Pulse Detonation Engines

The question

You can't hold a detonation still. But you can start one, let it run down a tube, and start another — over and over, like a machine gun. On 31 January 2008, a small aircraft flew over the Mojave Desert for ten seconds pushed by exactly that. Why not just fire a tube of detonations, again and again?

A cycle in four strokes

A is a tube with a valve at one end and an open nozzle at the other. Each cycle has four strokes, a little like a piston engine's:

Fill. The valve opens and fresh fuel–oxidizer mixture flows into the tube.
Detonate. The valve closes; an initiator (often a small pre-detonator, or a spark with a DDT section) starts a detonation at the closed end. It runs down the tube at the CJ speed — about 2 km/s — in half a millisecond.
Blow down. The high-pressure products rush out of the open end, while an expansion wave travels back to the closed end and lowers the pressure there. This takes several times longer than the detonation.
Purge. A slug of cool air separates the hot products from the next charge, so the fresh mixture is not ignited early by contact with hot gas.

ExperimentA pulse detonation engine, cycle by cycle

fill detonate blow down purge

Fill fraction100% of the tube

Purge slug20% of the tube

Supply pressure2.00 atm · faster filling

Cycle frequency—after two cycles

Impulse per cycle—5 cm bore

Impulse per unit fuel—relative units

Challenges0/3

Run two complete cycles and read the cycle frequency.
Which phase takes longest? Raise the supply pressure until filling takes less than a third of the cycle.
Partially fill the tube and beat the full-fill impulse per unit fuel by 20%.

A one-metre tube with a valve on the left and an open end on the right, run by the reactive Euler solver. Each cycle the valve opens and fresh mixture (mint) flows in; the valve shuts and an initiator fires; the detonation runs through the charge; the products blow down out of the open end; and a slug of cool air is let in to purge the tube before the next fill. The thrust comes from the pressure on the closed end — the lower trace. Times and frequencies are scaled to a hydrogen–air tube. Its supply pushes the fresh mixture in at 300–500 m/s, so it fires at roughly 170–210 Hz; refilled at a gentler 100 m/s, as in the estimate below, a metre-long tube manages about 50.

The thrust comes from the closed end. Behind the Taylor expansion of Lesson 4, the products near the thrust wall sit at a plateau of nearly 40% (about three-eighths) of the CJ pressure, and they push on the wall until the blowdown's expansion wave arrives. Every cycle delivers one push.

Impulse per bang, times bangs per second

A pulse detonation engine's average thrust is simply its impulse per cycle times its firing frequency. Wintenberger, Shepherd and colleagues at Caltech showed that the impulse of a fully filled tube is well captured by a single formula: $I = K\,V\,(p_3 - p_0)/\cdet{D_{CJ}}$ , where $p_3$ is the plateau pressure and $K \approx 4.3$ .

ExploreImpulse per bang, times bangs per second

Equivalence ratio φ1.00 · stoichiometric

Tube length1.00 m

Tube bore50 mm

Filling speed100 m/s

Firing frequency40 Hz

Impulse per cycle1.99 N·s

Fuel-based Isp4261 smixture-based 122 s

Max frequency54 Hzfill is 54% of the cycle

Mean thrust80 N

Challenges1/3

Find a fuel–air mixture with a fuel-based specific impulse above 4000 s.
Design a tube that can fire at 100 Hz or more.
Get 1 kN of mean thrust from a single hydrogen–air tube.

A PDE's thrust is its impulse per cycle multiplied by its firing frequency. The impulse comes from the pressure plateau left on the thrust wall behind the Taylor wave (Wintenberger and colleagues' model: I = K V (p₃ − p₀)/D_CJ, with K ≈ 4.3). The frequency is capped by the time it takes to detonate, blow down, purge and — above all — refill the tube.

Estimate first

A one-metre hydrogen–air pulse detonation tube is refilled at about 100 metres per second. Roughly how many times per second can it fire, in hertz?

1101001,00010,000100,000

Drag along the line to place your guess — each tick is ten times the last.

Why fill only part of the tube?

The partial-fill effect is one of the PDE's surprises. Filling only part of the tube and leaving the rest full of inert gas lowers the impulse per cycle, but raises the impulse per unit of fuel: the inert gas acts as a tamper, which the detonation products push on before they escape, so more of their energy goes into momentum. The penalty is less thrust per tube. Try it in the cycle simulation above.

Why PDEs never quite made it

PDEs were studied intensively from the 1990s to the 2010s, by the US Air Force, NASA, the Navy, General Electric and Pratt & Whitney among others. In 2008 the Air Force Research Laboratory flew a modified Long-EZ aircraft powered by a four-tube PDE. But the engine's problems were stubborn:

Initiation every cycle. Each cycle needs DDT, which takes length (Lesson 6), or a pre-detonator, which takes oxygen and complexity.
Valves must open and close tens to hundreds of times a second against detonation pressures and temperatures.
Low frequency and pulsing thrust, with the hardware vibrating at the firing rate.
Most of the cycle is spent not detonating — filling, purging and blowing down.

What if the detonation never had to stop? What if it could keep running into fresh mixture, continuously, while the mixture was being replaced behind it? That idea — first realised by Voitsekhovskii in 1959 — is the rotating detonation engine.

Check your intuition

What usually limits how often a pulse detonation tube can fire?

Recap

What to carry forward

A PDE cycles through fill, detonate, blow down and purge; thrust comes from the plateau pressure on the closed end.
Impulse per cycle ≈ $K V (p_3 - p_0)/D_{CJ}$ ; thrust = impulse × frequency.
Filling dominates the cycle, so PDEs fire at tens to a hundred hertz per tube.
Partial filling raises impulse per unit fuel at the cost of impulse per cycle.
Valves, repeated initiation and low frequency held PDEs back — motivating a detonation that never stops.

Next: bend the tube into a ring.