Why would sub-cooled LOX tanks need to "topped-off" until the last minute or so?

Question

Here is my understanding, let me know if I've got it right or wrong:

Until recently, most cryogenic propellants were at or close to their boiling points. Each unit of heat leaking into the tank would then boil off a corresponding unit of propellant and the temperature would stay constant. This is roughly like adding near boiling "make-up" water to a pot of boiling water. It might be a little cooler, but not much.

But in the case of sub-cooled LOX, the temperature is way below the boiling point, somewhere between 10 and 30 degrees C depending on the case. When heat leaks into the tank, it will raise the temperature of the LOX which then expands. A full tank would then overflow - remaining full but with less mass of LOX due to the density change.

There would be no boil-off to "make up" by topping it off. It would remain full but steadily decrease in density as it warmed up.

So for a rocket with first stage tank filled with well sub-cooled LOX, why would it need to be "topped-off" until the last minute or so before launch?

This video at T -00:05:05, video time 06:52, my approximate transcription of the narration:

Right now we’re just coming up on the five minute mark here, we are concluding the loading of the RP-1 on to the first stage […] and we are topping-off liquid oxygen as well on that first stage, and we’re going to keep topping that off for about two more minutes.

The video is already queue'd up at the appropriate time code (in this case I think the video edit is final):

Answer 1

At a pressure of 1 bar, the temperature of liquid boiling oxygen stabilizes at 90 K. For sub-cooling of LOX, the temperature should be lower. It is possible to cool LOX by forced evaporation by a pressure lower than 1 bar. But the LOX tank in a rocket should be as light as possible. If the pressure inside the tank is substantially lower than outside, extra strength and weight is necessary. But according to these papers: (1) (2) and (3) there is another method.

Cold helium gas is injected at the bottom of the tank and the bubbles raise in the LOX. At the surface of the bubbles, LOX evaporates into the bubble and cools the remaining LOX. But extra space is needed for the bubbles in the LOX and for the gas mixture of helium and oxygen above the liquid level. For topping off, the injection of helium is stopped and the remaining space is filled with LOX. Figure 8 of the first paper shows the effect of different helium gas temperatures. The cooling works best with helium at 85 K, but even helium at 150 K cools the LOX.

A bubble injected into the LOX consists of 100 % helium and 0 % oxygen at first. The LOX around this bubble would boil just like in a vaccum because the partial pressure of oxygen in this bubble is zero. Even a bubble consisting of 50 % helium and 50 % oxygen is able to cool LOX at 90 K. Without sub cooling in a tank with boiling LOX at 90 K, the gas above the liquid is 100 % oxygen and the partial pressure of oxygen is 1 bar. If the partial pressure of oxygen is lower than 1 bar in the gas above the liquid or inside the bubbles, the LOX is cooled by evaporation.

At the launch pad the LOX may be precooled using a heat exchanger with ground suplied liquid nitrogen boiling at 77.355 K. To save weight of the rocket, this heat exchanger should be outside the rocket but close to it. Liquid nitrogen and oxygen should not be mixed to avoid solving of nitrogen within the LOX. Cooling with helium bubbles may be used within the rocket LOX tank.

Answer 2

You guys are discussing anti-geyser systems like the one we used on the Space Shuttle ET-LO2 tank. But I didn't see the more obvious answer, the operational answer. Everyone was so focused on the thermodynamics and intricate differences between boiloff and evaporation... but nobody mentioned thermal conditioning of the engines.

How this is done depends on the engine(s) used, but in all cases (with cryogenic propellants) you have to chill down your engine inlet and all components that will touch cryos prior to startup or else you will have what we call a "bad day". In the case of the Shuttle, there was a constant bleed rate of something small for LO2 (on the order of a few pounds/sec, I think) but since LH2 used recirculation pumps they did not have that bleed. However, the Shuttle also had a constant Replenish rate to replace the LO2 lost due to boiloff and drainback. The ullage pressure dropped from about 17/18 psi at end of Topping down to about 15 psi(g) at Terminal Count.

The anti-geyser system was just a simple helium inject used to subcool the LOX so that at low flows/low liquid levels (eg during Slowfill) we wouldn't get Taylor Bubble formation in the feedline and a geyser event - we did not have to load extra propellant for that, but it did mitigate the LOX temps throughout tanking and Replenish.

Got off topic there. Some rockets will re-top to flight level shortly before liftoff to account for the propellant lost due to boiloff (WAY more prevalent than evaporation!) and engine thermal conditioning. Some vehicles, like the Shuttle, constantly replenish the levels to keep them at 100% until start of Terminal Count Sequence.