For our sizes (~12" dia), the rates will likely be on the order of a few
100 cc/hr for the best insulated, best thermal designs. The problem with accurate predictions is that the actual rate is so highly dependent on the nature of the experimental insert that hangs just above the free liquid surface. This requires calculations involving surface roughness and temperature of the bottom of the "Faraday Chamber", the gap between the bottom of this chamber and the top of the LHe, the radial gap between the OD of the Chamber and the ID of the dewar, the temp of the rotating ring assembly and the thermal contribution of the agitated He gas, etc. One textbook (Richardson) on cryodesign mentions average boil-off rates for actual (not ideal) experiments in "larger" dewars to be about 580 cc/hr. White calculates a boil-off rate of about 400 cc/hr from a 0.28 Watt thermal source immersed in LHe (although we do not have that exact situation) so that would imply an immersed thermal load of about 1/2 watt. World patent # WO/1994/026418 states for dewar diameters >~12", typical boil-off rates for the best insulated (near-ideal) systems are ~150 cc/hr.
GH called Quantum Technologies who manufacture dewars and the guy there (Calvin @ 604 222 5539) stated that for wide-mouthed LHe dewars with a tight-fitting long styrofoam plug/stopper down to almost the LHe level, the boil-off rate varied approx. linearly (!) with diameter: 3" dia -> ~200 cc/hr; 6" dia -> ~400 cc/hr; 12" dia -> ~800 cc/hr. While GH stated to Calvin he found this very hard to believe (expecting to find rate scaling at least as diameter2 ) Calvin explained that under equilibrium conditions this was the case. GH interpretation of this explanation was that if the annular area of the gap between the Styrofoam (or Faraday Chamber in our case) does not vary much with diameter (ie is so small as to be a negligible factor), then the main heat gain is mostly dependent on the circumferential length of the LHe/inner dewar wall interface which, of course, scales linearly with diameter.
GH also called International Cryogencis (James @ 317 297 4777) who gave more precise figures although he didn't know exactly under what conditions the data was taken.
GH suspects they were under near-ideal conditions. From them GH calculated the (linear!) scaling law to be B (boiloff in cc/hr) = 42.4D-176 where D is diameter in inches. Together with approximate costs of the dewar, we get for D=12", B=~330 cc/hr (~$5000): for D=18", B=~590 cc/hr (~$7000) and for D=24", B=~840 cc/hr (~$9500). These figures are lower than Calvin's but seem to be more in line with the other information.
GH would tentatively take the International Cryogenics data as a first pass. GH
is waiting for Janis (another Dewar manufacturer) to get back to him.
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From GH:
We have to define what we mean by "run"
before we can make any reasonable estimate of the quantity of LHe required both
for delivery and to be "on hand". Let's say Martin performed 200
"spins" (100 CW, 100 CCW) per run for his signal averaging
requirements. If each spin takes approx. 30 sec (see 2007 "Search
for..." paper) with another 30 sec between for immediate data crunching,
calibration, various system parameter checking, that's 200 minutes or approx 3
1/2 hours. It typically takes an hour or more to get a warm dewar down to LHe
temps even if LN2 is used as a pre-cooler. Also, you also cannot simply
"turn off" an experiment involving LHe - there must be an orderly
shut-down, even if the system is to be brought down to LHe temps the next day
for more runs. This shut-down process requires about 1/2 hour minimum. Thus I'm
suggesting that according to this model, 200 spins = 1 "run" per day
is a reasonalble target. And that's after the system has been shaken down.
From the figures I sent yesterday, a reasonable
average boiloff rate for a well-insulated >static< experiment might be
around 1/2 liter/hour. My guess is that with a spinning mass, this figure should
be at least 10 times more, or, say 5 l/hr. This is the subject of some pending
calculations. For a 4 hour experiment, that's 20 liters. In addition, about 5 l
may be required for initial cool-down and end-of-experiment warm up. This totals
25 l for a typical 6-hour "run" session. This should be checked with
Martin to see how far off it is but seems to square roughly with our Pod
spinning disk experiments which, although having a reasonably good thermal
design, nonetheless consumed about 1/2 of a 60 liter storage dewar per single
day's run.
Then there's the storage dewar boiloff rate which
is much smaller ~0.5 l/day for a typical 60 l storage dewar.
So I get about 1/4 of Scott's 100 l per daily "run" according to my
definition of "run". Therefore I recommend renting a 60 l dewar first
before considering a couple of 100+ l dewars. This will allow some essential
experiment shake-down time, even after several dummy runs with LN2. Don't forget
that LHe is a completely different animal than LN2 even tho' only 73K cooler!
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Marissa,
That's good news. However, I'd still have to try some of it in direct contact
with LHe. I'd start by making a "pulley" out of aluminum maybe a
couple of inches in diameter and an inch long, with a "tire" of PU
foam maybe 1/2" thick (by 1" long). This I would then dip into LHe in
a small cryostat to see if the foam shrank enough to break apart on the pulley.
Since you can't (usually) see what's happening at the LHe surface due to severe
condensation problems, you have to make some tests like this. I always prefer to
do this type of actual experiment first rather than to trust an extrapolation
from 20K to 4.2K and no contact with cryogen to direct contact with cryogen. If
that succeeded to some acceptable extent, I would then fabricate a small dewar
with cap from PU foam, if we can get chunks rather than sheets of it, and test
by filling with LHe. My gut feel is that it would not make an acceptable dewar
of the type Scott envisions except maybe for small-scale experiments where the
boiloff rate doesn't matter.
cheers - George ghathaway@ieee.org
George,
A friend of mine at Lockheed sent me data for the polyurethane foam (made by NCFI) that is sprayed over the large areas of the external tank. The foam is about 3 cm thick and the inside surface is in contact with the aluminum tank that contains liquid hydrogen (~20K). The aluminum wall is about 0.3 cm thick. The foam doesn’t shrivel up and the bulk foam is still strong enough to not shear off during takeoff.
Sorry about the insane units. Lockheed still hasn’t adjusted to the 21^st century. The lowest temperature on the graph gives a thermal conductivity of about 0.007 W/mK, which is just a bit lower then the value Scott used in his estimates (0.01 W/mK).
Marissa