Every few hundred microseconds, a detonation sweeps over the injector plate at two kilometres per second and drives the pressure on it up more than twentyfold. Within a few tens of microseconds, the injectors must be flowing again — fast enough to rebuild a fill layer several centimetres tall before the wave returns. How do you refill a chamber a hundred microseconds after it exploded?
The wave is the valve — and the valve leaks
An RDE has no valves: the wave itself shuts the injectors as it passes, because its pressure briefly exceeds the plenum's. That is elegant, but it has consequences:
- Blockage. For as long as the local chamber pressure exceeds the plenum pressure, no mixture can flow in.
- BackflowHot, high-pressure products pushed back into the injector passages after the wave passes. It delays refilling and can damage the injector.. Worse, the hot, high-pressure products are pushed back down the injector passages. When the pressure falls, those products have to be expelled before fresh gas can follow. In the worst case they reach the plenum — and if the plenum holds premixed gas, the engine can detonate its own supply.
- Injector recoveryThe time after the wave passes before the injectors can flow again, while the local chamber pressure is still above the plenum pressure.. The time from the wave's passage until fresh mixture is flowing again sets how much of each period the injectors actually work.
The cure is obvious — raise the plenum pressure relative to the chamber, so the wave blocks the injectors for less time — and so is its cost. (Raising the supply pressure through the same holes does little: the extra mass flow raises the chamber pressure too. In practice, a stiffer injector means smaller holes for the same flow.) The ratio of plenum to chamber pressure, the Injector stiffnessThe ratio of plenum to chamber pressure. Higher stiffness isolates the plenum from the wave but costs total pressure — the main penalty an RDE must beat., is total pressure thrown away before any combustion happens. A detonation can raise the pressure by a factor of two or three on average. An injector that drops it by half has already spent most of that gain.
Too stiff is not only wasteful. In the course's solver, fed with the same supply of mixture, an injector with a stiffness of about 6 is never blocked — so fresh mixture pours in right behind the wave, into products still well over 1000 K, and burns there: about a third of the heat comes out away from the front, and stray waves keep appearing. A soft injector (stiffness about 1.1) loses only 13% of the pressure but is blocked for a fifth of every lap and takes in a third less mixture. The working range lies in between.
Mixing in microseconds
Premixing the fuel and oxidizer upstream would solve the mixing problem — but a premixed plenum is a bomb waiting for one bad backflow event. So almost every RDE injects fuel and oxidizer separately and lets them mix in the chamber: typically, air enters through an annular slot or a ring of holes, and fuel is injected through small holes across the air stream, as jets in crossflow. They have until the next wave — a hundred microseconds or so — to mix.
Whatever is still unmixed when the wave arrives burns badly: some of it detonates weakly, some burns later as a flame behind the front, and some does not burn in the chamber at all. The result is a wave-speed deficit, more contact burning, and — if the layer is mixed badly enough — a wave that fails. Better mixing usually means smaller holes, stronger jets or colliding streams, all of which cost pressure drop: the same trade-off as before, in a different place.
Going deeper
Going deeper: injectors and plenums ring too
The wave hits each injector at the wave frequency, so it drives pressure oscillations back into the passages and the plenums. If an injector passage or a plenum has an acoustic resonance near that frequency (or a harmonic of it), the oscillations can grow — modulating the flow of fuel and oxidizer and feeding back on the wave. Researchers have traced mode switches, unstable wave counts and even counter-rotating waves to coupling between the chamber and the plenums. Designers tune passage lengths and plenum volumes to stay away from these resonances, much as rocket designers do (the rocket course's Lesson 7 on combustion instability tells the same story at lower frequency).
- The passing wave blocks the injectors, can drive backflow of hot products into them, and leaves a recovery time before fresh gas flows again.
- Injector stiffness (plenum/chamber pressure) shortens blockage and recovery but costs total pressure — the central trade-off of RDE design.
- Fuel and oxidizer are usually injected separately for safety; they have only ~100 µs to mix, and unmixed gas slows or kills the wave.
- Injectors and plenums can resonate with the wave frequency and drive mode changes.
Next: how many waves does an engine run — and who decides?