Successful Static Firing of Paraffin Hybrid Rocket Motor

This was the first test of the hybrid rocket motor design utilizing a paraffin based fuel. It was determined that centrifugal casting would be necessary to ensure proper case bonding of the fuel. This was done similarly to the casting of the ablative liners seen here. As the paraffin cooled during the casting process, I noted two observations. The first that the fuel appears to have partially separated on one end of the grain. Also, upon using a wooden block to center the grain during centrifugation, significant heat was produced in the area of contact causing a ring-shaped indentation to form withing the fuel port. This section was removed from both grains. Based on the preliminary cold-flow test results, I enlarged the injector orifice by a factor of roughly 1.37 in order to improve the expected O/F ratio and decrease operating time. A lower mass of nitrous oxide was also used in order to prevent the liner from being consumed. Here is a video of the test:

Test Stand

Motor Schematic

Nitrous Injector

From the footage, it is clear that the regression rate of the paraffin, even without oxidizer injection, is far to high given the setup, which is typical of an amateur hybrid rocket. A significant amount of paraffin was consumed before nitrous oxide injection even began. As a result of such high regression rates, the remaining paraffin as well as the liner was completely consumed without damage to the casing. This is illustrated in the video as the short-lived large smoky plume from the combusting paraffin shrinks to a narrow jet produced by the burning phenolic liner.

I predict that the remaining three paraffins will behave similarly with more extreme burn rate behavior in paraffins A and B. If this is the case -- validated through further testing, raw paraffin's implementation in amateur hybrid rockets may be limited to niche applications where massive oxidizer flows can be delivered and the fuel grain itself is significantly wider (Fintel). One possibility is the implementation as a booster stage for large and heavy sounding rockets. As for traditional rockets where the frontal diameter is minimized due to drag effects, a necessarily wide propellant grain is not optimal even when higher regression rates are desired. Thus, further testing will reveal the need to bring paraffin's regression rate under control and into the feasible domain of amateur sounding rockets.

In testing raw paraffins A, B, and D, minor changes to the fuel grain will be sought. Possibly a thin film (<.5mm) of opacified HTPB could be applied to the inner surface of the fuel port, acting as an ablative and being quickly consumed once oxidizer flow is initiated. Also, the nitrous injector will be further enlarged to compensate for the high regression rates attained with paraffin fuels.

If the prediction is validated through further testing, a polymeric addition to the paraffin will be sought in order to increase its melting point and viscosity substantially. Tsong-Sheng Lee and Hsin-Luen Tsai added HTPB to the paraffin mix with good results in their paper titled "Combustion Characteristics of a Paraffin-Based Fuel Hybrid Rocket. Some have even used hot-melt thermoplastic adhesives as additives (Fintel). Another option is to use the paraffin as the binding material for some kind of existing, permeable fiber matrix. One such material could be pieces of newspaper (Fintel) or cloth. I believe that this approach is extremely promising and under-documented making it perfect for investigation during the second phase of the experiment. Such an experiment will likely also lead to the development of new methods of fuel grain production and case bonding. To my knowledge, this exciting proposal has never been rigorously documented in scientific literature.

Unfortunately, P2 malfunctioned and the chamber pressure could not be recorded. Even without this information, the previous conclusions can still be drawn simply based on observations of the testing video. I still consider this test to be valid as it yielded a great deal of non-empirical data. Here is the voltage-time curve for the oxidizer feed pressure

P2 Output Voltage

 Per Bernoulli's equation, oxidizer flow was initiated at 43.70 seconds when the line pressure began to drop and appears to have ended at 49.52 seconds when the pressure reached zero. Fuel-oxidizer combustion appears only to have taken place over the 3.02 second interval between 43.70 seconds and 46.72 seconds. The liner burned from 46.72 seconds on to 47.42 seconds. Again by Bernoulli and the orifice discharge equation, we obtain that the pressure drop across the orifice is proportional to the fluid's dynamic pressure. Hence, we can say

P0 - P1 = q = k(P1 - P2)

where q is the dynamic pressure 

q = rho/2 * V^2

and P0(t) is the plot of static pressure in the tank. In other words, a good estimate for P0 is the curve extending from the constant portion of initial pressure and sloping down to meet the curve after the burn ended. 

Plot Showing P0

Thus, using only fluctuations in oxidizer line pressure, one gets a picture of the internal motor pressure's trend by taking

k * P2 = P1 * (k + 1) - P0

with an arbitrary value for k

Estimated Pressure Trends