This paper describes numerically the rapid deflagration-to-detonation transition (DDT) in detail in a high-frequency pulse detonation rocket engine. Different from traditional DDT, reactants are injected into the chamber from near the open end and travel toward the closed end. Previous experiments have implied that the gasdynamic shock by injecting in a confined space and the intensive turbulence generated by the high-speed jet play important roles in the detonation initiation, but explanations of how, when, and where the detonation is generated were not presented clearly due to the limitation of experimental observation. In this work, high-resolution two-dimensional simulations are performed to investigate this process employing a physical model similar to the experimental configuration. A new mechanism manifesting itself as a complicated vortex–flame interaction is found for the flame transition from a laminar to compressible or choking regime. It is discovered that the gasdynamic shock, after reflecting from the end wall, triggers the detonation through the gradient of reactivity with the hot spot formed by the collision of the shock and the flame. A dimensionless criterion defined by the ratio of the acoustic speed to the inverse gradient of the ignition delay time is applied to further describe the spontaneous wave propagation from the perspective of chem-physical dynamics. This criterion quantitatively gives a good prediction of the propagating mode from the subsonic deflagration to a developing detonation, even in such a complex scenario as encountered in this work.
References
1.
K.
Kailasanath
, “Review of propulsion applications of detonation waves
,” AIAA J.
38
, 1698
(2000
).2.
K.
Kailasanath
, “Recent developments in the research on pulse detonation engines
,” AIAA J.
41
, 145
(2003
).3.
Y.
Wang
, J.
Liang
, X.
Cai
, and Y.
Mahmoudi
, “Generation mechanism of a new type of unburnt gas pocket and its influences on the detonation-wave/boundary-layer interaction
,” Phys. Fluids
34
, 041704
(2022
).4.
G. D.
Roy
, S. M.
Frolov
, A. A.
Borisov
, and D. W.
Netzer
, “Pulse detonation propulsion: Challenges, current status, and future perspective
,” Prog. Energy Combust. Sci.
30
, 545
(2004
).5.
T.
Li
, X.
Wang
, B.
Xu
, and F.
Kong
, “An efficient approach to achieve flame acceleration and transition to detonation
,” Phys. Fluids
33
, 056103
(2021
).6.
G. B.
Goodwin
, R. W.
Houim
, and E. S.
Oran
, “Effect of decreasing blockage ratio on DDT in small channels with obstacles
,” Combust. Flame
173
, 16
(2016
).7.
G. B.
Goodwin
, R. W.
Houim
, and E. S.
Oran
, “Shock transition to detonation in channels with obstacles
,” Proc. Combust. Inst.
36
, 2717
(2017
).8.
W.
Zhao
, J.
Liang
, R.
Deiterding
, X.
Cai
, and X.
Wang
, “Flame–turbulence interactions during flame acceleration using solid and fluid obstacles
,” Phys. Fluids
34
, 106106
(2022
).9.
S.
Lai
, C.
Xu
, M. H.
Davy
, and X.
Fang
, “Flame acceleration and transition to detonation in a pre-/main-chamber combustion system,” Phys. Fluids
34
, 116105
(2022
).10.
M.
Cooper
, S.
Jackson
, J.
Austin
, E.
Wintenberger
, and J. E.
Shepherd
, “Direct experimental impulse measurements for detonations and deflagrations
,” J. Propul. Power
18
, 1033
(2002
).11.
J. P.
McGarry
and K. A.
Ahmed
, “Flame–turbulence interaction of laminar premixed deflagrated flames
,” Combust. Flame
176
, 439
(2017
).12.
B.
Knox
, D.
Forliti
, C.
Stevens
, J.
Hoke
, and F.
Schauer
, AIAA Paper No. AIAA 2011-663, 2011
.13.
R. W.
Houim
, A.
Ozgen
, and E. S.
Oran
, “The role of spontaneous waves in the deflagration-to-detonation transition in submillimetre channels
,” Combust. Theory Modell.
20
, 1068
(2016
).14.
D.
Liu
, Z.
Liu
, and H.
Xiao
, “Flame acceleration and deflagration-to-detonation transition in narrow channels filled with stoichiometric hydrogen-air mixture
,” Int. J. Hydrogen Energy
47
, 11052
(2022
).15.
H. D.
Ng
, “The effect of chemical reaction kinetics on the structure of gaseous detonations,” Ph.D. thesis, McGill University, Montréal, Québec, Canada (2005
).16.
K.
Fieweger
, R.
Blumenthal
, and G.
Adomeit
, “Self-ignition of S.I. engine model fuels: A shock tube investigation at high pressure
,” Combust. Flame
109
, 599
(1997
).17.
F. L.
Dryer
and M.
Chaos
, “Ignition of syngas/air and hydrogen/air mixtures at low temperatures and high pressures: Experimental data interpretation and kinetic modeling implications
,” Combust. Flame
152
, 293
(2008
).18.
A.
Jena
, H.
Singh
, and A. K.
Agarwal
, “Effect of swirl ratio on charge convection, temperature stratification, and combustion in gasoline compression ignition engine
,” Phys. Fluids
33
, 085113
(2021
).19.
S. M.
Walton
, X.
He
, B. T.
Zigler
, and A.
Atreya
, “An experimental investigation of iso-octane ignition phenomena
,” Combust. Flame
150
, 246
(2007
).20.
H.
Yang
and M. I.
Radulescu
, “Dynamics of cellular flame deformation after a head-on interaction with a shock wave: Reactive Richtmyer–Meshkov instability
,” J. Fluid Mech.
923
, A36
(2021
).21.
H.
Yamashita
, J.
Kasahara
, Y.
Sugiyama
, and A.
Matsuo
, “Visualization study of ignition modes behind bifurcated-reflected shock waves
,” Combust. Flame
159
, 2954
(2012
).22.
K. P.
Grogan
and M.
Ihme
, “Regimes describing shock boundary layer interaction and ignition in shock tubes
,” Proc. Combust. Inst.
36
, 2927
(2017
).23.
K. P.
Grogan
and M.
Ihme
, “Weak and strong ignition of hydrogen/oxygen mixtures in shock-tube systems
,” Proc. Combust. Inst.
35
, 2181
(2015
).24.
H.
Xiao
, R. W.
Houim
, and E. S.
Oran
, “Effects of pressure waves on the stability of flames propagating in tubes
,” Proc. Combust. Inst.
36
, 1577
(2017
).25.
O. J.
Teerling
, A. C.
McIntosh
, J.
Brindley
, and V. H. Y.
Tam
, “Premixed flame response to oscillatory pressure waves
,” Proc. Combust. Inst.
30
, 1733
(2005
).26.
A. Y.
Poludnenko
, “Pulsating instability and self-acceleration of fast turbulent flames
,” Phys. Fluids
27
, 014106
(2015
).27.
J.
Zhao
, L.
Zhou
, X.
Zhang
, K.
Li
, and H.
Wei
, “Experimental investigation of combustion modes and transition mechanism in confined combustion chamber
,” Combust. Flame
230
, 111451
(2021
).28.
J.
Zhao
, L.
Zhou
, K.
Li
, X.
Zhang
, J.
Pan
, R.
Chen
, and H.
Wei
, “Effect of diluent gases on end-gas autoignition and combustion modes in a confined space
,” Combust. Flame
222
, 48
(2020
).29.
L.
Zhou
, D.
Gao
, J.
Zhao
, H.
Wei
, X.
Zhang
, Z.
Xu
, and R.
Chen
, “Turbulent flame propagation with pressure oscillation in the end gas region of confined combustion chamber equipped with different perforated plates
,” Combust. Flame
191
, 453
(2018
).30.
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
).31.
V. N.
Gamezo
, A. M.
Khokhlov
, and E. S.
Oran
, “The influence of shock bifurcations on shock-flame interactions and DDT
,” Combust. Flame
126
, 1810
(2001
).32.
A. M.
Khokhlov
, E. S.
Oran
, and G. O.
Thomas
, “Numerical simulation of deflagration-to-detonation transition: The role of shock–flame interactions in turbulent flames
,” Combust. Flame
117
, 323
(1999
).33.
A. M.
Khokhlov
and E. S.
Oran
, “Numerical simulation of detonation initiation in a flame brush: The role of hot spots
,” Combust. Flame
119
, 400
(1999
).34.
F.
Ma
, J. Y.
Choi
, and V.
Yang
, “Thrust chamber dynamics and propulsive performance of single-tube pulse detonation engines
,” J. Propul. Power
21
, 512
(2005
).35.
F.
Ma
, Y.
Wu
, J. Y.
Choi
, and V.
Yang
, AIAA Paper No. AIAA 2003-0085, 2003
.36.
W.
Lu
, W.
Fan
, K.
Wang
, Q.
Zhang
, and Y.
Chi
, “Operation of a liquid-fueled and valveless pulse detonation rocket engine at high frequency
,” Proc. Combust. Inst.
36
, 2657
(2017
).37.
A.
Cutler
, B.
Beck
, J.
Wilkes
, J.
Drummond
, D.
Alderfer
, and P.
Danehy
, AIAA Paper No. AIAA 2005-1048, 2005
.38.
A.
Cutler
and J.
Drummond
, AIAA Paper No. 555, 2006
.39.
N.
Nguyen
and A.
Cutler
, AIAA Paper No. 4690, 2008
.40.
A.
Cutler
, AIAA Paper No. 4691, 2008
.41.
A. D.
Cutler
, “High-Frequency pulsed combustion actuator experiments
,” AIAA J.
49
, 1943
(2011
).42.
W.
Lu
, K.
Wang
, Q.
Zhang
, Y.
Wang
, and W.
Fan
, “Operation of a pulse detonation engine system at high frequency
,” Proc. Inst. Mech. Eng., Part G
230
, 886
(2016
).43.
I. R.
Hurle
, R. B.
Price
, T. M.
Sugden
, and A.
Thomas
, “Sound emission from open turbulent premixed flames
,” Proc. R. Soc. London, Ser. A
303
, 409
(1968
).44.
M. P.
Burke
, M.
Chaos
, Y.
Ju
, F. L.
Dryer
, and S. J.
Klippenstein
, “Comprehensive H2/O2 kinetic model for high-pressure combustion
,” Int. J. Chem. Kinet.
44
, 444
(2012
).45.
W.
Han
, J.
Huang
, G.
Gu
, C.
Wang
, and C. K.
Law
, “Surface heat loss and chemical kinetic response in deflagration-to-detonation transition in microchannels
,” Phys. Rev. Fluids
5
, 053201
(2020
).46.
T.
Ogawa
, V. N.
Gamezo
, and E. S.
Oran
, “Flame acceleration and transition to detonation in an array of square obstacles
,” J. Loss Prev. Process Ind.
26
, 355
(2013
).47.
X.
Lu
, C. R.
Kaplan
, and E. S.
Oran
, “Predictions of flame acceleration, transition to detonation, and detonation propagation using the Chemical-Diffusive Model
,” Combust. Flame
235
, 111705
(2022
).48.
R. B.
Bird
, “Transport phenomena
,” Appl. Mech. Rev
55
, R1
–R4
(2002
).49.
S.
Mathur
, P. K.
Tondon
, and S. C.
Saxena
, “Thermal conductivity of binary, ternary and quaternary mixtures of rare gases
,” Mol. Phys.
12
, 569
(1967
).50.
M.
Matalon
, C.
Cui
, and J. K.
Bechtold
, “Hydrodynamic theory of premixed flames: Effects of stoichiometry, variable transport coefficients and arbitrary reaction orders
,” J. Fluid Mech.
487
, 179
(2003
).51.
R.
Deiterding
, “Parallel adaptive simulation of multi-dimensional detonation structures,
” Ph.D. thesis, Brandenburg University of Technology (2003
).52.
R.
Deiterding
, “A parallel adaptive method for simulating shock-induced combustion with detailed chemical kinetics in complex domains
,” Comput. Struct.
87
, 769
(2009
).53.
N. N.
Janenko
, Die Zwischenschrittmethode Zur Losung Mehrdimensionaler Probleme Der Mathematischen Physik
(Springer-Verlag
, Berlin
, 1969
).54.
P.
Kaps
and P.
Rentrop
, “Generalized Runge-Kutta methods of order four with stepsize control for stiff ordinary differential equations
,” Num. Math
33
, 55
(1979
).55.
B.
van Leer
, “On the relation between the upwind-differencing schemes of Godunov, Engquist–Osher and Roe
,” SIAM J. Sci. Stat. Comput.
5
(1
), 1–20
(1984
).56.
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
).57.
L. E.
Bollinger
, M. C.
Fong
, and R.
Edse
, “Experimental measurements and theoretical analysis of detonation induction distances
,” ARS J.
31
, 588
(1961
).58.
L. E.
Bollinger
, “Experimental detonation velocities and induction distances in hydrogen-air mixtures
,” AIAA J.
2
, 131
(1964
).59.
E.
Wintenberger
, J. M.
Austin
, M.
Cooper
, S.
Jackson
, and J. E.
Shepherd
, “Analytical model for the impulse of single-cycle pulse detonation tube
,” J. Propul. Power
19
, 22
(2003
).60.
G.
Ciccarelli
and S.
Dorofeev
, “Flame acceleration and transition to detonation in ducts
,” Prog. Energy Combust. Sci.
34
, 499
(2008
).61.
Y. B.
Zeldovich
, “On the development of detonation in a nonuniformly heated gas,”Astro. Acta.
15
, 313
(1970
).62.
J. H.
Lee
, R.
Knystautas
, and N.
Yoshikawa
, Gasdynamics of Explosions and Reactive Systems
(Pergamon
, 1980
).63.
J.
Lawson
and J.
Shepherd
, “Shock and detonation toolbox installation instructions
” (California Institute of Technology
, Pasadena
, 2019
).64.
G. B.
Goodwin
, D.
Cantera
, see http://www.cantera.org for “Object-oriented software for reacting flows,” 2002
.65.
X. J.
Gu
, D. R.
Emerson
, and D.
Bradley
, “Modes of reaction front propagation from hot spots
,” Combust. Flame
133
, 63
(2003
).66.
Y. B.
Zeldovich
, “Regime classification of an exothermic reaction with nonuniform initial conditions
,” Combust. Flame
39
, 211
(1980
).67.
D.
Bradley
and G. T.
Kalghatgi
, “Influence of autoignition delay time characteristics of different fuels on pressure waves and knock in reciprocating engines
,” Combust. Flame
156
, 2307
(2009
).68.
L.
Bates
, D.
Bradley
, G.
Paczko
, and N.
Peters
, “Engine hot spots: Modes of auto-ignition and reaction propagation
,” Combust. Flame
166
, 80
(2016
).69.
D.
Bradley
, C.
Morley
, X. J.
Gu
, and D. R.
Emerson
, “Amplified pressure waves during autoignition: Relevance to CAI engines,” SAE transactions 2679
–2690
(2002
).70.
H.
Yang
and M. I.
Radulescu
, “Enhanced DDT mechanism from shock-flame interactions in thin channels
,” Proc. Combust. Inst.
38
, 3481
(2021
).© 2022 Author(s). Published under an exclusive license by AIP Publishing.
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