AIAA 2003-1171 Reactive Flow Phenomena in Pulse Detonation ... · PDF filepulse detonation...

AIAA 2003-1171

Reactive Flow Phenomena inPulse Detonation Engines

X. He and A. R. KaragozianUCLALos Angeles, CA

41st AIAA Aerospace SciencesMeeting and Exhibit

6–9 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.

AIAA–2003–1171

REACTIVE FLOW PHENOMENA INPULSE 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-dimensionalnumerical simulations, with simplified as well asfull reaction kinetics, of a single cycle pulse deto-nation engine (PDE). Focus of the present studiesis on 1) the presence of a nozzle extension at theend of the tube, and its effect on performance pa-rameters as well as noise characteristics, 2) critical“spark ignition” energies associated with the initia-tion of a detonation in the PDE tube, and 3) quan-tification of performance parameters associated withfull 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, andhence 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 devicewhich allows periodic ignition, propagation, andtransmission of detonation waves within a detona-tion tube, with associated reflections of expansionand compression waves which can act in periodicfashion to produce thrust

1, 2. A summary of the rel-

evant gasdynamics within the PDE tube is shown inFigure 1. The figure indicates ignition and propaga-tion of the detonation out of the PDE tube (Figures1a-c), reflection of an expansion fan into the tube(Figures 1de), reflection of the expansion fan from

∗Graduate Researcher†Professor; Associate Fellow, AIAA. Corresponding author

([email protected]).‡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 tobe drawn into the tube, and propagation of the ex-pansion fan out of the tube (Figures 1gh), with si-multaneous reflection of a compressive disturbanceinto the tube (Figures 1hij), which reflects fromthe 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 forpropulsion applications. This exploration has builton fundamental PDE work over several decades

1–4,

so that modern experimental diagnostic as well ascomputational methods may be used to bring aboutsignificant advances in the state of the art

2,4–6.

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 thethrust wall. The impulse is usually scaled to pro-duce the engine’s specific impulse, Isp,

Isp ≡ I

ρV g(2)

where ρ is the initial mass of the reactive gas mixturein the tube, V is the detonation tube volume (includ-ing the nozzle volume, if containing reactants), andg is the earth’s gravitational acceleration. As analternative performance parameter, the fuel-basedspecific impulse, Isp,f , is often used:

Isp,f ≡ Isp

Yf(3)

where Yf is the fuel mass fraction present within thepremixed reactants in the tube. Both Isp and Isp,f

1American Institute of Aeronautics and Astronautics

AIAA–2003–1171

are often used to compare performance among dif-ferent PDE configurations and also to compare PDEperformance with that of alternative engine cycles

7.

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 placeddownstream of the detonation tube. Cambier andTegner

4, for example, find that the presence of the

nozzle can have a significant effect on the impulseof a single cycle of the PDE. In 2D axisymmetricsimulations, 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 tubearea can produce monotonic increases in impulse I.Increasing the nozzle exit area causes a dropoff in Isp

until Aexit/Atube reaches 4.0, since the nozzle volumeincreases; for area ratios larger than this value, Isp

is seen to increase, suggesting that the impulse isincreasing faster than the nozzle volume increases,per equation (2).

In recent PDE experiments with nozzle exten-sions, Johnson

10observes 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 Cooperand Shepherd

6suggest that the relative impulse of a

PDE tube with a flared nozzle is lower than that for astraight nozzle at a given fill fraction (or percentageof the PDE tube initially filled with reactants). It isof interest to understand the mechanisms wherebynozzles can increase or decrease PDE performanceand 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 engineis quantification of the required energy input neededto ignite and sustain a propagating detonation wavefrom the closed end of the tube. Thermally initi-ated detonations via the deflagration-to-detonationtransition (DDT) have been examined over manyyears

11–13. When a mixture of reactants is ignited

by a bulk power deposition of limited duration, asequence of events is initiated which eventually re-sults in a sudden power burst or “explosion in theexplosion”, accelerating the flame front and leadingto 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 energyinput to be able to repetitively initiate a detonationfront.

Prior computational studies by our group pertain-ing to detonation phenomena in general

14and the

pulse detonation engine in particular15

involve bothone- and two-dimensional simulations, employingthe essentially non-oscillatory or ENO scheme

16–18

for spatial integration. An examination of the one-dimensional overdriven detonation

14suggests spe-

cific requirements for spatial resolution of the det-onation front to be able to obtain accurate wavespeeds, peak pressures, and frequencies of detona-tion oscillation. These ideas are incorporated into1D and 2D simulations of the single cycle PDE

15

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 enginewith simplified reaction kinetics.

The present study focused on using these highorder numerical schemes to study the behavior ofthe pulse detonation engine, using simplified as wellas complex reaction kinetics. Special attention waspaid to the PDE’s geometrical, flow, and reactioncharacteristics and their influence on performanceparameters as well as noise generation. NASA’s in-terest in the PDE for advanced vehicle propulsion

19

is incumbent upon the ability of the engine to ef-ficiently generate thrust without having to pay asignificant penalty in engine noise. While specificgeometries for PDE nozzle extensions may have theeffect of reducing the relative Isp, as suggested inrecent experiments

10, there may be benefits associ-

ated with noise reduction.

Problem Formulation and Numerical Methodology

The equations of mass, momentum, energy, andspecies conservation were solved in both one and twospatial dimensions, assuming inviscid flow. Singlestep reaction kinetics for CH4 − O2 and H2 − O2,as outlined in detail in He and Karagozian

15, as well

as full reaction kinetics for mixtures of H2 − O2,H2−O2−Ar, and H2−O2−N2 were employed. Bothstraight PDE tubes and tubes with nozzle extensionswere explored. In the 1D simulations, the compu-tational domain consisted primarily of the detona-tion tube or tube and nozzle (containing at least


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600 grid points), with only a few grid points ex-tending beyond the tube end in order to capturethe external pressure. In the 2D simulations, theair external to the detonation tube was assumed tobe uniformly at atmospheric pressure, and the com-putational domain extended well downstream of theend 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. Theeffects of employing a 1D pressure relaxation length(PRL), as done by Kailasanath and Patnaik

9, were

explored in our prior PDE study15

, but for most ofthe conditions examined, a relaxation length was notneeded in order to obtain equivalent results between1D and 2D simulations.

In cases where alternative nozzle geometries wereconsidered, 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, forexample, the governing equations reduce to the fol-lowing form:

∂

∂t�U +

∂

∂x�F =

1A

dA

dx( �H − �F ) + �S (4)

where the vectors containing conserved variables,flux terms, and source terms are:

�U =

ρ

ρu

E

ρY

�F =

ρu

ρu2 + p

(E + p)uρuY

(5)

�H =

0p

00

�S =

000

−KρY e−(

TAT

)

(6)

Here E may be written

E =p

γ − 1+

ρ(u2 + v2

)2

+ ρqY (7)

where ρ represents density, p is the static pressure,u is the x-component of the velocity vector, and γ

is the ratio of specific heats. q is a heat releaseparameter which characterizes the amount of en-ergy released during the reaction, and TA representsthe activation temperature. Y is the reactant massfraction, 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 nozzleshapes included a fifth order polynomial (configura-tion 1), a flared divergent section (configuration 2), anozzle section with a constant conical divergence an-gle (configuration 3), and a straight tube (configura-tion 4). In the simulations of PDEs with nozzles, thestraight portion of the PDE tube, of length L, wasassumed to be initially filled with reactants, whilethe nozzle section, of length Ln, was filled with inertgas (for a single step reaction, effectively products).In the simulations of straight PDE tubes without anozzle, the tube was assumed to be initially filledcompletely with reactants. Unless otherwise stated,the straight tube lengths L used in the present com-putations were 1 m, and the nozzle lengths Ln werealso 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 ofthe combustion reactions for H2−O2, H2−O2−Ar,and H2 −O2 − N2 (representing hydrogen-air) wereconsidered here; the latter mechanism contained 23elementary reactions and was part of the CHEMKINII library

20.

As in He and Karagozian15

, the present study usedthe Weighted Essentially Non-Oscillatory (WENO)method

21, a derivative of the ENO method

16–18for

spatial interpolation of the system of governingequations. The WENO scheme was fifth order ac-curate in smooth regions and third order accuratein the vicinity of discontinuities. The ENO/WENOschemes were tested on a variety of problems, in-cluding shock tubes with open ends, analogous tothe exit of the PDE

15, and that of the classical

one-dimensional, overdriven, pulsating detonation14

.For the single step kinetics simulations, the thirdorder total variation diminishing (TVD) Runge-Kutta method was used for time discretization. Forfull kinetics simulations, the method of operatorsplitting

22was used, whereby the system of govern-

ing equations (including N−1 species equations) was


AIAA–2003–1171

split into two separate equations, one which onlyincluded the advection-diffusion terms (solved viaWENO) and one which only included the reactionrate source terms. A stiff ODE solver, DVODE (avariation of VODE

23) was employed for the solution

of the rate equations; thermodynamic parametersand rate constants were obtained via the CHEMKINII subroutine

20.

A computational “spark” adjacent to the thrustwall was used to initiate the detonation at the startof the PDE cycle. This narrow, high pressure, hightemperature region (3 grid cells in width) was able toinitiate a propagating shock and ignite the reactants;the flame front then caught up with the shock, form-ing a detonation. As suggested by prior studies

11–13,

however, such thermal initiation of detonation de-pends very strongly on the initial rate of deposi-tion of energy in the reactants. This concept wasexplored 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 locationswithin and external to the detonation tube was alsocomputed. As done previously

15, these noise levels

were estimated by examining the Fourier transformof the time-dependent pressure measured at variouslocations within the computational domain. TheSPL 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 straightPDE tube, over a single cycle, is shown in Figure3 for a 2D axisymmetric configuration with a sin-gle step methane-oxygen reaction. Here the initia-tion and propagation of the detonation wave throughthe tube (Figures 3ab) and the exit of the shockfrom the tube and reflection of the expansion fanfrom the exhaust back into the tube (Figures 3cd)are clear. Our prior studies

15demonstrate that a

1D simulation of this same PDE tube quantitativelyyields a very similar pressure field evolution to thatof the 2D simulation, even without inclusion of a

1D pressure relaxation length. 1D simulations ofthe 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 thetube’s interior pressure without a PRL is, in mostcases previously explored

15, 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 1Dsimulations, 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 PDEtube with a single step CH4 − O2 reaction. Sincethe 1D simulations only resolved the flow within thePDE tube, comparisons were made only for inte-rior and tube exit noise levels. In all locations forthis case we observed the peak in pressure to appearclose to the frequency associated with the period ofthe PDE cycle, roughly 330 Hz. The noise levels atvarious tube locations are quantified in Table 1.

Location 2D SPL 1D SPLThrust Wall 212 dB 212 dBMid-tube 211 dB 211 dBTube 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), thenoise levels were nearly the same for 1D as for 2Dsimulations. The magnitudes of the noise levels wereclose to those quantified in PDE experiments

24,25.

The influence of the presence of the nozzle isshown in Figure 5, where the straight tube (nozzleconfiguration 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 of I, Isp, and Isp,f , while theconical nozzle (configuration 3) produced the low-est values. These findings were generally consistent


AIAA–2003–1171

with the observations of Johnson10

, i.e., that Isp,f

decreased with inclusion of a divergent exit nozzle.Our results were also consistent with those of Cam-bier and Tegner

4, 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 implicationsfor PDE noise estimates. Figure 6 shows the resultsof 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 differentnozzle configurations explored here. For example, inthe middle of the PDE tube, the straight nozzle caseproduced the smallest pressure perturbation at thePDE cycle frequency, yet at the end of the straightnozzle, the pressure and hence the SPL were bothlarger than those for the other nozzles, albeit ata higher harmonic (667 Hz) of the PDE cycle fre-quency (about 333 Hz). This behavior is reflected inTable 2 for SPL values at various locations.

Location Config. 1 SPL Config. 4 SPLThrust wall 212 dB 210 dBMid-tube 211 dB 208 dBTube end 205 dB 202 dBNozzle 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 inthe divergent nozzles as compared with that forthe straight nozzle. The lower pressure and SPLin the upstream portions of the straight nozzle(as compared with the divergent nozzles) possiblycould 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 unclearwhy the pressure perturbation of the higher har-monic (660 Hz) in the straight nozzle was so muchlarger than for the divergent nozzles. This and othernoise related issues require further exploration in thefuture.

The full kinetics simulations of the reactant-filled,straight PDE tube without a nozzle allowed a moredetailed examination of the detonation ignition andpropagation process to be made, in addition to morequantitative comparisons with experimental data.Figure 7 displays the evolution of the 2D pressurefield associated with the PDE tube and its sur-roundings, for a full H2 − O2 reaction. As seen inprior 2D simulations of the PDE but with simplifiedkinetics

15, the propagation of the detonation out of

the tube resulted in the propagation of a vorticalstructure 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 wasobserved, especially in the propagating shock/vortexstructure 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 fullkinetics simulations. Figure 8 shows the centerlinepressure distribution for a 1D, full kinetics simula-tion of an H2−O2 −Ar mixture, for different initialtemperatures and pressures in the 3 grid cell-wide“spark” adjacent to the thrust wall. Critical combi-nations of temperature and pressure were observedto be necessary for the classical ZND detonationstructure to evolve; if the initial energy depositionwas too small, a weak shock front did not ignite themixture 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 wererequired for ignition of a detonation.

Temp. Press. Energy (erg/cm2) Deton.?500K 3 atm 2.02 × 105 No1000K 3 atm 8.06 × 105 No1500K 3 atm 9.95 × 105 Yes2000K 3 atm 11.0 × 105 Yes1500K 5 atm 15.3 × 105 Yes1500K 2.5 atm 8.63 × 105 Yes1500K 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.


AIAA–2003–1171

Temp. Press. Energy (erg/cm2) Deton.?800K 1 atm 4.54 × 105 No900K 1 atm 4.89 × 105 No1000K 1 atm 5.18 × 105 Yes1200K 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 ignitionof a detonation were found to be different for thesedifferent reactions. In the case of H2 − O2 − N2,a critical energy deposition per unit area of about5×105 erg/cm2 was required for detonation, whereasfor the case of H2 −O2 −Ar, this critical value roseto about 8.5 × 105 erg/cm2.

The full kinetics simulations also allowed quanti-tative comparisons to be made between performanceparameters from the present simulations and thoseobtained by experiment (for a single cycle PDE) oranalysis. Table 5 below shows the current estima-tions of Isp for the PDE for H2−O2 and H2−O2−N2

(hydrogen-air) reactions, as compared with the anal-ysis and experiments described in Wintenberger

26

and the experiments of Zitoun27

and Schauer28

.

Study Isp, H2-air Isp, H2 − O2

Present 128.5 s 240 sWintenberger

26123.7 s 173 s

CIT expts.26

– 200 sZitoun expts.

27149 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 pulsedetonation 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 asIsp may decrease with increasing nozzle exit area,the noise generation at the nozzle exit may actu-ally be reduced, and hence these tradeoffs may beexplored through simplified reaction kinetics stud-ies. Simulations of PDE evolution with full chemi-cal kinetics suggested that specific minimum energydensities were required to enable the initiation of adetonation, and hence to sustain the PDE cycle. Fi-nally, it was observed that full kinetics simulationswere able to capture quantitatively the physical phe-nomena and corresponding performance parametersfor the PDE. Future studies will continue with thisquantitative comparison as well as noise generationissues relevant to the PDE.

Acknowledgments

This work has been supported at UCLA by NASADryden Flight Research Center under Grant NCC4-153, with Dr. Trong Bui and Dave Lux as technicalmonitors, and by the Office of Naval Research un-der Grant ONR N00014-97-1-0027, with Dr. WenMasters as technical monitor.

References

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[2] Kailasanath, K., “Recent Developments inthe Research on Pulse Detonation Engines”,AIAA Paper 2002-0470 (Invited), AIAA 40thAerospace Sciences Meeting, January, 2002.

[3] Helman, D., Shreeve, R. P., and Eidelman, S.,“Detonation Pulse Engine”, AIAA Paper 86-1683, June, 1986.


AIAA–2003–1171

[4] Cambier, J.-L. and Tegner, J. K., “Strategiesfor 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 FuelConcentration 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 forHigh Speed Flight”, Paper ID 17-5169, pre-sented at the 11th AIAA/AAAF InternationalConference on Space Planes and HypersonicSystems 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., “PerformanceEstimates of Pulsed Detonation Engines”, 28thSymposium (Intl.) on Combustion, 2000.

[10] Johnson, C., “The Effects of Nozzle Geometryon the Specific Impulse of a Pulse DetonationEngine”, Final Report 16.622, MIT, December,2001.

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[19] “Three Pillars for Success: NASA’s Responseto Achieve the National Priorities in Aeronau-tics and Space Transportation”, NASA Officeof 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.

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[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 CyclePulse Detonation Engine”, AIAA Paper 2001-3811, July, 2001.

[27] Zitoun, R. and Desbordes, D., “Propulsive Per-formances of Pulsed Detonations”, CombustionScience 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”, AIAAPaper no. 2001-1129, 2001.

a)

b)

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.


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0 0.5 1 1.5X (m)

0

0.1

0.2

0.3

0.4

0.5

Rad

ius

(m)

nozzle 1nozzle 2nozzle 3nozzle 4

Fig. 2: Different nozzle geometries explores inpresent 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 constantdivergence angle (configuration 3). In all case thereactants are assumed to lie initially upstream ofnozzle, in the constant area tube, while the nozzleitself contains inert gas.

X (m)

Pre

ssur

e(a

tm)

0 0.5 1 1.5 2 2.50

5

10

15

20

25

30

(a)

X (m)

Pre

ssur

e(a

tm)

0 0.5 1 1.5 2 2.50

5

10

15

20

25

30

(b)

X (m)

Pre

ssur

e(a

tm)

0 0.5 1 1.5 2 2.50

5

10

15

20

25

30

(c)

X (m)

Pre

ssur

e(a

tm)

0 0.5 1 1.5 2 2.50

5

10

15

20

25

30

(d)

Fig. 3: Evolution of the centerline pressure for astraight 2D axisymmetric PDE of 1 m length, attimes (a) 0.06 ms, (b) 0.15 ms, (c) 0.49 ms, and (d)2.89 ms.9

American Institute of Aeronautics and Astronautics

AIAA–2003–1171

0 0.001 0.002 0.003 0.004Time (sec.)

0

50

100

150

200

250

300

350

Sp

ecifi

c Im

puls

e (s

ec.)

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 anda temperature of 3000K in order to match the initialconditions for the 2D simulation.

0 0.001 0.002 0.003Time (sec.)

0

500

1000

1500

2000

2500

Imp

ulse

per

uni

t are

a (p

s.s)


0 0.001 0.002 0.003Time (sec.)

0

50

100

150

200

250

Isp

(se

c.)

0 0.001 0.002 0.003Time (sec.)

0

100

200

300

400

500

600

700

800

900

1000

1100

1200

1300

Isp

f (se

c.)

Fig. 5: Comparisons of time-dependent performanceparameters 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.


AIAA–2003–1171

0 2500 5000 7500 10000Frequency (HZ)

0

1

2

3

4

5

6

7

[P]/P

0


(a)

0 2500 5000 7500 10000Frequency (HZ)

0

0.5

1

1.5

2

2.5

3

3.5

4

[P]/P

0


(b)

0 2500 5000 7500 10000Frequency (HZ)

0

1

2

3

[P]/P

0


(c)

Fig. 6: Comparisons of pressure spectra: (a) in themiddle of the detonation tube, (b) at the end of thestraight part of the detonation tube, and (c) at theend of the nozzle. Results are shown for differentnozzle configurations (see Fig. 2).

50 100 150 200 250 300 350X (cm)

-50

0

50

100

150

200

Y (

cm)

(a)

50 100 150 200 250 300 350X (cm)

-50

0

50

100

150

200

Y (

cm)

9.66811E+069.09111E+068.51411E+067.93711E+067.36011E+066.78311E+066.20611E+065.62911E+065.05211E+064.47511E+063.89811E+063.32111E+062.74411E+062.16711E+061.59011E+06

(b)

50 100 150 200 250 300 350X (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 onecycle, with pressure given in units of dyn/cm2. Datashown are at times corresponding to (a) 0.15 ms, (b)0.47 ms, and (c) 1.34 ms. A H2 − O2 reaction wassimulated here with full chemical kinetics.


AIAA–2003–1171

0 10 20 30 40X (cm)

0

2E+06

4E+06

6E+06

8E+06

1E+07

1.2E+07

1.4E+07

1.6E+07

1.8E+07

Pre

ssur

e (d

yn/c

m2 )

Ps = 2.0 AtmPs = 2.5 AtmPs = 3.0 AtmPs = 5.0 Atm

(a)

0 10 20 30 40X (cm)

0

2E+06

4E+06

6E+06

8E+06

1E+07

1.2E+07

1.4E+07

1.6E+07

1.8E+07

Pre

ssur

e (d

yn/c

m2 )

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 temperature1500K and variable pressure, and (b) fixed pressure3 atm and variable temperature, each at time 0.2msec.


AIAA 2003-1171 Reactive Flow Phenomena in Pulse Detonation ... · PDF filepulse detonation...

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