Liquid Metal Alloy Oxygen Rocket
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A possible rocket for use on the moon could use fuel that is an alloy of aluminum with other metals to have a reasonably low melting temperature fuel. Calcium, magnesium, sodium, potassium, and silicon are candidate alloy components because they are relatively abundant on Luna. As a bi-propellant this alloy would need to be mixed with a large excess of oxygen for combustion to provide sufficient gas for a working fluid to expand as exhaust through a bell nozzle. The oxygen could also be used to cool the combustion chamber wall and the expansion nozzle. The resulting hot gas would drive the oxygen and fuel pumps before being injected into the combustion chamber. Having a single shaft for the for the oxygen and fuel pumps would be a problem since there would need to be a rotary seal where the shaft penetrates the oxygen housing to prevent oxygen from contacting the fuel before the combustion chamber. Having an electric generator driven by the hot oxygen as well as the oxygen pump might provide a solution. Then the fuel pump would be electrically driven. The fuel tank could be pressurized with hydrogen from a small tank of liquid hydrogen which would be used as necessary to maintain the pressure to the fuel pump input. A portion of that hydrogen could also fill the housing for the electric motor that drives the fuel pump. The oxygen tank could be pressurized initially with a small amount of helium gas. After engine start, some of the hot oxygen from the combustion chamber cooling could be diverted back to the oxygen tank through a loop that would heat the oxygen just enough to maintain pressure. Then oxygen from this loop would go on to the combustion chamber injector. If any additional heat is needed to keep the fuel relyably molten during the flight, a small amount of hot oxygen could be added to the fuel tank where it would burn and reheat the fuel.
The proportions of the various metal components of the liquid fuel would be determined by the cost and availability of each component on the moon and its contribution to keeping a low melting point and providing high specific impulse. NaK eutectic mixture is 22% sodium and 78% potassium. It melts at 9.4 degrees Farenheit or -12.6 degrees Celsius. So it is certainly not a difficult mixture to keep at a temperature at which it remains liquid to be handled by rocket engine turbo pumps. Aluminum and magnesium would raise the melting temperature of the alloy but would be added for the high energy they provide when burned in oxygen and their relative local abundance. Silicon would be added in such a proportion as would lower the melting point in a cost effective way. The whole alloy would be maintained in the fuel tank at a temperature well above its melting point to be sure that some local variation did not cause plating out of a higher melting composition. Multiple sheets of aluminum foil with vacuum between layers would provide adequate insulation so that the liquid metal fuel and the liquid oxygen would each stay at its proper temperature until pumped into the combustion chamber to be burned. The vacuum portion of this insulation is readily available on Luna.