This report is an account of research carried out from January to June 2000 on the feasibility of detonation initiation and impulse generation for small-scale pulse detonation engines. The initial work was focussed on the direct measurement of impulse using the ballistic pendulum technique for single detonations initiated in a tube with one end open to the atmosphere through a thin diaphragm. Three tubes were used: (1) 38-mm diameter by 1.5 m long. (2) 75-mm diameter by 0.6 m long. (3) 75-mm diameter by 1 m long. At the closed end of the tube, combustion was initiated by a low energy, less than 50 mJ, capacitor discharge system. A fast flame or detonation was created by transition to detonation. The effect of spirals and orifice plates was examined on propane- and ethylene-oxygen-nitrogen mixtures with varying initial pressure, equivalence ratio, and dilution amounts. A simple model for the impulse in prompt detonations was developed and calibrated. The results of our experiments were compared with this model

Austin, J. M.

Cooper, M.

Jackson, S.

Shepherd, J. E.

Sturtevant, B.

Wintenberger, E.

English

Caltech Authors - Main

1Small Scale Detonation Studies
Direct impulse measurements for detonations and deflagrations
J.M. Austin, M. Cooper, S. Jackson, E. Wintenberger, J.E. Shepherd, B. Sturtevant
Graduate Aeronautical Laboratories
California Institute of Technology
Pasadena, CA 91125
July 13, 2000
Explosion Dynamics Laboratory Report FM00-5
Prepared for General Electric, contract GE - PO A02 81655 under DABT-63-0-0001
Introduction
This report is an account of research carried out from January to June 2000 on the
feasibility of detonation initiation and impulse generation for small-scale pulse detonation
engines.  The initial work was focussed on the direct measurement of impulse using the
ballistic pendulum technique for single detonations initiated in a tube with one end open
to the atmosphere through a thin diaphragm.   Three tubes were used:  (1) 38-mm
diameter by 1.5 m long. (2) 75-mm diameter by 0.6 m long. (3) 75-mm diameter by 1 m
long.   At the closed end of the tube, combustion was initiated by a low energy, less than
50 mJ, capacitor discharge system. A fast flame or detonation was created by transition to
detonation.  The effect of spirals and orifice plates was examined on propane- and
ethylene-oxygen-nitrogen mixtures with varying initial pressure, equivalence ratio, and
dilution amounts. A simple model for the impulse in prompt detonations was developed
and calibrated.  The results of our experiments were compared with this model.
Experimental Setup
Direct measurements were made of the impulse delivered by a DDT-initiated detonation
or a fast flame.  The impulse was determined by measuring the displacement of a ballistic
pendulum in which a tube was suspended from the ceiling by steel wires (Fig. 1).  The
combustible mixture, initially contained in the tube by a thin diaphragm, was ignited by a
spark at the thrust wall.   Combustion products were free to expand out from the tube into
an unconfined volume.  Pressure histories were recorded, including the pressure at the
thrust wall which was then integrated for comparison with the ballistically-determined
impulse (Fig. 2).  Ionization gauges were used to determine the time-of-arrival of the
wave.  A calibration experiment was performed in which a detonation was directly
initiated in stoichiometric acetylene-oxygen with no obstacles present in the tube.  The
2ballistically-measured impulse was within 3.5% of the value obtained by integrating the
thrust-wall pressure trace.
Figure 1. Impulse measurement by a ballistic pendulum.
Figure 2. Sample pressure trace recorded at thrust wall.
Analytical Model
Experimental impulse measurements for detonations were compared with analytical
predictions.  The analytical model approximates the pressure history by two regions: an
approximately constant pressure region which begins with the passage of the Taylor wave
and ends with the arrival of the first characteristic of the reflected wave (usually an
expansion) at the thrust wall, and a second region which models the pressure decrease
through the remaining reflected wave.  The two regions are described by two parameters,
a and b (Fig. 3).  A similarity solution can be used to determine a and comparison with
experimental pressure histories shows excellent agreement. b is determined by
integrating the appropriate region of experimental and numerical pressure traces.  Both
experimental and numerical results indicate that the flow may be overexpanded by the
reflected rarefaction.  If this occurs, the impulse decreases from the peak value and care
must be taken in determining the impulse from the integrated pressure trace.
Detonation Tube
Clamps that attach 
tube to steel wires
Steel wires
Detonation Tube
ScaleFiducial
Dx
Deflection
Initial Position Fully Deflected Position
3 2
 1
 -c3
 c3
 UCJ
 t1 + t2
 t1
 thrust wall
       L
open end
 t
 x
 3
 Non-simple region
Figure 3. Gas dynamic processes inside the detonation tube.
 
 t 2   t 1  
 P 1  
 I g n i t i o n  
 t  
 P  
 P 2  
 P 3  
 t 3  
( )dttP
Pc
L
t
c
L
t
U
L
t
tCJ
ò
¥
D
D
====
23
1
3
3
3
21
ba
Figure 4. Idealized pressure trace used in the analytical model and parameter definitions.
The values of a and b will depend on the fuel concentration, initial pressure, and amount
of dilution. The value of a was evaluated using the single-g ideal detonation model and
found to be 1 < a < 1.1, weakly dependent on the detonation Mach number and ratio of
specific heats g.   An approximate value of 1.1 can be used for quick estimates of the
impulse. The values of b determined to be about 0.53 from numerical integration of
pressure traces.   The impulse is
( )÷÷ø
ö
ççè
æ ++D= ba
3
3 1
c
U
U
PAL
I CJ
CJ
where C3 is the sound speed at the end of Taylor wave.  The ratio UCJ/C3 is approximately
2 for fuel-oxygen-nitrogen mixtures, therefore the impulse is approximately
4V
U
PI
CJ
33.4 D=
where V is the tube volume,  V = AL.
Results
The impulse was directly measured for three tubes with length to internal diameter (L/d)
ratios of 40, 13 and 8. Various obstacle configurations were investigated, including
spirals of varying pitch, blockage plates and orifice plates.
Figure 5. Combustion products expanding out  from a detonation tube.  The initial
mixture was 2C2H4+6O2+2N2 at 100kPa.
The tube with L/d ratio of 8 had an internal diameter tube of 75 mm (3 in).  4 ionization
gauges and 4 PCB pressure transducers, including one positioned on the thrust wall, were
mounted along the tube.   Two spirals of different pitch (28 and 50mm) were used to
induce DDT in ethylene and propane in oxygen with increasing nitrogen dilution up to
air. The blockage ratio was held constant at 0.43.  Initial pressures ranged from 50-100
kPa. .  Different regimes of detonation, DDT and fast and slow flames were observed
with varying nitrogen dilution and some examples of pressure histories are given in
Appendix A.
Direct impulse measurements are shown in Fig. 7 for the two spiral configurations. There
is little difference in the impulse obtained for the two configurations and both agree quite
well with the theoretical predictions in mixtures where a detonation was recorded.  In
cases with higher nitrogen dilution, only a flame was observed.  The impulse obtained
was significantly reduced in these cases.
The tube with L/d ratio of 13 also has a 75 mm (3 in) internal diameter.  10 ionization
gauges and 4 pressure transducers, including one positioned in the thrust wall, were
mounted along the tube.  Measurements were carried out in stoichiometric ethylene-
oxygen mixtures with nitrogen dilution in a tube free of obstacles and with three different
5Figure 6.  Impulse measurements for stoichiometric C3H8-O2 mixtures with varying N2
dilution and initial pressure for two spiral configurations.  Impulse determined from the
ballistic pendulum is compared to values calculated from the theoretical model.
obstacle configurations: blockage plates spaced at one tube diameter were suspended
along the centerline of the entire tube by a single threaded rod, orifice plates were spaced
at one tube diameter both along the entire length of the tube and along half the length of
the tube in the upstream portion.  Each obstacle configuration had a blockage ratio of
0.43.  The inclusion of obstacles dramatically reduced the DDT times and distances (Fig.
7).  At 30kPa initial pressure, the obstacles reduced the DDT time and distance by 88.5%.
The obstacles allowed DDT to occur in mixture composed of up to 60% nitrogen.  With
no obstacles present, DDT was not achieved in mixtures with more than 30% nitrogen.
Only a fast flame could be initiated in ethylene-air.
Figure 7. Measured DDT time for stoichiometric C2H4-O2 mixtures with varying N2
dilution and initial pressure for three obstacle configurations.
The impulse increased by a factor of 2 over a fast flame when a highly diluted mixture
could be made to transition to detonation by the presence of obstacles (Fig. 8).  In
6mixtures in which DDT occurred in the absence of obstacles, the inclusion of obstacles
reduced the impulse measured by about 25%.    It is important to note that in these cases,
the impulse derived from the thrust-wall pressure trace overpredicts the impulse
measured by the ballistic pendulum by a factor of two since the pressure integration
neglects the momentum lost to drag over the obstacles.
The volume of the L/D = 13 tube is about twice that of the shorter tube discussed above
and with blockage or orifice plates of the same blockage ratio as the spirals, the measured
impulse is around twice that measured for the shorter tube for the same mixture.
Figure 8. Impulse measurements for stoichiometric C2H4-O2 mixtures with varying N2
dilution and initial pressure for three obstacle configurations.  Impulse determined from
the ballistic pendulum is compared to values obtained by integrating the thrust wall
pressure history and to values calculated from the theoretical model.
Summary
Including obstacles decreased the time needed for transition to detonation and enabled
transition in stoichiometric ethylene-oxygen and propane-oxygen mixtures with up to
60% N2 in 75-mm diameter tubes.  Without obstacles, detonation could only be initiated
in mixtures with up to 30% nitrogen in the 1-m long tube.  Detonation could not be
initiated in either fuel in stoichiometric mixtures with air.  The impulse obtained using
obstacles to produce a fast flame in fuel-air mixtures was about 1/2 of the theoretical
impulse predicted for prompt detonation.
The obstacles used were two spirals, repeated orifice plates and repeated central blockage
plates.  In all cases, the blockage ratio (obstructed area divided by total cross sectional
area) was 0.43.   No significant differences were observed between the effectiveness of
the different types of obstacles.   Including the obstacles reduced the measured impulse
by about 25% in cases where detonation could be initiated promptly without obstacles.
A simple model was developed to predict the impulse from a prompt initiation of
detonation.  This model agrees well with cases in which prompt detonation occurs and
7provides an upper bound for the impulse obtained in our testing.
Future Work
To conclude the first phase of this contract, additional tests are in progress to measure the
effect of exit end conditions on the ballistic impulse.  A flange, a straight extension, and a
cone will be placed at the end of the 75 mm diam, 1 m long tube to determine how these
influence the ballistic impulse for cases that have been examined previously in this study.
The next phase of the contract will involve development methods to reliably initiate
detonation in fuel-air mixtures. This work will proceed by constructing a proof of concept
device, implementing this as prototype initiator system on the 75-mm diameter tube,
measuring DDT times and impulses for fuel-air mixtures.  Initially the fuel will be
propane but a heated tube is also under development that will enable working with
aviation fuels such as Jet A and JP-10.
8Appendix A. Pressure histories recorded in C3H8-O2 mixtures with varying ß at 100kPa,
where ß is the ratio of N2 to O2 concentration in the initial mixture.  The tube has a L/d
ratio of 8.
Shot30: detonation
9Shot31: DDT
10
Shot33: Fast flame
11
Shot35: Slow flame


Small Scale Detonation Studies: Direct impulse measurements for detonations and deflagrations

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Small Scale Detonation Studies: Direct impulse measurements for detonations and deflagrations

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