Original
commentary posted in sci.space.tech newsgroup 2001
Revised
November 2001
The propellant combination of liquid hydrogen and liquid oxygen has a high exhaust velocity, and is thus favored for orbital transfer and interplanetary missions. In such missions, there can be waiting periods of days to months between when the propellant is launched from earth, and when the propellant is used for propulsion. Since both liquid oxygen and liquid hydrogen are cryogenic and only remain liquids at very low temperatures, the issue of the practical boiloff rate in space is important in mission planning. The boiloff rate for liquid hydrogen in space is also important for planning missions involving in-situ propellant production on Mars, using hydrogen imported from the earth. The boiloff rate for these propellants in low earth orbit was examined in the following study, carried out by Boeing, with Eldon E. Davis as Study Manager.
Future Orbital
Transfer Vehicle Technology Study, Volume II - Technical
Report
NASA Contractor
Report 3536
NASA 1982 (about 240 pages, soft cover)
The study examined strategies for propellant supply and storage options for a hypothetical fleet of reusable orbital transfer vehicles. The system included liquid hydrogen and liquid oxygen storage tanks in low earth orbit, refilled periodically by propellant brought up from the earth. The estimated boiloff rates for these tanks can be calculated from the raw data provided in the report:
|
Propellant |
Boiloff rate per day |
Boiloff rate per month |
|
Liquid Hydrogen |
0.127% |
3.81 % |
|
Liquid Oxygen |
0.016% |
0.49 % |
A tank set for on-orbit storage of propellants for a reusable orbital transfer vehicle contains a total of 59,400 kg of liquid oxygen and hydrogen, at a mixture ratio of 6 to 1 (given data). This equates to 8486 kg hydrogen, and 50,914 kg oxygen, before boiloff. The study assumed multilayer insulation consisting of 50 layers of double aluminized Kapton (0.15 mils thick), separated by Dacron net. Heat leakage includes that through the insulation, as well as through tank/shell struts and fill, feed and vent lines. The heat leakage causes a boiloff in this specific tank set of 0.45 kg/hour of liquid hydrogen, and 0.36 kg/hr of liquid oxygen. Given the loading of each propellant, this translates into the percentage losses seen above.
As an additional data point, a graph of boiloff vs. layers of insulation shows that if only 10 rather than 50 layers of insulation are used, the hydrogen boiloff rate is about 2.2 kg/hr rather than 0.45, and the oxygen boiloff rate is about 1.6 kg/hr rather than 0.36.
It should be noted that boiloff is governed by heat leakage, and the rate in kilograms per hour does not depend on the amount of propellant in the tanks. With partly filled tanks, the percentage loss per day or month would be higher. Also note that heat leakage is driven by surface area, while the original mass of propellant in the tanks is governed by volume. Thus, the smaller the tank, the faster the liquids will boil off (square/cube law ).
Boiloff rates in the Boeing study were estimated for tank sets in low earth orbit. Lower boiloff rates would be expected for tanks at a further distance from the sun. Lower boiloff rates can also be expected if tanks can be maintained at an angle which minimizes their cross-sectional area exposed to the sun, or tanks protected by a sunshade. The boiloff rates in low earth orbit thus most probably represent a worst case scenario, with better results to be expected for spacecraft on Mars trajectories etc.
Taking into account the enthalpy of vaporization, the oxygen tank heat flux across the walls is 0.36*213.1 = 76.7 kJ per hour. For the larger and colder hydrogen tank, the figure is 0.45*445 = 200.25 kJ per hour. The hydrogen tank is venting 0.45 kg/hour of very cold vapor, at just above the boiling point of liquid hydrogen. This vapor has a very high heat capacity, 12.24 kJ/kg*K. If the hydrogen vapor were conducted through a heat exchanger in thermal contact with the liquid oxygen tank, it would be warmed from approximately 20 K to approximately 90 K (exact temperatures depending on the pressure the tanks are maintained at). This has the capability of providing as much as (90-20)*12.24=857 kJ/hour of refrigeration. In other words, if desired the boiloff vapor from the hydrogen tank can be used to keep the liquid oxygen from boiling off entirely.
Although hydrogen is boiling off at nearly 4% per month, it is only 1/7 of the rocket propellant mix. Overall, the tank set in the example above is boiling off 0.45 + 0.36 = 0.81 kg of propellant per hour, which is 1% of the initial total mass per month. If boiled-off hydrogen were used to refrigerate the liquid oxygen tank, the propellant loss would be only 0.55% per month.