We have commonly observed that before engine start at T minus zero, for a very small moment before the exhaust gases gush out of the nozzle, the air around the nozzle is pulled in. For what reason can that be? Please explain in detail, relating to launch sequence.
One can see air/smoke getting "sucked in" in this awesome 500 fps video of a Saturn V launch starting at 0:35 seconds. Playback is 8x slower than realtime.
What you are seeing here is the initial cloud of dark smoke and flame from the gas generators being emitted through the turbopump exhaust and swirling around the base of the vehicle. Then when the mainstage of the engine ignites, the ambient air/smoke gets entrained in the exhaust plume and sucked down.
I can see the cloud stops coming out of the engine, but that's not evidence for air being pulled in. It could just as well mean that the condition of the gases coming out has changed to make them less visible.
There is nothing in the (nominal) startup sequence that can cause a sudden pressure drop (which would be required for air to be sucked into the engine).
The gases coming out are oxygen and possibly RP-1. These gases are pumped out by the turbopump which takes a few seconds to spool up to nominal speed. Ignition is done when the turbopump reaches a threshold speed (pressure at the injection site has to be above the chamber pressure, IIRC).
This video has some fascinating explanation and commentary on the ignition sequence of an F-1 (Saturn V main engine).
I had previously wondered about this vacuum-type phenomenon as well, after seeing this video, supposing for a few days that it was due to the brief "dump" of LOx through the engine (and out through the bell) that occurred when the main LOx valves opened.
This is explained starting at about 3:00 (though starting at 2:40 or so sets the stage better). The dumped LOx starts to vaporize as it depressurizes to the atmosphere, and I figured that because it is significantly cooling the air around it, it might produce a brief and local but potentially appreciable vacuum under the launch pad, which might be enough to "suck in" exhaust gas momentarily.
I think the explanation of entrainment makes more sense after reading it above (thanks, Organic Marble), as the LOx dump occurs long enough before the first engine ignition to make it an unlikely cause of the drawing in of the first exhaust plume.
The above video does explain the macro-level sequence of engine ignition (around 6:00); the middle engine ignites, then a 200-ms delay before another opposing pair, then another 200-ms delay before the final pair. The moderate amount of exhaust that comes back up around the base of the rocket surely pales in comparison to the amount produced by the remaining four F-1s, and the significant gas flow of those would probably easily entrain the exhaust that remains up around the base of the rocket.