What is an RDE?

As previously mentioned, a rotating detonation engine is an unconventional form of rocket engine that promises large efficiency gains compared to traditional propulsion technology. It does this by using the power of detonations. Now what exactly is a detonation, and don’t all rocket engines detonate fuel to work? The answer is no, traditional rocket engines use what is known as a deflagration. The difference between a detonation and a deflagration is a deflagration is when an explosion’s shockwave travels at less than the speed of sound. A detonation is when that shockwave travels at greater the speed of sound. Think of the difference between throwing a cup of petrol into a fire vs a stick of dynamite. This may just seem like a difference in semantics however the difference in the theoretical operation is dramatically different. The cycle of a detonation engine is a constant volume process compared to the constant pressure process seen in deflagration cycles. As seen in the following figure

This matters because the bigger the box the more work available during the cycle. So, the bigger the box the better and a detonation cycle has a very big box. When considering the ideal behaviour of the RDE it has the potential to be 20% more efficient then deflagration engines. A 20% increase in efficiency means you have to carry 20% less fuel or a rocket will be able to carry 20% more stuff. But this raises another question. Why if these rotating detonation engines are so good is no one using them. Well, this leads us on to the next part.

Why an RDE is hard to build?

One of the many difficulties of building an RDE is that the reaction itself is very unstable. A detonation is a single shock wave that travels faster than the speed of sound and while this is very powerful, a single moment of thrust is not enough to get a rocket into space or keep a plane in the air. To get around this a RDE sets off at least one detonation in a cylinder allowing it to spin around, hence “rotating”. This detonation is sustained by fresh fuel and oxidizer coming in from the bottom of the cylinder and lets out a large amount of thrust from the top. However, this is easier said than done. That shock wave can be traveling at speeds around 15 kHz. Meaning in a single second the wave will go all the way around the cylinder 15000 times. Imagine your car running at 900,000 rpm. It’s not exactly a stable reaction by itself. Let alone when other waves appear. When multiple waves appear at the same time, they can collide with each other or mess with the next’s fuel supply and just generally cause chaos.

Also, as you could probably expect this engine gets very hot and exerts an enormous amount of pressure on the engine. This provided a significant barrier for the first engineers working on RDEs in the 1950s. However modern advancements in material science and computational fluid dynamics have allowed engineers to design engines that facilitate stable reactions and can withstand them. In particular grcop-42 is a new alloy developed by NASA to handle the extreme operating conditions seen by an RDE. But how then if to make an RDE you need space age alloys and supercomputers running simulations am I a student with very limited resources going to make one.

How I plan to make one.

The key to approaching this complicated problem is to simplify it down based on your needs. Given that I have no requirement for thrust I plan on scaling down my RDE to a minimum. Making the development of my engine easier in several ways. First a smaller design will lead to a lower mass flow rate of fuel hopefully reducing the chances I inadvertently make a bomb. Secondly a smaller design will keep material and manufacturing costs to a minimum. However, my other requirement is actually achieving a somewhat stable rotating detonation. Smaller engine geometry works counter to this as the tighter the radius the harder it is for the reaction to sustain itself. So, my first problem is finding a reasonable minimum engine size that limits thrust and ensures stable operation. I plan to find this by stealing from people smarter than I. Researchers are a vain people. They spend all their days trying to figure stuff out just so they can show the world how they did it and get the sweet citations they so crave. Papers such as “Continuous Spin Detonations” by Fedor A. Bykovskii do a lot of the work for me having created equations that outline a reasonable minimum geometry to sustain a rotating detonation. This will largely negate any need to do complex simulation in the design of my engine.

Beyond the increase in efficiency another inherent benefit of the RDE is its simple geometry. Especially compared to hugely complex turbine jet engines with thousands of moving parts an RDE can essentially be simplified down to two cylinders bolted to a disk. My hope is that this makes manufacturing relatively simple and cheap with minimal points of failure. Regarding the advanced and expensive materials purpose built for modern RDEs that I don’t have access to, my plan is to just not use them. One inspiration for this project is from the creator Integza who managed to create a basic RDE out of 3d printed resin. The way he avoided the engine destroying itself is by running it at very short intervals around a second. Now if he can make an engine out of plastic that melts at around 100 degrees a mild steel engine with a melting point of 1350 degrees should be more than enough to handle short cycles.

To summaries my requirements for my design. The engine must run on a minimum mass flow rate ideally in the range of tens of grams per second. The engine must be able to function on bottle pressure alone with no complicated fuel delivery system. The engine will be designed to house a single detonation wave to increase the stability of the reaction. The engine must cost no more than $1500 and ideally less (if any of my previous projects are an indicator this requirement will likely be the first to be changed.). Finally, the engine should not kill me or anyone else and I will at least try and avoid grievous bodily harm.

What’s the first step?

The first step in the design of my engine is going to be fuel selection. RDEs can use a variety of fuels and I will need to pick one that proves to strike a balance between several required characteristics. Selecting the fuel will be the topic of the next update which if not already posted will be released soon.

UPDATE 1: Fuel selection

Choosing the best rocket fuel

Now that I’ve decided to make an RDE I immediately want to jump into CAD and start building the different parts. But because I don’t know what I’m doing, before that I’ll have to determine the minimum dimensions of the motor to ensure stable operation. This is luckily made very easy as the equations to determine this have been not only found before but conveniently packaged in “Small-size rotating detonation engine: scaling and minimum mass flow rate” by S. Connolly-Boutin1. The main take away from this article is that the dimensions of the RDE are determined by the detonation cell size. Detonations are formed out of a whole bunch of cells. The size of these cells will vary based on variables such as the type of gas detonated and the pressure the detonation is under. The smaller the cell size the smaller a mass flow rate I have to run.

Just to remind you I’m trying to have the minimum possible flow rate to reduce the likelihood I make a bomb, decrease the cost of gas per firing and to shrink the size motor making manufacturing easier. The first step in finding the geometry of the motor is to choose what gas I want to use.

What do I need in a fuel?

RDE’s can run on a variety of fuels. Basically, anything that detonates can be used as a fuel for an RDE. Most real examples of RDEs choose to use fuels like hydrogen, ethene, or methane. This is largely because these are fuels already in use in the rocketry industry. They are chosen based on a large number of factors such as their energy density and availability on other planets. However, for my purposes this is all really irrelevant. The properties of a gas that I care about is.

1. Small detonation cell size

The small cell size as previous mentioned is needed to reduce the mass flowrate of motor. However, this is not the only or even the most important factor in the selection of a gas for my project.

2. Availability

Availability is also of key concern. I am an undergrad student who is working on this currently with no affiliation with any other organization. So, I’m going to have to approach gas suppliers and ask for an unreasonably small amount of a highly dangerous gas and hope they don’t ask to many questions. For gases like acetylene or propane this probably isn’t going to be an issue but for the more specialized fuels I might run into some restrictions that prevent me from getting a hold of the fuel.

3. Cost

Another limitation of me being a uni student is that my budget for this project is very low. Remember I’m hoping to keep the total project cost to below $1500. The fact that a single cylinder of ethylene containing 1.8m3 of the gas costs roughly $500 a third of the total budget. Fuel costs seem like they have the potential to be the most expensive part of the project. The cheapest possible fuel would be ideal.

4. Safety

I understand that the very nature of the fuel needing to be explosive makes them inherently dangerous. However, I would like to keep this danger to a minimum. Ideally the gas will only be dangerous because it is explosive and preferably not carcinogenic, generally toxic, or radically unstable.

Which fuel am I going to use?

I don’t know. So, I’m going to assume I’m using all of them. The equations given are very simple and can easily be set up in an excel in a way that will let me do the geometry calculations for every fuel at once. While this may be marginally more work than just picking the fuel with the lowest detonation cell size it will make comparing fuels based on their other characteristics far easier. Also, in the very likely event that I choose the wrong fuel and change my mind later I would have already done all the calculations for the right one.

Calculations

The equations I will need to use are the following. Where

λ = detonation cell size (all cell sizes were found from GALCIT Explosion Dynamics Laboratory Detonation Database)

Detonation database reference	Chemical formula	Fuel – Oxidiser	Cell size	Pressure	Cell size at 101kpa	Annulus thickness min	Critical fill height min	Chamber length	Min chamber diameter	M dot min	M dot max
			mm	kPa	mm	mm	mm	mm	mm	kg/s	kg/s
at5a	H2	hydrogen-air	9.21	101.45	9.06	12.68	63.42	616.06	245.12
at57d	CH4	methain-O2	2.38	101.30	2.34	3.27	16.35	158.81	63.19	2.74	16.15
at21a	H2	hydrogen-O2	1.39	99.00	1.34	1.87	9.37	90.98	36.20	0.90	5.30
at154a	C3H8	propane – O2	8.25	13.87	1.11	1.55	7.77	75.49	30.04	0.62	3.65
at128b	C2H4	ethene – O2	4.72	11.43	0.52	0.73	3.66	35.54	14.14	0.14	0.81
at57f	C2H2	acetylene – O2	0.17	102.64	0.17	0.24	1.18	11.50	4.57	0.01	0.08

Finding an optimal fuel

Comparing the selection of 6 different fuel/oxidizer combinations gives us a good place to start when choosing a fuel. The smallest cell size comes from acetylene. This is fantastic news. With a minimum diameter of only 4.5mm and mass flowrate of 10-80g per second creating a small scale RDE within my desired specifications seems not only possible but conveniently easy. This is because acetylene has the added benefit of being very common meaning you can purchase it in small amount for a relatively low cost ($131 per m³). Its ubiquity in industry also means that there is an abundance of gas piping equipment such as mass flow rate regulators and check valves available for it. Acetylene being the best choice in terms of cell size is for my purposes the best outcome I could have hoped for.

Unfortunately, there is a catch. After jumping for joy at the prospect of being able to use such a common gas I found a problem. Acetylene is relatively unique in that it is not compressed into pressure vessels. Instead, it is dissolved into acetone and kept under pressure. Once that pressure is released the acetylene comes out of solution and out the top of the bottle. The issue with this is that this severely limits the maximum mass flow rate that these bottles are capable of. A rule of thumb is that you should not let out more than 1/15^th of the volume of the cylinder per hour of use. For most industrial applications this is not an issue however for my application I need a small volume of gas to be released very quickly at very high pressures. To achieve this with acetylene without a pump requires a manifold cylinder array. From BOC this starts at $3187. More than doubling the budget on fuel alone as well as making the logistics of transport much more difficult this unfortunately eliminates acetylene from the feasible options.

Moving up the list the two next best options in terms of cell size are ethene and propane. Propane would be the more ideal option of the two. This is largely because it is cheap, readily available as LPG and has acceptable minimum geometry requirements. However, one of the reasons that LPG is so reasonably priced and easily accessible is because it is stored in relatively low-pressure cylinders. BOC’s LPG cylinders only hold the gas at 700kpa. This is an issue as part of my design requirements is that I will not be using an external pump and will be relying entirely on bottle pressure to run the system. Having such a low pressure increases the likelihood of back flash in the engine and decreases its ability to deliver an adequate mass flowrate. Ethene (AKA ethylene) remedies this problem being stored at 6900kpa significantly increasing its ability to resist back flash and gives the best chance of supplying an adequate sustained mass flow rate. However (there is always a however) ethene comes with the minor drawback that it’s a controlled substance. Only available for agricultural and scientific purposes not amateur rocket programs.

Not with a bang but a whimper

Throughout this update we have identified the characteristics of an ideal fuel for our use case. Completed calculations for the approximate geometry of a small scale RDE and compared these criteria against actual fuels available. The results of this are that there currently isn’t a fuel that meets all the criteria that is needed for my application. To be clear small scale RDEs are not an unproven technology. Universities and research institutions make them all the time. However, the major difference between myself and them is that I was a little optimistic with the budget required for this project. Having also briefly looked into the cost of safe and appropriate plumbing system for this system I found the project budget fall far short of what would be required. For the reason that with the current resources available to me I would not be able to create a safe system that follows the theory, I’m going to put this project on the back burner. Who knows maybe when I start working in industry, I might be able to throw $10,000 at this project and see it become a reality. But for the minute with a uni budget this doesn’t seem feasible.

3 Responses

Id put money in don’t have to buy everything at once.

🤯 would love to get in on this.

Hi, my name is Mario Cestari, it wold be a pleasure try to help you. Find my LinkedIn, I am an undergraduate mechanical engineering student from Brazil.