The analysis on the interactions of a large-scale shearing vortex, an incident oblique shock wave, and a chemical reaction in a planar shear layer is performed by numerical simulations. The reacting flows are obtained by directly solving the multi-species Navier-Stokes equations in the Eulerian frame, and the motions of individual point-mass fuel droplets are tracked in the Lagrangian frame considering the two-way coupling. The influences of shock strength and spray equivalence ratio on the shock-vortex interaction and the induced combustion are further studied. Under the present conditions, the incident shock is distorted by the vortex evolution to form the complicated waves including an incident shock wave, a multi-refracted wave, a reflected wave, and a transmitted wave. The local pressure and temperature are elevated by the shock impingement on the shearing vortex, which carries flammable mixtures. The chemical reaction is mostly accelerated by the refracted shock across the vortex. Two different exothermal reaction modes could be distinguished during the shock-vortex interaction as a thermal mode, due to the additional energy from the incident shock, and a local quasi detonation mode, due to the coupling of the refracted wave with reaction. The former mode detaches the flame and shock wave, whereas the latter mode tends to occur when the incident shock strength is higher and local equivalence ratio is higher approaching to the stoichiometric value. The numerical results illustrate that those two modes by shock-vortex interaction depend on the structure of the post-shock flame kernel, which may be located either in the vortex-braids of post-shock flows or in the shock-vortex interaction regime.

1.
Y.
Tsujikawa
,
Y.
Tsukamoto
, and
S.
Fujii
, “
Performance analysis of scramjet engine with quasi-one-dimensional flow model
,”
Int. J. Hydrogen Energy
16
(
2
),
135
142
(
1991
).
2.
A.
Ferri
, “
Mixing-controlled supersonic combustion
,”
Annu. Rev. Fluid Mech.
5
(
1
),
301
338
(
1973
).
3.
F. E.
Marble
,
G. J.
Hendricks
, and
E. E.
Zukoski
, “
Progress toward shock enhancement of supersonic combustion processes
,” in
Turbulent Reactive Flows
(
Springer
,
New York, NY
,
1989
), pp.
932
950
.
4.
P. M.
Rubins
and
R. C.
Bauer
, “
Review of shock-induced supersonic combustion research and hypersonic applications
,”
J. Propul. Power
10
(
5
),
593
601
(
1994
).
5.
T.
Fujimori
,
M.
Murayama
,
J.
Sato
 et al, “
Improvement of flameholding characteristics by incident shock waves in supersonic flow
,”
Int. J. Energ. Mater. Chem. Propul.
5
(
1-6
),
330
(
2002
).
6.
A.
Ratner
,
J. F.
Driscoll
,
H.
Huh
 et al, “
Combustion efficiencies of supersonic flames
,”
J. Propul. Power
17
(
2
),
301
307
(
2001
).
7.
H.
Nakamura
,
N.
Sato
,
H.
Kobayashi
 et al, “
Combustion of transverse hydrogen injection with shock wave in a supersonic airstream
,” in
Proceedings of the 5th Asia-Pacific Conference on Combustion
,
Adelaide, Australia
,
17-20 July 2005
, pp.
465
468
.
8.
W.
Huang
,
Z.
Wang
,
J.
Wu
 et al, “
Numerical prediction on the interaction between the incident shock wave and the transverse slot injection in supersonic flows
,”
Aerosp. Sci. Technol.
28
(
1
),
91
99
(
2013
).
9.
T.
Mai
,
Y.
Sakimitsu
,
H.
Nakamura
 et al, “
Effect of the incident shock wave interacting with transversal jet flow on the mixing and combustion
,”
Proc. Combust. Inst.
33
(
2
),
2335
2342
(
2011
).
10.
A. A.
Shekarian
,
S.
Tabejamaat
, and
Y.
Shoraka
, “
Effects of incident shock wave on mixing and flame holding of hydrogen in supersonic air flow
,”
Int. J. Hydrogen Energy
39
(
19
),
10284
10292
(
2014
).
11.
R. P.
Fuller
,
P. K.
Wu
,
A. S.
Nejad
 et al, “
Comparison of physical and aerodynamic ramps as fuel injectors in supersonic flow
,”
J. Propul. Power
14
(
2
),
135
145
(
1998
).
12.
F. S.
Alvi
and
G. S.
Settles
, “
Physical model of the swept shock wave/boundary-layer interaction flowfield
,”
AIAA J.
30
(
9
),
2252-2258
(
1992
).
13.
N. T.
Clemens
and
M. G.
Mungal
, “
Large-scale structure and entrainment in the supersonic mixing layer
,”
J. Fluid Mech.
284
,
171
216
(
1995
).
14.
J.
Reveillon
and
L.
Vervisch
, “
Analysis of weakly turbulent dilute-spray flames and spray combustion regimes
,”
J. Fluid Mech.
537
,
317
347
(
2005
).
15.
S. K.
Aggarwal
, “
A review of spray ignition phenomena: Present status and future research
,”
Prog. Energy Combust. Sci.
24
(
6
),
565
600
(
1998
).
16.
X.
Jiang
,
G. A.
Siamas
,
K.
Jagus
 et al, “
Physical modelling and advanced simulations of gas–liquid two-phase jet flows in atomization and sprays
,”
Prog. Energy Combust. Sci.
36
(
2
),
131
167
(
2010
).
17.
Z.
Bouali
,
C.
Pera
, and
J.
Reveillon
, “
Numerical analysis of the influence of two-phase flow mass and heat transfer on n-heptane autoignition
,”
Combust. Flame
159
(
6
),
2056
2068
(
2012
).
18.
D.
Martínez-Ruiz
,
J.
Urzay
,
A. L.
Sánchez
 et al, “
Dynamics of thermal ignition of spray flames in mixing layers
,”
J. Fluid Mech.
734
,
387
423
(
2013
).
19.
A. L.
Sánchez
,
J.
Urzay
, and
A.
Liñán
, “
The role of separation of scales in the description of spray combustion
,”
Proc. Combust. Inst.
35
(
2
),
1549
1577
(
2015
).
20.
D. R.
Buttsworth
, “
Interaction of oblique shock waves and planar mixing regions
,”
J. Fluid Mech.
306
,
43
57
(
1996
).
21.
C.
Huete
,
J.
Urzay
,
A. L.
Sánchez
 et al, “
Weak-shock interactions with transonic laminar mixing layers of fuels for high-speed propulsion
,”
AIAA J.
54
(
3
),
966
979
(
2016
).
22.
C.
Huete
,
A. L.
Sánchez
,
F. A.
Williams
 et al, “
Diffusion-flame ignition by shock-wave impingement on a supersonic mixing layer
,”
J. Fluid Mech.
784
,
74
108
(
2015
).
23.
C.
Huete
,
A. L.
Sánchez
, and
F. A.
Williams
, “
Diffusion-flame ignition by shock-wave impingement on a hydrogen–air supersonic mixing layer
,”
J. Propul. Power
33
(
1
),
256
263
(
2016
).
24.
P. J. M.
Ferrer
,
G.
Lehnasch
, and
A.
Mura
, “
Compressibility and heat release effects in high-speed reactive mixing layers I. Growth rates and turbulence characteristics
,”
Combust. Flame
180
,
284
303
(
2017
).
25.
P. J. M.
Ferrer
,
G.
Lehnasch
, and
A.
Mura
, “
Compressibility and heat release effects in high-speed reactive mixing layers II. Structure of the stabilization zone and modeling issues relevant to turbulent combustion in supersonic flows
,”
Combust. Flame
180
,
304
320
(
2017
).
26.
X.
Wenxiong
,
H.
Yanji
,
X.
Qingyao
 et al, “
Generation and propagation of auto-ignition flame kernel caused by oblique shock in supersonic flow-field
,” in
21st AIAA International Space Planes and Hypersonics Technologies Conference
(
AIAA
,
2017
),
2120
.
27.
Y.
Zhang
,
B.
Wang
,
H.
Zhang
 et al, “
Mixing enhancement of compressible planar mixing layer impinged by oblique shock waves
,”
J. Propul. Power
31
(
1
),
156
169
(
2014
).
28.
B. E.
Poling
,
J. M.
Prausnitz
, and
J. P.
O’Connell
,
The Properties of Gases and Liquids
(
McGraw-Hill
,
New York
,
2001
).
29.
C. T.
Crowe
,
M. P.
Sharma
, and
D. E.
Stock
, “
The particle-source-in cell (PSI-CELL) model for gas-droplet flows
,”
J. Fluids Eng.
99
(
2
),
325
332
(
1977
).
30.
R. S.
Miller
,
K.
Harstad
, and
J.
Bellan
, “
Evaluation of equilibrium and non-equilibrium evaporation models for many-droplet gas-liquid flow simulations
,”
Int. J. Multiphase Flow
24
(
6
),
1025
1055
(
1998
).
31.
Y.
Ling
,
S.
Balachandar
, and
M.
Parmar
, “
Inter-phase heat transfer and energy coupling in turbulent dispersed multiphase flows
,”
Phys. Fluids
28
(
3
),
033304
(
2016
).
32.
E.
Loth
, “
Compressibility and rarefaction effects on drag of a spherical particle
,”
AIAA J.
46
(
9
),
2219
(
2008
).
33.
Y.
Ling
,
M.
Parmar
, and
S.
Balachandar
, “
A scaling analysis of added-mass and history forces and their coupling in dispersed multiphase flows
,”
Int. J. Multiphase Flow
57
,
102
114
(
2013
).
34.
C. K.
Westbrook
and
F. L.
Dryer
, “
Chemical kinetic modeling of hydrocarbon combustion
,”
Prog. Energy Combust. Sci.
10
(
1
),
1
57
(
1984
).
35.
G.
Lodier
,
C.
Merlin
,
P.
Domingo
 et al, “
Self-ignition scenarios after rapid compression of a turbulent mixture weakly-stratified in temperature
,”
Combust. Flame
159
(
11
),
3358
3371
(
2012
).
36.
J.
Verreault
,
A. J.
Higgins
, and
R. A.
Stowe
, “
Formation of transverse waves in oblique detonations
,”
Proc. Combust. Inst.
34
(
2
),
1913
1920
(
2013
).
37.
C.
Qian
,
W.
Bing
,
Z.
Huiqiang
 et al, “
Numerical investigation of H2/air combustion instability driven by large scale vortex in supersonic mixing layers
,”
Int. J. Hydrogen Energy
41
(
4
),
3171
3184
(
2016
).
38.
Z.
Ren
,
B.
Wang
,
Q.
Xie
 et al, “
Thermal auto-ignition in high-speed droplet-laden mixing layers
,”
Fuel
191
,
176
189
(
2017
).
39.
R. P.
Fedkiw
,
B.
Merriman
, and
S.
Osher
, “
High accuracy numerical methods for thermally perfect gas flows with chemistry
,”
J. Comput. Phys.
132
(
2
),
175
190
(
1997
).
40.
X.
Zhang
and
C. W.
Shu
, “
On maximum-principle-satisfying high order schemes for scalar conservation laws
,”
J. Comput. Phys.
229
(
9
),
3091
3120
(
2010
).
41.
X. Y.
Hu
,
Q.
Wang
, and
N. A.
Adams
, “
An adaptive central-upwind weighted essentially non-oscillatory scheme
,”
J. Comput. Phys.
229
(
23
),
8952
8965
(
2010
).
42.
K.
Luo
,
H.
Pitsch
,
M. G.
Pai
 et al, “
Direct numerical simulations and analysis of three-dimensional n-heptane spray flames in a model swirl combustor
,”
Proc. Combust. Inst.
33
(
2
),
2143
2152
(
2011
).
43.
W. D.
Smyth
and
J. N.
Moum
, “
Length scales of turbulence in stably stratified mixing layers
,”
Phys. Fluids
12
(
6
),
1327
1342
(
2000
).
44.
M. D.
Slessor
,
M.
Zhuang
, and
P. E.
Dimotakis
, “
Turbulent shear-layer mixing: Growth-rate compressibility scaling
,”
J. Fluid Mech.
414
,
35
45
(
2000
).
45.
S.
Lee
,
S. K.
Lele
, and
P.
Moin
, “
Eddy shocklets in decaying compressible turbulence
,”
Phys. Fluids A
3
(
4
),
657
664
(
1991
).
46.
R. S.
Miller
, “
Effects of non-reacting solid particle and liquid droplet loading on an exothermic reacting mixing layer
,”
Phys. Fluids
13
(
11
),
3303
3320
(
2001
).
47.
R. A.
Strehlow
,
Combustion Fundamentals
(
McGraw-Hill College
,
1984
).
48.
P. M.
Rubins
and
T. H. M.
Cunningham
, “
Shock-induced supersonic combustion in a constant-area duct
,”
J. Spacecr. Rockets
2
(
2
),
199
205
(
1965
).
49.
P.
Schroll
,
A. P.
Wandel
,
R. S.
Cant
 et al, “
Direct numerical simulations of autoignition in turbulent two-phase flows
,”
Proc. Combust. Inst.
32
(
2
),
2275
2282
(
2009
).
50.

This so-called local quasi detonation in the present study is different from the detonation defined in the classic theory. According to Strehlow’s definition,47 the energy that supports the detonation wave structure comes entirely from the exothermic chemical reaction. In addition, the shock-induced combustion means that the chemical reaction behind the leading shock does not necessarily affect the shock.48 For the present study, the leading shock is formed in the interaction between the vortex and incident shock wave, and the local combustion cannot be termed as a typical detonation wave according to the classic theory. However, the post-shock reaction increases the shock intensity by comparing the reacting and non-reacting cases. Therefore, the local combustion is termed as a quasi detonation or a detonation-like combustion, since the thermal energy to support the pressure wave partially comes from the incident shock, and partially is based on the post-shock reaction.

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