Why Detonate?

The question

A detonation is the thing most combustion engineers spend their careers preventing. It cracks engine blocks, flattens chemical plants and rips the hearts out of coal mines. Yet in 1940 the young Yakov Zel'dovich published a paper arguing that an engine should detonate its fuel on purpose. Why would anyone want an explosion inside an engine?

Two ways to burn

Light a mixture of fuel and air with a spark, and a flame spreads through it. The flame moves because heat and reactive radicals diffuse from the hot, burnt gas into the cold, fresh gas just ahead, warming it until it reacts. This kind of combustion is called . It is slow — a laminar hydrogen–air flame advances at about two metres per second; a methane flame at less than half a metre per second — and it happens at almost constant pressure. Every gas turbine, every jet engine and every gas cooker works this way.

There is a second way. Hit the same mixture with a strong enough shock wave, and the shock itself heats the gas to ignition. If the energy released behind the shock is enough to keep pushing it forward, the shock and the combustion lock together and race through the mixture at two kilometres per second. That is a . It does not wait for diffusion: it compresses the gas first and burns it immediately afterwards, so the burnt gas behind it is at fifteen to thirty times the original pressure.

RaceOne mixture, two ways to burn

Equivalence ratio φ1.00 · stoichiometric

Detonation speed1967 m/sMach 4.8

Flame speed in the tube14.2 m/sσ·S_L = 7.2 × 1.98 m/s

Speed ratio138×

Pressure behind the front14.9 atmvs ~1 atm for the flame

Challenges0/4

Ignite both tubes and watch the race.
Find a mixture whose detonation is more than 500 times faster than its flame.
Find a mixture that detonates to more than 35 atmospheres.
Race three different fuel–oxidizer pairs (0/3).

Two identical tubes, a metre long, closed at the left and filled with the same mixture. The top one is lit gently with a spark: a flame (deflagration) creeps along at a few metres per second, pushed by its own expanding gas. The bottom one is lit with a detonator: a detonation crosses the whole tube in half a millisecond. The purple traces are pressure. Time is slowed several thousand times.

Estimate first

How fast does a detonation travel through a stoichiometric hydrogen–air mixture at room conditions, in metres per second?

1101001,00010,000100,000

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

Heat added at higher pressure is worth more

Why should the pressure matter? Because of the second law. An engine turns heat into work by adding heat at high temperature and throwing away what it cannot use at low temperature. Any process that generates entropy on the way increases what must be thrown away. The question is how much entropy each way of adding the heat creates.

A gas turbine adds its heat at constant pressure: the Brayton cycle. The gas expands as it heats, and that expansion is "wasted": the heat goes in at a lower average temperature than it could. If you could add the same heat in a sealed box — at constant volume, the Humphrey cycle — the pressure would rise as the gas heated, and more of the heat could be turned into work. A detonation goes one step further: its leading shock compresses the gas before any heat is added, so the heat goes in at the highest temperature and pressure of all.

ExploreThree ways to add the same heat

Compression ψ = T₃/T₀2.00 · pressure ratio 11

Heat added q̃ = q/(c_pT₀)5.0

Brayton50.0%constant pressure

Humphrey61.4%constant volume

Detonation (FJ)63.2%detonation

Detonation advantage+13.2 ptsa Brayton engine would need ψ = 2.72

Challenges0/3

Watch the tour, or change both sliders.
Find conditions where detonation beats Brayton by more than 15 percentage points.
Find conditions where the advantage shrinks below 3 points. What kind of engine is that?

Ideal cycles for the same compressor (temperature ratio ψ) and the same heat added (q̃, in units of c_pT₀): constant pressure (Brayton, every gas turbine), constant volume (Humphrey) and detonation (Fickett–Jacobs). The efficiency is 1 − (heat rejected)/(heat added), and the heat rejected grows with the entropy produced on the way.

Going deeper
Going deeper: efficiency from entropy

For an ideal cycle that starts and ends at ambient pressure $p_0$ , the heat rejected is $c_p (T_5 - T_0)$ , where $T_5$ is the exhaust temperature after expanding back to $p_0$ . Because that expansion is isentropic, $T_5 = T_0\, e^{\Delta s / c_p}$ , where $\Delta s$ is the entropy added by the combustion. So

$\eta = 1 - \frac{c_p T_0}{q}\left(e^{\Delta s/c_p} - 1\right).$

For the same heat $q$ , the cycle with the smallest $\Delta s$ wins. Heat added at constant pressure gives $\Delta s = c_p \ln(T_4/T_3)$ ; at constant volume, $c_v \ln(T_4/T_3)$ , which is smaller since $c_v < c_p$ ; and across a detonation, the shock's compression means $\Delta s$ is smaller still. This is the analysis of Heiser and Pratt (2002), and the widget above uses it with $\gamma = 1.4$ .

A very old dream

People have chased constant-volume combustion for over a century. Holzwarth's explosion turbines of the 1900s fired charges in sealed chambers; the V-1's pulsejet of 1944 banged away at about 45 times a second. Zel'dovich's 1940 paper pointed out that a detonation would do better still. In 1957 Nicholls and colleagues at Michigan built the first experimental pulse detonation engines, and in 1959–60 Bogdan Voitsekhovskii in Novosibirsk achieved something stranger: a detonation that ran continuously around the inside of a ring-shaped channel. That is the ancestor of the rotating detonation engine, and the destination of this course.

The catch is that a detonation is violently unsteady. You cannot keep one standing still in a combustor the way you can a flame. Either you start a new one many times a second — the pulse detonation engine of Lesson 7 — or you let one run endlessly around a ring, refilling the ring just behind it — the rotating detonation engine of Lesson 8. Everything between here and there is about understanding the wave well enough to tame it.

Check your intuition

Where does a detonation cycle's efficiency advantage come from?

Recap

What to carry forward

Deflagration spreads by diffusion: metres per second, at nearly constant pressure. Detonation is a shock and a reaction zone locked together: about 2 km/s, with a 15–30× pressure rise.
For the same heat added, a detonation produces the least entropy of the three ideal cycles (Brayton, Humphrey, Fickett–Jacobs), so it is the most efficient.
The advantage is largest when the compressor does little, and shrinks as compression rises.
Detonations are unsteady: engines either pulse them (PDE) or let them spin around a ring (RDE).

Next: the physics of the shock wave itself — what happens when gas is hit faster than it can get out of the way.