(I got a private question about what the heck L* is anyway - my reply
might be useful to others also clawing their way up this rocketry
learning curve, and perhaps also provide impetus to clarify for the many
farther up that curve than I.)
AIUI, L* is defined as the ratio between a rocket chamber's volume and its throat area. Also
expressed as "characteristic length", which is how long that chamber volume would be if
its diameter was the same as the throat diameter. (Rather like Isp in seconds,
"characteristic length" is a fiction that's an aid to calculation - in this case of
chamber dwell time of combustion gases, if I understand correctly.)
L* effectively sets the average dwell time of a given element - say, a fuel
droplet - of the hot low-velocity combustion soup inside the chamber, before
that element reaches the throat and becomes cooler and higher-velocity.
This in turn defines how long on average there is for combustion to take place
inside the chamber and thus contribute usefully to exhaust velocity. (Leave
aside for now subtleties like what's happening in the expansion nozzle.) For a
liquid-motor injector at a given level of propellant mixing efficiency, there
will be some minimum L* below which combustion efficiency starts dropping
because of propellant exiting the nozzle before it's completely combusted.
At least that's my amateur understanding of L* as applied to liquids. I would
expect there's something roughly analogous for solids, but would not be at all
shocked if there are both nomenclature and detail differences.
Henry
This came up earlier, with several mentioning motor length as determining how high a metal particle fraction could usefully be included in an APCP solid motor.
My thought then was that ratio of chamber volume to throat area should be the main thing determining combustion dwell time of a particle within a solid motor, analogous to liquid motor L* determining how much time liquid fuel droplets have to combust.
You mention both volume and length as factors. Should I understand then that solid motor length is also a factor, even beyond the strict matter of how much it contributes to available combustion volume? IE, that a long skinny solid motor would combust metal particles more completely than a short fat one of identical internal volume?
And, out of curiosity, do solid motor designers even use L* as a design parameter? Or some equivalent, or partial equivalent?
Thanks for the very informative discussion of metal particles, BTW.
Henry
On 4/9/2018 6:36 AM, Jim Rosson wrote:
Note-When using high levels of any metal, be aware that a motor needs sufficient chamber volume and length to allow complete reaction of metal powder into reacted molecules. Failure to have large enough space, will result in metal slag collecting on nozzle and/or burning in plume (creating lower combustion efficiency than expected).