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The Falcon Heavy has 27 engines (Suck on it N-1!) in three sets of 9 (per core booster). SpaceX initially suggested they might need a couple of static fires to nail down the ignition sequence, since it turns out to be hard to get that many engines all running in very short time windows.

I had asked in a question about how the engines start whether the burning engines next to each other ignite the following engines or if they use TEA-TEB on all of them. The answer was they use ignitors on all the engines.

Now Falcon Heavy is of course, really running as three seperate boosters, connected. Thus no doubt the same is true.

But if an engine failed to ignite via TEA-TEB would the fact the other engines are rapidly burning ignite the Kerosene and LOX that would be pumping out of the unstarted engine?

I am sure they would shut the stack down when the sensors detect a failed start, but would the missed engine actually start from external ignition sources?

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    $\begingroup$ Details on Merlins are hard to come by, but in other engines, a failure to ignite causes the engine controller to close the propellant valves. $\endgroup$ – Organic Marble Dec 27 '17 at 14:43
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    $\begingroup$ Going off of Organic Marble, a failure to ignite may cause a hard-start, so the propellant valves are closed to prevent this $\endgroup$ – Jake Blocker Dec 29 '17 at 20:29
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In order to start the engine, you first have to start the gas generator to run the turbo pump. This means getting a flame up past the turbine and igniting the mixture in the gas generator combustion chamber. This seems unlikely.

Assuming the gas generator is somehow running but the main combustion chamber hasn't ignited, the propellant leaving the nozzle will burn outside the nozzle but will not generate much thrust.

According to Wikipedia the launch mass of a falcon 9 FT is 549,054 kg. That means a first stage propellant mass of around 400 metric tons, divided between 9 engines so around 44 metric tons each, with a burn time of 162 seconds, so 274 kg/s through a throat a few inches in diameter. It seems unlikely that the flame front will move back into the engine against such a flow, especially when you consider that the pressure gradient in the nozzle is 97 bar when the engine is operating nominally. That's a strong flow! (Which is kind of the point of a rocket engine.)

Whatever happens, it will not be under proper control, which is why the control system will shut an engine down if it is not operating nominally. If the engine did ignite (probably at reduced flow) it could go off with a big bang ("hard start") which could destroy it, as indicated in the other answer you linked.

I work with rather more mundane combustion equipment (boilers) and although this is not directly relevant, the control system on boilers always purges the combustion chamber of fuel before attempting ignition to avoid such an issue.

Note that the mixture from the unignited engine will probably vaporise before it begins to combust. Under normal ambient conditions (which is not the case in a rocket engine) a flame will propagate backwards along a pipe filled with an air/hydrocarbon explosive mixture at about 1 ft/s.

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    $\begingroup$ The pressure gradient is 97 bar when the engine is lit. This is a situation where the engine is not lit, the exhaust is cold and perhaps even a liquid. Look at videos of shuttle launches--pyrotechnics are fired below the engines. If the flame front couldn't get back into the engine from that why do it? $\endgroup$ – Loren Pechtel Dec 29 '17 at 22:36
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    $\begingroup$ @LorenPechtel: the pyrotechnics fired below the engine should also prevent the accumulation of larger quantities of hydrogen and oxygen. If such an accumulation is ignited late, an explosion may damage the shuttle and the launch pad. It is better to burn that hydrogen outside the engines as early as possible. $\endgroup$ – Uwe Dec 30 '17 at 11:21
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    $\begingroup$ @Uwe is correct, the shuttle "sparklers" were to burn off excess H2, not to start the engines. The shuttle engines had electronic igniters with their own propellant supplies, one in each preburner and one in the main chamber (basically little LO2/LH2 blowtorches). The solids were ignited by charges fired down the bore from the top. $\endgroup$ – Organic Marble Dec 30 '17 at 14:36
  • $\begingroup$ One should note that SpaceX does not use the "sparklers", as kerosene fuel is liquid at ambient temperatures and not easily ignited by sparks. $\endgroup$ – Skyler Jan 3 '18 at 18:06

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