In order to establish the burn area we use the following equation:
and for the grain volume we have:
We start off with a grain with the following dimensions:
Where Dc is the chamber inner diameter, xg is the spacing between the chamber and the grain, wg is the "width" of the grain, hg is the height of the grain, Ab is the effective burn area, Vg is the grain volume, Do is the outer grain diameter and Di is the grain inner diameter (the hollow part).This is the starting condition, but what about the final burn surface area? Is it larger or smaller than the initial surface area? If we assume that the burning is performed uniformly over the whole grain surface then the final effective burn surface would be:
By analysing the burn surface as a function of burn depth, we notice that the largest burn area occurs at the start up phase.Now, Ab is known and it's value is 5227.6102 mm^2. However, we might need to change this later. That is, the height of the grain. This is after all an iterative process in order to achieve the desired performance.
We also know that the total grain volume is 10053.0965 mm^3. By PROPEP we get that KNDX 65/35 has a density of 1.8897 g/cm^3 = 1.8897E-3 g/mm^3. Thus the grain mass is mg = 18.9973 g. Furthermore, this gives us the fuel and oxidizer masses mf = 6.6491 g and mo = 12.3483 g. This is put into PROPEP together with the earlier obtained maximum chamber pressure in order to estimate the combustion efficiency (i.e. specific velocity c*), specific impulse and a theoretical value of the total impulse! The c* will then be used to calculate the minimum nozzle throat area that we can have in order to build up the pressure level we want.
Next up is the thermodynamic calculations for this design. Stay tuned for more gory details!
Please read the safety guidelines before attempting anything like this on your own.
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