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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

Abstract

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.

Keywords

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

List of symbols

a

reaction progress degree

BR

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

CJ

Chapman–Jouguet

d

initiator tube (diffracting tube) diameter

dc

critical diameter

D

receptor tube diameter, diameter of inversed tube

Dch

diameter of chamber, 200 mm

DDT

deflagration to detonation transition

Ea

activation energy

h

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

H

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

k

d/λ, transmission ratio

kc

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

kDDT

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

klim

limit transmission ratio

kobst

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

k1,h

limit of head-on reflection transmission

k1,l

threshold value for lateral reflection transmission

k1-2

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

L

rectangular channel width

Lreignition

distance between the step and the re-ignition point

L0

reinitiation point at the wall

n

global reaction order

P0

initial pressure

RW1

first reflection of the flow in the inversed tube

RW2

second reflection of the flow in the inversed tube

Tc

post-shock temperature at the choking regime

W1

height of rectangular channel before diffraction

W2

height of rectangular channel after diffraction

Z

pre-exponential factor

Greek symbols

α

divergence expansion angle

γ

ideal gas polytropic coefficient

λ

detonation cell size

λc

cell size at critical detonation transmission to a free space

\({\frac{\lambda_c}{\lambda}}\)

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

PACS

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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