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Starship relies on tank pressure to gain it's full structural strength.

During reentry, the tank walls heat up, causing the ullage gas to heat up, causing pressure to rise. How will Starship prevent the tank from bursting due to pressure?

The most obvious answer is by venting gas. Then a second question arises. During landing, the walls cool down, causing the gas to cool down. How will Starship prevent the tank from crumpling?

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2 Answers 2

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1 Assuming that there are residual propellants:

When Starship re-enters most of the energy of re-entry will be absorbed or deflected by the tiles. Some heat will be absorbed into the tank, however as stated any resultant pressure build up can be vented to prevent over pressure.

Once landed the tiles will remain hot for some time and heat will continue to seep into the cryogenic tanks from the tiles and also from the stainless steel hull in contact with ambient temperatures. Venting of gas will take place to ensure that there is no over pressure event.

The rate of venting will decrease as the tiles cool until the tiles along with the rest of the hull approach ambient air temperature. At this point venting will still continue but at a much lower rate until all of the residual cryogenic propellants have boiled off.

At some point SpaceX will want to move the Starship so they may just leave the vents open or connect to ground infrastructure to pump or purge the remaining propellants.

The tank will never be in danger of crumpling on the ground (short of a structural failure) as there is no way for the pressure in the tank to reduce unless the ambient temperature drops to such an extent that the gases in the tanks start to condense and that would take a near cryogenic temperature which is no going to happen outside in southern Texas.

2 Assuming all of the cryogenic propellants boil off

Even making the unreasonable (in my opinion) assumptions that the entire tank and its contents would reach 1000 K during re-entry and all cryogenic liquids would boil off the pressure inside that tank would still not drop below 1 atm.

Assuming ideal gases, the combined gas law states that p1v1/t1 = p2v2/t2 and at constant volume this reduces to p1/t1 = p2/t2

The Raptor inlet pressure needs to be ~6 bar so the pressure in the tanks should not fall below that when in operation. After engine cut off the pressure will only increase and venting will occur as the tanks are heated. Gas will continue to be vented (at around 6-8bar) until the temperature reaches the assumed 1000 K. We will assume that the temperature then falls to 300K on landing.

So 6/1000 = p2/300

or 6*300/1000 = p2 = 1.8bar

So even assuming 1000K heating of the tank and its contents the pressure of the tanks will remain well above 1bar even after landing and cooling to ambient temperatures.

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    $\begingroup$ I love that you said "outside in southern Texas" as if it could happen in Maine or something. $\endgroup$ Commented Mar 19 at 18:22
  • $\begingroup$ I don't think the tiles will remain hot, based on demonstrations of Shuttle tiles that I have seen where someone handles a tile with their bare hands that was white hot moments before. The steel however will remain hot and cause the effects that you describe. As for structural strength, Starship can be ambient pressure when sitting on a stand, but whenever they move it they add some pressure (just not full tank pressure) to give it some more strength. The question is about landing so I would think the same is true. But to your point the residual heat should provide enough pressure for landing. $\endgroup$ Commented Mar 19 at 19:06
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    $\begingroup$ @StevePemberton my understanding matches Slarty's. I thought that part of the point of the tile-handling demo is that the tile is still very hot (frequently still visibly glowing), just an extremely poor conductor of heat $\endgroup$
    – Erin Anne
    Commented Mar 20 at 0:48
  • $\begingroup$ @ErinAnne - I remember that now. And doing some quick reading it seems the trick is to grab the edges which cool off faster. And you still may not necessarily be able to hold it for very long. But this also means that the tiles conduct heat into the steel more slowly, so there's a limit to how much heat they will transfer between the time when reentry heating ends and landing. But to the point of the answer they presumably transfer enough heat during that time to keep the tanks from cooling off too much. $\endgroup$ Commented Mar 20 at 1:40
  • $\begingroup$ @Steve Pemberton I don't think the tanks have any way to cool off. They contain cryogenic liquids which will only warm up as heat from the outside seeps in. $\endgroup$
    – Slarty
    Commented Mar 21 at 2:19
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You are correct in assuming the over-pressure is prevented through the use of pressure-release valves. (ref)

To address the part of your question that asks

During landing, the walls cool down, causing the gas to cool down. How will Starship prevent the tank from crumpling?

The first thing we need to ask is whether your assumption about the walls cooling down is accurate. After re-entry, the tank walls on the side not insulated with tiles would cool down and heat could travel outward through these walls. The tank walls on the other side are covered in tiles and are better insulated, so, all else being equal, there would be less heat flux through these walls. However, those tiles are going to be very hot after reentry. There may be inward heat flux from the tiles to the gas in the tank which would help to prevent the gas from cooling down.

However, let's proceed with the assumption that the gas would cool down and explore what could be done to maintain pressure and preserve structural integrity.

Elon Musk stated that the deorbit and landing burns are done with the header tanks (ref). It probably would not be advisable to have liquid propellants in the main tanks during reentry as they would be in contact with the hottest side of the ship, boil off rapidly, and thus be wasted. Such a design would reduce the payload capacity of the rocket by the amount of wasted propellant.

If, on average, the walls cool down after reentry, then to prevent the pressure from dropping too low, one option is to design the tanks to handle a peak pressure that is high enough to prevent the pressure from ever becoming too low. The other option is to increase the pressure in the main tanks by gasifying some of the propellant stored in the header tanks.

Internal pressure is also needed to compensate for the increasing ambient pressure outside the ship as its altitude decreases.

(Note: To explain the calculation, I roughly estimated some numbers. For example, I have no way of knowing what the peak temperature inside the tanks is but there's a comment below on why I went with 1000 °K.)

Let's hypothesize that the temperature in the tanks drops from a peak of 1000 °K at, say, 50 km altitude to 300 °K at 1km altitude. Let's also assume that the internal pressure needs to be maintained at 0.1 atm above the external pressure to maintain structural rigidity. Using the ideal gas law, we can calculate how many moles of gas need to be boiled off to maintain internal pressure difference.

$$PV=nRT$$

To do this, we first need to estimate the volume of the tanks. Since they hold approximately 1200 metric tons of liquid propellant, the density of liquid oxygen is 1141 kg/m3, the density of liquid methane is 424 kg/m3, and the mass ratio of a methalox rocket is 1kg of methane for every 3.6 kg of oxygen, we can work out that the volume of the methane tank is roughly...

$$1200000*1/(1+3.6)/424=615 m^3$$

and the volume of the oxygen tank is roughly

$$1200000*3.6/(1+3.6)/1141=823 m^3$$

Parameter Peak Heat After Cooling
Methane Tank Volume (m3) 615 615
Oxygen Tank Volume (m3) 823 823
Temperature (°K) 1000 300
External Pressure (Pa) (ref) 798 89880
Internal Pressure (Pa) 798+11000 89880+11000
Ideal Gas Constant 8.314 8.314
Moles in Methane Tank 873 24885
Moles in Oxygen Tank 1168 33290
Mass in Methane Tank (kg) 14 339
Mass in Oxygen Tank (kg) 37 1065

So, with these assumptions, Starship would need to boil off 324 kg of liquid methane and 1028 kg of liquid oxygen from its header tanks to keep the main tanks pressurized for structural rigidity.

However, there is evidence to suggest that the tanks can contain more pressure than what is needed to stay rigid. In that case, a higher internal tank pressure could be tolerated at peak heating to reduce the amount of propellant that needs to be gasified later to regulate the internal pressure - possibly to zero.

Update

A commenter expressed some surprise regarding the notion that the ship's tanks could heat up to as much as 1000 °K during reentry. If the ship's mass at reentry is 120,000 kg travelling at about 8000 m/s. This works out to a total kinetic energy of 3.84E+12 J. 100% of that energy is converted to heat, and most of that heat will go into the atmosphere if the thermal protection system does its job well. But if just 1% of that heat energy is absorbed into the vehicle, and distributed evenly, this works out to a vehicle temperature increase of...

$$3.84E+12 * 0.01 / (120000 * 502.416 J/(kg-K)) = 637 °K$$

... which, when added to the ship's initial temperature of perhaps 300 °K, would result in a temperature of 937 °K.

So how efficiently do tiles reject heat? I did find one reference on the Space Shuttle that said...

Black tiles work by reflecting about 90 percent of the heat they’re exposed to back into the atmosphere, while the tiles’ interior absorbs the rest. The tiles’ interiors radiate absorbed heat so slowly that after landing, the tiles take hours to cool.

In this interview, at around the 7-minute mark, Elon describes some of the advantages of stainless steel. He says..

anything above 200C for Carbon fiber or aluminum, you start falling off a cliff from a strength standpoint. But for steel you go 800°C and its fine. Even 1000°C can be fine.

In my example above, I used a value of 1000°K, which is 727°C.

He also said,

if the hull is steel, you can have thin heat shield tiles whereas if the hull is carbon fiber or aluminum you have to have thick heat shield tiles.

In footage from IFT4, it is possible to see the red-hot steel behind the heat shield tiles because some of the metal on the leeward side of a flap tore loose. enter image description here

From this Wikipedia article, the temperatures can be estimated from the color of the steel. Hot metal inside flap

However, it us unclear whether this steel is still protected by heat shield tiles.

The camera also captured a tile that tore loose which appears to be white hot one one side and red hot on the other. Loose tile

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    $\begingroup$ "Let's hypothesize that the temperature in the tanks drops from a peak of 1000 °K at, say, 50 km altitude to 300 °K at 1km altitude" is there any evidence at all that the cryogenic fuel tanks get to 1000K? $\endgroup$
    – Erin Anne
    Commented Mar 19 at 21:51
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    $\begingroup$ I challenge you to find any evidence at all of any re-entry vehicle structural temperatures to use to validate your random temperature numbers. There are lots of things inside a spacecraft that won't tolerate 1000K temperatures and it is harmful to credulous readers to confidently state they might get that hot without a shred of evidence. I'm voting to delete. $\endgroup$
    – Erin Anne
    Commented Mar 19 at 23:12
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    $\begingroup$ The onus is on you to provide evidence for the claims made in your answer. If you're answering a specific question with a vaguely related example calculation, that's even more grounds to delete. This is typical of the quality of answer you provide here, and I emphasize that including misleading details in these answers is leaving traps for future, lesser-informed readers. $\endgroup$
    – Erin Anne
    Commented Mar 20 at 1:04
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    $\begingroup$ The vote to delete always expresses the opinion of the voter about the answer. $\endgroup$
    – Erin Anne
    Commented Mar 20 at 5:05
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    $\begingroup$ phil1008 - that's a forward flap that is burning through, it's an aerodynamic surface not a tank wall. And it's presumably red hot (or whatever color on your chart) because the thermal protection failed in that region and the skin burned/tore off exposing the internal structure to the hot plasma. The initial beginning of the burn through earlier in the video appeared to possibly be the hinge area where the flap attaches to the fuselage, an area that Elon Musk had earlier identified as a possible vulnerable area. $\endgroup$ Commented Jun 7 at 20:26

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