Detonation Wave Simulator: Chapman-Jouguet Theory & Cell Structure

simulator advanced ~12 min
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D_CJ = 1850 m/s — stoichiometric hydrocarbon-air detonation

A stoichiometric hydrocarbon-air mixture at standard conditions detonates at approximately 1850 m/s with a pressure ratio of about 18, illustrating the extreme violence of detonation compared to deflagration.

Formula

D_CJ = √(2(γ²−1)·q + a₁²) (Chapman-Jouguet velocity)
P₂/P₁ = (1 + γ·M²)/(1 + γ) (normal shock relation)

Supersonic Combustion

A detonation wave is fundamentally different from ordinary burning. Where a flame deflagrates — propagating subsonically through thermal diffusion — a detonation couples a strong shock wave with an intense reaction zone, traveling at supersonic velocities (Mach 5–9 in typical gas mixtures). The shock compresses and heats the gas to ignition temperature, which then reacts and drives the shock forward in a self-sustaining cycle.

Chapman-Jouguet Theory

The CJ theory, developed in the early 1900s, treats the detonation as a discontinuity obeying conservation of mass, momentum, and energy. The CJ point is where the Rayleigh line is tangent to the Hugoniot curve — the unique solution where post-detonation flow is sonic. This gives the minimum stable detonation velocity, which depends on the mixture's heat release and thermodynamic properties.

Cellular Detonation Structure

Real detonations exhibit remarkable three-dimensional instability. Transverse shock waves create a cellular pattern that can be recorded on soot-coated foils placed inside detonation tubes. The cell size λ is the most important length scale in detonation dynamics — it determines critical tube diameter (d_crit ≈ 13λ), critical initiation energy, and detonation limits in various geometries.

Engineering Applications

Rotating detonation engines promise 5–15% efficiency gains over conventional gas turbines by exploiting the pressure gain from detonation rather than constant-pressure combustion. Meanwhile, understanding detonation limits is critical for explosion safety in chemical plants, mines, and fuel storage facilities. This simulation lets you explore the fundamental parameters governing these extreme combustion phenomena.

FAQ

What is a detonation wave?

A detonation is a supersonic combustion wave consisting of a leading shock front coupled with a rapid exothermic reaction zone. Unlike deflagration (subsonic burning), detonation propagates at velocities of 1500–3000 m/s with extreme pressure ratios, governed by the Chapman-Jouguet (CJ) theory.

What is Chapman-Jouguet velocity?

The CJ velocity is the minimum stable detonation speed for a given mixture. At this velocity, the flow behind the detonation front is exactly sonic relative to the wave. It depends primarily on the heat release per unit mass and the thermodynamic properties of the gas mixture.

What are detonation cells?

Real detonations are not perfectly planar — they exhibit a cellular structure of transverse waves that create a diamond-shaped pattern on soot foils. Cell size λ is proportional to the induction zone length and is a key parameter for predicting detonation limits and critical tube diameters.

How are detonations used in engineering?

Pulse detonation engines (PDEs) and rotating detonation engines (RDEs) exploit detonation's higher thermodynamic efficiency compared to constant-pressure combustion. Detonation also matters in explosion safety, mining, and military applications.

Sources

Embed

<iframe src="https://homo-deus.com/lab/combustion/detonation-wave/embed" width="100%" height="400" frameborder="0"></iframe>
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