SDN 0007.08

Pre-Cool System Experiments and Design

1. Introduction

The proposed pre-cool system for GNIRS consists of a cooling loop through which liquid nitrogen would flow and evaporate, thereby cooling the instrument structure to close to 77K. In order to do this the loop of pipe must be efficiently coupled to the cold structure. This document describes some experiments aimed at evaluating these “thermal clamps”.

2. Pre-Cool System Overview

The need for a pre-cool system and the basic requirements for such a system are outlined in SDN007.02. Briefly, in order to cool the instrument to operating temperature in <3 days, the structure must be cooled with liquid nitrogen to approximately 80K in about 1 day. This requires use of liquid nitrogen at an average rate of about 30 l/hr, equivalent to a cooling rate of ~1300 W (see SDN13.05 for a convenient summary of lN₂ properties). This assumes that the gas does not warm appreciably above 80K; if it does the same cooling will be achieved with less liquid.

One should note that this flow rate corresponds to about 5.4 l/s of room temperature gas, or about 1.5 l/s of 77K gas.

The basic design consists of a pipe routed around the periphery of the spectrograph structure. The design discussed in SDN007.02 assumed an average cooling path of ~0.5m, so attachment points are needed with this spacing or less. (One should note, though, that the cooling rate during most of the pre-cool is limited by the liquid nitrogen flow rate and not by thermal gradients; any less-than-ideal attachment scheme will only have an effect once the average bench temperature drop to around 120K.)

This routing leads to a length of the loop of about 7 m. The diameter of the pipe was determined by two considerations. We want to ensure that the transit time through the pre-cool system is long enough to ensure reasonable thermal coupling, and we are also concerned that too small a diameter will produce too high an exit velocity at the output. Typical fill tube diameters for large instruments are ½ inch, and initial fills take place with substantially higher flow rates without producing unsafe jets of cold gas. However, the volume of a line of ½ inch diameter is only 0.9 liters, which implies a transit time less than 1 second. (This assumes 77K gas, which would be appropriate for poor thermal coupling.) For a ¾ inch diameter pipe, the volume increases to 2 liters, and the transit time is then a little over 1 second, which seems more reasonable. Larger diameters become increasing unwieldy, so the ¾ inch diameter was adopted.

The next consideration was the type of pipe to be used. The pre-cool system needs to be simple, relatively free of welds or other joints, and must also allow removal of mechanisms and separation of the two bench sections. It must also be compliant so as to accommodate the effects of differential thermal contraction during the initial cooling stages, when the pre-cool system is at 77K and the structure is still near room temperature.

Two candidates were considered: stainless steel flex line, and copper refrigeration tubing. The first of these is something NOAO already uses for transfer lines and as a flexible interface in some dewar fill tubes. It has the advantage of being quite flexible, allowing easy assembly and disassembly of the pre-cool system. The only joints would be those associated with the fill/vent tubes in the dewar wall. The main concern was that the low conductivity of stainless steel and the corrugated design would lead to relatively poor heat transfer across the interface to the bench. The alternative was copper tubing. While this can be bent, some of the pre-cool routing requires sharper bends than can be readily accommodated by bending, and in these areas one would need to use 90-degree elbows. Given the greater stiffness, assembly and disassembly would be more difficult.

In both cases, the actual interface to the bench would have a similar design. It would be a block with a cylindrical bore which can be clamped down on the pipe, and which is then attached to the bench. These blocks (“clamps”) would be pre-assembled onto the pipe and then fastened to the bench as the pipe is bent to follow the intended routing.

3. Experiments

Given the attractions of the flex line from a strictly mechanical point of view, we decided to carry out some experiments to evaluate thermal performance of the competing pipe materials.

The experimental set-up consisted of an aluminum block installed in an insulated container (styrofoam picnic cooler). A single clamp of the design outlined above was attached to one end of the block, and a length of the pipe under study was run through the cooler wall and the clamp. The pipe was insulated on the outside, and attached to a 160 l storage dewar.

Diodes were installed at four locations: the top of the clamp, on the block near the clamp, on the block at the opposite end, and on the inside wall of the cooler. For the experiments, liquid nitrogen was flowed through the system and temperatures were recorded at roughly 5-minute intervals. The rate of flow was adjusted so that small amounts of liquid emerged from the end of the pipe. This setting was somewhat subjective (and not easy to do precisely with the valve on the storage dewar).

The experiment was run for three cases: a flex line of the type proposed, but with a ½ inch ID; the same line with indium solder wrapped in the corrugations to provide a better thermal contact, and ¾ inch (OD) copper tubing. Note that the OD of the flex line was close to ¾ inch as well (0.795 inch).

3.1. Results

The experiments were run for varying lengths of time, always at least 2 hours. The basic result was the same in all three cases: the block started cooling at a particular rate, and then cooled more gradually. It appeared that the temperature would eventually level out at in the vicinity of 200K, although none of the three experiments actually ran long enough to stabilize. This is presumably the point where the heat input into the cooler from the outside balances the cooling from the liquid nitrogen.

The simplest way to analyze the results is to consider only the initial part of the cooling curve, when external heat input is least. (One presumes that the heat input into the block is proportional to the temperature difference between it and the environment outside the cooler.) These results are summarized below. The cooling power is calculated using the mass of the block (9.5 kg) and the specific heat of aluminum at the relevant temperatures (0.85 J/g-K)

Initial Cooling Rates

A comparison of these results shows that the indium had only a modest effect; the copper pipe is better by a factor of about 1.6 .

A more detailed model of the cooling can be done in a variety of ways. If one assumes that the external heat input is proportional to the temperature difference between the block and ambient, and if one treats the heat capacity of the block as constant over the temperature range of interest, then an equation of the form

dT/dt = -a + b(T₀-T)

results, where a is the cooling term and b is a coefficient for the external heating. The heating term should be the same for all three tests; only a should vary. In fact this was not the case, which suggests that the coupling of the block to the outside world was not uniform. The best fit values of these coefficients are tabulated below. Plots of the fits to the first and last experiments are shown as well.

Corrected Cooling Rates

The cooling rates are not very different from the initial estimates given above, though allowance for external heat input does lead to slightly higher cooling estimates (20%).

The values fitted for b range from 0.38 to 0.27 (K/hr)/K (hr^-1). If one were to choose an average value for b the derived cooling rates would change by 10% or less (decrease for copper experiment, increase for flexline+In experiment).

The temperature drops across the block and between the body of the clamp and the adjacent portion of the block are both fairly small compared with the much larger temperature difference between the liquid nitrogen and the clamp body. However, as discussed below (Appendix A) the drop between the clamp and the block is not consistent from experiment to experiment, probably indicating non-uniform bolt torque. The drop across the block is much more consistent.

One should be able to confirm the heating rates, if the physical processes are symmetric, using data showing the block warming after the liquid flow was stopped. Only the first experiment was run (with data recording) long enough for significant warming to occur; the fit to the warming using the b value derived from the cooling shows much slower warming.

3.2. Discussion

As noted above, most of the thermal gradient occurs between the liquid nitrogen and the body of the clamp. There are two locations where it might occur – between the pipe wall and the clamp itself, or between the liquid and the wall of the pipe. The interface between the pipe and the clamp is not very different from that between the clamp and the plate, especially for the copper (smooth surface and high conductivity material). This implies a drop of at most a few tens of degrees; it could well be less since the surface area involved is actually larger. This strongly suggests that the largest resistance in the thermal path is the interface between the liquid and the pipe wall – the vapor barrier familiar to anyone who has ever cooled a dewar with liquid nitrogen. This interface is presumably similar for all three tests, and explains the similarity of the results.

The copper pipe does perform somewhat better, and there are two factors that probably contribute to this. One is that the resistance between the pipe and the clamp, though small, is undoubtedly higher for the flex line (see Appendix for more discussion). The other is that the copper pipe has enough lengthwise conduction to permit the effective length of the pipe/clamp contact to be somewhat greater than the mechanical length of the clamp; the conductivity of the flex line is much lower.

If the dominant source of resistance is the vapor layer at the pipe wall, then the cooling rate of the clamp should be roughly proportional to the area of the interface – the pipe circumference times the length of the clamp.

Use of the larger flex line (¾ in ID vs ½ in ID) should produce a cooling rate approximately 50% larger, and the clamp can be lengthened as well.

The tests above were done with a single clamp, and the nitrogen flow rate was adjusted to match the heat input. When the flow rate was increased in the tests with the flex line, the effective cooling did increase slightly. No attempt was made to quantify this effect, but it seems likely that the much higher flow rates required for a system dissipating 1300 W will lead to more efficient cooling in the initial stages of the pre-cool system, where the nitrogen is still largely liquid.

4. Design Guidelines

For ¾ inch ID flex line, the predicted cooling rate for a clamp of the same length is 112 W. The clamp length is 1.5 inches, so the sum of the length of the clamps should be around 18 inches to achieve a cooling power of 1300 W. Given the uncertainties in the analysis, some margin is surely desirable. A 50% margin would imply a total length in clamps of 27 inches.

In principle, the cooling will be distributed as the clamp length is distributed, although there may be some tendency for the clamps at the start of the loop to cool more effectively (per inch) than the clamps toward the end. Performance should not be significantly worse than that seen in the tests, however.

Appendix A – Conduction across Bolted Joints

The results and analysis above show that conduction across joints is not the limiting factor in the per-cool system design. It is interesting, however, to examine the joint performance.

A.1. Analytical Basis

A useful basis for the discussion is a PhD thesis by Jesse Maddren (1994, University of California, Santa Barbara). The thesis includes measurements of conductance across joints as a function of pressure, temperature, surface roughness, and material. Another thesis by John Fontenot (1968, Louisiana State University) provides more discussions on empirical models of contacts, but mainly at room temperature.

The experimental data for aluminum show that the conduction increases somewhat less than linearly with pressure, with a tendency to level off at pressures above 6 MPa. Conductivity is better across smoother surfaces; the effect is about a factor of 2 for a factor of 10 decrease in rms roughness.

The data also show better conductance if the pressure is increased and then decreased; this is interpreted as plastic deformation at the joint. One should note that without thermal compensation, this will occur naturally in GNIRS since the loading of bolted joints will be higher when warm than cold due to differential contraction of steel bolts and aluminum structures. The conductivity of the joint will therefore be better than predicted using the nominal bolt forces when cold – but not as good as it would have been if the bolt forces were maintained as the instrument cools.

For a surface roughness of ~115 microinches rms, the conductance (kW/m²-K) is about 20 at 3 MPa pressure, 31 at 6 MPa pressure, and 36 at 9 MPa pressure. The quoted experimental error is, however, fairly high – around 30%.

The air in the gap provides some conductivity as well, which may contribute a few kW/m²-K, based on the formulae in Fontenot. (Maddren’s data were taken in a vacuum; the conductivity of the residual air was measured to be negligible.)

A.2. Clamp Evaluation

Use of these data requires knowledge of the pressure distribution at the joint. The literature on the subject, cited by Maddren and Fontenot, shows that this is a function of both the joint geometry and the micro-structure of the joint. However, given the approximately linear nature of the dependence of conductance on pressure, one can argue that a rough estimate can be obtained using an average pressure.

The clamp was attached to the plate using two 6-mm bolts. Ed has done calculations showing that properly torqued bolts of this size will have a pre-load in excess of 1000 lb after cooling (equivalent to 9 kN total for 2 bolts). The area of the interface is 1.5 x 0.75 in or 7.26 cm². The average force at the interface is therefore ~12 MPa.

The conductance calculated from Maddren’s data would then be at least 36 kW/m²-K, which for the interface area translates to 26 W/K conductance across the joint. The conductance of the air in the gap might contribute another 10% or so. The first figure in section 3.1 shows a value much smaller than this, around 3.7 W/K; the second figure is closer, with a value of about 10.7 W/K. The third experiment was intermediate. As the system cools, the difference across the joint decreases, which is somewhat unexpected. This could be explained if the bolts are cooling after the clamp, thereby increasing pressure, or if a significant fraction of the external heat input goes into the clamp and hose. Both explanations are not particularly plausible. If one takes the smaller temperature difference at face value, the maximum conductance is around 35 W/K (flexline only experiment).

The range in conductance values does suggest that the bolts were not optimally torqued – although different clamps were used for the flexline and copper pipe, and these might have different contact properties.

A.3. Extrapolation to Bench Joints

The interfaces between the major bench sections are measured in hundred of square cm, and the average forces are certainly comparable (more care has been taken to ensure that these forces are, in fact, maintained). Scaling from the clamp, one predicts conductances well in excess of 1000 W/K based on theory, and around 1000 W/K based on the data. The conductance is likely to be lower at 60K than at 200K, but this still implies that heat flow across the bench of a few watts will result in temperature gradients across joints of 0.01K or less.

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