The authors examine the effects of inhomogeneity in the equivalence ratio on detonation propagation by using a set of two-dimensional numerical simulations of the detailed reaction chemistry of an H2/air mixture. A random field of fluctuations but with statistical characteristics is introduced, and several combinations of the root mean square (RMS) and characteristic length scales of the fluctuations are considered to investigate the evolutions of the cellular structure, speed of detonation, and shock pressure under these setups. The results indicate that an increase in the RMS enlarged the cell formed by the original triple points as well as the characteristic length scale to promote the transition from a single cellular pattern to a double cellular pattern. The large cell of the double cellular pattern was formed by triple points generated from local explosion, and the decoupling or curvature of the detonation wave within an extremely lean region was important for this process. Moreover, sustainable detonation propagation under these configurations benefited from the strong transverse detonation generated by the local explosion as well as the propagation of these original triple points along the stoichiometric region, where their collisions reinitiated detonation in the extremely lean region. The instantaneous and average speeds of detonation were calculated. The former followed the trend of evolution of the normalized potential instantaneous energy release, whereas the latter decreased with an increase in . However, the value of l had a non-monotonic influence that can be attributed to two factors.

1.
A. Y.
Poludnenko
,
J.
Chambers
,
K.
Ahmed
,
V. N.
Gamezo
, and
B. D.
Taylor
, “
A unified mechanism for unconfined deflagration-to-detonation transition in terrestrial chemical systems and type Ia supernovae
,”
Science
366
,
eaau7365
(
2019
).
2.
J.
Chambers
,
H. M.
Chin
,
A. Y.
Poludnenko
,
V. N.
Gamezo
, and
K. A.
Ahmed
, “
Spontaneous runaway of fast turbulent flames for turbulence-induced deflagration-to-detonation transition
,”
Phys. Fluids
34
,
015114
(
2022
).
3.
E. S.
Oran
,
G.
Chamberlain
, and
A.
Pekalski
, “
Mechanisms and occurrence of detonations in vapor cloud explosions
,”
Prog. Energy Combust. Sci.
77
,
100804
(
2020
).
4.
T.
Zhang
,
W.
Sun
,
L.
Wang
, and
Y.
Ju
, “
Effects of low-temperature chemistry and turbulent transport on knocking formation for stratified dimethyl ether/air mixtures
,”
Combust. Flame
200
,
342
(
2019
).
5.
F.
Ladeinde
and
H.
Oh
, “
Stochastic and spectra contents of detonation initiated by compressible turbulent thermodynamic fluctuations
,”
Phys. Fluids
33
,
045111
(
2021
).
6.
Z.
Yu
,
H.
Zhang
, and
P.
Dai
, “
Autoignition and detonation development induced by temperature gradient in n-C7H16/air/H2O mixtures
,”
Phys. Fluids
33
,
017111
(
2021
).
7.
M. B.
Luong
,
S.
Desai
,
F. E. H.
Pérez
,
R.
Sankaran
,
B.
Johansson
, and
H. G.
Im
, “
A statistical analysis of developing knock intensity in a mixture with temperature inhomogeneities
,”
Proc. Combust. Inst.
38
(
4
),
5781
5789
(
2020
).
8.
T.
Zhang
,
W.
Sun
, and
Y.
Ju
, “
Multi-scale modeling of detonation formation with concentration and temperature gradients in n-heptane/air mixtures
,”
Proc. Combust. Inst.
36
,
1539
(
2017
).
9.
S.
Prakash
and
V.
Raman
, “
The effects of mixture preburning on detonation wave propagation
,”
Proc. Combust. Inst.
38
,
3749
(
2021
).
10.
Y.
Liu
,
W.
Zhou
,
Y.
Yang
,
Z.
Liu
, and
J.
Wang
, “
Numerical study on the instabilities in H2-air rotating detonation engines
,”
Phys. Fluids
30
,
046106
(
2018
).
11.
T.
Sato
,
F.
Chacon
,
L.
White
,
V.
Raman
, and
M.
Gamba
, “
Mixing and detonation structure in a rotating detonation engine with an axial air inlet
,”
Proc. Combust. Inst.
38
,
3769
(
2021
).
12.
S.
Boulal
,
P.
Vidal
, and
R.
Zitoun
, “
Experimental investigation of detonation quenching in non-uniform compositions
,”
Combust. Flame
172
,
222
(
2016
).
13.
R. W.
Houim
and
R. T.
Fievisohn
, “
The influence of acoustic impedance on gaseous layered detonations bounded by an inert gas
,”
Combust. Flame
179
,
185
(
2017
).
14.
K. C.
Tang-Yuk
,
X.
Mi
,
J. H.
Lee
,
H. D.
Ng
, and
R.
Deiterding
, “
Transmission of a detonation wave across an inert layer
,”
Combust. Flame
236
,
111769
(
2022
).
15.
G.
Thomas
,
P.
Sutton
, and
D.
Edwards
, “
The behavior of detonation waves at concentration gradients
,”
Combust. Flame
84
,
312
(
1991
).
16.
Y.
Wang
,
C.
Huang
,
R.
Deiterding
,
H.
Chen
, and
Z.
Chen
, “
Propagation of gaseous detonation across inert layers
,”
Proc. Combust. Inst.
38
,
3555
(
2021
).
17.
P.
Honhar
,
C. R.
Kaplan
,
R. W.
Houim
, and
E. S.
Oran
, “
Role of reactivity gradients in the survival, decay and reignition of methane-air detonations in large channels
,”
Combust. Flame
222
,
152
(
2020
).
18.
L.
Boeck
,
F.
Berger
,
J.
Hasslberger
, and
T.
Sattelmayer
, “
Detonation propagation in hydrogen–air mixtures with transverse concentration gradients
,”
Shock Waves
26
,
181
(
2016
).
19.
L. R.
Boeck
,
J.
Hasslberger
, and
T.
Sattelmayer
, “
Flame acceleration in hydrogen/air mixtures with concentration gradients
,”
Combust. Sci. Technol.
186
,
1650
(
2014
).
20.
F.
Ettner
,
K.
Vollmer
, and
T.
Sattelmayer
, “
Mach reflection in detonations propagating through a gas with a concentration gradient
,”
Shock Waves
23
,
201
(
2013
).
21.
K.
Ishii
and
M.
Kojima
, “
Behavior of detonation propagation in mixtures with concentration gradients
,”
Shock Waves
17
,
95
(
2007
).
22.
D.
Kessler
,
V.
Gamezo
, and
E.
Oran
, “
Gas-phase detonation propagation in mixture composition gradients
,”
Philos. Trans. R Soc., A
370
,
567
(
2012
).
23.
W.
Han
,
C.
Wang
, and
C. K.
Law
, “
Role of transversal concentration gradient in detonation propagation
,”
J. Fluid Mech.
865
,
602
(
2019
).
24.
M.
Reynaud
,
F.
Virot
, and
A.
Chinnayya
, “
A computational study of the interaction of gaseous detonations with a compressible layer
,”
Phys. Fluids
29
,
056101
(
2017
).
25.
J.
Li
,
X.
Mi
, and
A. J.
Higgins
, “
Geometric scaling for a detonation wave governed by a pressure-dependent reaction rate and yielding confinement
,”
Phys. Fluids
27
,
027102
(
2015
).
26.
Y.
Wang
,
Z.
Chen
, and
H.
Chen
, “
Propagation of gaseous detonation in spatially inhomogeneous mixtures
,”
Phys. Fluids
33
,
116105
(
2021
).
27.
X.
Mi
,
A. J.
Higgins
,
H. D.
Ng
,
C. B.
Kiyanda
, and
N.
Nikiforakis
, “
Propagation of gaseous detonation waves in a spatially inhomogeneous reactive medium
,”
Phys. Rev. Fluids
2
,
053201
(
2017
).
28.
X.
Mi
,
E. V.
Timofeev
, and
A. J.
Higgins
, “
Effect of spatial discretization of energy on detonation wave propagation
,”
J. Fluid Mech.
817
,
306
(
2017
).
29.
X.
Mi
,
A.
Higgins
,
C.
Kiyanda
,
H.
Ng
, and
N.
Nikiforakis
, “
Effect of spatial inhomogeneities on detonation propagation with yielding confinement
,”
Shock Waves
28
,
993
(
2018
).
30.
A.
Cuadra
,
C.
Huete
, and
M.
Vera
, “
Effect of equivalence ratio fluctuations on planar detonation discontinuities
,”
J. Fluid Mech.
903
,
A30
(
2020
).
31.
C.
Huete
,
A. L.
Sánchez
, and
F. A.
Williams
, “
Theory of interactions of thin strong detonations with turbulent gases
,”
Phys. Fluids
25
,
076105
(
2013
).
32.
R.
Yu
and
X.-S.
Bai
, “
A fully divergence-free method for generation of inhomogeneous and anisotropic turbulence with large spatial variation
,”
J. Comput. Phys.
256
,
234
(
2014
).
33.
R. H.
Kraichnan
, “
Diffusion by a random velocity field
,”
Phys. Fluids
13
,
22
(
1970
).
34.
M. B.
Luong
,
F. E. H.
Pérez
, and
H. G.
Im
, “
Prediction of ignition modes of NTC-fuel/air mixtures with temperature and concentration fluctuations
,”
Combust. Flame
213
,
382
(
2020
).
35.
C. S.
Yoo
,
Z.
Luo
,
T.
Lu
,
H.
Kim
, and
J. H.
Chen
, “
A DNS study of ignition characteristics of a lean iso-octane/air mixture under HCCI and SACI conditions
,”
Proc. Combust. Inst.
34
,
2985
(
2013
).
36.
F.
Zhang
,
R.
Yu
, and
X.-S.
Bai
, “
Direct numerical simulation of PRF70/air partially premixed combustion under IC engine conditions
,”
Proc. Combust. Inst.
35
,
2975
(
2015
).
37.
T.
Sato
,
S.
Voelkel
, and
V.
Raman
, “
Detailed chemical kinetics based simulation of detonation-containing flows
,” in
Proceedings of the ASME Turbo Expo: Turbomachinery Technical Conference and Exposition
,
2018
.
38.
R.
Deiterding
, “
A parallel adaptive method for simulating shock-induced combustion with detailed chemical kinetics in complex domains
,”
Comput. Struct.
87
,
769
(
2009
).
39.
J.
Li
,
Z.
Zhao
,
A.
Kazakov
, and
F. L.
Dryer
, “
An updated comprehensive kinetic model of hydrogen combustion
,”
Int. J. Chem. Kinet.
36
,
566
(
2004
).
40.
X.
Zhang
,
H.
Wei
,
L.
Zhou
,
X.
Cai
, and
R.
Deiterding
, “
Relationship of flame propagation and combustion mode transition of end-gas based on pressure wave in confined space
,”
Combust. Flame
214
,
371
(
2020
).
41.
H.
Wei
,
X.
Zhang
,
H.
Zeng
,
R.
Deiterding
,
J.
Pan
, and
L.
Zhou
, “
Mechanism of end-gas autoignition induced by flame-pressure interactions in confined space
,”
Phys. Fluids
31
,
076106
(
2019
).
42.
W.
Chen
,
J.
Liang
,
X.
Cai
, and
Y.
Mahmoudi
, “
Three-dimensional simulations of detonation propagation in circular tubes: Effects of jet initiation and wall reflection
,”
Phys. Fluids
32
,
046104
(
2020
).
43.
W.
Zhao
,
J.
Liang
,
R.
Deiterding
,
X.
Cai
, and
X.
Wang
, “
Effect of transverse jet position on flame propagation regime
,”
Phys. Fluids
33
,
091704
(
2021
).
44.
K.
Kaneshige
and
J.
Shepherd
, “
Detonation database
,” Report No. FM97-8 (
California Institute of Technology
,
Pasadena, CA
,
1999
).
45.
C. K.
Westbrook
and
F. L.
Dryer
, “
Chemical kinetic modeling of hydrocarbon combustion
,”
Prog. Energy Combust.
10
,
1–57
(
1984
).
46.
M. I.
Radulescu
,
G. J.
Sharpe
,
C. K.
Law
, and
J. H.
Lee
, “
The hydrodynamic structure of unstable cellular detonations
,”
J. Fluid Mech.
580
,
31
(
2007
).
47.
Q.
Xiao
and
C.
Weng
, “
Effect of losses on hydrogen–oxygen–argon detonation cell sizes
,”
Phys. Fluids
33
,
116103
(
2021
).
48.
H.
Shimizu
,
A.
Hayashi
, and
N.
Tsuboi
, Study of detailed chemical reaction model of hydrogen-air detonation (
2001
).
49.
T.
Sato
,
S.
Voelkel
, and
V.
Raman
, “
Detailed Chemical Kinetics Based Simulation of Detonation-Containing Flows
,” in
Proceedings of the ASME Turbo Expo 2018: Turbomachinery Technical Conference and Exposition, Oslo, Norway, June 11–15, 2018
(ASME, 2018), Vol. 4A. (
American Society of Mechanical Engineers
,
2018
).
50.
S.
Voelkel
,
D.
Masselot
,
P. L.
Varghese
, and
V.
Raman
, “
Analysis of hydrogen-air detonation waves with vibrational nonequilibrium
,”
AIP Conf. Proc.
1786
,
070015
(
2016
).
You do not currently have access to this content.