Hybrid Fuel Rocket Final Report Aaron Oro, Brian Holman, Jamie Young, Nicholas Akiona Group: Units To Fix Me, ME140 Final Project Using the final nozzle design in Appendix A and a 5.375” fuel grain with the design shown to the right, our fourth and best firing -1 achieved a specific impulse (ISP) of 174.6 seconds . We reached this design by first selecting a target mixture ratio based on our analysis of the two major performance parameters: the stagnation pressure per unit mass flux ( c* ), and the thrust coefficient, ( CF ). As seen on the graphs presented in the Appendix B, a target mixture ratio of 3 resulted in near-peak properties for both of these values and thus the highest potential specific impulse. We then moved to develop the fuel grain. We had several objectives with our fuel grain. First, we wanted to burn enough fuel to keep the mixture ratio around 3. Secondly, after fouling1 in our initial fires, we wanted a larger open cross-sectional area to lower chamber pressure. Thirdly, after noticing that the oxygen flow rate decreased linearly across the firing period, we wanted to have a linear, neutral-to-regressive burn rate in our design. In addition to the fuel grain, we also established objectives for our nozzle. We needed supersonic flow at the exit, so we desired a throat area small enough to choke the flow . At the same time, however, we needed to have a large enough throat to manage back pressure and keep chamber pressure below the foul line. Additionally, we knew that we could minimize energy loss through the nozzle by using gradual tapers and by reaching perfect expansion at the outlet . Since the foul line pressure begins at approximately 1.1 MPa and we wanted a small safety factor, we aimed to size our nozzle throat to give us a peak chamber pressure of 1.0 MPa in our fourth fire and a more aggressive 1.05 MPa in our fifth. Over the course of several fires, we developed a highly accurate model with respect to both maximum chamber pressure due to the nozzle throat area and in the regression rate of the fuel grain design. Using our model, we were able to meet many of our objectives. As predicted, we achieved a peak chamber pressure of 0.99 MPa in our fourth fire and 1.04 MPa in our final fire, and were able to keep this chamber pressure below the foul line for the entire firing period. We also achieved a mixture ratio of 4 in our fourth (best) fire and improved this to 3.41 in our final fire, which was very close to the 3.39 our model had predicted. Utilizing the decrease in surface area that occurs when holes burn together, we also achieved the slightly regressive burn rate we intended; however, in our forth fire, the regression rate, while neutral, was not linear (see Appendix D). While we addressed this issue in the design of our fifth and final fuel grain, manufacturing limitations prevented us from fully demonstrating this improvement in the firing data. Nevertheless, with the fourth fuel grain and final nozzle, we still produced a quite respectable and very accurately predicted result.
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“Fouling” refers to when the chamber pressure is higher than the orifice pressure 1
Fuel Burn Regression Model In order to achieve the best results, it was essential to characterize how the HDPE fuel grain would burn over the course of the fire. Being able to predictably determine how different geometries of the fuel would burn under different conditions allowed us to then design our fuel grain to achieve desired results. We used two proven, theoretical fuel grain regression models as shown to the left2. Both models depended on empirical constants that had to be solved for using data and over the course of our fires, we were able to refine our model as we gathered more data. This allowed us to continue to develop more accurate constants. Our final model found that a=0.0080 [in3/g*sec] and that K=0.1763 [in*K/Pa*sec] for the equations above . We used these two models as they gave us a fuel grain regression rate based on different thermodynamic and geometric input parameters, giving us more flexibility and accuracy in our design. As we used the same hole diameters (0.15 - 0.30”) during all the fires, our model was repeatable throughout design iterations. We were able to then apply the model to predictably determine how our fuel would burn under three design parameters : (1) Po_max= ~1.05MPa (2) To = 3400K (3) mdot_O2 = constant across all fires. We designed for ~1.05MPa on the final fire as this would put us below the Orifice Choked Pressure line with a decent safety factor. The To value of 3400K was the theoretical chamber temperature maximum from our modeled HDPE at a mixture ratio of 3. This allowed us to design neutral/regressive burn rates as discussed above by creating pattern geometries in Solidworks and seeing how the initial holes would expand and burn fuel to get our desired mixture ratio and burn trend. As seen below and also in Appendix E, we were able to generate graphs relating geometry and thermodynamic properties to burn rate.
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http://web.stanford.edu/~cantwell/AA283_Course_Material/AA283_Course_Notes/Ch_10_Solid_Rockets_Cant well.pdf 2
By the 4th and 5th fire, our model was strong enough that we could make data driven predictions to determine the outcome of the mixture ratio, stagnation pressure and temperature and final fuel grain burn pattern for any design. The stagnation temperature and chamber pressure plots in Appendix C detailed how our modeled 1.0 MPa and 1.05 MPa was extremely accurate by the 4th and 5th fires . The major limitation of the modeled stagnation pressure was appropriately sizing the nozzle. In our 2nd and 3rd fire, our nozzle throat diameter was too small and led to a much higher Po than theoretically predicted. Appropriately sizing the nozzle throat diameter is crucial to the performance of both the model and the rocket. The accuracy of our fuel grain regression model can be seen in the actual final burn pattern of the HDPE fuel versus the predicted burn pattern. This is illustrated below for our 4th fire fuel grain. The link to the source code of the model can be found in Appendix F.
Nozzle Model and Design The nozzle is one of the two key aspects of our design. Through experimentation, we found that the nozzle throat diameter contributes substantially to the chamber pressure. Thus, one of our key goals was to properly size our nozzle so that it did not increase the chamber pressure and result in a foul. We managed this using the equation: A = c* m’ / P . throat total o Our experimental data gave us the mass flow rate of oxygen along with rough values for c*. By combining the oxygen mass flow rate with our ideal mixture ratio of three, we calculated the expected mass flow. Furthermore, we aimed for a peak P of 1.05 MPa to prevent a foul. The plot o below shows the ideal throat radius as a function of fire time. Since our main goal for the throat is to prevent a foul, we choose a throat diameter of 11/16” , slightly higher than the peak calculated value. Additionally, in order to minimize energy loss in the nozzle, we calculated an exit area that would allow for perfect expansion at the exit and used gradual tapers for the converging and diverging sections, 30 and 15 degrees, respectively . In our early analysis, we created a model for epsilon (exit area divided by throat area) for both frozen and dissociative flow. Through our first few fires, we found that we were operating roughly midway between frozen and dissociative flow, so we used the average value as our ideal 3
epsilon. This resulted in an exit diameter of approximately 1.05” . The final nozzle design that we used is included in the Appendix A.
Manufacturing Capabilities For the most part, manufacturing our nozzle was seamless, and we only manufactured one iteration during our entire design process (although we did slightly modify it a few times). However, manufacturing our fuel grain consistently presented us problems. Most notably, while using the manual mill, our drill bits experienced wandering between the top and bottom faces of approximately ± .020 in. This forced us to sacrifice a fire because our grain did not fulfill specifications. More importantly, it effectively ruined our 5th and final fire because burn areas that we had expected to be separate where unintentionally machined to close and burned together during our fire. This lead to lost mass through slivers and an uneven burn, both of which worked against our desire to maximize specific impulse. Drill bit wander also caused unwanted deflection when trying the machine overlapping holes. This was particularly problematic for us as we wanted to have a regressive fuel burn, and, in order to achieve this, we utilized overlapping holes that created pointed protrusions. We consistently found that drill bit wander left us with a design that was hard to align during firing and that significantly differed from our desired specifications. Although this problem of drill bit wander can be mitigated by using smaller section sizes (we mainly used 1.75 in. sections), this would just increase machining time and these sections would still experience some amount of wander. Therefore, as drill bit wander is a problem inherent to the mill itself, we believe that moving forward it would be much better to use a CNC to machine fuel grains. Not only would this fix the problem of wandering and allow for machining almost exactly to desired specifications, but also it would allow for the creation of more complex designs. It should also be noted that although we used the smaller 5.375 in. fuel grain for all of our fires, we believe that the 7.375 in grain would be better for maximizing specific impulse. We believe this because using the longer fuel grain would allow one to burn more fuel and therefore more easily reach our desired mixture ratio of 3. Although this was possible with the 5.375 in grain (up to about a mixture ratio of 3.4), it required a very low cross-sectional area, something that is hard to achieve while avoiding slivers. We suffered from this during our 5th fire as our grain had very low tolerances and we ended up getting silvers from areas burning together that we had wanted to keep separate. The longer grain would probably lead to reduced mixing since there is less space between the end of the grain and the opening of the nozzle, but we still believe now that that 7.375 in. grain is still the best option.
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Appendix - ME140 Hybrid Fuel Rocket Project
Appendix A - Final Nozzle CAD and Drawing
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Appendix B - C* and Cf Values and Efficiencies
Appendix C - Stagnation Pressure and Temperature Values
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Appendix D - Regressive Fuel Burn over Fire
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Appendix E - Additional Fuel Grain Regression Rate Models
Appendix F - Matlab Source Code and Final Presentation Link Final Presentation Link https://docs.google.com/a/stanford.edu/presentation/d/1sI2YHNw50GmXG_1J6djHLNdQ39 aUwDfW-S3404lhCGc/edit?usp=sharing Fuel Regression Rate MatLab Code https://www.dropbox.com/s/ouu9q8nuxpcr9j7/Fuel%20Grain%20Regression%20Model.zi p?dl=0
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ME140 Hybrid Fuel Rocket Project Final Reflections Aaron Oro: I spent the majority of my time working on the fuel grain regression modeling. I probably spent 25 hours overall on initially designing and then refining the model. From there I spent about 25 hours working on iterating over different fuel grain designs and seeing how the burn model applied. I spent 8 hours on writing the presentations, 8 hours preparing for the presentations and 3 hours at the rocket fires. I spent about 8 hours in the PRL assisting in machining. The most useful part of this project was designing and building a system to generate thrust and applying years worth of thermodynamics to one project. The least useful part of this project was the machining and not being able to accurately apply our models like we ideally would have liked. Nick Akiona: I spent around 16 hours on the manufacturing of the nozzle and fuel grains, an additional 6 hours doing modeling for the nozzle, 3 hours for rocket fires, 13 hours preparing for presentations, approximately 25 hours working on the general fuel grain design, and another 8 hours working on reports. The most useful part of this project was seeing how accurately we could predict real world rocket fires. The least useful part of this project was the extraneous amounts of time that we had to put into machining and the other logistical parts of the project that made this project challenging. To Future Groups (From Nick) : Start early. Make sure you create your models in the very beginning and then use your fires to tweak them. Ideally you only want to change one parameter at a time, so do your best to get an initial design that is closest to your intended final design. Talk to groups from previous years to get a few insights on key design aspects. Jamie Young: I probably spent somewhere close to 55-60 hours doing this project. I probably spent about 30 hours working in the machine shop machining parts and 25-30 hours working on analysis and going to firings. I think that the most useful part of the assignment was tangibly applying analysis to a physical project, and seeing how tangible machining and theoretical analysis combine in an engineering project. I thought the least useful part of this assignment was how inexact machining could be, specifically with such small tolerances. I’m pretty confident with regards to everything we did, and overall thought it was a good learning experience. To Future Groups (Jamie): Don’t take machining for granted. Not having grains within spec affected groups negatively more than most other parts of the project, and drill wander can really compromise your designs. Brian Holman: I, too, spent about 55-60 hours on this project. This included about 12 hours in the machine shop, but most of my time was spent designing and analyzing fuel grain designs with the information that Aaron’s regression model provided. I also spent a significant amount of time assisting with the modeling as well as presentation and report preparation. I think the most important part of the project was witnessing how analysis can inform a very detailed design, as this was the first class I’ve taken that has combined both analysis and actual manufacturing so thoroughly. The most challenging part of this project was the limited time allotted to us. I felt we had 9
a very good group; we started right away on the project and met nearly every day. However, even so, we felt very rushed between firings and machine shop sessions, often having only a few hours to analyze and design a new nozzle before having to make it on the mill. By the time we felt really confident in our model, we only had time to get in one final firing, and we barely had the chance to do even that. I feel that all groups would benefit from even just one or two more days to spend on this project, and if this comes at the expense of the other six projects in this class, I feel that it would be well worth the exchange. To future groups (Brian): ​ One thing we did well was get shop reservations. We planned ahead well enough to know what shop reservations we would about a week ahead and assigned each of us a specific reservation to make at midnight every night. The lathe and mill reservations fill up within fifteen seconds, but thanks to our diligence, we were able to obtain the reservations we needed and never had to sacrifice a fire due to not being able to get off a machining waitlist.
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