An Analysis of Detonation Wave Propulsion

Max Wen
11 min readFeb 3, 2024

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In December 2023, near the end of the new year, NASA tested its first full scale Rotating Detonation Rocket Engine. This would be the first step towards detonations in the space industry, allowing an almost 2 century old concept to reach reality. Discoveries in fluid dynamics and breakthroughs by computational analysis have accelerated the world of rocketry, potentially bringing us to a world with cheap and efficient space travel.

Before we begin, we must discuss how traditional liquid rockets work. If you have not read my past articles, here is a quick refresher; essentially, its like strapping a bomb to the back of a ship. Bombs need 3 things, heat, oxygen, and fuel. Traditional rocket engines pump both oxidizers and fuel into a combustion chamber, where it is ignited and launched out of the back of a rocket.

The Problem With Traditional Rocket Engines

2 terminologies rocket scientists use are deflagration and detonation, which measures how fast the combustion is; how fast the propellant burns in a combustion. Deflagration refers to when the propellant is burning at subsonic speeds or below the speed of sound. Detonation, in contrast, is when a combustion travels trough a propellant at speeds faster than sound/supersonic speeds. Detonations mainly occur in bursts because of the high energy release. Most rocket engines resort to a deflagration combustion process, for many reasons.[1]

  1. Detonations are extremely unstable because the faster-than-sound pressure waves stack up and cause a very unstable combustion, which is unpredictable and shaky. These 2 factors are a recipe for disaster in rocketry.
  2. The shockwaves produced poses a threat to the structure of rocket engines.
  3. When the propellant is being burnt unevenly in deflagration rockets, this causes instabilities within the combustion, which when swinging at 2000 rpm, will cause an explosion that destroys any engine
  4. Detonations are highly unstable due to high pressures so naturally, we can only fire them in pulses.
F1 Rocket Engine combustion instability; Credit to NASA

The instabilities of detonations come with the power it has, and because no one has dared to try controlling detonations, detonations stayed an idea. Now though, in a time where we understand detonations better and have better materials, detonations can go from an issue, to a solution. This means that trips to space are forced to remain both pricy and inefficient compared to detonation based engines.

Potential of Detonations

Although dangerous, detonations are much more energy efficient for a couple reasons. Because the propellant is being burnt much faster, it generates much more energy and generates a much faster exhaust velocity, which contributes towards a higher specific impulse, defined by thrust over weight flow rate of fuel. What this means is that we can extract more thrust with the same amount of fuel. Furthermore, detonations also create a much higher pressure release because of the faster combustions, doing more work and releasing more energy. Detonations have a 22.4% increase in atomic efficiency with hydrogen compared to normal gas turbines. Faster energy conversion, more energy production. The speed of a detonation can be described as the CJ(Chapman–Jouguet) velocity. In simple, this describes the minimum speed a detonation wave must be travelling at to sustain detonation without any change. This is a term used a lot when talking about detonations with the higher the CJ velocity, the better.[1, 2]

This graph shows the efficiency of a detonation cycle compared to a standard gas one

The efficiency is one of the main incentives to use detonations, but it is also the main incentive to avoid using detonations. Because of the high energy, the pressures and temperatures prove unstable and hard to control. That is the issue we are working on; create a system that utilizes the efficiency of detonations while also being practical and applicable to rockets.

Pulse Detonation Engines

The essence of Pulse Detonation Engines can be summed up to its name: Pulses of detonations. This engine works by igniting a propellant fulled chamber with one end open. Setting this off, we create a detonation wave that propagates through the chamber, creating thrust. These PDE systems, although not mainstream, were in consideration since the 1840s, with many papers being published and advancements in understanding mechanics, also discussing the potential application of it. Later on, many other universities and institutions contribute their insights on this topic, finding ways of optimizing detonation performance. [1, 5]

Ignition Cycle

The process of detonations is simple, it begins with the injection of both fuel and oxidizer(usually a hydrogen-oxygen mixture as that has the best results). Once the combustion chamber is filled, a detonation wave is ignited and should travel through the fuel at the CJ velocity. Next, rarefaction(Decrease in density) waves will propagate through the chamber from the closed end where the fuel is injected, to the open end. During this time, we can observe that the ignited fuel has a pressure that increases as it gets closer to the detonation, with the detonation wave being the highest point in pressure, where afterwards, the area with the unburnt fuel is at the lowest pressure. Once the detonation reaches the end, it creates rarefaction waves that travel through the high temperature and pressure propellent, which helps to expel it out of the combustion chamber. Afterwards, a blowdown occurs of all the excess propellent that accelerates it out using rarefaction waves and expansion. Finally, we have returned to the first step with an empty chamber ready to repeat this process.[4]

Credit to CHEMICAL PROPULSION INFORMATION AGENCY[4]

Fuel Systems

It is already known that rockets need both fuel and oxygen to work, but the question remains; How do PDEs satisfy these conditions? Well, for most rockets, PDEs utilize oxidizer and fuel valves both at the closed end or open end*, which inject periodically to maintain a detonation. The most common type of fuel and oxygen used would be a liquid hydrogen and oxygen mixture, as it has proven to be most efficient with a detonation speed of 2836 m/s and is common for traditional rockets. Open ended PDEs are another type of… PDEs. These utilize a system where the detonation is initiated at the open end, and as it makes its way to the closed end, it brings along pressure, which bounces back and expels the gas out, generating thrust. The fuel and oxygen are injected at the open end, typically using oxygen from drawn in air and gaseous fuel that may be hydrogen or hydrocarbons like methane. Open ended systems also characterize any type of engine utilizing eternal oxygen intakes, which are often used for aviation as, space travel requires an internal oxygen and fuel system because of the lack of oxygen in space.

*Injectors near the open end are mainly used for a more even mixing of fuel and oxidizer while injectors near the closed end are use for control

Small Changes, Big Results

A key discovery and difficulty was the importance of evenly spreading fuel and oxidizer. This posed a problem in detonation propulsion as, the less homogeneous(learned that from my science teacher) the mixture is, the more inefficient and unstable it is(due to uneven combustions). We have since solved this issue in PDEs by utilizing turbulence. This means we put an obstacle in the way of the combustion process, and because it collides with the different substances within a combustion chamber(fuel and oxidizer), it creates movement and causes them to mix better. The collisions with this obstacle create more even mixing and also creates a better spread of reactions/combustions.[3]

The left side shows the fuel and oxidizer valves while the spring represents an obstacle to create turbulence; Credit to Punjab Engineering College

There are 2 more things that can be changed about PDEs, the fuel they use and the design they use. For the fuel, it is most optimal for fuel to be a hydrogen-oxygen mix. Whether it is gaseous or liquid depends on the type of PDE(rockets used liquid, aviation uses gaseous). This fuel is preferred because 1, hydrogen holds high energy to mass ratio, creating more thrust 2, hydrogen and oxygen have a very optimal combustion characteristics that make it efficient, and 3, hydrogen is a very light weight fuel that is easily stored.

Graph of fuel comparisons [5]

Next would be the design of PDEs. A computational analysis done by Bhagyashree Nagarkar was done to test which nozzle inclination would be the most efficient. It proved that with an diverging nozzle, the CJ velocity increased and with a converging one, it decreased. This is because of the compressible flow theory, where when fluids are at high pressure and temperature conditions and they meet a converging diverging tube, the speed will increase because of the conservation of momentum and mass(This is a very scuffed explanation)[]. Furthermore, the placement of fuel and oxidizer valves also contributes to different outcomes. When oxygen and fuel are injected from the open end of a PDE, this typically allows for better mixing and distribution of fuel and oxidizer. On the other hand, having injectors near the closed end, where detonations typically occur, allows better control over injections. These 2 small design changes increase the efficiency of PDEs.[2]

A decrease in pressure shows an increase in velocity [2]

Rotating Detonation Rocket Engines

This next type of detonation based rockets is one that has the most potential in rocketry. This is because it solves an issue with detonation based engines which is that constant thrust isn’t maintained. RDREs solve this issue by simply firing pulses in a ring shape. What this means is that a detonation wave and fuel are travelling tangentially. This means that as fuel is added and burnt, the detonation wave is travelling around the annulus(ring shaped object). This ring shape also aids in distributing pressure as the pressure is dispersing around the body.[1]

Pressure distribution in RDREs [3]

Actually, the first ever display of an RDRE was when NASA was still trying to land on the moon. During this time, NASA was working on the F1 engine, which posed some issues. Due to the uneven burning of fuel, some parts in the combustion chamber were undergoing detonation over deflagration, causing the exhaust to swing at speeds of around 2000 rpm. This extreme oscillation was the first ever example of an RDRE, but during this time, rather than being an advancement in rocketry, this was a setback for NASA engineers that peeled apart engines like bananas. NASA actually solved this issue by using baffles, which separated fuel into smaller, more manageable areas. Later on, this issue would become what we know of as RDREs.[1]

NASAs first full scale RDRE at the Johnson Space Centre

Fuel Systems and Design Features

Built to withstand the immense pressures of detonations, RDREs are specially structured to disperse pressure. Usually, fuel in injected in a ring shape along the line of detonations while oxidizer is injected from a centre plate, but sometimes it can be the other way. Fuel and oxidizer are injected as the detonation wave propagates around the annulus which allows the pressure to be dispersed. The design of this system is made specifically for the harsh conditions within detonations. To put up with these pressures and temperatures, we need a propel material. Here, we can turn to NASA’s GRCop-42, an alloy designed and manufactured to withstand the heats and pressures in detonations. This copper/chromium/niobium is 3d printed for NASA’s RDRE, and because of the amazing advancements in metallic 3d printing, allows us to have designs accurate to 0.1 mm. This 3d printing also allows us to face another issue with the pressure within RDREs, back-flow. This refers to when fuel and oxidizers are spat back into injectors so to counter this, tesla valves are used. These valves have a clover shape which turns any fluid back around if it is travelling the wrong way, stoping itself from traveling any further.[1]

In the centre, there is an aerospike, which is a feat of engineering that tackles a major issue with normal rockets. The nozzle of traditional rockets are often bell shaped and so they have to compensate for external pressure. If the exhaust pressure is lower than the external pressure, this causes the atmosphere to push the exhaust in, a process called over expansion which decreases rocket efficiency, and when the external pressure is lower than the exhaust pressure, then the rocket efficiency is once again, decreased. Aerospikes on the other hand, are a spike shaped nozzle where exhaust travels along the outside of the nozzle. This solves this issue by have the eternal pressure press the exhaust onto the spike, so rather than decreasing efficiency, actually aid in sustaining it(the whole physics behind aerospikes are actually much more detailed).[6]

Credit to Everyday Astronaut(love this website)[6]

Where we’re Going

Detonations have went from an idea, to a reality. NASAs RDRE project was tested on a full scale near the end of 2023 and countless other institutions are tagging along. Since 2008, the American air force has been working on PDEs with countless other nations having successful tests. Although RDREs and PDEs aren’t the only detonation based engines, they are the ones that are closest to becoming reality. With this new world of rocket propulsion, we open up endless new opportunities for space travel. Detonations are way more fuel efficient than traditional deflagration rockets so we can foresee a rise in detonations in the near future. With the potential for space travel to be easily afforded, we create a chance for humanity to head to the stars as speeds never before reached. All we need are a few more discoveries in fluid dynamics and chemistry to make detonations a reality.

Sources:

  1. McManus, Brian, et al. How NASA Reinvented the Rocket Engine. YouTube, Real Engineering, 1 Apr. 2023, https://www.youtube.com/watch?v=RVxgyz_avQM&ab_channel=RealEngineering
  2. Nagarkar, Bhagyashree. Computational Analysis of Pulse Detonation Engine: Effects of Converging and Diverging Tube Geometries, San José State University, Dec. 2018, www.sjsu.edu/ae/docs/project-thesis/Shree.Nagarkar.F18.pdf
  3. Kailasanath, K. Review of Propulsion Applications of Detonation Waves, Office of Naval Research through the Mechanics and Energy Conversion Division and the U.S. Naval Research Laboratory., Sept. 2000, https://www3.nd.edu/~powers/kailas.2000.pdf
  4. Coleman, M. L. OVERVIEW OF PULSE DETONATION PROPULSION TECHNOLOGY, Defense Technical Information Center, Apr. 2001, https://apps.dtic.mil/sti/pdfs/ADA390257.pdf
  5. Shaw, Ian J., et al. “A Theoretical Review of Rotating Detonation Engines.” IntechOpen, IntechOpen, https://rest.neptune-prod.its.unimelb.edu.au/server/api/core/bitstreams/5e9a3d19-68a4-5eb2-9f7a-3e3c43e1cb67/content
  6. Dodd, Tim. “Are Aerospike Engines Better than Traditional Rocket Engines?” Everyday Astronaut, Everyday Astronaut, 27 Dec. 2020, https://everydayastronaut.com/aerospikes/

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Max Wen
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12 year old and future Aerospace Engineer! Debater, teacher, and problem solver, and innovator! Check out my Substack: https://substack.com/@maxwen