It takes a lot of fuel to launch something into space. Sending NASA‘s Space Shuttle into orbit required more than 3.5 million pounds of fuel, which is about 15 times heavier than a blue whale.
But a new type of engine – called a rotating detonation engine – promises to make rockets not only more fuel-efficient but also more lightweight and less complicated to construct.
There’s just one problem: Right now this engine is too unpredictable to be used in an actual rocket.
Researchers at the University of Washington have developed a mathematical model that describes how these engines work. With this information, engineers can, for the first time, develop tests to improve these engines and make them more stable.
The team published these findings Jan. 10 in Physical Review E.
“The rotating detonation engine field is still in its infancy. We have tons of data about these engines, but we don’t understand what is going on,” said lead author James Koch, a UW doctoral student in aeronautics and astronautics.
“I tried to recast our results by looking at pattern formations instead of asking an engineering question – such as how to get the highest performing engine – and then boom, it turned out that it works.”
A conventional rocket engine works by burning propellant and then pushing it out of the back of the engine to create thrust.
To start the reaction, propellant flows in the gap between the cylinders, and, after ignition, the rapid heat release forms a shock wave (starts at 11 seconds). After this start-up phase, a number of stable combustion pulses form that continue to consume available propellant. Credit: James Koch/University of Washington
“A rotating detonation engine takes a different approach to how it combusts propellant,” Koch said. “It’s made of concentric cylinders.
Propellant flows in the gap between the cylinders, and, after ignition, the rapid heat release forms a shock wave, a strong pulse of gas with significantly higher pressure and temperature that is moving faster than the speed of sound.
“This combustion process is literally a detonation—an explosion—but behind this initial start-up phase, we see a number of stable combustion pulses form that continue to consume available propellant.
This produces high pressure and temperature that drives exhaust out the back of the engine at high speeds, which can generate thrust.”
Conventional engines use a lot of machinery to direct and control the combustion reaction so that it generates the work needed to propel the engine. But in a rotating detonation engine, the shock wave naturally does everything without needing additional help from engine parts.
“The combustion-driven shocks naturally compress the flow as they travel around the combustion chamber,” Koch said. “The downside of that is that these detonations have a mind of their own. Once you detonate something, it just goes. It’s so violent.”
To try to be able to describe how these engines work, the researchers first developed an experimental rotating detonation engine where they could control different parameters, such as the size of the gap between the cylinders.
Then they recorded the combustion processes with a high-speed camera. Each experiment took only 0.5 seconds to complete, but the researchers recorded these experiments at 240,000 frames per second so they could see what was happening in slow motion.
After the initial shock wave, stable pulses of combustion continue to consume available propellant. Previously researchers didn’t understand how a specific number of pulses formed and why they can sometimes merge into one pulse, but this mathematical model developed by University of Washington researchers can help explain the underlying physics. Credit: Koch et al./Physical Review E
From there, the researchers developed a mathematical model to mimic what they saw in the videos.
“This is the only model in the literature currently capable of describing the diverse and complex dynamics of these rotating detonation engines that we observe in experiments,” said co-author J. Nathan Kutz, a UW professor of applied mathematics.
The model allowed the researchers to determine for the first time whether an engine of this type would be stable or unstable. It also allowed them to assess how well a specific engine was performing.
“This new approach is different from conventional wisdom in the field, and its broad applications and new insights were a complete surprise to me,” said co-author Carl Knowlen, a UW research associate professor in aeronautics and astronautics.
Right now the model is not quite ready for engineers to use.
“My goal here was solely to reproduce the behavior of the pulses we saw—to make sure that the model output is similar to our experimental results,” Koch said. “I have identified the dominant physics and how they interplay. Now I can take what I’ve done here and make it quantitative. From there we can talk about how to make a better engine.”
The gas turbine is one of the power devices widely used in aerospace, marine, electricity generation, and other fields. With the increasing demands for energy conservation and emissions reduction, how to achieve efficient use of fuel in gas turbines has become a popular research direction [1,2].
Therefore, it is urgent for researchers to develop advanced technologies on combustors of gas turbines. As one kind of pressure gain combustion, detonation theoretically can enhance the cycle performance of many conventional engines, including gas turbines [3,4].
Among the current mainstream detonation combustion propulsion devices, the rotating detonation engine has been recognized as the most promising one in recent years due to its unparalleled advantages in compact structure, one-time detonation initiation, better controllability, and steadier exhaust.
Since supersonic combustion in the rotating detonation combustor (RDC) involves complex chemical reactions, wave collisions and combustion instability [5,6], the coupling of the RDC and downstream components face severe aerodynamic, thermodynamic, and structural challenges in applications, which poses a potential hazard to the design of RDC and the evaluation of RDC-based engine performance.
Outlet parameters of RDC, mainly including temperature, pressure, and Mach number, directly determine the thrust [7,8], thermal efficiency [9–11], and combustor–turbine integration [12–14] of RDC-based engines.
Therefore, the unsteady outlet flow field control of the RDC with different nozzles is one focus of current research. Depperschmidt et al.  measured the RDC by using time-resolved particle image velocimetry (TR-PIV). Their research results show the non-uniform characteristics of the RDC outlet flow field. Rankin et al.
 experimentally and numerically studied the time-dependent static pressure distributions along the outlet nozzle of the RDC. Their results showed that combining the conical center body and converging–diverging nozzle could effectively control or eliminate the unsteady periodic exhaust flow.
Tellefsen  investigated the operating performance of an RDC with an aerospike nozzle and turbine. He indicated that outlet structure had no obvious impact on the propagation mode and speed of rotating detonation waves and pressure gain of the RDC. Considering the application of RDCs in gas turbines, Zhou et al. [18,19] experimentally analyzed the effect of a turbine guide vane on the propagation characteristic of a hydrogen–air rotating detonation wave and found that the addition of a turbine guide vane increased detonation wave speed and narrowed the stable operation scope.
However, the detailed information related to RDC exhaust was not shown in their research results. Fotia et al.  measured the propulsive performance of RDCs with four types of outlet configurations (even bluff body, recessed bluff body, open aerospike, and choked aerospike). From their test results, it can be observed that outlet configurations played a significant effect on thrust and specific impulse of the RDC and choked aerospike outlet behaved with better performance.
Naples et al. [21,22] experimentally tested the effect of RDC unsteady exhaust flow on the axial turbine performance in a T63 gas turbine engine. They mainly observed that RDC unsteadiness did not significantly affect turbine efficiency, while they did not discuss the response of the turbine to the RDC. Using particle image velocimetry (PIV) measurement, Dunn et al.  investigated the velocity field distribution at the outlet of the RDC and indicated that the exhaust velocity profiles were better at smaller outlet nozzle diameter and higher pressure conditions.
Bach et al.  explored the effects of different outlet structures on RDC performance and operation. From their experimental results, it was clearly seen that the outlet played an important role in controlling the detonation wave speed and pressure gain performance, which was different from that of Tellefsen .
Braun et al.  numerically investigated the unsteady performance of RDCs with different exhaust nozzles and found that using a straight duct nozzle could decrease pressure gain of about 27%.
Considering methane is the main component of natural gas, research on RDCs using methane–air is more valuable for engineering applications. However, methane is the hydrocarbon fuel with high activation energy, which means the realization of detonation with methane–air is not as easy as hydrogen–air or ethylene–air.
Thus, the combustor size needs to be larger than the others under the same initial conditions. The large scale chamber hampers the design of the experiment rig and imposes a huge burden on the numerical simulations. Therefore, in order to study the RDC with methane, many studies chose to add extra oxygen or hydrogen in the fuel to improve the chemical activity [26–29].
Besides, the minimum realization size of RDCs can be effectively reduced by increasing the initial pressure, as the detonation cell size is greatly affected by the initial pressure of the mixture [30–34].
More encouragingly, Peng et al.  achieved the methane–air RDC experiment with only a 100 mm chamber diameter by controlling the contraction ratio of the outlet Laval nozzle. This undoubtedly gives us more encouragement and valuable reference for the studies of methane–air RDCs.
From the above brief review, it is concluded that the downstream nozzle is one of the main factors that should be considered during the design of the RDC, especially for methane–air RDCs. However, to the best of the authors’ knowledge, the present published investigations still cannot fully explain the following questions.
(1) Can the downstream nozzle really affect the formation and propagation process of the detonation wave?
(2) As the downstream nozzle is adopted, how do the typical parameters at the outlet of the RDC change?
(3) Are the changes of parameters beneficial to the downstream component or not? Based on these motivations, the present study performs the three-dimensional numerical simulations to investigate the performance of the RDC under the action of a downstream nozzle (here mainly for a diverging nozzle).
The typical wave collisions in a rotating detonation combustor with a diverging nozzle is analyzed to understand the rotating detonation wave formation and propagation process.
On this basis, the changing of RDC flow field parameters under a diverging nozzle and different diverging angles are studied in detail.
More information: James Koch et al, Mode-locked rotating detonation waves: Experiments and a model equation, Physical Review E (2020). DOI: 10.1103/PhysRevE.101.013106