Burn rate simulation.

I felt the need for creating a program that can take any grain shape and analyze what the maximum burn depth would be. Noting that we are assuming ideal condition we therefore know that the burn time must be longer in reality since the burn rate increases with pressure and we use the burn rate under steady state conditions, i.e. maximum pressure.

The upper limit of the burn time is good to know since it has an impact on the chamber. Longer burn time will lower the tensile yield stress of the material and in this case it will melt the plastic casing if the grain doesn't burn quickly enough. How to obtain the upper limit of the burn time is probably more difficult and involves analysing the pressure buildup at the start up phase. I have not looked into this matter but my intuition tells me it's a matter of solving a linear (or linearized) ordinary differential equation and analysing the transient behaviour. It should depend on such things as throat diameter, burn surface as a function of time, initial available chamber volume and propellant density.

The tail off phase seems to me to be less interesting. But I'm sure the same ODE can be used for that as well.

Here are some screenshots from my program prototype with inhibited grain geometry, long grain and short grain:

Inhibited short grain:
Uninhibited short grain:
Long grain (uninhibited):
The distance field can then be used for finding the longest burn depth which can be done by analysing the smallest values in the distance field up to a given threshold value.

We can use these smallest field values to draw normals from the edges of the polygon (for those edges that it is possible) to these field points.

Then the largest surface normal pointing to the remaining depth field values is our burn depth. This depth is then used to calculate the ideal burn time tb.

Edit: Here's a recent update:


Just another thought on burn time.. The longest theoretical radial burn time is < 6.5/11.7162 = 0.55 s. This is still too short IMO. To get higher values an end burner must be used! Maybe a catalyst must be used.

As can be seen in the figures above, it doesn't matter which shape is used at the bottom end of the grain. The shape of the burn surface seem to always converge to a flat surface. :(.
At least I might utilize the initially increased burn area to get the pressure up quickly in the beginning.

If anyone has any hint on how to solve this problem, I'm all ears. Otherwise I'll have to make a regressive grain by shaping it as a solid cylinder but being unhibited, so it won't be an end burner. The burn surface will decrease with time.

A possibility would be to make a solid version of bates grain, but that would surely overpressurize.

Hmm.. maybe it will have to be an end burner after all. Seems I can't get around this in a smart way. I will just think about this a little more and then decide what to do.