A novel characteristic length of detonation relevant to supercritical diffraction


For stoichiometric C2H4–O2 and C2H2–O2 mixtures with or without argon dilution, the processes of detonation diffraction have been investigated in a two-dimensional setup through high-speed schlieren imaging, with the characteristic length and the stability of detonation varied by regulating the initial pressure and argon mole fraction of the mixture. In particular, a length relevant to the process of supercritical diffraction (i.e., distance from the channel end corner to reflection point of the transverse detonation on the channel end face, reflection point distance in short) was deduced from obtained sequential schlieren images and analyzed. The reflection point distance can be idealized for the infinitely wide donor channel, and thus, it can be a parameter in which properties intrinsic to each detonable mixture are manifested. Experimental results showed that the reflection point distance was roughly inversely proportional to the initial pressure for identical mixtures and independent of the width of the donor channel at high initial pressures. For a certain combination of the fuel and oxidizer, correlations between the reflection point distance and the initial partial pressure of fuel were very similar regardless of the argon mole fraction. Critical conditions of the diffraction problem could be given for the ratio of the reflection point distance to the channel width, and it was suggested that the critical value lies in a range of 3–5 and does not significantly depend on the stability of the mixture.

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D CJ :

Chapman–Jouguet (CJ) velocity

d dt :

Diameter of detonation tube

E a :

Activation energy

p 0 :

Initial pressure of mixture

p 0,f :

Initial partial pressure of fuel

l c :

Channel width

l r :

Reflection point distance

R :

Universal gas constant

T 0 :

Initial temperature

T vN :

von Neumann temperature

t oc :

Depth of observation chamber

y Ar :

Argon mole fraction

λ :

Detonation cell width

τ i :

Induction time

τ r :

Reaction time

χ :

Detonation stability parameter


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The authors thank Ken Matsuoka and Akira Iwakawa for fruitful discussions. This research was financially supported by the Nitto Foundation and the Japanese Society for the Promotion of Science (JSPS) KAKENHI Grant Numbers 17H06741, 17H03480, and 17K18937.

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Kawasaki, A., Kasahara, J. A novel characteristic length of detonation relevant to supercritical diffraction. Shock Waves 30, 1–12 (2020). https://doi.org/10.1007/s00193-019-00890-7

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  • Reflection point distance
  • Detonation dynamic parameters
  • Detonation diffraction
  • Critical tube diameter
  • Detonation stability
  • Schlieren imaging