On a Falcon 9 booster, does the central engine experience unique variations of its ISP due to its plume bordering the eight other plumes? If there is any influence, how does the ambient relative pressure evolve along the whole burn between lift off and main engine cutoff, in comparison with the other engines of the cluster?
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2$\begingroup$ Peter Beck, founder of RocketLabs, hinted in an interview that, using TVC (Thrust Vector Control), you can adjust the behavior of the whole engine cluster. So moving all the engines individually to create the best result for the cluster. I bet that the central engine does experience unique conditions and that the Falcon 9 also uses TVC to use/change those conditions. $\endgroup$– GittingGudCommented Jul 26, 2019 at 10:58
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1$\begingroup$ Beyond @GittingGud comment, I'm guessing any details would be highly proprietary and ITAR controlled. Someone with an academic interest in fluid dynamics of rocket engines would be the best person to speculate on a potential answer $\endgroup$– Carlos NCommented Jul 29, 2019 at 18:45
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1$\begingroup$ Here's a paper with a simulation of a 4 engine cluster. $\endgroup$– ChristophCommented Aug 23, 2019 at 12:23
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It is impossible that there is any influence, upon any of the engines, from the plumes bordering on each other. Any perturbation in a gas can only travel at the speed of sound in that gas; as the exhaust velocities are a multiple of the speed of sound in the exhaust gas, a perturbation can never travel back into the engine. See the classic by Huzel and Huang, "Modern Engineering for the Desing of Liquid Propellant Rocket Engines", chapter 2.
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2$\begingroup$ Were what you wrote correct, there would be no concern for the difference in specific impulse between sea level and vacuum. $\endgroup$ Commented Aug 23, 2019 at 15:55
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$\begingroup$ @DavidHammen Politely disagree. My answer is only about perturbations in an exhaust plume, and their speed of propagation. Of course the atmospheric and pressure conditions outside of the nozzle change with altitude, which explains the different specific impulse at sea level, altitude and vacuum. The two phenomena, contrarily to what you implicitly state, are not related. $\endgroup$ Commented Aug 24, 2019 at 11:40