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Numerical Study on Thermodynamic Efficiency and Stability of
Oblique Detonation Waves
Shikun Miao,∗Jin Zhou,†Zhiyong Lin,‡Xiaodong Cai,§and Shijie Liu‡
National University of Defense Technology, 410073 Changsha, People’s Republic of China
DOI: 10.2514/1.J056887
The stability of oblique detonation waves and the thermodynamic efficiency of the oblique detonation wave cycles
are studied systematically. The stability of oblique detonation waves is investigated with two-dimensional simulations
based on the open-source program AMROC (from “Adaptive Mesh Refinement in Object-Oriented C++”). The
results show that the oblique detonation waves with a smooth transition are more resistant to upstream disturbances,
requiring less time than the abrupt ones to recover their stable state. Subsequently, a theoretical analysis based on the
ideal thermodynamic cycle is carried out to investigate the thermodynamic efficiency of the oblique detonation cycles
under different inflow conditions. The efficiency loss is introduced to measure the difference in thermodynamic
efficiency between the oblique detonation waves and Chapman–Jouguet detonations. In addition, the influence of
initial compression, inflow velocity, equivalence ratio, and wedge angle on the efficiency loss are studied. Finally, the
optimum working condition is analyzed based on the stability of oblique detonation waves and the thermodynamic
efficiency of oblique detonation wave cycles, indicating that the oblique detonation waves in an oblique detonation
wave engine should be maintained in the shift area between the abrupt and the smooth transition.
Nomenclature
D= diameter of the disturbance
ER = equivalence ratio of the premixed combustible mixture
M1= Mach number of the incoming flow
P= pressure
Pdet = pressure behind the oblique detonation wave
Psh = pressure behind the oblique shock wave
P
1= total pressure before the oblique shock
P
2= total pressure behind the oblique shock
rl= refinement ratio of the refinement level l
T= temperature
Td= temperature of the disturbance
td= time when the disturbance is added to the flowfield
ti= chemical induction time
tr= total reaction time
trc = recovering time of the flowfield
ts= time when the oblique detonation wave becomes stable
again
U= velocity magnitude
UCJ = Chapman–Jouguet velocity
Ud= velocity of the disturbance
U2= flow velocity behind the oblique detonation wave or
shock wave
v= specific volume
X= length of the channel
Xd=xposition of the disturbance
Xw= distance between the wedge tip and the inlet of the
channel
Y= height of the channel
Yd=yposition of the disturbance
β= oblique shock or detonation wave angle
γ= ratio of specific heat
Δxmin = minimum grid width
δode = thermodynamic efficiency loss
εp= threshold value of the scaled gradient on pressure
εT= threshold value of the scaled gradient on temperature
ερ= threshold value of the scaled gradient on density
θ= wedge angle or deflection angle
ρ= density
Φ= velocity ratio
Φ= critical velocity ratio for the shift from smooth
transition to abrupt transition
ϕ= velocity ratio
Subscripts
0 = ambient state
1 = state of incoming flow
2 = state behind the detonation or shock waves
I. Introduction
DETONATION is considered a superior combustion method to
be used in hypersonic airbreathing propulsion, which is able to
work at a high flight Mach number and improve thermodynamic
efficiency [1–7]. In recent years, devices based on detonation have
been widely explored, among which the oblique detonation wave
engine (ODWE) is more appropriate for hypersonic airbreathing
propulsion. In the combustion chamber of an ODWE, the oblique
detonation wave (ODW) is initiated and stabilized by a wedge, and
combustion occurs near the detonation wave surface, which enables
structure simplification and size reduction of the combustion
chamber. However, recent research on oblique detonation has been
mostly concentrated on the structure and instability of the detonation
wave surface, whereas specialized investigations on the performance
of the ODWE are limited in quantity. Ashford and Emanuel [3]
evaluated the performance of an ODWE using a perfect gas
approximation versus a real gas model and compared it to a diffusive
scramjet engine. The results show that an ODWE gives comparable
performance to diffusive engines and offers several advantages (i.e.,
less drag, less engine heat transfer, and design flexibility).
Kailasanath [4] reviewed the development of detonation propulsion
and discussed the advantages of the detonation cycle over the isobaric
Brayton–Joule cycle. He argued that the thermodynamic efficiency
of the detonation cycle is prominently higher than the isobaric cycle,
which is close to that of the isochoric cycle. Valorani et al. [7]
Received 30 October 2017; revision received 27 February 2018; accepted
for publication 5 March 2018; published online 10 May 2018. Copyright ©
2018 by the American Institute of Aeronautics and Astronautics, Inc. All
rights reserved. All requests for copying and permission to reprint should be
submitted to CCC at www.copyright.com; employ the ISSN 0001-1452
(print) or 1533-385X (online) to initiate your request. See also AIAA Rights
and Permissions www.aiaa.org/randp.
*Ph.D Student, Science and Technology on Scramjet Laboratory,
Changsha, Hunan Province.
†Professor, Science and Technology on Scramjet Laboratory, Changsha,
Hunan Province; zj706@vip.sina.com (Corresponding Author).
‡Associate Professor, Science and Technology on Scramjet Laboratory,
Changsha, Hunan Province.
§Lecturer, Science and Technology on Scramjet Laboratory, Changsha,
Hunan Province.
Article in Advance / 1
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presented a mathematical model to predict the overall performance of
an ODWE, and all the relevant performance parameters can be
estimated with a first guess of the geometry of the vehicle, and
substantial results were achieved. Wolański [5] retrospected the
works on the detonation propulsion and mentioned Kindracki’s
studies on the performance of the ODWE. According to the analysis
in Kindracki’s thesis, the thermodynamic efficiency of the Fickett–
Jacobs cycle is the highest, which is higher than that of the
Brayton cycle by 20% and even slightly higher than that of the
Humphrey cycle.
Because of the complexity of detonation and the difficulty in
conducting experimental studies, the ODW has not been understood
clearly. Numerous theoretical and experimental problems still need to
be solved, especially by exploring all the dynamic states of the
detonation flow, to see if there indeed is a true operational window
where the detonation would be stabilized and robust [8]. To find that
operational window, the structure, stability, and behaviors of ODWs
when they are used in an ODWE should be further investigated.
Numerous studies have demonstrated that there are two kinds of
transition structures (i.e., smooth transition and abrupt transition). In
an abrupt transition, the change from the nonreactive shock to the
ODW is achieved abruptly, and they are separated by a triple point. In
a smooth transition, the nonreactive shock transits to an ODW
smoothly, without any triple points. These two kinds of transition
structures are shown in Fig. 1.
The transition structure has been investigated in recent years.
Papalexandris [9] studied numerically the transition structure of
wedge-induced ODWs, and the results show that a smooth transition
occurs when the wedge angle is small, whereas an abrupt transition
appears when the wedge angle is large. Figueira da Silva and
Dashaies [10] investigated the initiation of the wedge-induced ODWs
in the supersonic premixed mixtures of H2and air. A time ratio ti∕tr
(where tiand trare the induction time and the total reaction time,
respectively) is introduced to estimate the transition pattern.
According to the criterion, the abrupt transition is more likely to be
obtained when ti∕tr→1, whereas the smooth transition forms when
ti∕tr→0. Wang et al. [11] investigated the existence of the
transverse wave in the transition area through a simplified theoretical
method and numerical simulations. They proposed a criterion
associated to the ratio ϕU2∕UCJ to judge or predict the transition
pattern, where U2is the flow velocity behind the ODW, and UCJ is the
Chapman–Jouguet (CJ) speed of the ODW. When ϕ<1, a transverse
shock wave is generated, and an abrupt transition appears. However,
the transverse wave does not occur in the smooth transition when
ϕ>1. Teng and Jiang [12] carried out numerical simulations on the
two kinds of transition structures, and the difference in the oblique
shock angle and detonation angle was used to predict the transition
pattern of ODWs. That is, a smooth transition occurs for a small angle
difference, whereas an abrupt transition appears for a large angle
difference. The smooth transition shifts to abrupt transition when the
angle difference is about 15–18 deg. Furthermore, Teng et al. [13]
simulated ODWs to study the induction zone structures with different
incident Mach numbers. Three kinds of shock configurations (i.e., the
λ-shaped shock, X-shaped shock, and Y-shaped shock) were
observed at the end of the induction zone, which are all considered
abrupt transitions. In the most recent research of Teng et al. [14], the
initiation features of a wedge-induced ODW were investigated via
numerical simulations, where the effects of inflow pressure and Mach
number on the initiation structure and length were studied. The
results demonstrated that the two transition patterns depend strongly
on the inflow Mach number, whereas the inflow pressure has little
effect on the transition type.
The stability of the ODWs is one of the fundamental problems in
detonation propulsion. Li et al. [15,16] investigated the structure and
stability of the ODW and found that, once stabilized on the wedge
surface, the ODWs are not sensitive to disturbances from upstream
but will be affected by the postshock Mach number. This means that
the ODW is stable when the postshock flow is supersonic, but with
the existence of the subsonic area, the ODW becomes unstable and
even detaches from the wedge surface. Later, Li et al. [17] studied the
dynamic development of oblique detonation on accelerating
projectiles in ram accelerators using time-accurate numerical
simulations. Their results showed that a small change in the projectile
shape is sufficient to alter the overall detonation structure and
significantly affect the pressure distribution on the projectile. During
the acceleration, the location of the ODW moves upstream from one
reflected shock to another. However, once the detonation is stabilized
behind the upstream shock, it remains at the new location until the
transition to the next upstream shock occurs. Lefebvre and Fujiwara
[18] conducted numerical simulations on the ODWs on the blunt
bodies, and the ODWs with different incident Mach numbers and
blunt body sizes are compared. They argued that a smooth transition
is supposed to be formed on a small blunt body, whereas an abrupt
transition appears with a large blunt body size. For an abrupt
transition, when the incident Mach number is close to CJ Mach
number, the ODW becomes unstable and even propagates upstream.
Fusina [19,20] explored the structure and stability of ODWs near the
CJ point, and the results show that these quasi-CJ detonations have
high stability and are able to recover to their original state after
disturbed. Studies of Teng et al. [21] also showed that the oblique
detonation has strong resistivity to the perturbation of the incoming
flow. Choi et al. [22] carried out a comprehensive numerical study to
investigate the unsteady cell-like structures of ODWs in an incoming
flow with a fixed Mach number 7 over a wedge, and the effects of grid
resolution and activation energy are examined. The results indicated
that the ODW front remains stable for a low activation energy,
regardless of the grid resolution, but becomes unstable for a high
activation energy featuring a cell-like wave front structure, which is
just similar to a normal detonation wave. With a continuous increase
of the activation energy, the wave front will eventually transit from a
regular to an irregular pattern. Liu et al. [23] investigated the wedge-
induced ODWs at low incident Mach numbers via a Rankine–
Hugoniot analysis and numerical simulations. Their results showed
that the strengthening influence of the CJ detonation wave can lead to
an upstream propagation of the ODW, and during this process, a
Mach reflection wave configuration is always established on the
wedge surface. The upstream propagating ODW will be stabilized on
the wedge surface, with a short induction zone and extraordinary
stability. Lu et al. [24] reported a numerical study on the detonation in
a wedge channel, and the detonation waves were investigated with
a) Smooth transition b) Abrupt transition
Fig. 1 Schematic of ODWs with different structures.
2Article in Advance / MIAO ET AL.
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respect to two parameters (i.e., the incoming Mach number and
wedge angle). The results showed that subsonic pockets appearing
after some shock reflections might cause instability of the wave
system, thereby causing the wave to propagate upstream.
In fact, the stability and the structure of ODWs have often been
investigated separately in previous literature, and the emphasis has
always been placed on the condition when different transition patterns
occur. However, the differences between ODWs with different transition
patterns and the type of structure that is preferable in an ODWE have
been rarely researched, which help find an operational window.
In the present study, two-dimensional numerical simulations are
carried out based on a sophisticated code, AMROC (from “Adaptive
Mesh Refinement in Object-Oriented C++”)[25–30], which improves
the calculation efficiency with a high grid resolution. In recent years,
AMROC has been validated in multidimensional detonation
simulations [31–38]. First, the numerical method is introduced and
validated in Secs. II and III. Then, the stability of ODWs with different
transition patterns is studied through numerical simulations in Sec. IV.
A. In Sec. IV.B, the thermodynamic efficiency of oblique detonation
cycles is analyzed based on ideal thermodynamic cycles. Finally, the
optimum working condition of the ODWE is derived.
II. Numerical Method
Figure 2 shows a schematic of the simulations presented in this
work. The height and length of the channel are Y11 cm and
X6cm, respectively, and the wedge starts from Xw0.5 cm.The
slip reflecting boundary condition is used on the wedge surface and the
wall surface. The left boundary models the supersonic inflow
condition, and other boundaries are interpolated under the assumption
of zero first-order derivatives of all flow parameters. To mimic a
realistic working condition, high-enthalpy incoming supersonic
combustible mixtures are selected, which are hydrogen/air premixed
mixtures with a molecular proportion of H2:O2:N22×ER:1:
3.76, where ER is the equivalence ratio. To make a comparison and
validation, a representative inflow condition in [39] (i.e., T1872 K,
P163 kPa) is selected. The presence of a wedge in the supersonic
inflow induces an oblique shock first, and shock-induced combustion
occurs, resulting in the initiation of the ODW. Actually, previous
results [14,40] show that the inlet temperature and pressure havesmall
effects on the transition type of an ODW. Therefore, the inflow
temperature and pressure are kept unchanged in the present study, and
the numerical simulations are carried out with different equivalence
ratios, inflow velocities, and wedge angles.
Previous research [10,41,42] demonstrated that viscosity has
negligible effects on the ODW structure, and thus the numerical
simulations are based on reactive Euler equations. A detailed reaction
model with nine species and 19 steps is used. The stiff problem owing
to chemical reaction calculation is solved using the Godunov splitting
method. A second-order monotonic upwind scheme for conservation
laws (MUSCL)–total variation diminishing finite volume method is
adopted for convection flux discretization. To avoid a nonphysical
solution, a hybrid Roe–Harten-Lax-Van Leer Riemann solver is used,
and the van Albada limiter with MUSCL reconstruction is applied to
construct the second-order method in space. The MUSCL–Hancock
technique is used to match the requirement of the second-order
accurate time integration using the dynamically adaptive time step
with a target Courant–Friedrichs–Lewy number of 0.9.
III. Validation of Numerical Method
To establish a proper refinement strategy and mesh adaptation flag
parameters, the numerical method is validated in this section. An
inflow of P163 kPa,T1872 K,U11690 m∕s, and ER
0.25 is chosen, and the wedge angle is θ22 deg. The scaled
gradients for density, temperature, and pressure are set to be ερ0.1,
εT500, and εp4×105, respectively. The initial grid resolution
is 0.2 mm, and the refinement strategies are three-, four-, and five-
level, respectively. Refinement factors of r12,r22,r32, and
r42are used. The refinement factor rlis the ratio between the
spatial steps Δxland Δxl−1of levels land l−1, respectively (i.e.,
rlΔxl−1∕Δxl). The highest resolutions for the three refinement
strategies are Δxmin 0.05 mm,Δxmin 0.025 mm, and Δxmin
0.0125 mm, respectively. The stable ODWs with the three different
grid resolutions are shown in Fig. 3.
As shown in Fig. 3, the ODWs are initiated successfully, and an
extraordinary similarity is shown in the overall structure, which is
qualitatively consistent with previous studies [11,12,21,43]. The
wave angles of the ODWs are in good agreement, which are 51, 50.4,
and 50.3 deg, respectively. Thus, the mesh adaptation flag parameters
are effective. The pressure profiles along with a line parallel to the
wedge surface at a distance of 4 mm are illustrated in Fig. 4.
As observed in Fig. 4, the oblique shock wave and the primary
transverse wave of the ODW at Δxmin 0.025 mm are in good
agreement with those at Δxmin 0.0125 mm. However, there is a
small difference in the position of the waves at Δxmin 0.05 mm.
Additionally, when observed in detail, two other differences are
observed at Δxmin 0.05 mm.
1) The vortex along with the slip line at Δxmin 0.05 mm is not
well captured compared with the other two.
2) The induction length of the ODW at Δxmin 0.05 mm is
approximately 1 mm, whereas it is approximately 2 mm at Δxmin
0.025 mm and Δxmin 0.0125 mm, which is consistent with the
theoretical value (i.e., 1.984 mm).
Therefore, it can be concluded that the major structures are well
resolved with the four- and five-level mesh adaptation. To save
calculation resources, the four-level refinement strategy with the
refinement factors r12,r22, and r32is eventually selected
for the numerical simulations, which guarantees the reliability of our
conclusions.
IV. Result and Analysis
A. Stability of Oblique Detonation Waves with Different Transition
Patterns
The performance of an ODWE depends on the stability of the
ODWs. In the present study, in a similar way to previous studies
[20,23,44–46], a disturbance is added to the stable flowfield to study
the stability of the ODW. When the ODW is stabilized on the wedge, a
disturbance of Td2000 K,Ud0m∕s, and D3mm(Td,Ud,
and Dare the temperature, velocity, and diameter of the disturbance
area, respectively) is inserted at the position of Xd2cm,
Yd3cm, which is removed 30 μslater. The species and density of
the disturbance area are the same as those in the incoming flow. The
inflow velocity is U11690 m∕s, and the equivalence ratio is
Outflow
Outflow
Supersonic
Inflow
Wedge
Wall
x
y
State 1
ODW
State 2
Fig. 2 Schematic of the calculation model.
Article in Advance / MIAO ET AL. 3
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ER 0.25. A stable ODW with an abrupt transition structure is
formed, which is shown in Fig. 5a. The primary triple point A is the
intersection point of the induced shock wave, the ODW, and the
primary transverse wave, which is also the position where the ODW
starts. The primary transverse wave reflects on the wedge surface, and
the reflected shock wave passes across the slip line, resulting in the
interaction between the reflected wave and the ODW, where a new
triple point B is formed. Actually, the formation of triple point B
increases the strength and stability of the ODW [11]. The high-
temperature disturbance is added to the flowfield at a time of 500 μs,
and the evolution of the ODW is shown in Fig. 5.
As shown in Fig. 5, after the disturbance is inserted, the supersonic
combustible mixture is ignited, and the disturbing shocks interact
with the ODW. At the time of 535.77 μs, the triple point and
transverse wave are destroyed, and a local decoupling of the ODW
occurs. The decoupling area reaches its maximum at a time of
551.76 μs. Soon afterward, as the disturbed area propagates
downstream, the decoupling area becomes smaller, and it is finally
replaced by the reinitiation of a local detonation with two new triple
points at the time of 573.56 μs. However, the newly formed triple
points are weak, and they propagate downstream and gradually fade
away. At the time of 757.11 μs, the ODW surface becomes smooth,
Fig. 3 Flowfield structures with different refinement strategies.
4Article in Advance / MIAO ET AL.
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as shown in Fig. 5f, and maintains the same state for a period. It is
shown that the structure of the ODW changes significantly, where the
primary transverse wave reflects back and forth between the slip line
and the wedge surface instead of passing across the slip line. Actually,
this kind of structure is similar to the situation of 0.8 <ϕ<0.9 in
[11], which is considered to be a critical detonation. Then, at the time
of 904.90 μs, a new triple point C is formed just above the primary
triple point A, and the flowfield gradually becomes stable and
recovers the initial state.
According to the simulation results, a parameter trc (the recovering
time) is defined as trc ts−td, where tsis the time when the
ODW becomes stable again after the disturbance is removed. In this
Paper, tsis determined by comparison between pressure profiles of
the ODW flowfield at a different time. tdis the time when the
disturbance is added to the flowfield. Based on this definition, the
recovering time for the case in Fig. 5 is trc 773.55 μs.
When the inflow velocity is increased to 1900 m∕s, while the other
parameters are kept unchanged, an ODW with a smooth transition is
formed, as shown in Fig. 6a. The same disturbance as before is added
into the flowfield at the time of 200 μs, and the evolution of the ODW
is shown in Fig. 6.
It is shown that, after the disturbance is inserted, the disturbing
shock waves intersect with the ODW surface, leading to the
formation of the triple point D. With the occurrence of the triple point,
the transition structure shifts to an abrupt one, as shown in Figs. 6d
and 6e. However, this abrupt transition is not stable, and as the triple
point and the transverse wave weaken and disappear, the ODW
recovers the initial state and becomes stable again at the time of
384.19 μs. That means trc 184.19 μs.
It is suggested that, when disturbed, the stabilized ODWs, with both
abrupt or smooth transitions, can recover to their initial state. However,
the ODW with a smooth transition requires less time than the abrupt
one. Actually, the structure of the abrupt transition is more complicated
than the smooth one. When the ODW is disturbed, a reconstruction of
the triple points and transverse waves is required for the restabilization
of the ODW, which takes much more time. Comparatively, the ODW
with a smooth transition has a simple wave structure and is easy for it to
recoverthe initial state.Therefore, the ODWwith a smooth transitionis
more stable. Besides, the flowfield behind the ODW with a smooth
transition is entirely supersonic, whereas the ODW with an abrupt
transition is partially subsonic, especially the area near with the triple
points and transverse waves. Actually, Li et al. [16] mentioned that,
when the flowfield is partially subsonic, the ODW may become
unstable, even detaching from the wedge and moving upstream, which
is consistent with the present simulation results.
Recent studies [47] have concluded that the transition structure
depends on the pressure ratio Pdet∕Psh , where Pdet and Psh are the
pressure behind the ODWand the pressure behind the induced shock
wave, respectively. When the pressure ratio is large, a transverse wave
forms in the transition, leading to an abrupt transition. When the
pressure ratio is small, a series of compressional waves occur, leading
to a smooth transition. Through numerical simulation and theoretical
analysis, a critical pressure ratio of 1.3 was obtained for the shift
between the abrupt and smooth transition.
Additional simulations are conducted under different inflow
velocities, equivalence ratios, and wedge angles, and ODWs with
different transition patterns are observed. The same disturbances are
added to the flowfields, and the results showed that the ODWs with a
smooth or an abrupt transition could all recover the initial state after
being disturbed. However, there are significant differences in
recovering time, which is closely related to the transition structure of
the ODWs. The recovering time of ODWs and the pressure ratios are
shown in Fig. 7.
As shown in Fig. 7, the ODWs with a smooth transition are more
stable and resistant to the disturbance, requiring less time to recover
the initial state after disturbed. For the ODW with a smooth transition,
the recovering time changes in a small range. However, for the ODW
with an abrupt transition, the recovering time increases substantially
with the increase of pressure ratio.
Therefore, in view of the stability of the ODW, the smooth
transition is preferable in an ODWE. Actually, a higher level of
overdrive is needed to suppress the instability of the ODW [48] and
obtain a smooth transition, which will inevitably reduce the
thermodynamic efficiency of the ODWE. How the thermodynamic
efficiency changes for different transition structures and how to
determine the operational window will be analyzed.
B. Analysis on Thermodynamic Efficiency of Oblique
Detonation Waves
1. Loss of Thermodynamic Efficiency
Theoretically, the CJ detonation cycle has the highest
thermodynamic efficiency. However, in an ODWE, a successfully
initiated and stabilized ODW is usually overdriven. In particular, to
inhibit the instability of the ODW, the overdrive factor needs to reach
over 1.77 [48]. Under the circumstances, the entropy of the detonation
cycle is increased, leading to the loss of thermodynamic efficiency.
Therefore, for an ODWE, considering its thermodynamic efficiency
under the CJ condition is not enough; it is necessary to conduct an
analysis on the thermodynamic cycles of the overdriven ODWs.
The atmospheric pressure and temperature at an altitude of 27 km
are chosen to be the initial state of theoretical analysis. In all cases, the
fuel–air mixture is initially compressed adiabatically from P0
1.88 kPa to P163 kPa before chemical reaction. Then, chemical
reaction occurs through a CJ detonation and an overdriven oblique
detonation, respectively. After the chemical reaction, the products of
combustion are expanded adiabatically to P163 kPa. Finally, the
system is returned to its initial state. The work done during the two
cycles is obtained from the enclosed area in Fig. 8. The wedge angle
to initiate the ODW is θ22 deg, and the inflow velocity is
U12400 m∕s. The thermodynamic cycles are shown in Fig. 8.
Because all processes, except for the detonation combustion, have
been maintained, the work done or relative thermodynamic efficiency
of the two combustion processes can be obtained by comparing the
two areas. For determining the efficiency, the work output is divided
by heat release. The calculation results show that the cycle efficiency
of the CJ detonation is 39%, whereas that of the ODW is 35%. This
means that a noteworthy efficiency loss is observed in the ODW
thermodynamic cycle. As shown in Fig. 8, the adiabatic expansion
line is tangent with the Rayleigh line for a CJ detonation cycle.
During the detonation combustion, the system is compressed from
state 1 to state 2, and the work is negative. Then, the system does
positive work during the adiabatic expansion from state 2 to state 3.
However, for an ODW cycle, at the beginning of the adiabatic
expansion, the adiabatic line is below the Rayleigh line, which means
that the work is still negative. That is why there is an efficiency loss,
and the size of area A is the amount of the efficiency loss.
Hereinafter, the efficiency loss is defined to measure the difference
in cycle efficiency between the overdriven ODWs and the CJ
detonations, which is expressed as
Δ
x
min
=0.0125 mm
Δ
x
min
=0.025 mm
Δ
x
min
=0.05 mm
P (kPa)
Primary
transverse
wave
Deflagration
Oblique shock
600
500
400
300
200
100
0
0.0 1.0 2.0 3.0
X (cm)
4.0 5.0 6.0
Fig. 4 Pressure profiles of the flowfields with different grid resolutions.
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Fig. 5 Evolution of the ODW affected by the upstream disturbance.
6Article in Advance / MIAO ET AL.
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δode ηCJ −ηode
ηCJ
(1)
where ηCJ and ηode are the thermodynamic efficiency of the CJ
detonation cycle and the ODW cycle, respectively. The efficiency loss
of the ODWE under different working conditions is now analyzed.
2. Effects of Initial Compression
Previous research [4] has mentioned that the amount of initial
compression changes the cycle efficiency. There are some changes in
relative values, but in all of these cases, the efficiency of the
detonation process is close to that of the constant-volume process and
significantly better than that of the constant-pressure process. It is
concluded that, for an ODWE, the amount of initial compression
affects the efficiency loss apparently. Generally, the efficiency loss
decreases remarkably with the increase in initial compression.
Particularly, when the compression is larger than 30, the efficiency
loss becomes small and changes slightly. Therefore, a large initial
compression is preferable in ODWE applications because it generates
a higher cycle efficiency. However, in the present Paper, the emphasis
is placed on the relation between transition structure and efficiency
loss; thus, further analysis on the initial compression is not presented
here, and the amount of initial compression is kept unchanged in the
present Paper.
Generally, the transition structure of ODWs with a certain
supersonic combustible mixture is decided by the equivalence ratio,
inflow velocity, and wedge angle. In the following section, the
emphases are placed on the effects of these factors on the
thermodynamic efficiency.
Fig. 6 Evolution of the ODW affected by the upstream disturbance.
Article in Advance / MIAO ET AL. 7
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3. Effects of Inflow Condition
In an ODWE, the inflow condition plays a vital role in cycle
efficiency. Hereinafter, the parameters of state 0 and the pressure
and temperature of state 1 are kept unchanged, with an initial
compression of 33.5, and the efficiency losses under different
equivalence ratios, inflow velocities, and wedge angles are analyzed.
The efficiency losses versus equivalence ratios with different inflow
velocities are shown in Fig. 9.
It is indicated that the thermodynamic efficiency changes
significantly under different inflow conditions, which remarkably
affects the performance of the ODWE. For a given inflow velocity,
the increase in equivalence ratio raises the heat release of the
detonation combustion, and the ability for work is also enhanced,
which reduces the efficiency loss. However, with the increase in
equivalence ratio, the detachment angle of the ODW is reduced.
When the wedge angle is close to the detachment angle, a slight
increase in efficiency loss occurs. This is because when the ODW is
close to the detachment state, the strength of the shock is weak and the
detonation wave surface is lifted, leading to a lateral expansion,
which generates an additional efficiency loss. Meanwhile, the ODWs
close to the detachment state are always unstable and are likely to
propagate upstream, which is supposed to be avoided. The
comparison between cases of different inflow velocities indicates that
the increase in inflow velocity results in a large efficiency loss but
provides a wider range for the ODWs to be stabilized on the wedge
surface. Under this condition, an increase in equivalence ratio can
reduce the efficiency loss. Therefore, the ODWE is more applicable
to hypersonic propulsion, where the ODW tends to be stable in a large
range of equivalence ratios.
To perform a further study on the influence of the inflow velocity
on the efficiency loss, a case of P163 kPa,T1872 K,
θ22 deg, and ER 0.25 is simulated with different inflow
velocities, and the efficiency losses versus the inflow velocities are
shown in Fig. 10.
It is revealed that, under the given condition, the efficiency loss
decreases before U11800 m∕sand gradually increases after that
position. That is to say, a minimum efficiency loss is achieved near
the position of U11800 m∕s. The reasons are as follows; when the
flowfield reaches the equilibrium state, the heat release rate is fixed
under a given equivalence ratio, and the influence of inflow velocity
can be explained through the shock relation. The total pressure ratio
for a shock wave can be calculated by Eq. (2):
P
2
P
1
1
2γ
γ1M2
1sin2β−γ−1
γ11∕γ−12
γ1
1
M2
1sin2βγ−1
γ1γ∕γ−1(2)
where P
1and P
2are the total pressure before and behind the shock
wave, γis the specific heat ratio, M1is the inflow Mach number, and β
is the angle of the shock wave. It is inferred from Eq. (2) that the loss
of total pressure is related to the normal Mach number (i.e., M1sin β).
For a given temperature, an increase in inflow velocity means an
increase in the inflow Mach number, which generates a decrease in
the wave angle β. With regard to the weak shock, when the flow
deflection angle approaches the detachment angle, the wave angle β
drops fast with the increase in the inflow Mach number, leading to the
decrease of M1sin β. Therefore, the total pressure ratio increases,
which results in a smaller efficiency loss. However, this phenomenon
just happens in a small range, and a further increase in the inflow
Mach number will lead to the increase of M1sin β, and then the total
pressure ratio will drop, generating a larger efficiency loss. As a
result, although the increase in inflow velocity broadens the range of
stabilization and increases the stability of ODWs, the consequent
efficiency loss should not be neglected in ODWE applications.
The ODW is initiated by a wedge in the ODWE, where the wedge
angle plays an important role in the initiation and the thermodynamic
efficiency of the ODW. A case under the condition of P163 kPa,
T1872 K,ER 0.25, and U11870 m∕sis chosen to explore
the relation between efficiency loss and wedge angle. The efficiency
losses versus equivalence ratios with different wedge angles are
shown in Fig. 11, and the relation between efficiency loss and wedge
angle is shown in Fig. 12.
Pdet /Psh
Recovering time (
μ
s)
1.1 1.15 1.2 1.25 1.3 1.35 1.4 1.45 1.5
0
200
400
600
800
Abrupt transition
Smooth transtion
Fig. 7 Recovering time and pressure ratios for different transition
patterns.
Fig. 8 Ideal thermodynamic cycles of a CJ detonation and an
overdriven ODW.
ER
δ
ode
0 0.2 0.4 0.6 0.8 1
0
0.05
0.1
0.15
0.2
0.25
1690 m/s
1800 m/s
2000 m/s
2175 m/s
2300 m/s
2400 m/s
Fig. 9 Efficiency losses vs equivalence ratios with different inflow
velocities, T1872 K,P163 kPa,θ22 deg.
U
1
(m/s)
1600 1800 2000 2200 26002400
0.04
0.06
0.08
0.1
0.12
δ
ode
Fig. 10 Diagram of efficiency losses vs inflow velocities.
8Article in Advance / MIAO ET AL.
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It is observed from the two figures that the efficiency loss is
affected by the wedge angle, and this loss increases remarkably with
the increase in wedge angle. The effects of wedge angle on the
efficiency loss mainly come from the blocking effects of the wedge.
When the wedge angle increases, the blocking area increases, leading
to a larger loss of total pressure; thus, the efficiency loss increases.
Besides, the same phenomenon showed in Fig. 9 is also observed in
Fig. 11, that is, when the wedge angle approaches the detachment
angle, the efficiency loss increases slightly. The reason is also the
same as in Fig. 9.
As a result, in view of the stability and the thermodynamic
efficiency, a qualitative understanding on the selection of the working
condition of the ODWE has been achieved. First, the wedge angle is
the crucial factor in the thermodynamic efficiency of an ODWE. A
small wedge angle is preferable on the premise of the initiation and
stabilization of the ODWs, and it determines the maximum
thermodynamic efficiency of the ODWE. Second, the increase of the
inflow velocity leads to a larger efficiency loss, but it increases the
stabilizing range of the ODWs. Under this condition, a large
equivalence ratio generates a higher thermodynamic efficiency.
Besides, a state near the detachment condition usually results in a
slightly higher efficiency loss along with a weak stability, which
should be avoided in ODWEs.
However, in the real engine, whether a strong stability and a high
thermodynamic efficiency can be achieved concurrently remains to
be answered, which is analyzed in the following section.
C. Optimum Working Condition Analysis
As mentioned previously, the transition pattern is actually
dependent on the pressure ratio Pdet∕Psh . With the increase in
pressure ratio, the transition pattern changes from a smooth one to an
abrupt one. Based on this, the efficiency losses and the pressure ratios
are calculated, and they are listed in Fig. 13.
As shown in Fig. 13, the statistics are divided into six areas, among
which areas 3 and 6 are not worthy of consideration because no data
points exist. In area 1, the pressure ratios are small, which means that
the transition structures are smooth. The ODWs in this area are of
stronger stability, but the efficiency losses are also prominent. In
area 4, the efficiency losses are lower, and they are even close to the
efficiency of CJ detonations. However, the pressure ratios of the
ODWs in this area are all larger than 1.5; that is to say, the transition is
overwhelmingly abrupt. Under this condition, the stability and
resistivity of the ODWs are comparatively weak. When disturbed, it
takes much more time for the ODWs to recover the stable state.
Besides, the wave angles are close to the detachment angle, indicating
that the ODWs are likely to propagate upstream under this condition.
Thus, the ODWs in area 4 are also disadvantageous for ODWE
applications. With regard to areas 2 and 5, the pressure ratios are in
the range of 1.2–1.5, which is located in the shift area between
smooth and abrupt transition. The efficiency losses of ODWs in area
2 are relatively higher just because the wedge angles for these ODWs
are large. However, for ODWs in area 5, the stability is stronger, and
the efficiency losses are relatively lower. Therefore, an ODW located
in the shift area between smooth transition and abrupt transition with
a proper wedge angle (i.e., an ODW in area 5) is better for ODWE
applications.
According to recent studies [47], the velocity ratio ΦU1∕UCJ is
used to find the shift area. There is a critical velocity ratio Φfor a
given wedge angle θ, which can be calculated with an empirical
formula (i.e., Φ0.0012θ2−0.0579θ2.072). When Φ<Φ,
an abrupt transition appears, and when Φ>Φ, a smooth transition
occurs. Therefore, the velocity ratio Φshould be kept in a range near
the critical value Φwith a proper limit error.
V. Conclusions
The stability and thermodynamic efficiency of oblique detonation
waves (ODWs) with different transition patterns (i.e., smooth
transition and abrupt transition) are studied systematically, and the
optimum working condition of the oblique detonation wave engine
(ODWE) is summarized based on the results. According to numerical
simulations based on AMROC, when a high-temperature disturbance
is added into the flowfields of stable ODWs, there are large
differences in the stability and resistivity of the ODWs. Specifically,
an ODW with a smooth transition has stronger stability, requiring less
time to recover to the stable state, whereas the ODW with an abrupt
transition needs much more time to reconstruct the wave structure for
the restabilization of the flowfield. In addition, the thermodynamic
efficiency of the ODWs under different inflow conditions is analyzed
through a theoretical method, and the results indicate that the initial
compression, inflow condition, and wedge angle influence the cycle
efficiency remarkably. The increase in inflow velocity leads to a
larger efficiency loss but provides a wider range of equivalence ratios
for ODWs to be stabilized. In contrast, the increase in the equivalence
ratio leads to a higher heat release rate and thus results in lower
wedge angle/(deg)
15 20 25 30
0
0.05
0.1
0.15
δ
ode
Fig. 12 Relation between efficiency loss and wedge angle.
ER
0 0.1 0.2 0.3 0.4 0.5 0.6
0
0.05
0.1
0.15
18 deg
19 deg
20 deg
21 deg
δ
ode
Fig. 11 Efficiency losses vs equivalence ratios under different wedge
angles.
Pdet /Psh
1 1.2 1.4 1.6 1.8
0
0.1
0.2
0.3
Abrupt transition
Smooth transition
4
3
5
6
2
1
δ
ode
Fig. 13 Statistical results of thermodynamic efficiency and pressure
ratio.
Article in Advance / MIAO ET AL. 9
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efficiency loss. The optimum working condition analysis is
conducted according to the stability and thermodynamic efficiency of
the ODWs. The results are divided into six areas, among which area 5
is preferable for ODWEs. In other words, the ODWs located in the
shift area between the smooth and abrupt transition are stable and
resistant and, therefore, are better for ODWE applications. Finally,
according to [47], the shift area can be calculated with an empirical
formula, which is expressed as Φ0.0012θ2−0.0579θ2.072.
Acknowledgment
This work is supported by National Natural Science Foundation of
China (numbers 91441101 and 51476186).
References
[1] Pratt, D. T., Humphrey, J. W., and Glenn, D. E., “Morphology of
Standing Oblique Detonation Waves,”Journal of Propulsion and
Power, Vol. 7, No. 5, 1991, pp. 837–845.
doi:10.2514/3.23399
[2] Powers, J. M., and Stewart, D. S., “Approximate Solutions for Oblique
Detonations in the Hypersonic Limit,”AIAA Journal, Vol. 30, No. 3,
1992, pp. 726–736.
doi:10.2514/3.10978
[3] Ashford, S. A., and Emanuel, G., “Oblique Detonation Wave Engine
Performance Prediction,”Journal of Propulsion and Power, Vol. 12,
No. 2, 1996, pp. 322–327.
doi:10.2514/3.24031
[4] Kailasanath, K., “Review of Propulsion Applications of Detonation
Waves,”AIAA Journal, Vol. 38, No. 9, 2000, pp. 1698–1708.
doi:10.2514/2.1156
[5] Wolański, P., “Detonative Propulsion,”Proceedings of the Combustion
Institute, Vol. 34, No. 1, 2013, pp. 125–158.
doi:10.1016/j.proci.2012.10.005
[6] Avrashkov, V., Baramovsky,S., and Levin, V., “Gasdynamic Features of
Supersonic Kerosene Combustion in a Model Combustion Chamber,”
2nd International Aerospace Planes Conference, AIAA Tech.
Paper 1990-5268, 1990.
doi:10.2514/6.1990-5268
[7] Valorani, M., Digiacinto, M., and Buongiorno, C., “Performance
Prediction for Oblique Detonation Wave Engine (ODWE),”Acta
Astronautica, Vol. 48, No. 4, 2001, pp. 211–228.
doi:10.1016/S0094-5765(00)00161-2
[8] Stewart, D. S., and Kasimov, A. R., “State of Detonation Stability
Theory and Its Application to Propulsion,”Journal of Propulsion and
Power, Vol. 22, No. 6, 2006, pp. 1230–1244.
doi:10.2514/1.21586
[9] Papalexandris, M. V., “A Numerical Study of Wedge-Induced
Detonations,”Combustion and Flame, Vol. 120, No. 4, 2000,
pp. 526–538.
doi:10.1016/S0010-2180(99)00113-3
[10] Figueira da Silva, L. F., and Dashaies, B., “Stabilization of an Oblique
Detonation Wave by a Wedge: A Parametric Numerical Study,”
Combustion and Flame, Vol. 121, Nos. 1–2, 2000, pp. 152–166.
doi:10.1016/S0010-2180(99)00141-8
[11] Wang, A. F., Zhao, W., and Jiang, Z. L., “The Criterion of the Existence
or Inexistence of Transverse Shock Wave at Wedge Supported Oblique
Detonation Wave,”Acta Mechanica Sinica, Vol. 27, No. 5, 2011,
pp. 611–619.
doi:10.1007/s10409-011-0463-7
[12] Teng, H. H., and Jiang, Z. L., “On the Transition Pattern of the Oblique
Detonation Structure,”Journal of Fluid Mechanics, Vol. 713, No. 6,
2012, pp. 659–669.
doi:10.1017/jfm.2012.478
[13] Teng, H. H., Zhang, Y. N., and Jiang, Z. L., “Numerical Investigation on
the Induction Zone Structure of the Oblique Detonation Waves,”
Computers and Fluids, Vol. 95, No. 3, 2014, pp. 127–131.
doi:10.1016/j.compfluid.2014.03.001
[14] Teng, H. H., Ng, H. D., and Jiang, Z. L., “Initiation Characteristics of
Wedge-Induced Oblique Detonation Waves in a Stoichiometric
Hydrogen–Air Mixture,”Proceedings of the Combustion Institute,
Vol. 36, No. 2, 2017, pp. 2735–2742.
doi:10.1016/j.proci.2016.09.025
[15] Li, C., Kailasanath, K., and Oran, E. S., “Stability of Oblique
Detonations in Ram Accelerators,”30th AIAA Aerospace Sciences
Meeting and Exhibit, AIAA Paper 1992-0089, 1992.
doi:10.2514/6.1992-89
[16] Li, C., Kailasanath, K., and Oran, E. S., “Detonation Structures
Behind Oblique Shocks,”Physics of Fluids, Vol. 6, No. 4, 1994,
pp. 1600–1611.
doi:10.1063/1.868273
[17] Li, C., Kailasanath, K., Oran, E. S., Landsberg, A. M., and Boris, J. P.,
“Dynamics of Oblique Detonations in Ram Accelerators,”Shock Waves,
Vol. 5, Nos. 1–2, 1994, pp. 97–101.
doi:10.1007/BF02425040
[18] Lefebvre, M. H., and Fujiwara, T., “Numerical Modeling of Combustion
Processes Induced by a Supersonic Conical Blunt Body,”Combustion
and Flame, Vol. 100, No. 1, 1995, pp. 85–93.
doi:10.1016/0010-2180(94)00044-S
[19] Fusina, G., Sislian, J. P., and Parent, B., “Formation and Stability of Near
Chapman–Jouguet Standing Oblique Detonation Waves,”AIAA
Journal, Vol. 43, No. 7, 2005, pp. 1591–1604.
doi:10.2514/1.9128
[20] Fusina, G., Sislian, J. P., and Parent, B., “Computational Study of
Formation and Stability of Standing Oblique Detonation Waves,”42nd
AIAA Aerospace Sciences Meeting and Exhibit, AIAA Paper 2004-
1125, Jan. 2004.
doi:10.2514/6.2004-1125
[21] Teng, H. H., Zhao, W., and Jiang, Z. L., “A Novel Oblique Detonation
Structure and Its Stability,”Chinese Physics Letters, Vol. 24, No. 7,
2007, pp. 1985–1988.
doi:10.1088/0256-307X/24/7/055
[22] Choi, J. Y., Kim, D. W., Jeung, I. S., Ma, F., and Yang, V., “Cell-Like
Structure of Unstable Oblique Detonation Wave from High-Resolution
Numerical Simulation,”Proceedings of the Combustion Institute,
Vol. 31, No. 2, 2007, pp. 2473–2480.
doi:10.1016/j.proci.2006.07.173
[23] Liu, Y., Wu, D., Yao, S. B., and Wang, J. P., “Analytical and Numerical
Investigations of Wedge-Induced Oblique Detonation Waves at Low
Inflow Mach Number,”Combustion Science and Technology, Vol. 187,
No. 6, 2015, pp. 843–856.
doi:10.1080/00102202.2014.978865
[24] Lu, F. K., Fan, H., and Wilson, D. R., “Detonation Waves Induced by a
Confined Wedge,”Aerospace Science and Technology, Vol. 10, No. 8,
2006, pp. 679–685.
doi:10.1016/j.ast.2006.06.005
[25] Deiterding, R., “Parallel Adaptive Simulation of Multi-Dimensional
Detonation Structures,”Ph.D. Dissertation, Brandenburg Univ. of
Technology Cottbus, Cottbus, Germany, 2003.
[26] Deiterding, R., “Detonation Structure Simulation with AMROC,”
International Conference on High Performance Computing and
Communications, Vol. 3726, edited by L. T. Yang, Springer, Berlin,
2005, pp. 916–927.
doi:10.1007/11557654_103
[27] Deiterding, R., “A High-Resolution Method for Realistic Detonation
Structure Simulation,”Proceedings of the 10th International Conference
Hyperbolic Problems, edited by W. Takahashi, and T. Tanaka, Vol. 1,
Yokohama Publishers,Yokohama, Japan, 2006, pp. 343–350.
[28] Deiterding,R., “AParallel A daptiveMethod for S imulating Shock-Induced
Combustion with Detailed Chemical Kinetics in Complex Domains,”
Computer & Structures, Vol. 87, Nos. 11–12, 2009, pp. 769–783.
doi:10.1016/j.compstruc.2008.11.007
[29] Deiterding, R., “Parallel Adaptive Simulation of Weak and Strong
Detonation Transverse-Wave Detonation Structures in H2-O2
Detonations,”Parallel Computational Fluid Dynamics: Recent
Advances and Future Directions, DEStech Publ., Lancaster, 2010,
pp. 519–534.
[30] Deiterding, R., “High-Resolution Numerical Simulation and Analysis
of Mach Reflection Structures in Detonation Waves in Low-Pressure
H2-O2-Ar Mixtures: A Summary of Results Obtained with the Adaptive
Mesh Refinement Framework AMROC,”Journal of Combustion,
Vol. 2011, May 2011, pp. 1–18.
doi:10.1155/2011/738969
[31] Cai, X. D., Liang, J. H., Lin, Z. Y., Deiterding, R., and Liu, Y.,
“Parametric Study of Detonation Initiation Using a Hot Jet in Supersonic
Combustible Mixtures,”Aerospace Science and Technology, Vol. 39,
Dec. 2014, pp. 442–455.
doi:10.1016/j.ast.2014.05.008
[32] Cai, X. D., Liang, J. H., Lin, Z. Y., Deiterding, R., Qin, H., and Han, X.,
“Adaptive Mesh Refinement-Based Numerical Simulation of
Detonation Initiation in Supersonic Combustible Mixtures Using a
Hot Jet,”Journal of Aerospace Engineering, Vol. 28, No. 1, 2013, Paper
04014046.
doi:10.1061/(ASCE)AS.1943-5525.0000376
[33] Liang, J. H., Cai, X. D., Lin, Z. Y., and Deiterding, R., “Effects of a Hot
Jet on Detonation Initiation and Propagation in Supersonic Combustible
10 Article in Advance / MIAO ET AL.
Downloaded by UNIVERSITY OF SYDNEY on May 18, 2018 | http://arc.aiaa.org | DOI: 10.2514/1.J056887
Mixtures,”Acta Astronautica, Vol. 105, No. 1, 2014, pp. 265–277.
doi:10.1016/j.actaastro.2014.08.019
[34] Cai, X. D., Liang, J. H., Lin, Z. Y., Deiterding, R., and Zhuang, F. C.,
“Detonation Initiation and Propagation in Nonuniform Supersonic
Combustible Mixtures,”Combustion Science and Technology, Vol. 187,
No. 4, 2015, pp. 525–536.
doi:10.1080/00102202.2014.958223
[35] Cai, X. D., Deiterding, R., Liang, J. H., and Mahmoudi, Y., “Adaptive
Simulations of Viscous Detonations Initiated by a Hot Jet Using a High-
Order Hybrid WENO–CD Scheme,”Proceedings of the Combustion
Institute, Vol. 36, No. 2, 2017, pp. 2725–2733.
doi:10.1016/j.proci.2016.06.161
[36] Cai, X. D., Liang, J. H., Deiterding, R., Che, Y. G., and Lin, Z. Y.,
“Adaptive Mesh Refinement Based Simulations of Three-Dimensional
Detonation Combustion in Supersonic Combustible Mixtures with a
Detailed Reaction Model,”International Journal of Hydrogen Energy,
Vol. 41, No. 4, 2016, pp. 3222–3239.
doi:10.1016/j.ijhydene.2015.11.093
[37] Cai, X. D., Liang, J. H., Deiterding, R., and Lin, Z. Y., “Adaptive
Simulations of Cavity-Based Detonation in Supersonic Hydro-
geneoxygen Mixture,”International Journal of Hydrogen Energy,
Vol. 41, No. 16, 2016, pp. 6917–6928.
doi:10.1016/j.ijhydene.2016.02.144
[38] Cai, X. D., Liang, J. H., Deiterding, R., and Lin, Z. Y., “Detonation
Simulations in Supersonic Combustible Mixtures with Nonuniform
Species,”AIAA Journal, Vol. 54, No. 8, 2016, pp. 2449–2462.
doi:10.2514/1.J054653
[39] Han, X., “Research on Detonation Initiation and Propagation
Mechanisms in Supersonic Premixed Flows,”Ph.D. Dissertation,
National Univ. of Defense Technology, Changsha, PRC, 2013.
[40] Lin, Z. Y., “Research on Detonation Initiation and Development
Mechanisms in Elevated Temperature Supersonic Premixed Mixture,”
Ph.D., National Univ. of Defense Technology, Changsha, PRC, 2008.
[41] Li, C., Kailasanath, K., and Oran, E. S., “Effects of Boundary Layers on
Oblique Detonation Structures,”31st Aerospace Sciences Meeting,
AIAA Paper 1993-0450, 1993.
doi:10.2514/6.1993-450
[42] Oran, E. S., Weber, J. W.,Stefaniw, E. I., Lefebvre, M. H., and Anderson,
J. D., “ANumerical Study of a Two-Dimensional H2–O2–Ar Detonation
Using a Detailed Chemical Reaction Model,”Combustion and Flame,
Vol. 113, No. 1, 1998, pp. 147–163.
doi:10.1016/S0010-2180(97)00218-6
[43] Teng, H. H., Ng, H. D., and Jiang, Z. L., “Initiation Characteristics of
Wedge-Induced Oblique Detonation Waves in a Stoichiometric
Hydrogen–Air Mixture,”Proceedings of the Combustion Institute,
Vol. 36, No. 2, 2017, pp. 2735–2742.
doi:10.1016/j.proci.2016.09.025
[44] Buckmaster, J., “The Structural Stability of Oblique Detonation
Wav es,”Combustion Science and Technology, Vol. 72, Nos. 4–6,
1990, pp. 283–296.
doi:10.1080/00102209008951652
[45] Teng, H. H., Zhao, W., and Jiang, Z. L., “A Novel Oblique Detonation
Structure and Its Stability,”Chinese Physics Letters, Vol. 24, No. 7,
2007, pp. 1985–1988.
doi:10.1088/0256-307X/24/7/055
[46] Fusina, G., Sislian, J. P., and Parent, B., “Formation and Stability of
Near Chapman–Jouguet Standing Oblique Detonation Waves,”AIAA
Journal, Vol. 43, No. 7, 2005, pp. 1591–1604.
doi:10.2514/1.9128
[47] Miao, S. K., Zhou, J., Liu, S. J., and Cai, X. D., “Formation Mechanisms
and Characteristics of Transition Patterns in Oblique Detonations,”Acta
Astronautica, Vol. 142, Jan. 2018, pp. 121–129.
doi:10.1016/j.actaastro.2017.10.035
[48] Grismer, M. J., and Powers, J. M., “Numerical Predictions of Oblique
Detonation Stability Boundaries,”Shock Waves, Vol. 6, No. 3, 1996,
pp. 147–156.
doi:10.1007/BF02510995
Y. J u
Associate Editor
Article in Advance / MIAO ET AL. 11
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