Autogenous pressurization with sub-cooled propellant

Question

In his IAC 2016 talk, Elon Musk said (at 28m 4s in the video) that the ITS booster tanks would use autogenous pressurization. This means there is gaseous oxygen resp. methane in the tank. To stay gaseous, its temperature must be above the boiling point.

On the other hand, the liquids are sub-cooled, i.e. their temperatures are far below the boiling point.

So we have "warm" gas and "cold" liquid in the same tank. How does this work out? Wouldn't the gas quickly condense, causing the pressure to drop? And respectively, wouldn't the liquid heat up and eventually boil?

I could imagine that it works for the booster, as the tanks are emptied so quickly that there won't be time to reach equilibrium anyway. But what about the spaceship? Is it also using autogenous pressurization? The diagram shows smaller tanks embedded in the spaceship tanks, could this be a helium pressurization system like in the Falcon 9?

Note: This web-based tool by NIST may be useful to determine and visualize thermophysical properties of fluids used in rockets.

Answer 1

Once the tanks are no longer full, there's no point in keeping the propellants subcooled. When you start the engines, you just have to control the rate at which the tank and propellant warm up, to keep the pressure below its limit.

The warm gas you inject into the headspace to pressurize the tank will start warming up the surface of the liquid. You'll have to stay ahead of the cooling down and condensation of this gas.

So there's a balancing act between two limits.

Answer 2

There is nothing wrong with a substance existing in both a liquid form and a gas form at the same time, like in this case. In fact, that is where the equilibrium is!

Firstly, there is not really such a thing as a liquid in a vacuum, it will always attempt to fill it*, as the boiling point gets lower with the decreased pressure.

Le Chatelier's principle is the law preventing the process from going towards any extreme, either all gas or all liquid:

• If the liquid starts to boil, the pressure increases, rising the boiling point, and the phase transitions consumes heat, lowering the temperature
• If the gas starts to condense, the pressure decreases, lowering the boiling point, and the process is exothermic, releasing heat so the temperature rises.

Any attempt by the system to go towards either extreme is resisted.

"sub-cooled" as the term is used in this setting, means that the temperature of the liquid is below the equilibrium point (the boiling point), but a transition is not going to go fast. The only way to get the liquid to leave the sub-cooled state more quickly would be to supply heat externally, as the process is endothermic. Also, the system is self-balancing: If you remove fuel from the tank and lower the pressure, some of the liquid boils until an equilibrium is reached again. Then it stops boiling. lastly, fuel tanks are well insulated, and once surrounded by vacuum, the heat-flow is extremely slow. Like any other cryogenic system, it requires a little refrigeration to be kept liquid in the long term.

_{*There are factors that can keep the liquid from boiling to fill the vacuum, like surface tension and some intermolecular forces, but those factors can generally be ignored.}

Answer 3

In fact, the system of sib-cooled (chilled) cryogenic liquid and its vapour (gas) is more stable than the same liquid near the boiling point. Condensation on the free surface of the liquid propellant is driven mainly by diffusion which is a slow process. From the other side, a sudden splash may increase the free surface a hundred times because of droplets and provoke rapid pressure drop. Such splash may be caused by energetic manoeuvre (belly flop). Even raptor motors being switches to landing tanks the pressure oscillations are among the suspected cause of landing failure of SN 8 and 9. _

Answer 4

Here is my current understanding of the situation.

Reading Disposition of the Oxidizer Tank in Rockets with Autogenous Pressurization and this and this answer, it seems that autogenous pressurization of propellants is not used on sub-cooled propellants but instead happens when the temperature of the propellants (and tank internal surface) is at the boiling point. Adding additional heat will build pressure, or maintain pressure while propellants are leaving the tank.

The main advantage of sub-cooling is to increase the density so that a tank which is completely full can hold a larger mass of propellant. Once a propellant begins to be depleted (used) and say 10% or 20% has been used, there is no further major advantage for it to be at a temperature below boing point, except perhaps a bit of thermal inertial if heating in space is not sufficiently insulated. However, until that point, an inert gas should be used for pressurization.

edit: as @oefe pointed out in a comment below, in the recent video Making Humans a Multiplanetary Species starting at about 32:38, Elon Musk discusses advantages of maintaining sub-cooled temperatures for liquid propellants including reduction in cavitation within the turbo pumps. This is discussed further in How (actually) do sub-cooled propellants reduce cavitation within turbo pumps and make feed easier?

I don't think a propellant can easily be both sub-cooled and self-pressurized "autogenously" simultaneously, which I think is the key point of asking your question.

Heat could be added to the closed system within the tank or by passing a small amount of propellant through a heater and re-introducing it. I think in general "autogenous pressurization" refers to such a system, which may or may not meet the thermodynamic definition of a "closed system".

(some plots of published data on LOX and RP-1 density vs temperature can be found in Does the NK-33 engine require subcooled kerosene so cold that it turns to wax?)