Post on 06-Apr-2018
8/3/2019 X. He and A. R. Karagozian- Reactive Flow Phenomena in Pulse Detonation Engines
1/13
AIAA 2003-1171
Reactive Flow Phenomena inPulse Detonation Engines
X. He and A. R. Karagozian
UCLA
Los Angeles, CA
41st AIAA Aerospace Sciences
Meeting and Exhibit
69 January 2003Reno, Nevada
For permission to copy or to republish, contact the American Institute of Aeronautics and Astronautics,
1801 Alexander Bell Drive, Suite 500, Reston, VA, 20191-4344.
8/3/2019 X. He and A. R. Karagozian- Reactive Flow Phenomena in Pulse Detonation Engines
2/13
AIAA20031171
REACTIVE FLOW PHENOMENA IN
PULSE DETONATION ENGINES
X. He and A. R. Karagozian
Department of Mechanical and Aerospace EngineeringUniversity of California, Los Angeles, CA 90095-1597
Abstract
This paper describes one- and two-dimensional
numerical simulations, with simplified as well as
full reaction kinetics, of a single cycle pulse deto-
nation engine (PDE). Focus of the present studies
is on 1) the presence of a nozzle extension at the
end of the tube, and its effect on performance pa-
rameters as well as noise characteristics, 2) criticalspark ignition energies associated with the initia-
tion of a detonation in the PDE tube, and 3) quan-
tification of performance parameters associated with
full kinetics simulations of the PDE and compari-
son of these data sets with available experimentaldata. The present simulations demonstrate the abil-
ity to predict PDE reactive flow phenomena and as-
sociated performance and noise characteristics, and
hence have promise as a predictive tool for the evo-
lution of future PDE designs.
Introduction and Background
The Pulse Detonation Wave Engine (often calledthe Pulse Detonation Engine or PDE) is a device
which allows periodic ignition, propagation, and
transmission of detonation waves within a detona-
tion tube, with associated reflections of expansion
and compression waves which can act in periodic
fashion to produce thrust1,2
. A summary of the rel-
evant gasdynamics within the PDE tube is shown in
Figure 1. The figure indicates ignition and propaga-
tion of the detonation out of the PDE tube (Figures
1a-c), reflection of an expansion fan into the tube(Figures 1de), reflection of the expansion fan from
Graduate ResearcherProfessor; Associate Fellow, AIAA. Corresponding author
(ark@seas.ucla.edu).Copyright (c) 2003 by X. He Published by the American
Institute of Aeronautics and Astronautics, Inc., with permis-sion.
the thrust wall (Figures 1ef), allowing reactants to
be drawn into the tube, and propagation of the ex-
pansion fan out of the tube (Figures 1gh), with si-
multaneous reflection of a compressive disturbance
into the tube (Figures 1hij), which reflects from
the thrust wall, ignites the fresh reactants, and re-
initiates the cycle. Because the PDE concept holdspromise for high thrust density in a constant vol-
ume device requiring little or no rotating machinery,a number of groups have been exploring PDEs for
propulsion applications. This exploration has built
on fundamental PDE work over several decades14
,so that modern experimental diagnostic as well as
computational methods may be used to bring about
significant advances in the state of the art2,46
.
Performance parameters commonly used to char-
acterize the pulse detonation engine include the im-
pulse, I, typically defined as
I A
0
ptw(t)dt (1)
where A is the area of the thrust wall and ptw(t)
is the time-dependent pressure differential at the
thrust wall. The impulse is usually scaled to pro-
duce the engines specific impulse, Isp,
Isp I
V g(2)
where is the initial mass of the reactive gas mixture
in the tube, V is the detonation tube volume (includ-
ing the nozzle volume, if containing reactants), and
g is the earths gravitational acceleration. As an
alternative performance parameter, the fuel-basedspecific impulse, Isp,f, is often used:
Isp,f IspYf
(3)
where Yf is the fuel mass fraction present within the
premixed reactants in the tube. Both Isp and Isp,f
1
American Institute of Aeronautics and Astronautics
8/3/2019 X. He and A. R. Karagozian- Reactive Flow Phenomena in Pulse Detonation Engines
3/13
AIAA20031171
are often used to compare performance among dif-
ferent PDE configurations and also to compare PDE
performance with that of alternative engine cycles7
.
Overviews of past and ongoing numerical simu-
lations of PDEs are described in recent articles byKailasanath
2,8,9
. Other recent simulations have fo-
cused on various flow and geometrical features ofthe PDE, including the effects of nozzles placed
downstream of the detonation tube. Cambier and
Tegner4
, for example, find that the presence of the
nozzle can have a significant effect on the impulse
of a single cycle of the PDE. In 2D axisymmetric
simulations, which employ a second order TVD (to-
tal variation diminishing) scheme, they find that in-
creasing the ratio of the nozzle exit area to the tube
area can produce monotonic increases in impulse I.
Increasing the nozzle exit area causes a dropoff in Ispuntil Aexit/Atube reaches 4.0, since the nozzle volume
increases; for area ratios larger than this value, Ispis seen to increase, suggesting that the impulse is
increasing faster than the nozzle volume increases,
per equation (2).
In recent PDE experiments with nozzle exten-
sions, Johnson10
observes a decrease in the fuel
specific impulse for converging-diverging nozzles ascompared with straight nozzles or converging noz-
zles. Similarly, tests as well as modeling by Cooper
and Shepherd6
suggest that the relative impulse of a
PDE tube with a flared nozzle is lower than that for a
straight nozzle at a given fill fraction (or percentageof the PDE tube initially filled with reactants). It is
of interest to understand the mechanisms whereby
nozzles can increase or decrease PDE performance
and what the associated changes in engine noise lev-
els may be.
Another issue of interest with respect to the suc-
cessful performance of the pulse detonation engine
is quantification of the required energy input needed
to ignite and sustain a propagating detonation wave
from the closed end of the tube. Thermally initi-
ated detonations via the deflagration-to-detonation
transition (DDT) have been examined over manyyears
1113
. When a mixture of reactants is ignited
by a bulk power deposition of limited duration, a
sequence of events is initiated which eventually re-
sults in a sudden power burst or explosion in the
explosion, accelerating the flame front and leading
to formation of a propagating detonation. Since the
PDE tube is designed to operate in a cyclical man-
ner, it is of interest to quantify the required energy
input to be able to repetitively initiate a detonation
front.
Prior computational studies by our group pertain-
ing to detonation phenomena in general14
and the
pulse detonation engine in particular15
involve bothone- and two-dimensional simulations, employing
the essentially non-oscillatory or ENO scheme1618
for spatial integration. An examination of the one-
dimensional overdriven detonation14
suggests spe-
cific requirements for spatial resolution of the det-onation front to be able to obtain accurate wave
speeds, peak pressures, and frequencies of detona-
tion oscillation. These ideas are incorporated into
1D and 2D simulations of the single cycle PDE15
with single step reaction kinetics. The studies sug-gest that useful performance and noise related esti-
mates may be obtained even from one-dimensionalcomputations of the pulse detonation wave engine
with simplified reaction kinetics.
The present study focused on using these high
order numerical schemes to study the behavior of
the pulse detonation engine, using simplified as well
as complex reaction kinetics. Special attention was
paid to the PDEs geometrical, flow, and reaction
characteristics and their influence on performance
parameters as well as noise generation. NASAs in-
terest in the PDE for advanced vehicle propulsion19
is incumbent upon the ability of the engine to ef-
ficiently generate thrust without having to pay asignificant penalty in engine noise. While specific
geometries for PDE nozzle extensions may have the
effect of reducing the relative Isp, as suggested in
recent experiments10
, there may be benefits associ-
ated with noise reduction.
Problem Formulation and Numerical Methodology
The equations of mass, momentum, energy, and
species conservation were solved in both one and two
spatial dimensions, assuming inviscid flow. Single
step reaction kinetics for CH4 O2 and H2 O2,
as outlined in detail in He and Karagozian
15
, as wellas full reaction kinetics for mixtures of H2 O2,H2O2Ar, and H2O2N2 were employed. Both
straight PDE tubes and tubes with nozzle extensions
were explored. In the 1D simulations, the compu-
tational domain consisted primarily of the detona-
tion tube or tube and nozzle (containing at least
2
American Institute of Aeronautics and Astronautics
8/3/2019 X. He and A. R. Karagozian- Reactive Flow Phenomena in Pulse Detonation Engines
4/13
AIAA20031171
600 grid points), with only a few grid points ex-
tending beyond the tube end in order to capture
the external pressure. In the 2D simulations, the
air external to the detonation tube was assumed to
be uniformly at atmospheric pressure, and the com-
putational domain extended well downstream of the
end of the tube, in general at least one and one halftube lengths downstream and at least two tube di-
ameters away from the detonation tube in the di-
mension perpendicular to the axial dimension. The
effects of employing a 1D pressure relaxation length
(PRL), as done by Kailasanath and Patnaik9
, were
explored in our prior PDE study15
, but for most of
the conditions examined, a relaxation length was not
needed in order to obtain equivalent results between
1D and 2D simulations.
In cases where alternative nozzle geometries were
considered, a locally 1D flow approximation was em-
ployed to represent nozzle shapes of slowly vary-ing cross-sectional areas A(x). In this quasi-one-dimensional case, with a single step reaction, for
example, the governing equations reduce to the fol-
lowing form:
tU +
xF =
1
A
dA
dx( H F) + S (4)
where the vectors containing conserved variables,
flux terms, and source terms are:
U =
u
E
Y
F =
u
u2 + p
(E+ p)u
uY
(5)
H =
0p
0
0
S =
00
0
KY eTA
T
(6)
Here E may be written
E =p
1+
u2 + v2
2+ qY (7)
where represents density, p is the static pressure,u is the x-component of the velocity vector, and
is the ratio of specific heats. q is a heat release
parameter which characterizes the amount of en-
ergy released during the reaction, and TA represents
the activation temperature. Y is the reactant mass
fraction, which varies from 0 to 1, while K is the
reaction-rate multiplier for the reaction source term.
Through equation (4) it became possible, in an ap-
proximate way, to represent the effects of nozzle ge-
ometry in 1D PDE simulations.
Four different nozzle extension shapes were ex-plored here; these are shown in Figure 2. The nozzle
shapes included a fifth order polynomial (configura-tion 1), a flared divergent section (configuration 2), a
nozzle section with a constant conical divergence an-
gle (configuration 3), and a straight tube (configura-
tion 4). In the simulations of PDEs with nozzles, the
straight portion of the PDE tube, of length L, was
assumed to be initially filled with reactants, while
the nozzle section, of length Ln, was filled with inert
gas (for a single step reaction, effectively products).
In the simulations of straight PDE tubes without a
nozzle, the tube was assumed to be initially filled
completely with reactants. Unless otherwise stated,
the straight tube lengths L used in the present com-putations were 1 m, and the nozzle lengths Ln were
also 1 m.
For the simulations involving complex reaction ki-
netics, the equations (5) - (7) were replaced by rela-
tions for the straight PDE tube (with A(x) constant)
but with N 1 species equations for the N speciesinvolved in the reactions. Full kinetics simulations of
the combustion reactions for H2O2, H2O2Ar,
and H2 O2 N2 (representing hydrogen-air) were
considered here; the latter mechanism contained 23
elementary reactions and was part of the CHEMKINII library
20.
As in He and Karagozian15
, the present study used
the Weighted Essentially Non-Oscillatory (WENO)
method21
, a derivative of the ENO method1618
for
spatial interpolation of the system of governingequations. The WENO scheme was fifth order ac-
curate in smooth regions and third order accurate
in the vicinity of discontinuities. The ENO/WENO
schemes were tested on a variety of problems, in-
cluding shock tubes with open ends, analogous to
the exit of the PDE15
, and that of the classical
one-dimensional, overdriven, pulsating detonation
14
.For the single step kinetics simulations, the third
order total variation diminishing (TVD) Runge-
Kutta method was used for time discretization. For
full kinetics simulations, the method of operator
splitting22
was used, whereby the system of govern-
ing equations (including N1 species equations) was
3
American Institute of Aeronautics and Astronautics
8/3/2019 X. He and A. R. Karagozian- Reactive Flow Phenomena in Pulse Detonation Engines
5/13
AIAA20031171
split into two separate equations, one which only
included the advection-diffusion terms (solved via
WENO) and one which only included the reaction
rate source terms. A stiff ODE solver, DVODE (a
variation of VODE23
) was employed for the solution
of the rate equations; thermodynamic parameters
and rate constants were obtained via the CHEMKINII subroutine
20
.
A computational spark adjacent to the thrust
wall was used to initiate the detonation at the startof the PDE cycle. This narrow, high pressure, high
temperature region (3 grid cells in width) was able to
initiate a propagating shock and ignite the reactants;
the flame front then caught up with the shock, form-
ing a detonation. As suggested by prior studies1113
,
however, such thermal initiation of detonation de-
pends very strongly on the initial rate of deposi-
tion of energy in the reactants. This concept was
explored in the present studies by altering the ini-tial temperature and pressure in the computational
spark to be able to determine minimum input en-
ergy densities leading to detonation initiation.
In addition to the standard performance parame-
ters used to characterize the PDE (I, Isp, and Isp,f),
the sound pressure level (SPL) at various locations
within and external to the detonation tube was also
computed. As done previously15
, these noise levelswere estimated by examining the Fourier transform
of the time-dependent pressure measured at various
locations within the computational domain. The
SPL was then computed based on peak pressuresin the Fourier spectrum. In most cases these peaksoccurred at the PDE cycle frequency.
Results
An example of the temporal evolution of the pres-
sure distribution along the centerline of a straight
PDE tube, over a single cycle, is shown in Figure
3 for a 2D axisymmetric configuration with a sin-
gle step methane-oxygen reaction. Here the initia-
tion and propagation of the detonation wave through
the tube (Figures 3ab) and the exit of the shockfrom the tube and reflection of the expansion fan
from the exhaust back into the tube (Figures 3cd)
are clear. Our prior studies15
demonstrate that a
1D simulation of this same PDE tube quantitatively
yields a very similar pressure field evolution to that
of the 2D simulation, even without inclusion of a
1D pressure relaxation length. 1D simulations of
the PDE tube do not precisely replicate the pres-
sure and Mach number evolution at the tube end,
with or without a PRL. Yet the evolution of the
tubes interior pressure without a PRL is, in most
cases previously explored15
, sufficiently close to that
obtained from the 2D simulations so as to producesimilar PDE performance estimates. This is shown,
for example, in Figure 4, which compares the spe-
cific impulse for 2D simulations with that for 1D
simulations, with and without inclusion of a PRL.
Time-series pressure data at specific locationswere used to estimate the noise generated at vari-
ous points in the flowfield over a single PDE cycle.
Estimates of the sound pressure level were made us-
ing both 1D and 2D simulations of the straight PDE
tube with a single step CH4 O2 reaction. Sincethe 1D simulations only resolved the flow within the
PDE tube, comparisons were made only for inte-rior and tube exit noise levels. In all locations for
this case we observed the peak in pressure to appear
close to the frequency associated with the period of
the PDE cycle, roughly 330 Hz. The noise levels at
various tube locations are quantified in Table 1.
Location 2D SPL 1D SPL
Thrust Wall 212 dB 212 dB
Mid-tube 211 dB 211 dB
Tube end 202 dB 203 dB
Table 1. Computed sound pressure level (SPL) at vari-
ous locations within the tube (thrust wall, center of tube,
and tube end). Results are computed from both 2D and
1D simulations of the CH4 O2 reaction.
Consistent with the evolution of the pressure fieldand the performance parameters (e.g., Figure 4), the
noise levels were nearly the same for 1D as for 2D
simulations. The magnitudes of the noise levels were
close to those quantified in PDE experiments24,25
.
The influence of the presence of the nozzle is
shown in Figure 5, where the straight tube (nozzle
configuration 4) had the same length as the tubeswith the divergent nozzles. Again, a CH4 O2 sin-
gle step reaction was used in this set of simulations.
Interestingly, the straight tube was observed to pro-
duce the highest values ofI, Isp, and Isp,f, while the
conical nozzle (configuration 3) produced the low-
est values. These findings were generally consistent
4
American Institute of Aeronautics and Astronautics
8/3/2019 X. He and A. R. Karagozian- Reactive Flow Phenomena in Pulse Detonation Engines
6/13
AIAA20031171
with the observations of Johnson10
, i.e., that Isp,fdecreased with inclusion of a divergent exit nozzle.
Our results were also consistent with those of Cam-
bier and Tegner4
, in that Isp decreased for nozzle-
to-tube area ratios of 4.0 (examined here).
The fact that the straight tube produced the high-
est thrust (resulting from the highest sustained pres-sure at the thrust wall) has interesting implications
for PDE noise estimates. Figure 6 shows the results
of taking the Fourier transform of the time depen-
dent pressure within (Figure 6ab) and at the end
(Figure 6c) of the tube/nozzle, for the four different
nozzle configurations explored here. For example, in
the middle of the PDE tube, the straight nozzle caseproduced the smallest pressure perturbation at the
PDE cycle frequency, yet at the end of the straight
nozzle, the pressure and hence the SPL were both
larger than those for the other nozzles, albeit at
a higher harmonic (667 Hz) of the PDE cycle fre-quency (about 333 Hz). This behavior is reflected in
Table 2 for SPL values at various locations.
Location Config. 1 SPL Config. 4 SPL
Thrust wall 212 dB 210 dB
Mid-tube 211 dB 208 dB
Tube end 205 dB 202 dB
Nozzle end 188 dB 208 dB
Table 2. Computed sound pressure level at various lo-
cations within the tube (thrust wall, center of tube, PDE
tube end) and at the nozzle exit for two different noz-
zle configurations (see Figure 2). Results are computed
from quasi 1D simulations of the CH4 O2 reaction.
The above behavior likely resulted from the weak-
ened downstream-propagating shock that formed in
the divergent nozzles as compared with that forthe straight nozzle. The lower pressure and SPL
in the upstream portions of the straight nozzle
(as compared with the divergent nozzles) possibly
could have resulted from stronger reflected expan-
sion waves that occurred at the contact surface be-
tween reactants and air at the start of the noz-
zle. While there were clear tradeoffs between perfor-mance and nozzle exit noise conditions, it is unclear
why the pressure perturbation of the higher har-
monic (660 Hz) in the straight nozzle was so much
larger than for the divergent nozzles. This and other
noise related issues require further exploration in the
future.
The full kinetics simulations of the reactant-filled,
straight PDE tube without a nozzle allowed a more
detailed examination of the detonation ignition and
propagation process to be made, in addition to more
quantitative comparisons with experimental data.
Figure 7 displays the evolution of the 2D pressure
field associated with the PDE tube and its sur-roundings, for a full H2 O2 reaction. As seen in
prior 2D simulations of the PDE but with simplified
kinetics15
, the propagation of the detonation out of
the tube resulted in the propagation of a vortical
structure coincident with the shock and simultane-ous reflection of an expansion fan back into the tube.
Increased complexity in the wave structures as com-
pared with that for simplified reaction kinetics was
observed, especially in the propagating shock/vortex
structure downstream of the tube exit.The influence of the initial pressure and tempera-
ture (and resulting energy deposition) on initiationof a detonation wave was studied using these full
kinetics simulations. Figure 8 shows the centerline
pressure distribution for a 1D, full kinetics simula-
tion of an H2O2Ar mixture, for different initial
temperatures and pressures in the 3 grid cell-wide
spark adjacent to the thrust wall. Critical combi-
nations of temperature and pressure were observed
to be necessary for the classical ZND detonation
structure to evolve; if the initial energy deposition
was too small, a weak shock front did not ignite the
mixture and thus did not transition to a detonation,
as seen by the solid lines in Figures 8ab. Tables 3and 4, for H2 O2 Ar and H2 O2 N2 reac-
tions, respectively, quantify the conditions that were
required for ignition of a detonation.
Temp. Press. Energy (erg/cm2) Deton.?
500K 3 atm 2.02 105 No
1000K 3 atm 8.06 105 No
1500K 3 atm 9.95 105 Yes
2000K 3 atm 11.0 105 Yes
1500K 5 atm 15.3 105 Yes
1500K 2.5 atm 8.63 105 Yes
1500K 2.0 atm 7.3 105 No
Table 3. Initial temperatures, pressures, and input
energies for a computational spark used to ignite a
H2 O2 Ar mixture, and determination of the possi-
bility of detonation ignition.
5
American Institute of Aeronautics and Astronautics
8/3/2019 X. He and A. R. Karagozian- Reactive Flow Phenomena in Pulse Detonation Engines
7/13
AIAA20031171
Temp. Press. Energy (erg/cm2) Deton.?
800K 1 atm 4.54 105 No
900K 1 atm 4.89 105 No
1000K 1 atm 5.18 105 Yes
1200K 1 atm 5.64 105 Yes
Table 4. Initial temperatures, pressures, and input
energies for a computational spark used to ignite a
H2 O2 N2 mixture, and determination of the possi-
bility of detonation ignition.
As expected, the critical input energies for ignition
of a detonation were found to be different for these
different reactions. In the case of H2 O2 N2,
a critical energy deposition per unit area of about
5105 erg/cm2 was required for detonation, whereas
for the case of H2 O2 Ar, this critical value rose
to about 8.5 105 erg/cm2.
The full kinetics simulations also allowed quanti-tative comparisons to be made between performance
parameters from the present simulations and those
obtained by experiment (for a single cycle PDE) or
analysis. Table 5 below shows the current estima-
tions ofIsp for the PDE for H2O2 and H2O2N2(hydrogen-air) reactions, as compared with the anal-
ysis and experiments described in Wintenberger26
and the experiments of Zitoun27
and Schauer28
.
Study Isp, H2-air Isp, H2 O2
Present 128.5 s 240 s
Wintenberger26 123.7 s 173 s
CIT expts.26
200 s
Zitoun expts.27
149 s 226 s
Schauer expts.28
113 s
Table 5. Comparison of specific impulse for single cycle
PDE between the present simulations and corresponding
experiments and modeling efforts, as noted.
While the present simulations appeared quantita-
tively to replicate the experimentally observed per-
formance parameters reasonably well, detailed com-
parisons of the pressure field evolution and noise es-timates require further examination and are the sub-
ject of continued studies.
Conclusions
High resolution numerical simulations of pulse
detonation engine phenomena revealed useful infor-
mation that may be used in future PDE designs.
Simulations of the effects of the presence of a di-
vergent nozzle downstream of the PDE tube sug-gested that, while performance parameters such as
Isp may decrease with increasing nozzle exit area,
the noise generation at the nozzle exit may actu-
ally be reduced, and hence these tradeoffs may be
explored through simplified reaction kinetics stud-
ies. Simulations of PDE evolution with full chemi-
cal kinetics suggested that specific minimum energy
densities were required to enable the initiation of a
detonation, and hence to sustain the PDE cycle. Fi-
nally, it was observed that full kinetics simulations
were able to capture quantitatively the physical phe-
nomena and corresponding performance parametersfor the PDE. Future studies will continue with this
quantitative comparison as well as noise generation
issues relevant to the PDE.
Acknowledgments
This work has been supported at UCLA by NASA
Dryden Flight Research Center under Grant NCC4-
153, with Dr. Trong Bui and Dave Lux as technical
monitors, and by the Office of Naval Research un-
der Grant ONR N00014-97-1-0027, with Dr. Wen
Masters as technical monitor.
References
[1] Eidelman, S., Grossmann, W., and Lottati, I.,
Review of Propulsion Applications and Nu-
merical Simulations of the Pulsed Detonation
Engine Concept, J. Propulsion and Power,
7(6), pp. 857-865, 1991.
[2] Kailasanath, K., Recent Developments in
the Research on Pulse Detonation Engines,AIAA Paper 2002-0470 (Invited), AIAA 40th
Aerospace Sciences Meeting, January, 2002.
[3] Helman, D., Shreeve, R. P., and Eidelman, S.,
Detonation Pulse Engine, AIAA Paper 86-
1683, June, 1986.
6
American Institute of Aeronautics and Astronautics
8/3/2019 X. He and A. R. Karagozian- Reactive Flow Phenomena in Pulse Detonation Engines
8/13
AIAA20031171
[4] Cambier, J.-L. and Tegner, J. K., Strategies
for Pulsed Detonation Engine Performance Op-
timization, Journal of Propulsion and Power,
14(4), pp. 489-498, 1998.
[5] L. Ma, S.T. Sanders, J.B. Jeffries, and R.K.
Hanson, Monitoring and Control of a PulseDetonation Engine using a Diode-Laser Fuel
Concentration and Temperature Sensor, Proc.
of the Comb. Inst., 29, 2002, to appear.
[6] Cooper, M. and Shepherd, J. E., The Ef-
fec of Nozzles and Extensions on Detona-tion Tube Performance, AIAA Paper 02-3628,
38th AIAA/ASME/SAE/ASEE Joint Propul-
sion Conference, July, 2002.
[7] Povinelli, L. A., Pulse Detonation Engines for
High Speed Flight, Paper ID 17-5169, pre-
sented at the 11th AIAA/AAAF InternationalConference on Space Planes and Hypersonic
Systems and Technologies, Orleans, France,
Sept. 29 - Oct. 4, 2002.
[8] Kailasanath, K., A Review of PDE Research
Performance Estimates, AIAA Paper 2001-
0474, AIAA 39th Aerospace Sciences Meeting,
January, 2001.
[9] Kailasanath, K. and Patnaik, G., Performance
Estimates of Pulsed Detonation Engines, 28th
Symposium (Intl.) on Combustion, 2000.
[10] Johnson, C., The Effects of Nozzle Geometry
on the Specific Impulse of a Pulse Detonation
Engine, Final Report 16.622, MIT, December,
2001.
[11] Oppenheim, A. K., Manson, N., and Wagner,
H. G., Recent Progress in Detonation Re-
search, AIAA Journal, Vol. 1, pp. 2243-2252,
1963.
[12] Lee, J. H. S., Initiation of Gaseous Detona-
tion, A. Rev. Phys. Chem., Vol. 28, pp. 74-104,
1977.
[13] Sileem, A. A., Kassoy, D. R., and Hayashi, A.
K., Thermally Initiated Detonation through
Deflagration to Detonation Transition, Proc.
Royal Soc. London A, Vo. 435, pp. 459-482,
1991.
[14] Hwang, P., Fedkiw, R., Merriman, B.,
Karagozian, A. R., and Osher, S. J., Numeri-
cal Resolution of Pulsating Detonation Waves,Combustion Theory and Modeling, Vol. 4, No.
3, pp. 217-240, 2000.
[15] He, X. and Karagozian, A. R., Numerical Sim-
ulation of Pulse Detonation Engine Phenom-
ena to appear in the SIAM Journal of Scien-
tific Computing, 2003.
[16] Harten, A., Osher S. J., Engquist, B. E.,
and Chakravarthy, S. R., Some Results on
Uniformly High-Order Accurate Essentially
Nonoscillatory Schemes, J. Appl. Numer.
Math., Vol. 2, pp. 347-377, 1986.
[17] Shu, C.W. and Osher, S., Efficient Imple-
mentation of Essentially Non-Oscillatory Shock
Capturing Schemes II, Journal of Computa-tional Physics, Vol. 83, pp. 32-78, 1989.
[18] Fedkiw, R.P., Merriman, B., Osher, S., High
accuracy numerical methods for thermally per-
fect gas flows with chemistry, Journal of Com-
putational Physics, Vol. 132, No. 2, pp. 175-190,
1997.
[19] Three Pillars for Success: NASAs Response
to Achieve the National Priorities in Aeronau-
tics and Space Transportation, NASA Office
of Aeronautics and Space Transportation Tech-
nology, 1997.[20] Kee, R. J., Miller, J. A., and Jefferson, T. H.,
CHEMKIN: A general purpose, problem in-
dependent, transportable, Fortran chemical ki-
netics code package, Sandia National Labora-
tories Report SAND80-8003, 1980.
[21] Jiang, G. S. and Shu, C. W., Efficient Imple-
mentation of Weighted ENO Schemes, Journal
of Computational Physics, Vol. 126, pp. 202-
228, 1996.
[22] Strikwerda, J. C., Finite Difference Schemes
and Partial Differential Equations, Wadsworthand Brooks, 1989.
[23] Brown, P. N., Byrne, G. D., and Hindmarsh, A.
C., VODE: A variable coefficient ODE solver,
SIAM J. Scientific Statistical Computing 10,
pp. 1038-1051, 1989.
7
American Institute of Aeronautics and Astronautics
8/3/2019 X. He and A. R. Karagozian- Reactive Flow Phenomena in Pulse Detonation Engines
9/13
AIAA20031171
[24] Schauer, F., private communication.
[25] Perkins, H. D., private communication.
[26] Wintenberger, E., Austin, J. M., Cooper, M.,
Jackson, S., and Shepherd, J. E., An Analyt-
ical Model for the Impulse of a Single Cycle
Pulse Detonation Engine, AIAA Paper 2001-3811, July, 2001.
[27] Zitoun, R. and Desbordes, D., Propulsive Per-
formances of Pulsed Detonations, Combustion
Science and Technology, Vol. 144, pp. 93-114,
1999.
[28] Schauer, F., Stutrud, J., and Bradley, R., Det-
onation Initiation Studies and Performance Re-
sults for Pulsed Detonation Engines, AIAA
Paper no. 2001-1129, 2001.
a)
)
c)
reactants
reactantsproducts
products
detonation
products
reflected expansion wave
products
expansion wave
d)
e)
detonation front
propagating detonation
f)
g)
h)
i)
j)
reactants
enterproducts
reactants
reactants
reactants
reactants
reflected expansion wave
expansion wave
reflected compression wave
compression wave
shock/detonation reflection
Fig. 1: The generic Pulse Detonation Engine (PDE)
cycle.
8
American Institute of Aeronautics and Astronautics
8/3/2019 X. He and A. R. Karagozian- Reactive Flow Phenomena in Pulse Detonation Engines
10/13
AIAA20031171
0 0.5 1 1.5
X (m)
0
0.1
0.2
0.3
0.4
0.5
Radius(m)
nozzle 1nozzle 2
nozzle 3nozzle 4
Fig. 2: Different nozzle geometries explores in
present computations. These include straight tubes
(configuration 4), flared divergent sections (config-uration 2), divergent sections with inflection (con-
figuration 1), and a nozzle section with a constant
divergence angle (configuration 3). In all case the
reactants are assumed to lie initially upstream of
nozzle, in the constant area tube, while the nozzleitself contains inert gas.
X (m)
Pressure(atm)
0 0.5 1 1.5 2 2.50
5
10
15
20
25
30
(a)
X (m)
Pressure(atm)
0 0.5 1 1.5 2 2.50
5
10
15
20
25
30
(b)
X (m)
Pressure(atm)
0 0.5 1 1.5 2 2.50
5
10
15
20
25
30
(c)
X (m)
Pressure(atm)
0 0.5 1 1.5 2 2.50
5
10
15
20
25
30
(d)
Fig. 3: Evolution of the centerline pressure for a
straight 2D axisymmetric PDE of 1 m length, at
times (a) 0.06 ms, (b) 0.15 ms, (c) 0.49 ms, and (d)
2.89 ms.9
American Institute of Aeronautics and Astronautics
8/3/2019 X. He and A. R. Karagozian- Reactive Flow Phenomena in Pulse Detonation Engines
11/13
AIAA20031171
0 0.001 0.002 0.003 0.004
Time (sec.)
0
50
100
150
200
250
300
350
SpecificImpulse(sec.)
2D simulation1D without pressure relaxation1D with pressure relaxation
Fig. 4: Comparisons of time-dependent specific im-
pulse for both 1D and 2D axisymmetric simulationsof the PDE tube with a CH4 O2 reaction, takenfrom He and Karagozian
15
. 1D simulations explored
the use of a pressure relaxation length l = 0.5L.
Here the 1D simulations incorporated a computa-
tional spark consisting of a pressure of 10 atm and
a temperature of 3000K in order to match the initial
conditions for the 2D simulation.
0 0.001 0.002 0.003
Time (sec.)
0
500
1000
1500
2000
2500
Impulseperunit
area(ps.s
)
nozzle 1nozzle 2nozzle 3nozzle 4
0 0.001 0.002 0.003
Time (sec.)
0
50
100
150
200
250
Isp(sec.)
0 0.001 0.002 0.003
Time (sec.)
0
100
200
300
400
500
600
700
800
900
1000
1100
1200
1300
Ispf(sec.)
Fig. 5: Comparisons of time-dependent performance
parameters computed from 1D simulations using dif-
ferent nozzle geometries. Results shown are for im-
pulse I, specific impulse Isp, and fuel specific impulseIsp,f. The reaction of methane and oxygen was sim-
ulated.
10
American Institute of Aeronautics and Astronautics
8/3/2019 X. He and A. R. Karagozian- Reactive Flow Phenomena in Pulse Detonation Engines
12/13
AIAA20031171
0 2500 5000 7500 10000
Frequency (HZ)
0
1
2
3
4
5
6
7
[P]/P
0
nozzle 1nozzle 2nozzle 3nozzle 4
(a)
0 2500 5000 7500 10000
Frequency (HZ)
0
0.5
1
1.5
2
2.5
3
3.5
4
[P]/P0
nozzle 1nozzle 2nozzle 3nozzle 4
(b)
0 2500 5000 7500 10000
Frequency (HZ)
0
1
2
3
[P]/P0
nozzle 1nozzle 2nozzle 3nozzle 4
(c)
Fig. 6: Comparisons of pressure spectra: (a) in the
middle of the detonation tube, (b) at the end of the
straight part of the detonation tube, and (c) at the
end of the nozzle. Results are shown for different
nozzle configurations (see Fig. 2).
50 100 150 200 250 300 350
X (cm)
-50
0
50
100
150
200
Y(cm)
(a)
50 100 150 200 250 300 350
X (cm)
-50
0
50
100
150
200
Y(cm)
(b)
50 100 150 200 250 300 350
X (cm)
-50
0
50
100
150
200
Y(cm)
(c)
Fig. 7: Temporal evolution of the 2D planar pres-sure field within and external to the PDE over one
cycle, with pressure given in units of dyn/cm2. Data
shown are at times corresponding to (a) 0.15 ms, (b)
0.47 ms, and (c) 1.34 ms. A H2 O2 reaction was
simulated here with full chemical kinetics.
11
American Institute of Aeronautics and Astronautics
8/3/2019 X. He and A. R. Karagozian- Reactive Flow Phenomena in Pulse Detonation Engines
13/13
AIAA20031171
0 10 20 30 40
X (cm)
0
2E+06
4E+06
6E+06
8E+06
1E+07
1.2E+07
1.4E+07
1.6E+07
1.8E+07
Pressure(dyn/cm
2)
Ps = 2.0 AtmPs = 2.5 AtmPs = 3.0 AtmPs = 5.0 Atm
(a)
0 10 20 30 40
X (cm)
0
2E+06
4E+06
6E+06
8E+06
1E+07
1.2E+07
1.4E+07
1.6E+07
1.8E+07
Pressure(dyn/cm
2)
Ts = 500KTs = 1000KTs = 1500KTs = 2000K
(b)
Fig. 8: Centerline pressure distribution for the H2
O2 reaction with full kinetics, for different compu-
tational spark conditions: (a) fixed temperature
1500K and variable pressure, and (b) fixed pressure
3 atm and variable temperature, each at time 0.2
msec.
12
American Institute of Aeronautics and Astronautics