 Hello everybody. I'm Aleksandar Agapean and I'm going to be presenting my capstone thesis on hybrid engine, hybrid rocket engine optimization through open control techniques. So firstly let's discuss the three main types of rocket engines. They are solid rocket motors, liquid rocket engines, and hybrid rocket engines. The main difference in these names is actually self-explanatory. Solid rocket motors utilize solid-face fuel and oxidizer. Liquid rocket engines utilize liquid-face fuel and oxidizer and the hybrids are a mix of the two. Often utilizing solid-face fuel and liquid oxidizer, while other configuration also exists. The hybrid rocket engines will be the focus of my work that I'll be discussing next. Looking at the advantages and disadvantages of these models, we can see that SRMs or solid rocket motors are very high in thrust, offer high thrusts, are very simplistic in nature, are the cheapest to manufacture and have long storage stability. However, they are not throttle-able, which is why they're mostly used as rocket boosters on larger rockets and have very low specific impulse because of inefficient combustion. LREs are the most expensive, most complex, but also offer the highest specific impulse or efficiency and high thrust and throttle-ability. The cost and complexity is the main issue with them and as well as the fact that they have to utilize a larger volume of fuel to operate. Hybrids actually are in the middle ground between the two, taking the advantages of the simplicity from the solid rocket motor side and the having a cost that's less than the LREs as well as the ability to throttle is one of their advantages. The disadvantages and the focus of my study, however, was the propellant ratio shifts during operation, which are caused by the regression of the fuel. So looking at the hybrid structure, we can notice the solid fuel casing inside as well as the cross-sectional area of the fuel grain. During operation, the solid fuel grain would expand causing the burn area to enlarge, which itself would induce a lot of fuel particles released at unit time as compared to the oxidizer. Because of that, we can get inefficient ratios that are, because there is a stoichiometric ratio which needs to be held to have complete combustion. In this case, we might have some shifts of that ratio causing inefficient combustion, which in effect lowers the specific impulse or efficiency of the engine. So the motivation of this study and research was to control the oxidizer valve of the engine eliminate the OF ratio shifts, which result in efficiencies and try to increase the overall efficiency of the engine as well as the thrust. Now let's take a look into some background that was needed to present all of this. Firstly, we can see we can get our thrust equations for our rockets and because we're working with an ideal case and mostly rockets are designed to be ideal at the range where they're operated, we considered the pressures to be the same and an ideal nozzle to be present, just both for simplistic calculations and as well as actual designs work like that. We can also use the formula we just derived and integrated through time to get the total impulse, which will be the measure of our efficiency. Moving forward, modeling the mass flow rate summation and the OF ratio, we can also take into a look the effect I mentioned earlier, which was the fuel regression that's causing all of the inefficiencies. The regression area is modeled by the following formula you see there, which we can see is proportional to the inverse square of the radius of the initial radius of the fuel grain. From this, we can also derive the mass flow rate and related to the radius, which will after some integration processes of the regression equation would allow us to finally reach the mass flow rate history function, which allows us to simulate the change in mass flow rate of the fuel throughout time for any specific given fuel type with the regression coefficients, as well as the engine parameters. Coming to the engine parameters, for this research, the Hydra 3x student-built engine parameters were used to perform all the calculations, as well as 14 different fuels with their given experimentally found regression rate coefficients and flux exponents were used for the simulation. You said students make these engines? Yes, yes. Okay, we'll make sure. All right. So moving into the work that was actually done, because we found out that the OF ratio was the oxidizer flow rate proportional over mass flow rate of the fuel, in order to keep that stable, we want to control the oxidizer in the same manner that the fuel is being changed. For that, plugging in the oxidizer equation allows us to receive the control function that the oxidizer mass flow rate valve needs to follow in order to achieve what we have. From experimenting with this function, it was it occurred that it was too complex to be solved analytically. Therefore, it had to be numerically approximated using MATLAB. So you can see that we've used VPA solve software and we approximated the mass, what we now call the theoretical mass flow rate function, which is what it has to follow and it is simulated for all the different fuel types, which are all the different lines you can see on the graph. So we know that the controller must follow these functions and we also know that we need an analytical form if we want to have a digital controller that's going to do this. So in order to have that, we need to approximate the theoretical control function or TCF, which we have done a couple of approximations of. I'll show the two most viable ones next. So firstly, we decided to do a power approximation since the mass flow rate itself was proportional to 1 over T. The fitting was done and the following proportionalities of the coefficient and exponent were found. Yielding what we call the power control function, where A is the regression rate coefficient of the fuel and N is the flux exponent. Plotting this graph results in an average r squared of 0.9927, which is not bad at all. And we can see the similar behavior with the theoretical control function. However, one significant problem is that we now have problematic vertical asymptotes at T equals 0 seconds. This would result in infinite values of oxidizer, which the computer would not be able to handle and are physically impossible. For this reason, we decided to recalculate the theoretical control function while keeping one of the variables stable and varying the other and vice versa. This would allow us to find better correlations between the variables in our next fitting. This is flux exponent varied, regression rate kept constant, and this is the reverse. So we keep the flux exponent constant and vary the regression rate. Using the recalculated theoretical control function graphs, we're able to perform the better radical approximation using origin pro, which yielded us in the following coefficients for each of the fuels, which were then fitted using MATLAB to the regression rate coefficient and the flux exponent, resulting in the following proportionalities. Yes. This is all one direction. There's no feedback. No, this is an open loop controller. I'll be coming to that in a second. You'll think the final form of what we call the better radical control function. While plotting the better radical control function, we can see almost identical behavior to the theoretical control function. We have very high r-squares for n. It's a hundred percent correlation, and for the a-average is 0.998. It's an overall better fit for the numerical approximations, and we have resolved the issues of the infinities as per the equation at t equals zero. We no longer have infinite values. Since this is going to be working on a rocket engine, and it has to be ignited in a way, we also want to simulate the opening of a valve, and this was done using the general square root formula with the same coefficients that were found in the in the better radical approximation to match the slopes, and we can use the following function to calculate the intersection points in time for each fuel where the where we simulate the valve and then start controlling valve opening and then start controlling the valve after. So plugging everything back into the original equations we use from literature, we can find the thrust simulate thrust equation, which we're going to use to simulate everything, and we can see from the thrust equation that we actually need an oxidizer input. So for a no-control case oxidizer input would include the valve simulation and then constant values for every fuel. This would look something like that, and without control we result in the following thrust simulations for every fuel. We can see the thrust simulation is above and the operational oxidizer to fuel ratio shifts below. As we can see we notice the effect of the shifts throughout operation with no control case. For this we designed something called the Prometheus open-loop controller, which combines the valve approximation function with the Belihadek approximation function with a knot at t equals t intersection, which we found previously. The following is the input of the oxidizer for utilizing Prometheus open-loop controller or POLC for every different fuel that we simulated, and these are the thrust simulations that we have. As you can see all of the oxidizer to fuel ratio shifts were eliminated during the entire operation. However, we did experience a slight decrease in thrust. For this we went to mythology and constructed the inverse of our Prometheus controller or our Epimetheus open-loop controller. We derived a new inverse Belihadek configuration, which is the inverse of the Belihadek, which was used for the EOLC case. Resulting in the following inputs of the oxidizer mass flow rate, which are increasing as we can see, and these result in the following thrust values for each fuel. We can see that we did achieve a thrust increase. However, we have some we have worse OF shifts than we had before. So concluding from this, we can say that the POLC controller is actually very useful at eliminating the OF shifts of during operation. It does decrease the efficiency by a maximum of 61.9 percent, however. The efficiency losses have a positive correlation with our flux exponent of the fuel, so the more it increases the more it decreases we have. It is also very useful if thrust is not a big issue and the main goal is to eliminate the effects of the fuel regression. The EOLC, on the other hand, does worsen the OF ratios, but does have a theoretical maximum increase of 292.6 percent. This is because of some missing constraints, which are going to be fixed in the future and discussed in the future work. The flux exponent has a positive correlation with the increase in efficiency with this one, and it's good for increasing thrust overall without carrying much for the OF shifts, and both of these controllers work well for engines with various burn times, so it's not going to suddenly turn off the engine because we had previous experience with that simulation. The future work for this thesis concludes constraining the thrust simulations to be more realistic. This will include modeling a saturation point for the valve, which would not allow us to have infinitely increasing oxidizer values. We're also currently working on a manuscript that we're preparing to publish this research, as it was not done before. Future entails designing actual closed loop, so a feedback loop system, probably utilizing model reference adaptive control, which will be necessary if this were to use on an actual hybrid rocket, as it has to take external disturbances into consideration. There's a lot of disturbances that, so we want to take those into account. That's why we want to do a closed loop controller in the future, and after the finalization of every addition, we're going to test all of the controllers mentioned above on an actual static stand in order to compare the theoretical results with the actual results of different fuels, control versus no control. In my acknowledges, I'd like to thank Dr. Hiracha for for everything, essentially, being the supporter of this very very tiring journey. As well as most of my friends and alumnus who are part of all of this and my parents, so thank everybody so much, I wouldn't be here without any of you. Thank you. Also, have you researched other engines, for example, constant burn surface engines? Yes. Actually, currently, the problem with hybrid with the OF ratio is solved by creating a fuel grain, just like I showed you with a star pattern, with a pattern that has constant area throughout its operation. So that's how they're solving it, but however my approach was to have a more easily manufacturable cylindrical burn surface that would be controlled from an external controller, essentially. So I'm trying to make the problem solvable for many different cases of the fuel as well as a simpler manufacturing process. So again, when we talk about the oxidizer, what is the correlation with the atmospheric air as an oxidizer in the whole process? So what are you saying using atmospheric air for combustion? Well, since you are in the atmosphere, and then it is getting changed, and then you are also using another chemical as main oxidizer. So is it somehow also using atmospheric air as an oxidation process? Yeah, actually no, because the combustion chamber is at very high pressures, compared to the atmospheric pressure. So essentially the main process is going on inside, and we're actually feeding pure oxygen, in our case, pure liquid oxygen. So the 21% or even lower, if you're higher up, is not going to have any effect on the combustion process. Pure liquid oxygen wouldn't work. You have to have a different kind of oxidizer. Well, yes. I mean, I just said an example. Also, like we can have NO2, N2O2. We have carbon inside, etc. So HPDB and aluminum would require... Would require a different, yeah. Obviously, so this was a general approach, so we don't focus on what oxidizer is being used. This was just to make sure that it's viable. And it looks like it might be. I have not a technical question. Just I'm curious to learn from, like how you come up with this idea or like, was it suggested with somebody, how you come up that this should be your capstone subject? This has been my dream since I was six. Me and my dad was behind there. We always watched every possible thing, starting with, you know, the shuttle launches, documentaries about space. We had a telescope. I've been watching at the stars since I was five. And ever since I wanted to be in this field. I didn't fully understood, honestly, like, every big news. But something like, how are you sure why it is... I'm convinced that this is something new that you're doing. Like, why no one else, like having this many research institutes all over the world, conducting many different types of research, especially for the rocket science, haven't done any similar kind of research. It was interesting for me, too, and I figured that I wanted to do something with rocketry. This wasn't the first thing that came to mind. But then the hybrid rocket engines were actually first theorized and made possible in the early 1970s during the space race, and were quickly abandoned because of the effects of the regression, because they have a much stronger liquid rocket engine, and the developers of those have enough funds to make the complex ones work. My guess is that it was just abandoned starting then, because I haven't found anything that has to do with controlling the regression rates or controlling the... having any sort of a controller in the hybrid rocket engine. Thank you. The first hybrids flew in the 1930s. Yeah, yeah, it's a bit late. I mean, like, academically. They were very complex and they were a trust holder. Yeah. Thank you.