Shock Waves

, Volume 19, Issue 1, pp 11–23 | Cite as

Detonation diffraction through different geometries

  • Rémy SorinEmail author
  • Ratiba Zitoun
  • Boris Khasainov
  • Daniel Desbordes
Original Article


We performed the study of the diffraction of a self-sustained detonation from a cylindrical tube (of inner diameter d) through different geometric configurations in order to characterise the transmission processes and to quantify the transmission criteria to the reception chamber. For the diffraction from a tube to the open space the transmission criteria is expressed by d c  = k c ·λ (with λ the detonation cell size and k c depending on the mixture and on the operture configuration, classically 13 for alkane mixtures with oxygen). The studied geometries are: (a) a sharp increase of diameter (D/d > 1) with and without a central obstacle in the diffracting section, (b) a conical divergent with a central obstacle in the diffracting section and (c) an inversed intermediate one end closed tube insuring a double reflection before a final diffraction between the initiator tube and the reception chamber. The results for case A show that the reinitiation process depends on the ratio d/λ. For ratios below k c the re-ignition takes place at the receptor tube wall and at a fixed distance from the step, i.e. closely after the diffracted shock reflection shows a Mach stem configuration. For ratios below a limit ratio k lim (which depends on D/d) the re-ignition distance increases with the decrease of d/λ. For both case A and B the introduction of a central obstacle (of blockage ratio BR = 0.5) at the exit of the initiator tube decreases the critical transmission ratio k c by 50%. The results in configuration C show that the re-ignition process depends both on d/λ and the geometric conditions. Optimal configuration is found that provides the transmission through the two successive reflections (from d = 26 mm to D ch = 200 mm) at as small d/λ as 2.2 whatever the intermediate diameter D is. This configuration provides a significant improvement in the detonation transmission conditions.


Detonation Diffraction Re-initiation Soot track records Shock reflection Mach stem 

List of symbols


reaction progress degree


\({=\dfrac{\rm obstacle surface}{\rm tube cross section}}\), blockage ratio




initiator tube (diffracting tube) diameter


critical diameter


receptor tube diameter, diameter of inversed tube


diameter of chamber, 200 mm


deflagration to detonation transition


activation energy


distance between the initiator tube end and the closed end of the inversed tube


distance between the inversed tube open end and the combustion chamber wall


d/λ, transmission ratio


d c /λ, critical transmission ratio to a free space


limit value when the deflagration to detonation transition takes place in the reinitiation process


limit transmission ratio


threshold value corresponding to wall reinitiation in the case of a central obstacle


limit of head-on reflection transmission


threshold value for lateral reflection transmission


limit of transmission through the two successive shock reflections in inversed tube


rectangular channel width


distance between the step and the re-ignition point


reinitiation point at the wall


global reaction order


initial pressure


first reflection of the flow in the inversed tube


second reflection of the flow in the inversed tube


post-shock temperature at the choking regime


height of rectangular channel before diffraction


height of rectangular channel after diffraction


pre-exponential factor

Greek symbols


divergence expansion angle


ideal gas polytropic coefficient


detonation cell size


cell size at critical detonation transmission to a free space


k/k c  = (d/λ)/k c , dimensionless transmission limit


47.40.Rs 82.40.Fp 82.20.Wt 


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Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  • Rémy Sorin
    • 1
    • 2
    Email author
  • Ratiba Zitoun
    • 1
  • Boris Khasainov
    • 1
  • Daniel Desbordes
    • 1
  1. 1.Laboratoire de Combustion et de DétoniqueENSMA, CNRS UPR 9028Futuroscope CedexFrance
  2. 2.CEA, DAM, DIFArpajonFrance

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