SpaceX Starship : Texas Prototype(s) Thread 24 : Discussion

[TomH]

We do not know how much of the liquid that is heated to above ambient boiling point but the whole point of subcooling is to minimize it...

Can you cite a source to verify that? I can see that as a benefit, however, wasn't sub-cooling first applied in F9 (to both fuel and oxidizer) to induce densification and allow greater energy to be contained in tanks of equal/original volume? I have never read that the purpose of sub cooling in SS/SH is to minimize ambient boiling rather than mass and energy densification.

Also, I don't remember reading much re. whether prop will be kept at cryo or subchilled in accumulation tankers and in storage when produced on Mars.

[gsa]

I've attached some screenshots from the LabPadre highlight reel.  I have questions...

1. The stringers do not frost because of the way they are connected to the hull - thermal conductivity is too low. If you would get an image with better quality, you would see that there is frost in between the stringers.
2. The valve uses a disk that rotates around its diameter in order to open/close. If the rotation axis is horizontal and the upper part goes outwards it will lead to the effect we observe.
3. When a valve is fully open (i.e. a disk is normal to the hull) the force of gravity begins to pull a stream down.

[eriblo]

We do not know how much of the liquid that is heated to above ambient boiling point but the whole point of subcooling is to minimize it...

Can you cite a source to verify that? I can see that as a benefit, however, wasn't sub-cooling first applied in F9 (to both fuel and oxidizer) to induce densification and allow greater energy to be contained in tanks of equal/original volume? I have never read that the purpose of sub cooling in SS/SH is to minimize ambient boiling rather than mass and energy densification.

Also, I don't remember reading much re. whether prop will be kept at cryo or subchilled in accumulation tankers and in storage when produced on Mars.

I could have expressed that better - I simply meant that they use subcooling to minimize propellant temperature in order to maximize density which would be pointless if they then let it just sit there and heat up.

[Alberto-Girardi]

Zack stated: "There are no pipes on the inside of the tank that connect to these valve".

What evidence to we have that this is the case?

I think Radical Moderate has the right idea.

John

I agree, we need prof to say that the vent goes straight through the tank wall to the tank interior.

If this is true the vent wasn't liquid methane, so we simply misidentified a big "normal" vent (composed of gaseouse propellant and condensed water droplets) for  a stream of liquid methane exiting and then vaporizing making a lot of condensed water (that is what gives the white colour)?  Because other than the fill line level being aboce vent level there isn't any proof the vent was of liquid, andwe don't know of the former  argument holds.

[edzieba]

Zack having good fun on his jump-to-conclusions mat. Frost line does not equal liquid level (liquid will be above it during fill, and below it after as walls continue to chill down), vents are not necessarily direct holes into the tank (e.g. internal plumbing to apex), and no liquid was observed being ejected (LCH4 falls under gravity just like any other liquid). We also don't even know if the ullage was all (or mostly) CH4 rather than the He we know has been used for ground tank pressurisation in the past (because He ullage does not collapse if left unattended).
His scheme to try and vent via Starship's QD is also pointlessly Rube Goldberg: if it were even a problem in the first place, taking an apex tapoff from the top of the forward dome and routing it straight out to the side through the interstage would get the vent outboard without messing with the plumbing of another vehicle (which itself is already in use by that vehicle).

[sebk]

Except, if all of that was true a huge gush of liquid would flow out

That is what happened.

Wrong.

If the vent inlet was below liquid level it would be a "waterfall" (or rather methanefall). It woudn't be carried by the wind as it was, it would look like a water from a hose (enveloped with tons of condensation). Just 10cm over would mean 6.5 cubic meters of liquid leaving in seconds. That would be a true methanefall. The flow would be order of magnitude bigger than a form a firehose. It would rain downward.

I would recommend Zack and the team do some sanity check of their claims. Try to visualize what would happen if the claim were true. Since it didn't happen, the chain of claims is broken somewhere. That's it.

[chopsticks]

Except, if all of that was true a huge gush of liquid would flow out

That is what happened.

It would rain downward.

Really? I thought most or all of it simply boiled off quite fast. Besides, we DID see some actual liquid here and there raining downward before it evaporated. In one of the views you could see some small plumes.

[eriblo]

I wondered it the fact that the plume sinks could tell us anything about the composition. However, the density of methane at the ambient boiling point is higher than air. The cross over is ~30 K higher so the only conclusion would be that it was not warm gas.

BTW, since the heat capacity of methane is higher than that of air the density of the methane/air mixture will initially decrease even more before approaching that of air as it is diluted further. As the methane heats up it will start to segregate out and rise but I assume that this process is relatively slow compared to the mixing in the plume.

Except, if all of that was true a huge gush of liquid would flow out

That is what happened.

Wrong.

If the vent inlet was below liquid level it would be a "waterfall" (or rather methanefall). It woudn't be carried by the wind as it was, it would look like a water from a hose (enveloped with tons of condensation). Just 10cm over would mean 6.5 cubic meters of liquid leaving in seconds. That would be a true methanefall. The flow would be order of magnitude bigger than a form a firehose. It would rain downward.

I would recommend Zack and the team do some sanity check of their claims. Try to visualize what would happen if the claim were true. Since it didn't happen, the chain of claims is broken somewhere. That's it.

I initially assumed we would be able to see significant liquid content as well but this appears to not be the case if it is vented as a spray (either due to the velocity or because it is already mixed with gas).

Cooling 1 kg of air down to the boiling point of methane takes ~210 kJ, which means that 1 m³ of ambient air can evaporate ~0.5 kg of liquid methane. The resulting mixture will decrease slightly in volume and retain ~1/3 of the jet velocity which suggest that it would require a deeper analysis to differentiate between an initial plume caused by a large amount of cold gas as opposed to a smaller volume of gas/liquid spray.

_{EDIT due to premature posting.}

[sebk]

Except, if all of that was true a huge gush of liquid would flow out

That is what happened.

It would rain downward.

Really? I thought most or all of it simply boiled off quite fast. Besides, we DID see some actual liquid here and there raining downward before it evaporated. In one of the views you could see some small plumes.

It cannot. Notice if you spill liquid nitrogen it will take quite a while to evaporate. Liquid methane has ~2.5 higher heat of vaporization (511kJ/kg vs 201kJ/kg)  and over ~2x less density i.e. it takes about 11x more heat to evaporate the same volume of liquid methane. It takes about 233MJ evaporate cubic meter of liquid methane. You'd have to chill over 900 cubic meters of air down to 100K to evaporate that. If you're chilling the air just to the dew point (about 6K on that day) you'd need
over 32000 cubic meters of it just for one cubic meter i.e. 455kg.

If the liquid were merely 10cm above the vent level, it'd be 6.4x the amount. Zack is talking nonsense here.

NB. look up Sn4 testing and methane sometimes spilling form the flare stack. The gulps are clearly visible as burning liquid, and despite those were gulps and they were burning it took it a while to cook off.

[sebk]

I wondered it the fact that the plume sinks could tell us anything about the composition. However, the density of methane at the ambient boiling point is higher than air. The cross over is ~30 K higher so the only conclusion would be that it was not warm gas.

BTW, since the heat capacity of methane is higher than that of air the density of the methane/air mixture will initially decrease even more before approaching that of air as it is diluted further. As the methane heats up it will start to segregate out and rise but I assume that this process is relatively slow compared to the mixing in the plume.

Except, if all of that was true a huge gush of liquid would flow out

That is what happened.

Wrong.

If the vent inlet was below liquid level it would be a "waterfall" (or rather methanefall). It woudn't be carried by the wind as it was, it would look like a water from a hose (enveloped with tons of condensation). Just 10cm over would mean 6.5 cubic meters of liquid leaving in seconds. That would be a true methanefall. The flow would be order of magnitude bigger than a form a firehose. It would rain downward.

I would recommend Zack and the team do some sanity check of their claims. Try to visualize what would happen if the claim were true. Since it didn't happen, the chain of claims is broken somewhere. That's it.

I initially assumed we would be able to see significant liquid content as well but this appears to not be the case if it is vented as a spray (either due to the velocity or because it is already mixed with gas).

Cooling 1 kg of air down to the boiling point of methane takes ~210 kJ, which means that 1 m³ of ambient air can evaporate ~0.5 kg of liquid methane. The resulting mixture will decrease slightly in volume and retain ~1significant

But the air is not getting chilled down to the boiling point of methane. On that day it would take just ~6K to get it down to the dew point. Which means ~35x more air volume just chilled to the dew point.
 
Also even if the liquid were totally obscured, we'd see the entire plume falling like a waterfall, not being carried by the wind.

[eriblo]

Here is my attempt at some (mostly upper) bounding numbers for the Potentially World Ending Methane Vents of Doom:

I am using WolframAlpha for physical properties/calculations and some rough pixel counting from the NSF livestream. Please feel free to find mistakes.

Two vents, total ~140 s.
IIRC temperature was 19 °C with a dew point of 13 °C. This  means air is 1.2 kg/m³ with 10 g/kg of water.
Wind speed from the plume movement on the South/North views: 7m/s.
Average specific heat capacity of air is 1.0 kJ/kg.
Average specific heat capacity of methane (gas) is 2.2 kJ/kg.
Specific heat of vaporization of methane is 510 kJ/kg.


Vent opening
The vent has a plate welded on with a smaller hole that looks to be ~13 cm diameter. Assuming John's maximum ullage pressure of 6 bar absolute from above :

Venting gas, worst case: Choked flow at opening, methane at 6 bar, 150 K is 34 kg/s, total 5 t.

Venting liquid, worst case: Bernoulli equation for methane at 95 K and 5 bar pressure drop gives 280 kg/s, total 40 t.


Vent size
The air flow across the initial vent plume is enough to mostly vaporize any liquid content (as we do not see the plume bending significantly downwards under gravity). Estimating the vent cross section to the wind is hard due to the rapid expansion downwind but I get range of 30 m² - 70 m². Note that most of the liquid in the plume would likely evaporate well before it starts to be deflected.

Using 0.5 kg methane per m³ of air and 7 m/s wind gets a range of 100 kg/s - 250 kg/s or a total of 15 t - 35 t

Any vented gas would at most be a few t.


Final plume size
Comparing to the stack the downwind plume expands to a diameter of ~50 m and then disperses (hard to tell because it interacts with the ground and extends beyond most video views).

At this point it has a flow of 12000 m³/s (neglecting wind gradient) and has warmed enough that all the water evaporates, i.e. 6 K below ambient.

Venting gas at boiling point (400 kJ/kg): 250 kg/s, total 35 t.

Venting liquid at boiling point (910 kJ/kg): 110kg/s, total 15 t.

This assumes a homogenous plume and should be an upper bound.


Conclusions
It looks like both plume appearance and size is inconsistent with the maximum gas vent rate, not to mention the amount of ullage gas available (even with rapid boiling).

My guess is a spray with significant liquid content totaling towards the lower range (i.e. on the order of 10 t).

[eriblo]

I wondered it the fact that the plume sinks could tell us anything about the composition. However, the density of methane at the ambient boiling point is higher than air. The cross over is ~30 K higher so the only conclusion would be that it was not warm gas.

BTW, since the heat capacity of methane is higher than that of air the density of the methane/air mixture will initially decrease even more before approaching that of air as it is diluted further. As the methane heats up it will start to segregate out and rise but I assume that this process is relatively slow compared to the mixing in the plume.

Except, if all of that was true a huge gush of liquid would flow out

That is what happened.

Wrong.

If the vent inlet was below liquid level it would be a "waterfall" (or rather methanefall). It woudn't be carried by the wind as it was, it would look like a water from a hose (enveloped with tons of condensation). Just 10cm over would mean 6.5 cubic meters of liquid leaving in seconds. That would be a true methanefall. The flow would be order of magnitude bigger than a form a firehose. It would rain downward.

I would recommend Zack and the team do some sanity check of their claims. Try to visualize what would happen if the claim were true. Since it didn't happen, the chain of claims is broken somewhere. That's it.

I initially assumed we would be able to see significant liquid content as well but this appears to not be the case if it is vented as a spray (either due to the velocity or because it is already mixed with gas).

Cooling 1 kg of air down to the boiling point of methane takes ~210 kJ, which means that 1 m³ of ambient air can evaporate ~0.5 kg of liquid methane. The resulting mixture will decrease slightly in volume and retain ~1significant

But the air is not getting chilled down to the boiling point of methane. On that day it would take just ~6K to get it down to the dew point. Which means ~35x more air volume just chilled to the dew point.
 
Also even if the liquid were totally obscured, we'd see the entire plume falling like a waterfall, not being carried by the wind.

Any gas/liquid mixture will obviously be at the boiling point. Once all the liquid has evaporated you will have a air/ice/methane mixture with a density of 2 kg/m³ - 3 kg/m³ which will rapidly decrease with as it mixes with more air. I think the key is a relatively high velocity spray as opposed to a more continuous jet.

[chopsticks]

And if it's a spray rather than a jet of liquid, it would aerosolize and evaporate quite quickly no? An example would be sprayer attachment on a garden hose. I don't know what kind of valves are used on these vents (butterfly?), but if it's mostly liquid that sprays out of it, would it perhaps create the effect that we saw? Something in the valve that could cause liquid to spray? Or maybe the ullage pressure itself would be enough to cause this?

I hadn't considered the possibility before that there might be internal piping to the top of the dome. I would love some proof for or against this theory if any proof exists. In any case, there was some liquid visible that quickly evaporated.

I didn't think that this could be so complicated!

[chopsticks]

Conclusions
My guess is a spray with significant liquid content totaling towards the lower range (i.e. on the order of 10 t).

Just to be sure that I understand. You are assuming an internal pipe to the top of the dome that leads to the vent? If this is your assumption, the only way that both liquid and gas could have come out is if the tanks were being overfilled and the vent opened up as a safety. In this scenario, there would have been liquid methane inside the internal pipe leading to the vent, so when the vent opened, pure liquid methane came shooting out followed by gaseous methane (or helium?).

[eriblo]

Conclusions
My guess is a spray with significant liquid content totaling towards the lower range (i.e. on the order of 10 t).

Just to be sure that I understand. You are assuming an internal pipe to the top of the dome that leads to the vent? If this is your assumption, the only way that both liquid and gas could have come out is if the tanks were being overfilled and the vent opened up as a safety. In this scenario, there would have been liquid methane inside the internal pipe leading to the vent, so when the vent opened, pure liquid methane came shooting out followed by gaseous methane (or helium?).

My intent was to base that post on what can be observed on the outside without speculating on whats on the inside

Previously I just assumed that the vents were connected to the apex of the dome - the gas volume controls the pressure and venting the gas is up to an order of magnitude more efficient than venting the liquid. There are however some points to consider:

They might be oversized due to potentially being thrusters or needing to quickly reduce pressure during some part of the flight. Thus venting liquid in an emergency might be sufficient (if wasteful), especially if a rapid increase in gas volume is less likely with subcooled propellant. During thruster/depress operations the propellant level is not a problem.

They might nominally not be covered if the ullage volume is somewhat larger than what we have expected. Might need more margin with subcooled propellants and might start out extra conservative - easy to add pipes later.

There might be some convoluted scenario where it is better to vent liquid rather than gas due to the higher mass flow.


Now I am wondering about connecting some of the vents to the dome apex and some directly into the tank...

[OTV Booster]

Here is my attempt at some (mostly upper) bounding numbers for the Potentially World Ending Methane Vents of Doom:

I am using WolframAlpha for physical properties/calculations and some rough pixel counting from the NSF livestream. Please feel free to find mistakes.

Two vents, total ~140 s.
IIRC temperature was 19 °C with a dew point of 13 °C. This  means air is 1.2 kg/m³ with 10 g/kg of water.
Wind speed from the plume movement on the South/North views: 7m/s.
Average specific heat capacity of air is 1.0 kJ/kg.
Average specific heat capacity of methane (gas) is 2.2 kJ/kg.
Specific heat of vaporization of methane is 510 kJ/kg.


Vent opening
The vent has a plate welded on with a smaller hole that looks to be ~13 cm diameter. Assuming John's maximum ullage pressure of 6 bar absolute from above :

Venting gas, worst case: Choked flow at opening, methane at 6 bar, 150 K is 34 kg/s, total 5 t.

Venting liquid, worst case: Bernoulli equation for methane at 95 K and 5 bar pressure drop gives 280 kg/s, total 40 t.


Vent size
The air flow across the initial vent plume is enough to mostly vaporize any liquid content (as we do not see the plume bending significantly downwards under gravity). Estimating the vent cross section to the wind is hard due to the rapid expansion downwind but I get range of 30 m² - 70 m². Note that most of the liquid in the plume would likely evaporate well before it starts to be deflected.

Using 0.5 kg methane per m³ of air and 7 m/s wind gets a range of 100 kg/s - 250 kg/s or a total of 15 t - 35 t

Any vented gas would at most be a few t.


Final plume size
Comparing to the stack the downwind plume expands to a diameter of ~50 m and then disperses (hard to tell because it interacts with the ground and extends beyond most video views).

At this point it has a flow of 12000 m³/s (neglecting wind gradient) and has warmed enough that all the water evaporates, i.e. 6 K below ambient.

Venting gas at boiling point (400 kJ/kg): 250 kg/s, total 35 t.

Venting liquid at boiling point (910 kJ/kg): 110kg/s, total 15 t.

This assumes a homogenous plume and should be an upper bound.


Conclusions
It looks like both plume appearance and size is inconsistent with the maximum gas vent rate, not to mention the amount of ullage gas available (even with rapid boiling).

My guess is a spray with significant liquid content totaling towards the lower range (i.e. on the order of 10 t).

Six bar is the tank rating. At the tank bottom it is the sum of methane weight and ullage pressure. IIRC, John calculated the liquid methane to contribute 3.99 bar at full tank. That leaves ullage at ~2 bar max.

This needs a sanity check as I can't find the referenced post and could easily have LOX and LCH4 switched.

Anyway, I did this screen grab from the NSF feed. It shows both tanks venting at the same time - something that SX should be allergic to. Either this vent was unplanned or had an inert component. I found this while searching for a video I saw showing the beginning of the vent. Didn't find it.

At vent initiation there were a few gobs spewed out that fell in a manner consistent with liquid. Not much, and for less than a second. This doesn't mean that there wasn't more liquid than initially apparent. More could have been hidden in the gaseous plume - or not.

We need Elon to step up and put us out of our misery.


Edit: found it and yes, I did booger the numbers. LCH4 ullage pressure should range between 2.4 and 4.9 bar.

[eriblo]

Here is my attempt at some (mostly upper) bounding numbers for the Potentially World Ending Methane Vents of Doom:

I am using WolframAlpha for physical properties/calculations and some rough pixel counting from the NSF livestream. Please feel free to find mistakes.

Two vents, total ~140 s.
IIRC temperature was 19 °C with a dew point of 13 °C. This  means air is 1.2 kg/m³ with 10 g/kg of water.
Wind speed from the plume movement on the South/North views: 7m/s.
Average specific heat capacity of air is 1.0 kJ/kg.
Average specific heat capacity of methane (gas) is 2.2 kJ/kg.
Specific heat of vaporization of methane is 510 kJ/kg.


Vent opening
The vent has a plate welded on with a smaller hole that looks to be ~13 cm diameter. Assuming John's maximum ullage pressure of 6 bar absolute from above :

Venting gas, worst case: Choked flow at opening, methane at 6 bar, 150 K is 34 kg/s, total 5 t.

Venting liquid, worst case: Bernoulli equation for methane at 95 K and 5 bar pressure drop gives 280 kg/s, total 40 t.


Vent size
The air flow across the initial vent plume is enough to mostly vaporize any liquid content (as we do not see the plume bending significantly downwards under gravity). Estimating the vent cross section to the wind is hard due to the rapid expansion downwind but I get range of 30 m² - 70 m². Note that most of the liquid in the plume would likely evaporate well before it starts to be deflected.

Using 0.5 kg methane per m³ of air and 7 m/s wind gets a range of 100 kg/s - 250 kg/s or a total of 15 t - 35 t

Any vented gas would at most be a few t.


Final plume size
Comparing to the stack the downwind plume expands to a diameter of ~50 m and then disperses (hard to tell because it interacts with the ground and extends beyond most video views).

At this point it has a flow of 12000 m³/s (neglecting wind gradient) and has warmed enough that all the water evaporates, i.e. 6 K below ambient.

Venting gas at boiling point (400 kJ/kg): 250 kg/s, total 35 t.

Venting liquid at boiling point (910 kJ/kg): 110kg/s, total 15 t.

This assumes a homogenous plume and should be an upper bound.


Conclusions
It looks like both plume appearance and size is inconsistent with the maximum gas vent rate, not to mention the amount of ullage gas available (even with rapid boiling).

My guess is a spray with significant liquid content totaling towards the lower range (i.e. on the order of 10 t).

Six bar is the tank rating. At the tank bottom it is the sum of methane weight and ullage pressure. IIRC, John calculated the liquid methane to contribute 3.99 bar at full tank. That leaves ullage at ~2 bar max.

This needs a sanity check as I can't find the referenced post and could easily have LOX and LCH4 switched.

Anyway, I did this screen grab from the NSF feed. It shows both tanks venting at the same time - something that SX should be allergic to. Either this vent was unplanned or had an inert component. I found this while searching for a video I saw showing the beginning of the vent. Didn't find it.

At vent initiation there were a few gobs spewed out that fell in a manner consistent with liquid. Not much, and for less than a second. This doesn't mean that there wasn't more liquid than initially apparent. More could have been hidden in the gaseous plume - or not.

We need Elon to step up and put us out of our misery.


Edit: found it and yes, I did booger the numbers. LCH4 ullage pressure should range between 2.4 and 4.9 bar.

Yes I used the 4.9 bar max rounded to 6 bar absolute.

While not optimal I do not think there is an absolute inhibit for venting both tanks simultaneously. You still want to control the pressures and that vent will not increase oxygen concentration but that much. If both vents were low velocity liquid it would be more of a concern 

[TheRadicalModerate]

Here is my attempt at some (mostly upper) bounding numbers for the Potentially World Ending Methane Vents of Doom:

I am using WolframAlpha for physical properties/calculations and some rough pixel counting from the NSF livestream. Please feel free to find mistakes.

Two vents, total ~140 s.
IIRC temperature was 19 °C with a dew point of 13 °C. This  means air is 1.2 kg/m³ with 10 g/kg of water.
Wind speed from the plume movement on the South/North views: 7m/s.
Average specific heat capacity of air is 1.0 kJ/kg.
Average specific heat capacity of methane (gas) is 2.2 kJ/kg.
Specific heat of vaporization of methane is 510 kJ/kg.


Vent opening
The vent has a plate welded on with a smaller hole that looks to be ~13 cm diameter. Assuming John's maximum ullage pressure of 6 bar absolute from above :

Venting gas, worst case: Choked flow at opening, methane at 6 bar, 150 K is 34 kg/s, total 5 t.

Venting liquid, worst case: Bernoulli equation for methane at 95 K and 5 bar pressure drop gives 280 kg/s, total 40 t.


Vent size
The air flow across the initial vent plume is enough to mostly vaporize any liquid content (as we do not see the plume bending significantly downwards under gravity). Estimating the vent cross section to the wind is hard due to the rapid expansion downwind but I get range of 30 m² - 70 m². Note that most of the liquid in the plume would likely evaporate well before it starts to be deflected.

Using 0.5 kg methane per m³ of air and 7 m/s wind gets a range of 100 kg/s - 250 kg/s or a total of 15 t - 35 t

Any vented gas would at most be a few t.


Final plume size
Comparing to the stack the downwind plume expands to a diameter of ~50 m and then disperses (hard to tell because it interacts with the ground and extends beyond most video views).

At this point it has a flow of 12000 m³/s (neglecting wind gradient) and has warmed enough that all the water evaporates, i.e. 6 K below ambient.

Venting gas at boiling point (400 kJ/kg): 250 kg/s, total 35 t.

Venting liquid at boiling point (910 kJ/kg): 110kg/s, total 15 t.

This assumes a homogenous plume and should be an upper bound.


Conclusions
It looks like both plume appearance and size is inconsistent with the maximum gas vent rate, not to mention the amount of ullage gas available (even with rapid boiling).

My guess is a spray with significant liquid content totaling towards the lower range (i.e. on the order of 10 t).

A few comments:

1) The condition you're describing is one where liquid isn't completely covering the vent, but rather one where the flow across the top of the liquid is enough to loft spray into the flow, correct?

But that doesn't account for the position of the frost line, which is well above the vent.  So you should see a pure liquid flow (which should look like a stream, with a narrowly expanding cloud of water condensation), followed by mixed vapor-spray (which should look like what you're describing), followed by pure vapor (which should look like a rapidly expanding cloud). 

Note that edzieba thinks that the frost line and the liquid level aren't one and the same.  I don't know if he's right or not, but that could be a conceivable explanation for why you're getting vapor+spray, rather than pure liquid.

It's freakin' complicated!

2) I think that gsa is right above, and the transient on the beginning of the vent looks like it's the flow being directed upward as a butterfly-like valve is opening.  That's a partially throttled flow, which probably isn't choked.  If it truly is a butterfly valve (which seems... unreliable?), then flow ought to become choked as the valve opens fully and becomes parallel with the flow.

3) You calculated 10g/kg of water content, but you didn't seem to factor in its enthalpy of vaporization (2.26kJ/g).  So you're adding roughly 23kJ of heat to each kg of air as the water condenses.

4) ISTM that you really need to be figuring out how much volume of ambient air you need to mix with a volume of vapor+liquid methane (possibly with inert gas mixed in) before the temperature of the mixture rises above the dew point.  I don't think the mass helps you very much.

5) Don't forget that there were probably water ice chunks blown off of the area around the vent when it opened up.  Those could easily be mistaken for LCH4 blobs.

6) I searched in vain for a photo of a dome-flip that yielded any interesting information.  But, in addition to the argument that SpaceX would be extremely conservative with their air/methane mixtures, to avoid blowing up their multi-billion-dollar hunk of infrastructure, there's another argument:  If the vent goes straight through and SpaceX just screwed up on the liquid level, then there's way too much ullage space at the top of the tank.  They need just enough of an ullage bubble for two purposes:

a) Fine-tuning of the pressure control.
b) Keeping ullage pressure high enough until the autogenous hot gas can take over.

If the vent is nominally above the fill level, they'll have the whole dome as ullage, plus maybe half a meter of cylinder.  That's maybe... 50m³?  That doesn't make sense.

[TheRadicalModerate]

There might be some convoluted scenario where it is better to vent liquid rather than gas due to the higher mass flow.

There is a not-very-convoluted scenario where it's better to vent liquid:  A fuel dump as part of an emergency abort/reentry.  You need to get the wet down-mass down to the point of viability.

But that would likely be a vent near the bottom of the tanks, not the top.  I'd guess that you'd want to vent directly from the prop distribution manifold.  Near the top would be useless after getting to orbit, because the liquid level will be many meters below it.

Now I am wondering about connecting some of the vents to the dome apex and some directly into the tank...

Mod the prop dump scenario, I can't think of a reason why you'd nominally vent liquid--especially on the pad.  If they actually did vent liquid during the WDR, I'm sure the EPA is on its way with the proctoscope.

All that said, I also can't think of a reason why they wouldn't have assembled the vent inlet and its piping down to the cylindrical portion before doing the dome-flip, so a recent good photo of the inside of a methane dome that shows the interior of the dome but doesn't show the requisite plumbing (either Starship or SuperHeavy should be largely the same in this regard) would be fairly strong evidence of a straight-through vent, rather than one with an inlet near the top of the dome.

[Slothman]

What if there really is a "snorkel" to the top of the dome, but the gas inside it recondensed due to being submerged in subcooled propellant? That would explain an initial spray