Now, let us see a video of a GM cryocooler that we have bought at IIT Bombay it is from a Leibold company and from that you can see an actual machine I am not going to run this machine, but you can see different parts of these machines. So, just now we saw this machine for the sake of understanding a demo video of GM cooler at IIT Bombay just shown. You just saw how does the compressor look what are this flex line what is this cold head and you could see in video how are they placed how do they look like how are the sizing and thing like that. So, let us have a look at a GM cryocooler Gafford McMoron cryocooler and what you are seeing right now is a Gafford McMoron cryocooler with a compressor at this place and the cold head or expander head at this end. Now, here you can see that the compressor is connected to the cold head using this flexible lines and this is a compressor and you can see this compressor with a high pressure and low pressure line connected from this compressor and this is a helium compressor of around 8 kilowatt power capacity and this is also a power cord which connects the power to the wall the rotary wall of the GM cryocooler alright. This is a high pressure line this is a low pressure line this is where you can read the pressures and this is the on and off switch of this compressor and as you will see further that the gas will get compressed from here the gas will go from here to the cold head and the low pressure gas will come back to the compressor and to the capsule inside and a water cooling arrangement. Now, what you also see from here is a water cooling arrangement the water will go as in late water will come out late from this it will go to the chiller and again the water will enter from this place cold water will take the heat of compression from this place it will enter it will take the heat of compression it will come as hot water from this and it will again go back to the chiller and it will come back again from this particular port. This compressor is normally a 3 phase it has a 3 phase power supply what you see is a lie bolt compressor now here or the lie bolt GM cryocooler and these are the flexible lines of around 6 to 8 meter length it could be 20 meter also in order that compressor could be kept as much away from the cold head. Now, come to this point and what you see here is a cold head now from where you can see that the high pressure line comes from here the low pressure line will take the gas from here. What you see now is a valve the rotary valve this particular housing has the rotary valve the high pressure gas comes inside the rotary valve which is housed in this and this is the motor which is driving this rotary valve and the power supply to this motor comes from the compressor and that also one can see that it should run at 1 hertz or 2 hertz that also can be decided by the input that can be given on the compressor. So, here this housing has the rotary valve which is driven by this motor we have seen how this rotary valve works. So, for some time the rotary valve will allow the high pressure gas to go from here to the cold head and the low pressure gas will go will leave this place through this port and it will go to the compressor to get charge again to get compressed again alright. So, now what you see below this flange this is this is the cold head which is connected to this flange and this flange will sit on the vacuum vessel which I will show you later. So, this is the cold head now this is the first stage and this is the second stage of the GM cryocooler. Now this is a 10 k cryocooler. So, I get around lowest temperature of the order of 8 to 10 Kelvin at this point which is the second stage and I get the first stage temperature of around 30 to 35 Kelvin at the first stage at this point. This houses the displacer 2 stage displacer driven by the motor which is kept or it can possibly get driven by itself if you got a pressure drop across the displacer and this is called as free displacer in that case. The displacer will go up and down with the frequency that you maintain as 1 hertz or 2 hertz and displacer also houses the regenerator. This is the second stage this is the first stage here and what you see here is the first stage and what you see here also is a silicon dad which has been kept here to measure the temperature at this particular point. We can measure the first stage temperature at this point and similarly we got a 2 stage. Now you can see this flange over here which is copper. So, anything if I want to connect anything to be cooled by the first stage can be connected to this different holes or this could serve as a radiation shield for the second stage. One can put a radiation shield across this second stage. The entire thing has to go under vacuum. So, that there is no 300 Kelvin radiation that is coming or you do not have air around this alright. So, you can see that above this what you have got is a first stage regenerator. Below this in the displacer housed is a second stage regenerator which normally will have because it is a 10 K cryocooler it will have lead balls as the regenerator material while the first stage will have stainless steel mesh as a first stage regenerator material. What you see also the circuit of the first stage and the second stage silicon diode in order to measure the temperature. Now this is the second stage. So, here the second stage whatever you want to cool will be conductively coupled to the second stage of the GM cryocooler. Now if I want to test the performance of the GM cryocooler we have made this vacuum jacket and in this vacuum jacket this 2 stage GM cryocooler will be put in alright. So, this flange can be taken off and the flange with the GM cryocooler can be put in in this case. So, this is basically the vacuum jacket to test the performance of GM cryocooler. It is a 2 stage machine which is capable of reaching a temperature of around 10 Kelvin. The lowest temperature possibly is around 10 Kelvin, but normally it is referred to as 10 Kelvin cryocooler 10 Kelvin machine. So, what are the different components of a GM cryocoolers? The basic components of any GM cryocooler as are as listed below. It has got a helium compressor. The working fluid is normally helium and therefore it will have a helium compressor which could be a scroll type, a screw type or a reciprocating type. Normally it is a scroll type machine basically. Then we got a flex line and this is what we call as flexible line actually. It is a short form given as flex lines and we have got a HP line and LP line. In order to keep the compressor away from the expander or the cold head this flex line could be 6 meter line or could be 20 meter lines. So, that means compressors vibrations will not reach the cold head. In some cases the cold head vibrations are very very detrimental. For example, on a MRI machine where the system sits that the compressor is kept outside of the building in fact. So, that there is no noise there are no vibration transferred to the cold head. So, the flex line does the purpose that it will allow the temperature gas to come from the compressor and to come to the cold head. Then of course, the regenerator and the dispenser. The regenerator as we just saw is housed in the displacer and it is a very important component is the regenerator which has got regenerator materials sitting there. It is a regenerator matrix which plays a very important role in the functioning of any cryocooler. In the next lectures I will show what is regenerator materials and everything look like, but for the time being we will just go ahead with theory. As we are talking about every time this wall mechanism the rotary wall mechanism it could be solenoid wall it could be puppet wall this is the most important thing. And therefore, a GM cooler will have a helium compressor flex line the regenerator displacer the cold head for example, and the wall mechanism. These are very important aspects of a GM cryocooler. Finally, we have to cooling arrangement for helium compressor the heat of compression has to be taken care by this cooling arrangement normally it is a chilled water and chilled water at around 8 degree centigrade or 15 degree centigrade will inlet will be inlet to the helium compressor and it will take the heat and go back it will get cooled and again come back. So, basically it is normally chilled water arrangement sometimes it could be air cooled also some compressors are air cooled also. And therefore, this is very important what kind of arrangement has been made over here for a compressor cooling. Now, let us come to the regenerators of a cryocooler. The regenerator is the most vital component and is often called as heart of the cryocooler. So, entire design of a cryocooler will basically depend on the regenerating capacity. What does the regenerator do? The regenerator stores the heat and therefore, everything depends on the storing capacity of heat by the regenerator. What is the storing capacity is m is a mass of the regenerator into Cp the specific heat capacity of the regenerator material. The regenerator houses the material and through this material the gas flows that means, the regenerator has to have some porosity. The regenerator has to allow this gas to pass to this material and in such a way that there will be very good heat transfer between the gas or the working fluid and the material that are stored as regenerator matrix. So, the major design aspects I will say the major aspects of the regenerator therefore, are the dimensions length and diameter. So, the regenerator dimension makes a very important impact on the functioning of a cryocooler. Depending on what kind of compressor what kilowatt compressor you are using that means, how much is the flow rate of the machine. In comparison to that we have to have a capacity of the regenerator which are determined by the length and the diameter of the regenerator alright. So, regenerator material will be housed in this dimensions it will have its volume and this regenerator matrix should be able to take the heat given by this gas during its travel through this regenerator. And therefore, the dimension of the regenerator you have to calculate very very critically. The material what material you choose because the material is a very important this is the material which stores heat. So, its heat capacity variation with temperature because you are going to work at low temperature and we have seen in the materials earlier that the heat capacity goes on the reducing as the temperature gets reduced. Therefore, you have to choose such a material which has got higher heat capacity at low temperature comparatively higher heat capacity at low temperature. Also the thermal conductivity of this material also is important because this is what will determine the diffusivity of the material also alright. So, there are very important thermo physical property of the material that has to be used as regenerator matrix material. It has to have very high heat capacity at low temperature in comparison with the heat capacity of the gas which is flowing through this. So, we should say that the ratio of heat capacity of matrix to that of gas will be infinite basically in order to have a very good heat transfer alright. So, this is going to decide what is the lowest temperature that could be attained by this cryocooler because at that particular temperature the regenerator will get saturated that means it cannot take any more heat from the gas the matrix gets saturated. So, this is a very important aspect of the regenerator. As I said the gas the working fluid travels through this matrix material and therefore, it has to have some porosity and this porosity allows the gas to travel through this matrix material. It also allows to have a good heat transfer between the gas and the matrix material. So, we need to have a good porosity in optimum porosity through this material. What is the working temperature? What is my what is my working temperature range I am talking about? Am I talking about 30 Kelvin machine? Am I talking about 10 Kelvin machine? Am I talking about 4 Kelvin cryocooler? According to which the material will change. So, working temperature will decide the material. So, if I want to have a cryocooler working around 30, 40 Kelvin I will I will use stainless steel mesh while if I want to work at very low temperature I can go for lead balls or magnetic materials I will talk about that in the next slide. This is what I talked about the heat transfer between the working fluid and the material has to be perfect. But you know that when you got to have perfect heat transfer you will have more pressure drop. So, what I want is perfect heat transfer at the same time I would like to have minimum pressure drop and therefore, one has to play between this porosity and the sizing of this matrix material. This is very important aspect. I would like to have maximum heat transfer and minimum pressure drop in the regenerator. Because regenerator has got some porosity it will have a good heat transfer but moment is got less porosity it will have a very high pressure drop and this is very important aspect. So, the regenerators in general the material with I just told you with high heat capacity is chosen as regenerator material. This is because the energy exchange between the working gas and the matrix is directly dependent on the relative heat capacity. As I just said that the heat capacity of the matrix material should be infinitely as much as high as possible it should be as high as possible as that of the heat capacity of the gas. As seen in the earlier lectures it is important to note that the CP of the there is a specific heat capacity of the material decreases with the decrease in temperature alright. In certain cases it comes very close to 0 even and therefore, such materials need not be used as regenerator material in this case. Very often a combination of various rare earth materials or the magnetic material which we call as is used in the regenerator material because they show very high heat capacity at low temperature. They may not normally have very high capacity but at low temperature they show a transition and suddenly the CP value increases and this particular property of magnetic material is exploited in this regenerator. For example, here I am going to show you some regenerator material at temperature less than 50 Kelvin. So, we are talking about let us say stainless steel and this is a green this is CP value and we are talking about volumetric heat capacity alright. So, volumetric heat capacity is going to come down below 50 Kelvin and therefore, it cannot be used below let us say 30 Kelvin till 30 to 40 Kelvin I can use stainless steel and normally the stainless steel material is such that it can be made in the form of meshes that means the gas can flow through these meshes thereby having a good heat transfer between the gas and stainless steel mesh. So, here we are seeing the variation of volumetric heat capacity with temperature as shown the material like SS are not preferred at lower temperature let us say less than 30 Kelvin due to low heat capacity. So, what do I do? I during if I want to have a 10 Kelvin machine for example, from here you can see that I got a lead over here and this lead can be used because it has got substantially high heat capacity as compared to that of stainless steel below let us say 50 Kelvin. So, normally if I want to come and reach down to 10 to 15 Kelvin I normally will use lead. So, I can have stainless steel in the first stage and I can use lead in the second stage as regenerator material agreed this is a very important aspect. So, material like lead can be used for second stage if I want to reach 10 Kelvin, but what happens if I want to reach 4 Kelvin? I cannot use lead anymore I cannot use stainless steel anymore, but you can see these two curves having high CP variation and this is what I talked about these are all rare earth materials or magnetic materials and this is ribium 3 nickel and neodymium for example, these materials have got low CP let us say to 10 Kelvin, but suddenly below 8 Kelvin these are transition and this is called as transition of second order suddenly this transition goes up and the CP value goes up and this CP now is comparably quite high as compared to that of lead and stainless steel and this property is exploited in a second stage of the regenerator for a cryocooler for any cryocooler in order to reach around 4 Kelvin and temperatures below. So, materials like lead, ribium 3 nickel, neodymium, what we are not shown is holonium copper all these materials can be used at low temperature because they exhibit high heat capacity at low temperature. However, these materials cannot be made into the form of meshes like lead. The lead, ribium 3 nickel, neodymium are normally made in the spherical forms they are in a ball forms up around 0.2 to 0.1 millimeter diameter and this is what it is used in the regenerator of the second stages. So, in a single stage normally in a GM system stainless steel meshes are used in two stages let us say around 10 Kelvin we will have first stage stainless steel mesh, second stage lead balls. If I want to have a 4.2 Kelvin temperature or a 4 K machine we can have first stage we can have stainless steel plus lead in the first stage if this something referred as hybrid regenerator and second stage we can have lead plus ribium 3 nickel and this is very important that how much stainless steel should be there, how much lead should be there, how much lead and ribium 3 nickel should be there these are very important design aspect of regenerator and lot of computational fluid dynamics is normally used to understand how this regenerator would play a role in determine the lowest temperature that could be generated by this cryocoolers. The third important aspect which I had touched was the wall mechanism. So, we talked about regenerator material which we talked about the Gifford-Macman cryocooler functioning and let us see now in brief the wall which is a very very important component of the GM cryocooler. What does this wall do as I told you earlier the wall generates the kind of pressure pulse I want the wall basically will determine for how much time it should take to reach maximum pressure for how much time the maximum pressure should remain constant how much time it should take to come down from maximum pressure to low pressure and for how much time the low pressure should remain all these things are taken care by the wall mechanism or therefore, the wall design is very very critical. As mentioned earlier the sequential opening and closing of the wall mechanism generates the required pressure variation or the pressure pulse. The rotary wall should operate at an optimum frequency we have seen that the GM cryocooler functions at 1 to 2 hertz or 1 to 3 hertz let us say this optimum frequency is very important at what frequency it should 1.5 hertz 1.4 hertz this is what not lot of people would even work at. So, one has to find out what is this optimum frequency and this will be that will be decided by the pressure pulse that is wall will generate and of course, what is my cold head volume what is my first stage volume second stage volume and thing like that various aspects. The schematic and the working of most commonly used rotary wall is explained in the next slide. So, just for example, lot of papers have published how these rotary walls work and from one paper we have taken and but lot of people will not even reveal how these walls work in those cases because it is a very important commercial secrets. But as far as some published information is available we have tried to transfer this knowledge to you just to understand how does a simple rotary wall work. So, this is what is just a schematic of a rotary wall. The various parts of a rotary wall are shown over here. So, you have got a rotary mechanism and therefore, drive mechanism this could be a motor basically driving this wall unit. So, let us say this is a wall unit and the gas high pressure gas will come from some side the low pressure gas will come from other side and ultimately what you get from here is a pressure pulse this is going to go to the cold head. So, what you see here is a drive mechanism what you see is a high pressure and a low pressure port. So, you got a high pressure gas which is coming like this and low pressure gas which is going into this plane into the plane of this board basically. So, you got a low pressure wall opening somewhere over there what you have got a rotor and stator. So, a rotor is as shown over here this rotor is getting rotary motion from this motor which is shown over here and you got a stator. So, as you see a rotor is going rotating while stator is going to be remaining stationary and this rotor and stator are hard pressed on each other basically and this is most important thing they should be hard pressed and therefore, you will have some spring loaded directly on them I have not shown the schematics of that, but it should be ensure that this rotor and stator are absolutely pressed hard against each other. The rotor is driven by a drive mechanism maintaining a perfect seal in a system that means this rotor and stator because they are going to be you know press hard against them they will not leak I mean the high pressure gas and low pressure gas should not get leaked again this all right. So, this is very important and you can see that the special slots are cut on the rotor and the stator the slotted rotor and the stator discs connect the cryocular to HP and the LP line respectively this is very important now this curvature how long this is what is at what angle is happens this is what is going to decide how much time it takes to to increase the pressure and decrease the pressure and how much time it should be kept at what is the diameter of this all these will decide pressure pulse mechanism all right. So, let us see now the high pressure position is something like this you can see the slotted mechanism and this is the port which goes to the cryocular and high pressure gas has opened and suddenly the disc has taken this position because of which these two openings are open. So, this entire area over here is getting filled with high pressure gas and the gas now travels from this to these two openings which is these two openings are meant open to the high pressure gas because of the motion of the rotor the rotor has moved in such a way that this ports cryocular got in touch with the high pressure and therefore, high pressure gas has moved through this ports and will go to the cryocular when the slots of the rotor disc match with the stator as shown the high pressure gas from the compressor flows to the cryocular. In this way the high pressure gas will go to the cryocular in this position the low pressure is completely closed to this gas the gas cannot see this low pressure gas at all and when the position comes like this now the low pressure position gets open and the gas which travel now from cryocular to the compressor and this gas will come like that this port is not any more open to the high pressure side basically. So, entire area as I said was open earlier to the high pressure side now suddenly low pressure gas will come like that and it will enter this hole which is connected through this hole to the LP port cycle spend some time to understand this drawing basically, but I am just going to show you some schematic with the rotation of the rotor disc at a particular instant the slots on the rotor disc are masked and getting closed now in this position the hole in the stator is unmasked it gets open and therefore, this open gets open it goes to this it gets it connects now cryocular to the LP port as shown in this figure and therefore, now the LP gets open it goes here it gets connected after sometime again the rotor gets open the high pressure gas will come again this position will come and the cycle continues. This is a schematically very simple for me to possibly explain, but it is not very very simple to fabricate and demonstrate them in practice because many times you can find that there could be now you got a high pressure over here you got a low pressure here and there could be some clearance there could be some leakage past these if the rotor and stator are not very very hard pressed over here this is a very important aspect otherwise the gas can get short circuited the HP can get in touch with LP and the gas can just flow like this this is very important therefore, this should ensure that the rotor and stator are absolutely leak tight there is no they are hard pressed against each other. Coming finally, to the applications of gm cryocular what we have seen is what is the gm cooler how does it compare with sterling cycle what we saw after that is also how does the gm cryocular function then we also saw what are the important aspects of a regenerator in a gm cryocular which we also saw that for multi staging how do we go for low temperature and with respect to multi stage temperature two stage temperature how do the regenerator matrix material change. We just touch upon lastly the wall mechanism the importers of a rotary wall the rotor and the stator and how do they function and ultimately just to complete the task related to gm cooler where do we apply where do we find applications of gm cryoculars gm cryoculars has got tremendous application in fact gm coolers have made cryogenics very very popular or to reach commercial destinations. So, gm cryoculars find application in the following area MRI machine every MRI machine is having a gm cryocular sitting on it which does the functioning of shield cooling many times or even recondensing cryoculars. So, MRI machine is a very important area where gm cryoculars find its application cryo pumps. So, all these cryo pumps which produce clean vacuum houses a gm cryocular a 10 k gm cryocular basically which produces clean vacuum for various mains laboratories or micro electronics laboratories and thing like that nitrogen liquefier a single stage cryocular can be used to produce nitrogen liquid nitrogen basically. So, this is very important application again cryo probes. So, we will lot of NMR cryostats use cryo probes to cool the electronics so that to increase the signal to noise ratio and therefore, very popular equipment for NMR user is a cryo probe or a cold probe basically to get a very high signal to noise ratio. There are some very important area where cryoculars are needed in almost you know 100s and 200s and thing like that they are now in 1000s for MRI machine for example, very important 1000 for MRI machine may be 10000 for cryo pumps and thing like that. So, very important area gm cryocular normally finds applications in these machines also find applications for very low temperature physicists and scientific applications. So, very important R and D application R and D group who want to do experiments at low temperature use gm cryoculars. Summarizing Gifford and McMone were the first to present the idea of introduction of valves in 1950 a gm system has a valve mechanism to control regulate the flow between the compressor and the regenerator displacer assembly. For an optimum performance the relation between the pressure pulse generated by the valve mechanism and expander displacer is vital. A gm system can reach much lower temperatures as compared to sterling system, but may require a high powered compressor due to the inefficiency of the valves. Multi staging is done to reach lower and lower temperatures you can get less than 4.2 Kelvin or a 10 Kelvin system whatever you want. The basic components of a gm cryocular are helium compressor, flex lines, regenerators, displacer, valve mechanism etcetera. The choice of regenerator material is dependent on the lowest working temperature of the cryocular. So, if I want to have a single stage machine to reach 30 Kelvin I can use stainless steel mesh as the regenerator matrix material. If I want to go to two stage a 10 K machine I can have first stage with SS mesh and second stage may have lead balls of spherical nature. If I want to go to a two stage machine reaching around 4.2 Kelvin the first stage could be stainless steel mesh plus lead balls, second stage could be lead balls per ilmen 3 nickels. This is just a guideline it could be 100 percent stainless steel mesh also while second stage can have lead balls plus ilmen 3 nickels. So, it is left to the design of a regenerator for that particular application. Finally, commercially available cryoculars have rotary walls to control regular flow and this is the rotary wall is the moving component which is a very important design aspect of a gm cryocular. Finally, I have got a self assessment exercise given please go through that kindly assess yourself for this lecture alright and we are going some answers at the end. So, please assess yourself and see how much questions you can answer. Thank you very much.