Predicting Non-Standard Grains
The "Two" Grain Motor
Hit Reload if you don't see motor burn animation image
Goal of this experiment is to find a way to correlate the results
of the static testing results of the two grain 24mm motor with the results of simming the
motor with the SRM.xls file
The standard use of SRM.xls has the multiple grains (N) the same size/length as each other.
It also has all the grain ends inhibited (Ends=0) or all ends not inhibited (Ends=1).
However these motors have grains that differ in length and often one end inhibited and the other not.
It is hoped that the sim results of the SRM.xls thrust curve vs time can be made to
correlate with static test thrust curve vs time results. This would preferably be by adjusting input rather
than the more complicated approach of changing the internal calculations within SRM.xls
The motor was constructed as per the image above. The red areas shows the non-inhibited
surfaces along with the ignitor.
The motor was then ignited on a static test stand to measure thrust.
This is a spring weight scale. The static burn is videotaped and the thrust over time is plotted by analyzing
each frame for thrust. The video captures 30 frames per second.
The sim results are obtained by entering the chamber and grain data into the Excel file and solving for output.
Once these graphs are available they are roughly compared for maximum thrust, burn time, and if the thrust curve is
neutral, progressive, or regressive.
Any obvious differences in the sim file are addressed by changing input into the SRM.xls file.
Of course the input changes need to reflect reality so the focus is changes that reflect the non-standard
construction of these grains.
The first graph shows the static results in red. The Sim results are in black.
This sim is two fully cored grains with both ends exposed. KN~100.
As expected the sim curve is too high The actual motor (top of page) is not two grains of the same length but more like 1.5 grains.
At first one might think we could change the number of grains in the sim from 2 to 1.5
However when I posed this idea to the SugPro group Richard Nakka replied that doing so would not only effect the total core length calculations (the desired effect)
but would also mis-calculate the number of exposed ends.
Richard's suggestion was to take both grains and average their length. This average becomes the length input. Now the number of grains can stay at 2.
The caveat is that the grain lengths can not be so short as to reach 0 before the Tweb reaches 0.
Below is the graph that shows the comparison of the new "grains averaged" sim to the static results:
Now the area under the curve (area represents approximate total impulse) maximum thrust, and burn time are close. However the actual burn is not neutral but somewhat progressive.
This is to be expected since some of the grain ends are inhibited.
Re-running the sim with ends inhibited (Ends = 0) gives the following graph:
This looks closer but the second half of the burn is not as progressive as the sim.
Here is where I went outside of the box and tried entering a value of Ends=0.5
This makes intuitive sense and possibly mathematical sense? Looking at the SRM calculated tables it looked like the grain length was losing one Tweb (web-thickness) as Tweb approached 0.
This is good but I wasn't sure if this might be throwing something else off. I posed this "outside of the box" workaround idea to the
SugPro group. Richard Nakka replied that it will work to sim a grain(s) with one end inhibited and the other end
Below is a graph comparison where the value in SRM.xls for Ends=0.5
The different grain lengths are still averaged as in the previous graph so both workarounds are in play in the graph below:
The sim values give this motor a designation of D25.
The static data (converted to Newtons) and entered in Engedit.exe gives a motor designation of D19
The first motor of this design (#53) had an static data Engedit calculated designation of D16, hence on my starting page I call these motors my "D16s"
One aspect of these motors that is not addressed in the sim workarounds is that as the core surface burns then simultaneously the propellant beyond the dead end core also burns to a depth that
is theoretically equal to the initial Tweb. To account for this is probably beyond adjusting inputs.
The only way I can see to account for this is to "re-program" the Excel macros
to calculate an incremental addition to grain/core length that increases (in the forward direction) as the Tweb decreases.
Since the unhibited end would burn decreasing the length then the length of this second grain would actually stay the
same. While the nozzle end grain would decrease in length by one Tweb during the burn.
The circular area at the end of the core would also increase incrementally as the burn progresses and would need to
I would consider tackling this aspect of the burn as well except that I am already able to obtain simmed thrust curves close enough to static for my purposes using the two workarounds.
My main use is to make a motor that will work without over or under pressurization. Another purpose is to have the simmed thrust data to make .eng files for RocSim
so that I can "fly" my hypothetical simmed motors in my hypothetical simmed rockets in RocSim.
I can then optimize my real rockets to my real motors (or vice-versa.) Once the motors are built and static data available then that data is used for the RocSim flight sims.
The other reason I'm not tackling further fine tuning of the sims is because I am trying to avoid too much math and avoid "programming altogether.
To further test this process one could try a variety of motor/grain configurations to see if these workarounds
keep the predictive value of SRM.
See the results for:
The one grain motor
The standard "two" grain motor...That link is this page
The two grain booster motor
The two full grain motor
The three grain motor
Another question is the reproducibility of these small motors. Too much variation in performance would make all this
"fine tuning" of the sims a mute point. The one grain page listed above includes 2 static motors side by side.
Click Here to see a preliminary comparison of four standard "two" grain motor statics.
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