Lesson 8 of 14

The Rotating Detonation Engine

Bend the detonation tube into a ring, feed it from the bottom, and a single detonation can chase its own tail thousands of times a second — no valves, no re-ignition. How it works, where it came from, and a live solver to run one yourself.

5 min2 live simulations
you are here
The question

A pulse detonation engine spends most of its life waiting: for the tube to refill, for the products to leave, for the valve to cycle. The detonation itself lasts half a millisecond. What if the detonation never had to stop?

Bend the tube into a ring

Take the PDE's tube and bend it until its ends meet. Now a detonation launched into it never reaches an end: it runs round and round. Of course, it would consume all the mixture in one lap — unless fresh mixture keeps being fed in behind it.

So feed it. Make the ring an AnnulusThe ring-shaped gap between two coaxial cylinders that forms an RDE’s combustion chamber, typically 5–20 mm wide. — the gap between two coaxial cylinders, typically 5 to 20 millimetres wide — and inject fuel and oxidizer through holes in its closed end. The mixture flows axially into the chamber. The detonation runs around the annulus, burning the layer of fresh mixture that has accumulated since it last passed; behind it, the injectors start refilling; and the burnt gas, turned by the wave, expands axially out of the open end. That is a Rotating detonation engineAn engine in which one or more detonation waves run continuously around an annular chamber, consuming fresh mixture injected through the bottom..

Live solverA rotating detonation, computed in your browser
25% of the wall
changes the mass flow; takes effect live
Waves running0
Wave speed—most RDEs run at 70–95%
Frequency—scaled to a 15 cm H₂–air engine
Fill height—laps run: 0
Challenges0/3
  • Watch the wave complete a full lap.
  • Keep two waves running for two laps.
  • Starve the engine until the detonation dies.
A genuine finite-volume solution of the reactive Euler equations on a 128 × 48 grid: the annulus is unrolled into a rectangle that wraps around at the sides, with the injector plate at the bottom and the open exit at the top. Fresh mixture (mint) is fed through choked micro-nozzles from a plenum, whenever the local pressure is below the plenum's. Nothing in the picture is scripted: the detonation, its fill layer, the oblique shock and the injector blockage all emerge from the equations. The model gas has a single-step chemistry and is far coarser than a real engine, so read the trends, not the decimals.

Three things that a PDE needs, an RDE does not:

  • Valves. The wave itself is the valve. As it passes over an injector, its pressure briefly exceeds the plenum's and the flow stops; about ten microseconds later (roughly 4% of a lap, in the course's solver), the pressure has fallen and the injector reopens.
  • Re-initiation. The detonation is started once and then sustains itself as long as it finds fresh mixture ahead.
  • Waiting. Filling and detonation happen at the same time, in different places around the ring. The engine is continuously busy.

From outside, the engine is steady: mass flows in steadily and out steadily. Only an observer riding the chamber wall sees the violent pulsing — and the wave as seen from the wall is steady too, in its own rotating frame.

A short history

The idea is older than it looks. In 1959, Bogdan Voitsekhovskii at the Lavrentyev Institute of Hydrodynamics in Novosibirsk observed a detonation spinning continuously in a disc-shaped chamber fed with acetylene and oxygen. In the 1960s, Nicholls and colleagues at Michigan tried, with limited success, to build rocket chambers on the same principle. For decades the Novosibirsk group, led by Fedor Bykovskii, kept experimenting and established most of the empirical rules this course uses.

The field exploded in the 2000s and 2010s, driven by Piotr Wolański's group in Warsaw, the US Naval Research Laboratory and Air Force Research Laboratory, and groups in Japan, China, France and elsewhere. In July 2021 a JAXA sounding rocket, S-520-31, fired an RDE in space for the first time. In 2023 NASA's Marshall Space Flight Center ran a copper-alloy rotating detonation rocket engine for 251 seconds at thousands of pounds of thrust.

How fast does it spin?

A wave of speed D\cdet{D} in an annulus of mean diameter dd completes a lap in πd/D\pi d/D seconds. With nn waves running, a pressure sensor on the wall sees

f=n Dπd.f = \frac{n\,\cdet{D}}{\pi d}.

ExploreHow fast does it spin?
1.00 · stoichiometric
150 mm
1
85% · 1672 m/s
1.0 atm
Frequency3.55 kHzwhat a pressure sensor hears
Each wave spins at212,856 rpm
Time between waves282 µsthe time the injectors have to refill
Cell width11 mmcircumference = 43 cells
Challenges0/2
  • Find a design that rings above 10 kHz.
  • Make a single wave spin faster than a million rpm.
The wave frequency is set by geometry and chemistry alone: f = n·D/(π·d), where n is the number of waves, D their speed and d the mean diameter of the annulus. The ring is slowed down by the factor shown.
Estimate first
A single detonation wave runs around a 15 cm hydrogen–air RDE at 85% of the CJ speed. What frequency does a pressure sensor on the wall record, in hertz?
1101001,00010,000100,0001,000,00010,000,000
Drag along the line to place your guess — each tick is ten times the last.
Check your intuition
An RDE is scaled up to twice the diameter, with the same mixture and the same number of waves. What happens to the wave frequency and to the time available for refilling?
Recap
What to carry forward
  • An RDE is an annulus fed through its closed end; one or more detonations run around it continuously, burning the fresh layer injected since they last passed.
  • The wave is its own valve, it is lit once, and filling and burning happen simultaneously in different places.
  • Pioneered by Voitsekhovskii (1959) and Bykovskii; first flown in space by JAXA in 2021; run for minutes by NASA in 2023.
  • Wave frequency: f=nD/(πd)f = nD/(\pi d) — kilohertz for laboratory engines.

Next: freeze the wave and look closely at the flow around it.

Finished this lesson?Mark it complete to track your progress through the course (saved in this browser).
Up next · Lesson 9Inside the AnnulusWhat does a parcel of gas see as the wave sweeps past?Keep going →