SYSTEM DESIGN NOTE
SDN0007.02 - Instrument Cool Down
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Prepared by
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Date
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Approved by
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Date
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Rev.
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Rev Date
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J Elias/Dick Joyce
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6/17/99
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N. Gaughan
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6/17/99
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B
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5/12/00
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1. Introduction
The purpose of this document is to provide a preliminary calculation of the cooling time for the GNIRS design. Designs both with and without a liquid nitrogen “jump-start” system are discussed. Some relevant information on Phoenix is presented in an appendix.
Revision A comprises a somewhat better treatment of heat inputs during cool-down.
2. Basic Parameters
For the purposes of this analysis, the cold mass of the instrument is assumed to be 700 kg., with the bulk of it consisting of 6061 Al (based on 5/00 weight budget). It is assumed that the instrument is to be cooled from 293K to 60K. The specific heat of 6061 Al varies significantly over this temperature range (from about 200 J/kg/K at 60K to about 870 J/kg/K at 293K); a reasonable rough average is 650 J/kg/K.
Hence the amount of heat to be removed is about 1.1 x 108 J. This ignores any heat input into the instrument from radiation, conduction, or other sources during the cooling process.
2.1 Cool-Down with Cryocoolers
The baseline cryocooler complement for the instrument comprises two Leybold “150” heads and two Leybold “130” heads. If the heads were somehow coupled to the cold structure so that there were no thermal gradients, cooling would proceed with maximum efficiency. Earl Pearson’s thermal analysis gives an average total cooling power for the four heads under these assumptions of ~650W. (Note that because the cooling curves of the heads and the heat capacity of the structure are both functions of temperature, the averages ought to be weighted – but for the purpose of this simple-minded calculation, a straight average is good enough.)
Division yields a time of 47 hours. This is optimistic in several regards. External heat inputs are likely to be many tens of watts, increasing the time required by 10-15%. More important, the assumption of perfect coupling to the cryocoolers is incorrect. The cooling power is roughly half of the value quoted above when the head first stage temperature is ~50K.
Reducing the cold mass by 100 kg. would decrease the cooling time to about 40 hours.
The cooling curves from the manufacturer that were used don’t provide information for higher head temperatures, so cooling power was assumed to be flat above ~90K. The measurements of Phoenix and information on other heads (see below) suggest that cooling power near room temperature might be around 1000W.
We are also considering use of a different model of Leybold heads, the RGD5/100-1. Based on the cooling curves in the manual, the average power per head is around 150 W over the temperature range of interest, for a cool-down time for 700 kg. of 51 hours.
2.2 Liquid Nitrogen
How much would a “jump-start” system help? The heat of vaporization of liquid nitrogen is about 1.61 x 105 J/l, which could be used to cool the instrument to close to 77K. The total heat to be removed is somewhat in excess of 90% of the total, with the amount needed to get from 77K to 60K only about 3 x 106 J (because heat capacity of 6061 at this temperature range is lower). The amount of liquid nitrogen required is about 660 l of liquid, or about 430 cubic meters of gas (STP).
The time to cool down with the jump start is in principle very short. If the jump start system was capable of pre-cooling the entire instrument to 77K – not just the structure – the time for the cryocoolers to take it from 77K to 60K would be a few hours.
3. Further Refinements
3.1 Cryocooler Cooling
3.1.1 Thermal Distribution System
The least plausible assumption in the calculation in 2.1 is that of perfect coupling between the cold mass and the cryocoolers. In reality, the heads are connected to the structure at a limited number of points, and the coupling medium (usually copper braid) has some thermal resistance. In order for heat to flow from the structure to the cryocooler first stages, there must be a thermal gradient.
What this means is that the cryocooler heads are systematically colder than the average of the instrument structure. At lower temperatures, efficiencies are less, so cool-down times are longer. The schematic cooler efficiency curves used are flat down to about 90K, so the thermal gradients affect the cooling time only after the point where the cryocooler heads drop below this temperature.
The copper braid used in NOAO instruments has a cross-section of 5 x 10-5 m2; 20 of these therefore have a cross-section of 0.001 m2. At ~100K, OFHC copper has a conductivity of ~470 W/m/K. If the average length of the copper is 0.2 m, the temperature gradient for 650W of heat flow is well in excess of 200K – which indicates (confirming experience) that the cryocooler heads will cool down very rapidly.
An average conductivity for copper over a larger temperature range is around 400 W/m/K, so the copper braids have (collectively) a gradient of ~0.5 K/W. A little iteration with the cooling curves indicates that if the structure end of the braid is still at 293K, the maximum cooling power for the four heads is around 450W (head temperatures ~70K). The cooling power is reduced to ~300W (head temperatures ~50K) when the other end of the braid is ~200K, and 200W (head temperatures ~40K) when the other end of the braid is ~140K. At lower temperature, the conductivity of copper rises sharply, so the gradient calculations are more complicated.
If there are no gradients within the structure, one can do a crude analysis (also neglecting external heat inputs) as follows. Note that all the times listed below scale with the cold mass.
In estimating the cooling time, it is necessary to
make allowances for heat inputs in the system as well as cooling. The dominant
input is radiation, which is assumed to be ~90W when the structure is cold
(worst case lab environment – see SDN007.01). The radiation load reaches
this value once the structure has cooled even slightly. Conduction is assumed
to be 30W when the structure is cold.
Table 1 – Cool-Down Time with 20 Copper Straps
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Temperature Range (K)
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Ave Heat Cap. (J/kg/K)
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Ave. Cooling Power (W)
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Total Heat (J)
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Time (hours)
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293-200
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800
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285
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5.2 x 107
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51
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200-140
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700
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140
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2.9 x 107
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58
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140-60
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450
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30
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2.5 x 107
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231
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Total
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1.1 x 108
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340
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This time is much longer than the value arrived at in 2.1. This is because of the external heat load as well as the thermal gradients. Doubling the number of copper straps would help significantly. Calculating as above, we would get:
Table 2 – Cool-Down Time with 40 Copper Straps
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Temperature Range (K)
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Ave Heat Cap. (J/kg/K)
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Ave. Cooling Power (W)
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Total Heat (J)
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Time (hours)
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293-200
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800
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530
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5.2 x 107
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27
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200-140
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700
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310
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2.9 x 107
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26
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140-60
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450
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110
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2.5 x 107
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63
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Total
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1.1 x 108
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116
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This time is within a factor of three of the simple-minded calculation. Although 40 straps sound horrendous, the actual mass of copper is still rather modest – less than 4 kg. Note that to maintain a given temperature differential when straps are lengthened, the cross-section must also increase proportionately, so doubling the length increases the mass of copper by a factor of four.
The calculations ignore the effects of joints in the system; clamped copper braid will present some thermal resistance, and a more effective joint needs to be considered.
The real design should try to minimize the amount of copper braid used to that required for flexibility; to cover additional distance a rigid “bus-bar” design should be used.
A calculation similar to that for Table 2 can be done for 4 RGD 5/100 heads:
Table 3 – Cool-Down Time with 40 Copper Straps & RGD 5/100 Heads
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Temperature Range (K)
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Ave Heat Cap. (J/kg/K)
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Ave. Cooling Power (W)
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Total Heat (J)
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Time (hours)
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293-200
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800
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430
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5.2 x 107
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34
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200-140
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700
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250
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2.9 x 107
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32
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140-60
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450
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80
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2.5 x 107
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87
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Total
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1.1 x 108
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153
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This time is about 30% longer than the time with the larger heads. The difference is not as large as the nominal difference in cooling power, because the lower cooling capacity leads to a smaller temperature gradient on the copper, which allows the smaller heads to run somewhat warmer, with higher cooling capacity.
The times above (Tables 2 and 3) are 5-6 days. These values are not really acceptable.
3.1.2 Structural Gradients
All of the above calculations neglect any gradients in the structure itself. If the main structure is taken as a slab 0.5m x 0.05m x 2m, cooled at the center and with the heat input at the ends, the gradients will be ~0.27 K/W (average conductivity 150 W/m/K). This gradient is comparable to that in the copper strapping, but it is pessimistic in several regards. First of all, the heat is distributed over the structure, and is (if anything) concentrated towards the center, where the bulk of the mechanisms are supported. Second, the effective cross-section has probably been under-estimated as well. Finally, the copper strapping could be distributed to a certain extent, reducing the path lengths between large masses and the cooler heads.
Even so, temperature gradients over the structure are not likely to be much below 0.1 K/W unless an elaborate thermal distribution system is installed. This means that temperature differences of up to 60K are possible. Examination of Tables 1 and 2 suggests that this in turn will increase cooling times by perhaps 1/3 over the quoted values. More precise values will require detailed thermal modeling – but the times are already uncomfortably long.
For the simple structure used above, the mass is only 135 kg, which is inconsistent with a more realistic assumption that about 2/3 of the total mass of 700 kg. is in structure. Of course, not all the structural mass will be distributed in such a way as to assist with cooling, but it is reasonable to suppose that the gradients above are conservative.
3.1.3 Mechanism Gradients
The discussion has neglected the fact that a large fraction of the heat capacity is in the form of mechanisms – lumps of mass, so to speak – which may not be well-coupled to the structure. This issue is best addressed by design rather than analysis, since it should be possible to couple all of the larger mechanisms fairly efficiently to the instrument structure.
A rough calculation can be performed to illustrate this. If the moving mass of a mechanism weighs 10 kg and is coupled to the bench through a single copper strap of 10 cm. length, that strap has a thermal resistance of 5 K/W. The heat in the mechanism is roughly 1.5 x 106 J. If the mechanism cools over 72 hours, there must be an average heat flow of slightly under 6 W, which implies an average temperature difference of ~30K.
This shows that with a fairly simple connection the mechanism is capable of “tracking” the bench reasonably well. This is consistent with the time constant estimated from the numbers above, 6500 J/K x 5 K/W or 9 hours. If we examine the later stages of cooling in more detail, we see that the cooling rate of the bench (Table 2) is about 1.3 K/hr. At these lower temperatures the heat capacity of Al is down to roughly 350 J/kg/K, or 3500 J/K for the mechanism. Hence heat flow must average about 1.2 W. At the lower temperatures, the copper strap’s conductivity has risen somewhat and the resistance is around 3.5 K/W – so the temperature difference is down to around 4 K. The cooling time constant is now around 4 hours, so the mechanism should get within a degree of the bench in under 8 hours.
These numbers can be scaled for other mechanism masses or more (or fewer) connecting straps. It should be noted that thermal conduction through bearings and drive trains is neglected and may help significantly. Also, during the early stages of cool-down, radiation can be significant. If the mechanism has an area of 0.1 m2, and has unit emissivity, the net radiation if it is at 300K and the surrounding are 30K colder is 5 W – almost the same as the thermal conduction through the strap neglecting radiation! Radiative cooling drops rapidly with temperature; it is down by an order of magnitude halfway through the cool-down and is certainly not significant at the very end.
This calculation does not consider cooling times for optical elements such as the camera lenses and the prisms.
3.1.4 Conclusions
The analysis up to this point indicates that with four cryocoolers, the most optimistic cool-down time is 2 days, and more realistic estimates are 5 days or more. Times well in excess of this are possible unless some care is taken with the thermal design, particularly coupling of the heads to the structure (thermal distribution system).
3.2 Jump-Start System
3.2.1 Liquid Nitrogen Pre-Cool
As shown in 2.2, a jump-start system has the potential of substantially reducing the cool-down time of the instrument. The analysis in 2.2 examined the amount of liquid required to cool the instrument to 77K, without looking at time scales or how that amount of liquid would be handled.
If the distribution system is taken as a simple manifold that runs the length of the instrument and back, so that the average path length is 0.5 m and the cross-section is now roughly 0.05 m x 2 m, the thermal gradient will be 0.033 K/W. For a temperature differential of 216K (room temperature – 77K), this translates into heat flow of 6500W. The heat capacity of liquid nitrogen (above) is equivalent to 45 W-hr/l, so this rate corresponds to 144 l/hr. The system cools with an exponential tail rather than linearly; it still should reach ~80K (ignoring external heat input) within 24 hours.
This rate of liquid nitrogen consumption is fairly high; gas production is about 1.6 cubic meters/minute. At a rate of only 30 l/hr the nominal cool-down is just under 22 hours (heat/power) but will in fact also have an exponential tail when consumption drops below 30 l/hr. The cool-down time to ~80 K will therefore be more than 24 hours, and the time to reach 60K with the cryocoolers must be added (see below). On the other hand, the cryocoolers will be operating, and will help somewhat as the bench approaches 80K.
Note that these calculations assume the ability to continue flowing liquid nitrogen into the system more or less continuously over a period of 24 hours or more. This would require either an automatic system with a capacity of 500 l or more, or periodic attention round the clock for a system with less capacity (or a slightly less efficient cool-down).
The mechanism cool-down (see 3.1.3) will be similar to that without the jump-start, but with the difference that the cooling must be faster, so the temperature differentials will be larger. Since the latter stages of cool-down are the slowest, the mechanism temperature will tend to converge on the bench temperature, and during the final cool-down below 80 K the mechanisms should cool down in much the same way as with the cryo-coolers only. This description of the mechanisms applies to lenses and prisms as well, unless their time constants are comparable to that of the jump start system itself, in which case the lag between the bench and the optics will be greater than for a slower cool-down.
3.2.2 Final Cool-Down
The cool-down from 80K to 60K can be calculated for the “40 braid” case used above (Table 2). At these relatively low temperatures (range 30-80K), the conductivity of copper is significantly higher than the values used in Tables 1 and 2; the thermal gradient is roughly 0.15 K/W, for an initial cooling power of roughly 250 W (total for four heads). Cooling power for a structure temperature of ~60K is about 180 W. This implies a cooling time of about 4 hours, but consideration of external heat inputs (see SDN007.01) suggests that they should run about 120 W (worst case), leaving only 60-130 W for cooling. Cooling time from 80 to 60 K is thus close to 14 hours. (The structure would then continue to cool below 60 K in the absence of thermal control.)
What would happen if the two one-stage cryocoolers were eliminated? One could retain the same thermal distribution system, but connect it to only two heads. The heads then run somewhat warmer than in the 4-head model, so the gradients and hence heat flow are reduced; the cooling power is about 160 W at 80K structure temperature and 100 W at 60 K. The actual cooling capacity is over half that of the four heads, but excess cooling capacity over external thermal inputs is much, much less: time to reach 60 K is probably in excess of a day, and depends critically on the balance between cooling capacity and heat inputs near 60 K. One could increase the efficiency of the thermal distribution system or add MLI to reduce heat input. Halving the gradients would give a cooling power of roughly 210 W at 80K and 140 W at 60K. This is still rather marginal.
Note that if the RGD 5/100 heads are used, the 2-head case is even worse.
3.2.3 Manifold Design
It is worth noting that the design of the manifold mainly affects the tail of the cool-down since it is unlikely that we would be running it at maximum capacity initially.
For the simple layout discussed above the manifold has a total length of roughly 5 m. If it also has a cross-section of 10 cm2, its volume would be ~5 l. The gas volume corresponding to 30 l/hr of liquid is about 5.4 l/sec (STP). The liquid would have to evaporate in about a second, and the gas would have an exit velocity of roughly 5 m/sec (18 km/hr).
If the manifold is simply aluminum pipe with 3 mm (1/8 in.) wall and total length is assumed to be 6 m. (allowance for connections), its weight is roughly 5 ½ kg. This is comparable to the weight of the cryocooler thermal distribution systems discussed above. A system with double the pipe diameter would have double the weight and four times the capacity; this would simplify control of the liquid. (20 l. of gas [STP] corresponds to 0.03 l. of liquid, or about 3 seconds worth of use at 30 l/hr.)
Once the pre-cool is complete, the manifold can become a heat source rather than a sink. Also, since it will be cooled below 77K, it will be capable of condensing air if left open to atmosphere. The fill and vent tubes should be designed to limit thermal conduction, and the manifold should (probably) be evacuated and sealed during further cooling and operation of the instrument. If the manifold remains a permanent part of the instrument, some means of monitoring internal pressure is required (which should be part of the general instrument diagnostics and not an “eye-ball” read-out in the dome).
If a jump start system is installed, there is no obvious advantage to removing it unless weight is truly at a premium. If it is never used once delivered to Gemini, one could break the connections to the outside and leave it permanently under vacuum (open to dewar inside).
3.2.4 Conclusions
With a jump-start system the cool-down divides into four phases, of roughly similar duration. There is an initial rapid cool-down, during which the limiting factor is either liquid nitrogen consumption (limitations of handling) or concerns about rapid changes in temperature. The second phase is one in which the maximum cooling rate is set by coupling of the structure to the nitrogen system, and the third phase is where the cryocoolers cool the structure below 77 K. Once the structure reaches the desired temperature (60K), the mechanisms will require some time to get close enough for operation.
Heroic efforts to shorten any one of the phases are not warranted, since the best one could do would be a reduction in total cool-down time of about 1/3. On the other hand, a poor design that lengthens one of the phases significantly is not good.
4. Conclusions and Issues
The analysis investigated two approaches to cooling the instrument: cryocoolers alone, and cryocoolers aided by a jump start system.
The cooling time in the first approach is dominated by the design of the thermal distribution system. An efficient system will have significant mass, although it may be possible to design it to properly locate the center of gravity, and thus replace some ballast mass.
The most optimistic cooling time using cryocoolers alone is 2 days, and this is wildly optimistic. With good design, it appears that a time around 5 days is feasible. The level of analysis of this design note is not enough to guarantee that the time will be below 4 days, unless cold mass is significantly under the assumed value of 700 kg.
The jump-start system adds a level of complexity to the system, which mainly has operational impact. With the liquid nitrogen pre-cool, the total cool-down time is around 2 days, but will not be much less (if it is less). Installation of a jump start system does not allow one to easily remove two of the cold-heads, nor does it significantly simplify the thermal distribution system. The time saved per cool down is likely to be 3 days or more.
5. Recommendations
Based on the conclusions above, a simple jump-start system is recommended. The emphasis should be on simplicity of design and operation. At the same time, an efficient thermal distribution system is needed to ensure rapid cool-down from 80K to operating temperature, and to provide the option of cooling without the jump-start system with reasonable performance (but not necessarily under 4 days).
Appendix: Phoenix Cool-Down
This appendix has been adapted from material supplied by Dick Joyce.
A.1.General Comments
I looked at Jay's cooling models using our experience with Phoenix as a baseline.Phoenix has a cold mass on the order of 220 kg and uses two 065 Balzers coolers.The first stages are attached to the instrument bench (actually the collimator box)by a total of 16 copper braid straps.The cross-sectional area of these braids was that estimated by Jay (5 cm2), but their average length was shorter, on the order of 10 cm.
While I would be very reluctant to scale the observed Phoenix cooldown by factors such as relative mass, coldhead capacity, number of straps, etc., to estimate a cooldown time for GNIRS, it does make sense to look at the general shape of the cooling curve.In particular, if one takes Jay's fiducial temperatures (293, 200, 140, and 60), it is instructive to compare the relative times to achieve these temperatures in Phoenix with those estimated by Jay's model.
The first figure is a time plot of the temperatures of one of the 1st stage cryocooler heads (the temperature sensor is actually on the cooling strap mounting plate which is bolted to the cooler stage) and a point on the collimator box, plotted at intervals of two hours.It is evident that the heads cool off to about 140 K almost immediately.The bench itself cools at an initial rate of about 6.5 K/hr (except for the grating, which cooled more slowly, intrinsic offsets in the various temperature sensors masked obvious gradients in the bench itself).Assuming a mass of 220 kg, this works out to an initial cooling power of 320 w and a thermal conductance of the straps of approximately 2.2 w/K.This is virtually identical to what Jay estimated for 20, somewhat longer, straps.
The second figure plots the temperature difference between the 1st stage heads and the bench, as well as the cooling rate of the bench and the effective thermal resistance of the cooling straps (temperature difference/ cooling rate).The latter figure drops significantly when the bench gets below 100 K, reflecting the lower heat capacity of the Al and the improved thermal conductance of the straps.In other words, the bench continues to cool at a reasonable rate (2.5 - 3 K/hr), even though the temperature difference to the cold heads has dropped to less than 30 K.In the case of Phoenix, the bench temperature continues to decrease to the order of 50 K; if we were to control the bench to stabilize at 60 K, it would be essentially cooled after 63 hours, although some of the optics would take longer.
A comparison with Jay's cooldown table is instructive.
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Temperature Range (K)
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Time (Jay's estimate for
40 Copper Straps) |
Phoenix (Observed)
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293 - 200
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27
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18
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200 - 140
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26
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16
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140 - 60
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63
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29
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Total
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116
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63
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While it may be premature to read too much into this, it suggests that the overall thermal model is likely to be a good approximation. The GNIRS thermal distribution system will require some thought and perhaps CROC tests of methods to increase the thermal conductance between the braided straps and their mounting surfaces. (Note by JHE – the fact that the times aren’t a constant ratio is plausibly due to causes discussed in the main text: the head cooling capacity is greater at high temperatures than the cooling curves used, so the 293-200 K cool-down will go faster than the model. The exact amount of heat input into the instrument affects that last stage particularly, so less conduction or radiation would improve the 63 hours substantially.)
A.2. Liquid Nitrogen Precool
Since the external review committee specifically addressed the issue of LN2 precooling, it is incumbent on us to investigate this. As Jay's numbers point out, the jump-start does have the potential of decreasing the overall cooldown time, primarily by being so efficient at removing heat during the earlier stages where the heat capacity of the structure is the greatest.As always, there are arguments both pro and con:
1.A precool system is yet another part of the instrument to be designed, fabricated, and integrated.
2.Obtaining the calculated cooling requires filling the manifold with LN2 at a rate sufficient to maximize the cooling power, but low enough to ensure that the liquid vaporizes completely within the manifold.A real system might be more complex than a cooling tube to which one simply attaches a large cryostat, opens the valve, and walks away.
3.Cooling the bench quickly does not ensure that all the mechanisms will attain operating temperature within this reduced time frame.Alternatively, one will need to ensure that delicate structures, such as the optics, are not thermally shocked by the rapid cooling rate.We could (and probably should) measure the cooling of an optical element (a rough blank of BaF2, for example) in the equivalent of our lens cell using temperature sensors on the material itself.One would obviously not want to install sensors on an actual lens.
4.The precool system adds operational and safety issues which Jay has addressed.
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