AIAA JOURNAL
Vol. 41, No. 10, October 2003
Numerical Analysis of First and Second Cycles
of Oxyhydrogen Pulse Detonation Engine
¤
†
Soshi Kawai and Toshi Fujiwara
Nagoya University, Nagoya 464-8603, Japan
In the present study, numerical analysis of pulse-detonation-engine (PDE) cycles such as combustion, exhaus-
tion, and fuel-injection phases is performed. A numerical scheme that is second-order accurate in time and space,
MacCormack-total-variation-diminishing scheme, was used to solve the Navier–Stokes equations, where a simpli-
ed two-step chemical reaction model is introduced. The dependence of fuel-injection time on 1) the opening width
of intake port, 2) reservoir pressure, and 3) injection angle is studied. Through the numerical analysis of PDE-cycle
operation, the time required for each phase is estimated for each model PDE; the dependence on PDE tube length
and the time required for PDE operation are studied. The performances (such as impulse and thrust density) of
four straight model PDEs that have different tube lengths are estimated and compared with the theoretical result
of Endo–Fujiwara analysis. The useful formula for impulse per unit area, which is similar to the expression in the
theoretical analysis, is derived from the numerical analysis.
Introduction
In studying PDE, a key issue would be how to generate a
Chapman–Jouguet (CJ)/quasi-CJdetonationin a short distanceand
howto realizehigh-frequencyoperation.Therefore,investigationof
fuel injection and subsequentignition has become unavoidableand
important.
DETONATION phenomenon is the interaction between a
front-running shock wave and subsequent coupled combus-
tion, generating a high pressure and temperature that is basically
uncontrollablein comparison with conventional ames. The direc-
tion of research has mostly been prevention of or protection from
hazard.
For several years, however, there has been a trend to control
detonation propagation and to utilize its high power and high-
density energy in positive directions like pulse detonation engine
A
In the present work, a two-dimensional cycle analysis of PDE
containing an Ar-diluted stoichiometric oxyhydrogen mixture is
performed. To achieve a high-frequency-running engine, we pay
attention specically to the exhaustion and injection process for
the second cycle, where the burned gas generated in the rst cy-
cle still remains within PDE. A second-order MacCormack-total-
variation-diminishing(TVD) schemeisusedtosolveNavier–Stokes
1
(
PDE) ; Eidelman and Grossmann reignited the study of PDE.
Pulse-detonation-engine research has spread widely recently be-
cause it is considereda good candidatefor an aerospacepropulsion
9
equations where a simpli ed two-step chemical reaction model is
2
introduced.
system of the next generation.
The operationalprinciple of PDE can be explained briey in the
following. As a simple example, a rocket-engine-typePDE opera-
tion of cylindricalshape is considered.The cycle operationof PDE
consistsof the four phases, which are fuelsupply,ignition,combus-
tion, and exhaustion.As shown in Fig. 1, a mixture of hydrogenfuel
and oxygen is supplied into PDE, followed by the ignition of mix-
tureby an igniterplacedover the closedupstreamend. The combus-
tion wave is acelerated to a detonation and propagates downstream
in PDE. Thereafter, the detonation wave is emitted from PDE exit,
with the burnedgas beingexhausted.By repeatingsuch four phases,
PDE generates thrust.
Mathematical Model and Numerical Method
Governing Equations and Numerical Method
The governing equations are two-dimensional Navier–Stokes
ones, containing the mass-conservationequations for two progress
variables® (induction reaction) and ¯ (exothermic reaction):
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One-dimensionalnumericaland theoreticalanalysesof PDE have
been performed by numerous workers3¡6 without considering in-
jection phase and diffusive transportprocesses(viscosity,heat con-
ductivity,and diffusion).In one-dimensionalanalysis, furthermore,
it is dif cult to treat fuel injection and mixing process, which
are the longest time-consuming processes during PDE operation.
Two-dimensional numerical analyses of PDE also have been per-
where
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formed by some workers.7 In these studies, however, diffusive
transport processes and fuel injection in PDE operation were not
considered.
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Received 15 March 2002; revision received 6 March 2003; accepted
0
1
for publication 7 May 2003. Copyright °c 2003 by Soshi Kawai and
0
Toshi Fujiwara. Published by the American Institute of Aeronautics and
Astronautics, Inc., with permission. Copies of this paper may be made for
personal or internal use, on conditionthat the copier pay the $10.00per-copy
fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers,
MA 01923; include the code 0001-1452/03 $10.00 in correspondence with
the CCC.
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Graduate Student, Department of Aerospace Engineering; kawai@ ab.
@
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eng.isas.ac.jp. Student Member AIAA.
†
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Professor, Department of Aerospace Engineering.
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