Exhaust plume length variation across different rocket types

In rockets we see exhaust plume smaller and bigger. I know length has some relation with the fuel mixture ratio (not confident about it).

How to calculate, or at least understand, the variation in the wide variation in the apparent length of the exhaust plume of different rocket/engine combinations?

edited Jul 30, 2018 at 11:30

asked Jul 30, 2018 at 10:09

Amar

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$\begingroup$ I guess we should call it an "exhaust plume" rather than a flame. Most of the combustion or reaction takes place within the engine or body (depending on type) and the heat generated is used to produce expansion in the nozzle to generate momentum. $\endgroup$
– uhoh
Jul 30, 2018 at 10:52
$\begingroup$ If you only account for the clearly visible part ("flame"), it also depends on the type of fuel: hydrogen burns basically invisible (see: RS-68). Kerosene on the otherhand produces a fairly long "flame" (see: Merlin). $\endgroup$
– DaGroove
Jul 30, 2018 at 10:55
$\begingroup$ @uhoh, I am actually looking if there is some formula with which we can calculate the plume length for different propellants. $\endgroup$
– Amar
Jul 30, 2018 at 11:27
2

$\begingroup$ @Amar I'm confident there will not be a single formula that works across multiple propellants, engine types, sizes, flow-rates, nozzle expansion ratios, etc. There are so many factors that go into the visibility of a plume, most of which has to do with several different secondary processes that each produces a different spectrum of light. See for example What is the cause of the blue light from LH2/LOX rocket engines? and also How do rocket propellant combinations rank in terms of “brightness”? $\endgroup$
– uhoh
Jul 30, 2018 at 12:11
$\begingroup$ @Amar also see the as-yet unanswered What makes exhaust from aluminum-based SRB propellant so bright? as well as How bright is a rocket launch?. Then look at Why do the exhaust flames from cryogenic stage engines appear to be separated from the nozzle? $\endgroup$
– uhoh
Jul 30, 2018 at 12:12

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