Behavior of air in a submersible implosion

Question

I hope that this community could help to clarify some unproven but widespread claims regarding the implosion of the Titan submersible.

Background: The 2023 Titan submersible incident created a wide interest in the physics of implosion. Media and general public articles often claim that "when a submarine hull collapses, it moves inward at about 671 m/s... so that the time required for complete collapse is about one millisecond". The article continues by saying that the air inside a sub has a fairly high concentration of hydrocarbon vapors. When the hull collapses, the air auto-ignites, and an explosion follow the initial rapid implosion (so bodies incinerate and are turned to ash and dust instantly).

Numbers may slightly differ in different articles, but the fundamental point is that it is a very fast process. Moreover, I keep hearing that the persons inside the submersible were vaporized due to the heat from the compressed air: it is easy to find (unproven) claims that an implosion at this depth is so fast (~1500 mph) that it creates thermal energy almost as hot as the Sun (~4000 C) followed by an explosion, all in a few milliseconds.

The question: Is it possible to verify the accuracy of those claims thanks to standard thermodynamics estimates? For example, the fact that air possibly reached Sun temperatures does not prove that the bodies were vaporized because of this (it probably depends on some heat conduction timescale, but the process is too fast so the destructive effect is most likely to be purely mechanical).

My considerations: The mechanism is adiabatic compression, but a requirement of that happening is that the air cannot escape in any way. Now, if the submersible sprang a leak, and the hull would otherwise remain intact, that would be true, but since there has been a catastrophic failure of the hull, does it still holds that the air cannot escape? I can very well imagine air being forced into the water. And even if the air can't escape, it liquefies at about 75 bars, as that's the pressure of the critical point of the air. How would that change the picture?

Answer 1

I'm going to try to put this adiabatic compression "cooking" problem to bed once and for all. When I was a college intern working a "co-op" assignment, I worked a strike duty assignment in a unit that was pouring liquid lead into molds. We had a large furnace burner lit, burning natural gas with a flame temperature of 1083 C, that was placed on a valve that lead flowed through to ensure that the valve didn't freeze up. During the cold of winter, I was curious and passed my right forearm quickly through the blue flame (approximately 0.1 second time interval). The flame flow felt a bit "different" regarding its density compared to normal air, but I didn't feel any substantial heat. I proceeded to do this again, slowing down my arm slightly, getting to a time interval of approximately 0.25 seconds in the flame. Again, I didn't feel any substantial heat but the hair on my forearm was singed, so I didn't try to move any slower through that flame than I already had.

For the submersible implosion, even if the adiabatic compression involved a temperature of 5000+ C, the time interval was on the order of a few milliseconds, in the range of 100-250 times shorter than my forearm was in the flame at 1083 C. There is just NO WAY that the occupants of that submersible could be cooked by the high temperature of adiabatic compression of air over that short of a time interval, and I know this from a personal experiment, not theoretical data.

Answer 2

The compression should be adiabatic or very nearly so- you say that this is only the case if the air doesn't "escape." Where do you envision it escaping to?

The air wouldn't be "forced into the water" either- the water is at a greater pressure, so it will flow in. This is essentially how fume hoods work- they keep a pressure differential that keeps outside air flowing in and the fumes from flowing out.

Then a rough computation of the final temperature is pretty simple. For an adiabatic process, $P^{1-\gamma}T^\gamma$ is constant, where $\gamma\approx 1.4$ for air. $\gamma$ goes down with temperature, but this should be good enough for a rough approximation.

Then $T=T_0\left(\frac{P_0}{P}\right)^{\left(\frac{1-\gamma}{\gamma}\right)}$. With $P/P_0=400$ and $T_0=300~\rm K$, this gives about $1700~\rm K$. If there are hydrocarbon vapors in the air, it's certainly plausible that they would auto-ignite. This is basically how a diesel engine works.

I'm skeptical of the implication that the bodies would have incinerated, instantly or otherwise. By the time the air is compressed enough to ignite, most of the internal volume of the sub would have been replaced by water that is moving extremely fast. The internal volume of the pressure hull is around $4~\rm m^3$. Pressure can be thought of as a type of energy density, and the pressure of around $400$ atmospheres is equivalent to $40~\rm MJ/m^3$, or $160~\rm MJ$ for the total volume of the pressure hull. By comparison, a kilogram of gasoline has only about $48~\rm MJ$. In order to be comparable to the energies involved in the implosion, then, there would need to be more than 3 kilograms of gasoline in the air in the pressure hull.

Considering that there are about 5 kilograms of air in $4~\rm m^3$ at 1 atmosphere and reasonable temperatures, it's safe to say that air with that many hydrocarbons in it would be wholly unbreathable. Assuming a still-high level of 10 grams of hydrocarbons per cubic meter (more than ten times allowable workplace limits per OSHA), the energy released would be only around $2~\rm MJ$. Not nothing, but essentially negligible compared to the violence of the implosion.

In short, I think an explosion is quite likely but it is unlikely to have any real effect since the energies involved in the implosion itself are much greater than the chemical energy of the hydrocarbons likely to be in the air.