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The Apollo and Shuttle spacecrafts used fuel cells for the production of electric energy and water. The hydrogen and oxygen for the fuel cells were stored as a supercritical fluid at a temperature close to the critical point to increase density without using very high pressure.

But how were those fuel cell tanks loaded on the launch pad? The temperature of gaseous high pressure oxygen and hydrogen was too high, the boiling temperature of those liquified gases was too low. The boiling point of O2 at 1bar is 90.188 K ​(−182.962 °C, ​−297.332 °F) and the Critical point is at 154.581 K, 5.043 MPa or 50.43 bar.

Did they fill the tanks with the proper amount of liquified gases, closed the valves and waited (may be using the tank heaters to speed up) for temperatures and pressures to raise to the wanted values for the supercritical fluids?

See also these related questions 1 2.

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I don't have a good reference that explicitly states it for this one but I think your conjecture is correct: filled from ground and hydraulically pressurized to a low pressure as liquified gases, then turn the heaters on to get into the supercritical range.

The shuttle Power Reactant and Supply Distribution Handbook (not online) has charts showing how long it takes to pressurize to operating range using the heaters. The chart description says

Oxygen Tank Heaters Pressurization - Expected tank pressures are shown as functions of time for various fill quantities. Initial pressure is 15 psia. Heaters are operated on GSE power.

Apollo may have been different - the reference in this answer says

Initial pressurization from fill to operating pressures is accomplished by GSE.

This could mean either hydraulic pressurization from GSE, or GSE-powered heater operation as in the case of Shuttle, it's not clear.

GSE = Ground Support Equipment

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    $\begingroup$ Heating a closed vessel can’t change the density of its contents: it’s still the same mass in there. So if the goal is to maximize the enclosed mass, it has to be loaded at/near the storage pressure & temperature contour. $\endgroup$ – Bob Jacobsen Oct 10 '19 at 14:11
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    $\begingroup$ @BobJacobsen Heating a closed vessel can’t change the density if the vessel is filled completely with either liquid or gaseous oxygen. But what if the vessel is filled with about 80 % liquid and 20 % gaseous oxygen? $\endgroup$ – Uwe Oct 10 '19 at 14:26
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    $\begingroup$ I wish KSC had published their procedures and rules like JSC did! There's a frustrating lack of information about ground ops. $\endgroup$ – Organic Marble Oct 10 '19 at 15:05
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    $\begingroup$ @BobJacobsen there's another line in the PRSD Manual that says "Ground Pressurization: Hydraulic" so the chart title may have misled me. When I found that line "Initial Pressure is 15 psia" I interpreted the chart the way I wrote the answer, but it definitely isn't explicitly stated. $\endgroup$ – Organic Marble Oct 10 '19 at 15:10
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    $\begingroup$ @uwe if you fill, close valves and heat, the overall mass isn’t changing any more. It looks like the fill ends up at (close to) final P and T before closing off. $\endgroup$ – Bob Jacobsen Oct 10 '19 at 15:55
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Page 303 of the Apollo Operations Handbook contains information about the temperature at the time of fill:

enter image description here

The boiling temperature of LOX is ​−297.332 °F, of LH2 is −423.182 °F, so we may conclude the fuel cell tanks are loaded with LOX and LH2.

In the diagramms of the tank isothermes found by Organic Marble: enter image description here

we find the temperature for a loading of 100 % LOX is -280 °F, very close to the boiling temperature.

So I think filling the tanks with LOX and LH2 first and then pressurizing them with gaseous O2 and H2 to about 900 and 240 psia was the easiest way.

But to load the right amount of LOX and LH2, there should be level sensors for the liquids or weight sensors for the tanks. The capacitive gauges are designed for supercritical fluids to measure tank quantity during flight. But may be they could be used with supercritical fluids in zero gravity as well as for liquids on the launch pad.

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