Mixing and Combustion of Rich Fireballs
F. Pintgen and J. E. Shepherd
Graduate Aeronautical Laboratories
California Institute of Technology
Pasadena, CA 91125
U.S.A.
GALCIT Report FM2003-004
October 14, 2003
prepared for Sandia National Laboratory
Albuquerque, NM USA
Abstract
A series of experiments was carried out to investigate the effect of fireball composition
on secondary combustion. The fireball was created from a 1.5 liter balloon filled with
a propane-oxygen mixture (1
<
Φ
<
3) and initiated by a detonation. Two initiation
locations and two initiator strengths were studied. Two pencil pressure gauges located
at 0.6 and 1.2 m and in some experiments, simultaneous high-speed imaging, were used
as diagnostics. For Φ
>
1, the incompletely oxidized products from the primary burn
mix with the surrounding air and may be oxidized in a secondary combustion process.
The unique feature of the present experiments was a repeatable secondary pressure
pulse for sufficiently rich mixtures. The secondary pressure rise was observed repeatably
for all initiation configurations. The nature of the secondary pressure pulse is a strong
function of the initial equivalence ratio. For Φ = 1 and 1.5, no secondary pressure waves
are observed. An acoustic analysis of the measured pressure histories has been carried
out to infer the rate of volume displacement and the total volume displaced by the
secondary combustion. The results of the acoustic analysis are in reasonable agreement
with both a simplified thermodynamic model predicting the total volume displacement
assuming constant-pressure combustion for the secondary burn and the analysis of the
fireball luminosity of the high-speed images.
For nearly stoichiometric mixtures, Φ = 1 and 1.5, the leading blast wave peak pres-
sures and impulses are comparable with the previously-measured gaseous and high explo-
sive blasts when the energy content of the balloon only is used to formulate Sachs scaling
variables. Due to a much slower combustion process than detonation for Φ
>
2 the peak
pressure of the leading wave rapidly decreases below the energy-equivalent reference blast
values as the equivalence ratio is increased. The Sachs-scaled impulse agrees well with
the predictions on the basis of the energy in the balloon alone for 2.75
>
Φ
>
1.
One of the key results of the present study has been the documentation of the existence
i
of the secondary pressure wave. The present study has emphasized the acoustic nature of
the secondary pressure waves and the origin of these pressure waves due to the processes
at the interface between the fireball and the atmosphere. The presence of the secondary
pressure peak and the higher impulses indicate that there is the potential for significant
enhancement of the blast through secondary combustion.
ii
Contents
Abstract
i
List of Figures
v
List of Tables
xi
1 Introduction
1
2 Experimental Setup
3
3 Results
7
3.1 Initiator Characterization
. . . . . . . . . . . . . . . . . . . . . . . . . .
7
3.2 Propane-oxygen Initiator Mixture
. . . . . . . . . . . . . . . . . . . . . .
7
3.3 Sachs-scaled Results
. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
12
3.4 Acetylene-oxygen Initiator Mixture
. . . . . . . . . . . . . . . . . . . . .
19
3.5 Initiation Location
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
20
3.6 Analysis of Secondary Combustion Process
. . . . . . . . . . . . . . . . .
25
3.7 Acoustic Approach to Secondary Combustion
. . . . . . . . . . . . . . .
30
3.8 High-speed camera imaging
. . . . . . . . . . . . . . . . . . . . . . . . .
36
4 Conclusions
41
4.1 Future Directions
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
43
Bibliography
45
A Plots
47
A.1 Peak pressure
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
47
A.2 Impulse
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
50
A.3 Time to Secondary Pressure Peak
. . . . . . . . . . . . . . . . . . . . . .
52
A.4 Pressure traces
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
53
A.5 Species shift during expansion
. . . . . . . . . . . . . . . . . . . . . . . .
55
A.6 Pencil gauge calibration
. . . . . . . . . . . . . . . . . . . . . . . . . . .
57
B Highspeed movies
59
C Shotlist
87
D Initial balloon shape
89
iii
iv
List of Figures
1
Major products calculated for a constant volume combustion for a
propane-oxygen mixture as a function of the equivalence ratio.
. . . .
3
2
Initiation locations
. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3
3
Detailed drawing of initiator tube and set-up
. . . . . . . . . . . . . .
4
4
Schematic of plumbing for balloon filling procedure.
. . . . . . . . . .
5
5
Plan view of blast room with location of fire ball center and blast pencil
gauges.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5
6
Photograph of actual test rig
. . . . . . . . . . . . . . . . . . . . . . .
6
7
Example pressure traces of experiment with initiator charge only
. . .
7
8
Pressure traces obtained from the pencil gauges at 0.6 and 1.2 m.
. . .
9
9
Peak pressure measured for C
3
H
8
-O
2
initiator mixture.
. . . . . . . . .
10
10
Mach number obtained from shock jump conditions for C
3
H
8
-O
2
initia-
tor mixture.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10
11
Delay between blast wave and secondary pressure peak for C
3
H
8
-O
2
initiator mixture. Center initiation location.
. . . . . . . . . . . . . . .
11
12
Maximum positive impulse obtained from integrating the pressure trace.
C
3
H
8
-O
2
initiator mixture. Center initiation location.
. . . . . . . . .
11
13
Point in time at which the maximum positive impulse (Fig.
12
) occurs.
C
3
H
8
-O
2
initiator mixture. Center initiation location.
. . . . . . . . .
11
14
Delay between blast wave and secondary pressure peak for C
3
H
8
-O
2
and
C
2
H
2
-O
2
initiator mixture. Center initiation location.
. . . . . . . . .
11
15
Amount of fuel and oxidizer for different equivalence ratios.
. . . . . .
13
16
Balloon charge energies for varying equivalence ratio.
. . . . . . . . . .
13
17
Ratio for temperature and number of moles of reactants to expanded
products as a function of equivalence ratio.
. . . . . . . . . . . . . . .
14
18
Sachs-scaled peak pressure vs. distance based on energy content
E
1
.
C
3
H
8
-O
2
initiator mixture. Center initiation location.
. . . . . . . . .
14
19
Sachs-scaled impulse based on
E
1
vs. distance. C
3
H
8
-O
2
initiator mix-
ture. Center initiation location.
. . . . . . . . . . . . . . . . . . . . . .
14
20
Sachs-scaled impulse based on
E
2
vs. distance based on energy content
E
2
. C
3
H
8
-O
2
initiator mixture. Center initiation location.
. . . . . . .
14
21
Peak pressure of blast wave vs. equivalence ratio for stoichiometric
C
2
H
2
-O
2
and C
3
H
8
-O
2
initiator mixtures. Center initiation location.
.
20
22
Mach number of blast wave derived from shock jump conditions for sto-
ichiometric C
2
H
2
-O
2
and C
3
H
8
-O
2
initiator mixtures. Center initiation
location.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
20
23
Comparison of Sachs’
E
1
-scaled blast wave peak pressure vs. scaled
distance for the C
2
H
2
-O
2
initiator mixture. Center initiation location.
Gauge locations: 0.6 m and 1.2 m.
. . . . . . . . . . . . . . . . . . . .
21
v
24
Peak blast wave pressure and peak pressure of secondary pressure rise
vs. equivalence ratio for stoichiometric C
2
H
2
-O
2
initiator mixture. Cen-
ter initiation location.
. . . . . . . . . . . . . . . . . . . . . . . . . . .
21
25
Comparison of blast wave pressure and peak pressure of secondary pres-
sure rise for C
2
H
2
-O
2
and C
3
H
8
-O
2
initiator mixtures. Center initiation
location. Gauge location: 0.6 m.
. . . . . . . . . . . . . . . . . . . . .
21
26
Comparison of blast wave pressure and peak pressure of secondary pres-
sure rise for C
2
H
2
-O
2
and C
3
H
8
-O
2
initiator mixtures. Center initiation
location. Gauge location: 1.2 m.
. . . . . . . . . . . . . . . . . . . . .
21
27
Impulse for C
2
H
2
-O
2
and C
3
H
8
-O
2
initiator mixture. Center initiation
location.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
22
28
Comparison of secondary wave peak time for C
2
H
2
-O
2
and C
3
H
8
-O
2
initiator mixtures. Center initiation location. Gauge location: 0.6 m.
.
22
29
Comparison of blast wave pressure for center and bottom initiation
locations. C
2
H
2
-O
2
initiator mixture.
. . . . . . . . . . . . . . . . . .
23
30
Comparison of Mach number derived from the shock jump condition
for center and bottom initiation locations. C
2
H
2
-O
2
initiator mixture.
23
31
Comparison of blast wave pressure and peak pressure of secondary pres-
sure rise for center and bottom initiation locations. C
2
H
2
-O
2
initiator
mixture. Gauge location: 0.6 m.
. . . . . . . . . . . . . . . . . . . . .
23
32
Comparison of blast wave pressure and peak pressure of secondary pres-
sure rise for center and bottom initiation locations. C
2
H
2
-O
2
initiator
mixture. Gauge location: 1.2 m.
. . . . . . . . . . . . . . . . . . . . .
23
33
Comparison of impulse derived from pressure traces for center and bot-
tom initiation locations. C
2
H
2
-O
2
initiator mixture.
. . . . . . . . . .
24
34
Comparison of point in time at which maximum impulse occurs for
center and bottom initiation locations. C
2
H
2
-O
2
initiator mixture.
. .
24
35
Delay between blast wave peak pressure and peak pressure of secondary
pressure rise for center (c) and bottom (b) initiation locations. C
2
H
2
-O
2
initiator mixture.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
24
36
Comparison of the
E
1
-Sachs-scaled impulse derived from pressure traces
for center and bottom initiation locations. C
2
H
2
-O
2
initiator mixture.
24
37
Schematic of model process used to analyze the primary and secondary
combustion events.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
25
38
Major products of state 1 and state 2 calculated for a constant volume
combustion for a propane-oxygen mixture as a function of the equiva-
lence ratio.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
27
39
Thermodynamic properties of state 1 calculated for a constant volume
combustion for a propane-oxygen mixture as a function of the equiva-
lence ratio.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
27
40
Shift in major species for chemically-equilibrated isentropic expansion
to atmospheric pressure calculated for Φ=1.
. . . . . . . . . . . . . . .
27
vi
41
Volume-temperature relationship for chemically-equilibrated isentropic
expansion to atmospheric pressure calculated for different equivalence
ratios of the primary combustion.
. . . . . . . . . . . . . . . . . . . . .
27
42
Volume-temperature relationship illustrating the dependence of heat
capacity ratios on equivalence ratio.
. . . . . . . . . . . . . . . . . . .
29
43
Temperature at states 3 and 4.
. . . . . . . . . . . . . . . . . . . . . .
29
44
Specific volume at states 3 and 4.
. . . . . . . . . . . . . . . . . . . . .
29
45
Volumes calculated for different states in the model cycle based on the
1.5 l charge as a function of initial equivalence ratio.
. . . . . . . . . .
29
46
Volume displacement rate calculated from Eq.
7
using the pressure his-
tory obtained at 0.6 m. Shot 106, Φ = 2.5.
. . . . . . . . . . . . . . .
32
47
Volume displacement rate calculated from Eq.
7
using the pressure his-
tory obtained at 0.6 m. Shot 106, Φ = 2.5.
. . . . . . . . . . . . . . .
32
48
Volume displacement rate calculated from Eq.
7
for both gauge locations.
32
49
Shot 174, Φ = 2.5. Volume displacement rate calculated from Eq.
7
using the pressure history obtained at 0.6 m.
. . . . . . . . . . . . . .
33
50
Volume displacement rate calculated from Eq.
7
using the pressure his-
tory obtained at 1.2 m. Shot 174, Φ = 2.5.
. . . . . . . . . . . . . . .
33
51
Volume displacement rate calculated from Eq.
7
for both gauge loca-
tions. Shot 174 and 175, both Φ = 2.5.
. . . . . . . . . . . . . . . . .
33
52
Volume displacement ∆
V
derived from integrating the volume displace-
ment rate
Q
shown in Fig.
51
and Fig.
48
. Φ = 2.5, C
3
H
8
-O
2
and
C
2
H
2
-O
2
initiator mixture.
. . . . . . . . . . . . . . . . . . . . . . . .
35
53
Volume displacement ∆
V
derived from integrating the volume displace-
ment rate
Q
shown in Fig.
51
and integrated volume of fireball from
high speed video. Shot 106. Φ = 2.5, C
3
H
8
-O
2
initiator mixture. The
delay time of
R/c
is included.
. . . . . . . . . . . . . . . . . . . . . . .
35
54
Luminous volume of fireball determined by analyzing the high-speed
video for shots at several different equivalence ratios. C
3
H
8
-O
2
initiator
mixture.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
35
55
Sequence of high-speed movie for Φ = 1.5 (shot 111).The complete
sequences for all high-speed movies is shown in Sec.
B
.
. . . . . . . . .
36
56
Luminosity derived from high-speed videos by averaging the luminosity
of each frame and normalizing by the peak luminosity.
. . . . . . . . .
38
57
Transit time ∆
t
that a blast wave needs to travel from the balloon edge
(0.07 m) to the gauge located at 0.6 m and 1.2 m as a function of the
blast wave peak pressure measured at the corresponding gauges.
. . .
39
A.1.1 Peak pressure for C
3
H
8
-O
2
initiator. Center initiation location.
. . . .
47
A.1.2 Peak pressure for C
3
H
8
-O
2
initiator. Center initiation location.
. . . .
47
A.1.3 Peak pressure for C
3
H
8
-O
2
initiator. Center initiation location.
. . . .
47
A.1.4 Peak pressure for C
2
H
2
-O
2
initiator. Center initiation location.
. . . .
47
A.1.5 Peak pressure for C
3
H
8
-O
2
and C
2
H
2
-O
2
initiator. 0.6 m. Center initi-
ation location.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
48
vii
A.1.6 Peak pressure for C
3
H
8
-O
2
and C
2
H
2
-O
2
initiator. 1.2 m. Center initi-
ation location.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
48
A.1.7 Peak pressure for center and bottom initiation location. 0.6 m. C
2
H
2
-
O
2
initiator mixture.
. . . . . . . . . . . . . . . . . . . . . . . . . . . .
48
A.1.8 Peak pressure for center and bottom initiation location. 1.2 m. C
2
H
2
-
O
2
initiator mixture.
. . . . . . . . . . . . . . . . . . . . . . . . . . . .
48
A.1.9
E
1
-Sachs-scaled impulse for both initiator mixtures versus Sachs-scaled
distance. Center initiation location.
. . . . . . . . . . . . . . . . . . .
49
A.1.10
E
1
-Sachs-scaled peak pressure for center and bottom initiation location
versus Sachs-scaled distance. C
2
H
2
-O
2
initiator mixture.
. . . . . . . .
49
A.1.11
E
2
-Sachs-scaled impulse for both initiator mixtures versus Sachs-scaled
distance. Center initiation location.
. . . . . . . . . . . . . . . . . . .
49
A.1.12
E
2
-Sachs-scaled peak pressure for center and bottom initiation location
versus Sachs-scaled distance. C
2
H
2
-O
2
initiator mixture.
. . . . . . . .
49
A.2.1 Impulse for both initiator mixtures versus equivalence ratio. Center
initiation location.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
50
A.2.2 Maximum impulse point in time for both initiator mixtures versus
equivalence ratio. Center initiation location.
. . . . . . . . . . . . . . .
50
A.2.3 Impulse for both initiation locations versus equivalence ratio. C
2
H
2
-O
2
initiator mixture.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
50
A.2.4 Maximum impulse point in time for both initiation lo actions versus
equivalence ratio. C
2
H
2
-O
2
initiator mixture.
. . . . . . . . . . . . . .
50
A.2.5
E
1
-Sachs-scaled impulse for both initiator mixtures versus Sachs-scaled
distance. Center initiation location.
. . . . . . . . . . . . . . . . . . .
51
A.2.6
E
2
-Sachs-scaled impulse for both initiator mixtures versus Sachs-scaled
distance. Center initiation location.
. . . . . . . . . . . . . . . . . . .
51
A.2.7
E
1
-Sachs-scaled impulse for center and bottom initiation location versus
Sachs-scaled distance. C
2
H
2
-O
2
initiator mixture.
. . . . . . . . . . . .
51
A.2.8
E
2
-Sachs-scaled impulse for center and bottom initiation location versus
Sachs-scaled distance. C
2
H
2
-O
2
initiator mixture.
. . . . . . . . . . . .
51
A.3.1 Time to secondary pressure peak for both initiator mixtures versus
equivalence ratio. Center initiation location.
. . . . . . . . . . . . . . .
52
A.3.2 Time to secondary pressure peak for both initiation locations versus
equivalence ratio. C
2
H
2
-O
2
initiator mixture.
. . . . . . . . . . . . . .
52
A.4.1 Examples of pressure traces for replica tests obtained from the pencil
gauge at 0.6 m. C
3
H
8
-O
2
initiator mixture. Center initiation location.
53
A.4.2 Examples of pressure traces for replica tests obtained from the pencil
gauge at 1.2 m. C
3
H
8
-O
2
initiator. Center initiation location.
. . . . .
54
A.5.1 Pressure-volume relationship for chemically-equilibrated isentropic ex-
pansion to atmospheric pressure calculated for different equivalence ra-
tios of the primary combustion.
. . . . . . . . . . . . . . . . . . . . . .
55
A.5.2 Shift in OH and H mole fraction for chemically-equilibrated isentropic
expansion from state 1 to state 2 to atmospheric pressure.
. . . . . . .
55
viii
A.5.3 Shift in O
2
and O mole fraction for chemically-equilibrated isentropic
expansion from state 1 to state 2 to atmospheric pressure. Note that Φ
only ranges from 1 to 2.
. . . . . . . . . . . . . . . . . . . . . . . . . .
55
A.5.4 Shift in major species for chemically-equilibrated isentropic expansion
from state 1 to state 2 to atmospheric pressure calculated for Φ=1.
. .
55
A.5.5 Shift in major species for chemically-equilibrated isentropic expansion
from state 1 to state 2 to atmospheric pressure calculated for Φ=1.5.
.
56
A.5.6 Shift in major species for chemically-equilibrated isentropic expansion
from state 1 to state 2 to atmospheric pressure calculated for Φ=2.
. .
56
A.5.7 Shift in major species for chemically-equilibrated isentropic expansion
from state 1 to state 2 to atmospheric pressure calculated for Φ=2.5.
.
56
A.5.8 Shift in major species for chemically-equilibrated isentropic expansion
from state 1 to state 2 to atmospheric pressure calculated for Φ=3.
. .
56
A.6.1 Calibration curves obtained from shock tube experiments for the two
pencil gauges used.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
57
B.1
Shot 113, frames 5 to 34, Φ
= 1
.
. . . . . . . . . . . . . . . . . . . . .
60
B.2
Shot 113, frames 35 to 49, Φ
= 1
.
. . . . . . . . . . . . . . . . . . . .
61
B.3
Shot 113. Pressure traces from the pencil gauges located at 0.6 and 1.2 m.
61
B.4
Shot 110, frames 5 to 34, Φ
= 1.5
. . . . . . . . . . . . . . . . . . . .
62
B.5
Shot 110, frames 35 to 49, Φ
= 1.5
.
. . . . . . . . . . . . . . . . . . .
63
B.6
Shot 110. Pressure traces from the pencil gauges located at 0.6 and 1.2 m.
63
B.7
Shot 111, frames 5 to 34, Φ
= 1.5
. . . . . . . . . . . . . . . . . . . .
64
B.8
Shot 111, frames 35 to 49, Φ
= 1.5
.
. . . . . . . . . . . . . . . . . . .
65
B.9
Shot 111. Pressure traces from the pencil gauges located at 0.6 and 1.2 m.
65
B.10 Shot 112, frames 5 to 34, Φ
= 1.5
.
. . . . . . . . . . . . . . . . . . . .
66
B.11 Shot 112, frames 35 to 49, Φ
= 1.5
.
. . . . . . . . . . . . . . . . . . .
67
B.12 Shot 112. Pressure traces from the pencil gauges located at 0.6 and 1.2 m.
67
B.13 Shot 107, frames 5 to 34, Φ
= 2
.
. . . . . . . . . . . . . . . . . . . . .
68
B.14 Shot 107, frames 35 to 49, Φ
= 2
.
. . . . . . . . . . . . . . . . . . . .
69
B.15 Shot 107. Pressure traces from the pencil gauges located at 0.6 and 1.2 m.
69
B.16 Shot 108, frames 5 to 34, Φ
= 2
.
. . . . . . . . . . . . . . . . . . . . .
70
B.17 Shot 108, frames 35 to 49, Φ
= 2
.
. . . . . . . . . . . . . . . . . . . .
71
B.18 Shot 108. Pressure traces from the pencil gauges located at 0.6 and 1.2 m.
71
B.19 Shot 109, frames 5 to 34, Φ
= 2
.
. . . . . . . . . . . . . . . . . . . . .
72
B.20 Shot 109, frames 35 to 49, Φ
= 2
.
. . . . . . . . . . . . . . . . . . . .
73
B.21 Shot 109. Pressure traces from the pencil gauges located at 0.6 and 1.2 m.
73
B.22 Shot 103, frames 5 to 34, Φ
= 2.5
.
. . . . . . . . . . . . . . . . . . . .
74
B.23 Shot 103, frames 35 to 49, Φ
= 2.5
.
. . . . . . . . . . . . . . . . . . .
75
B.24 Shot 103. Pressure traces from the pencil gauges located at 0.6 and 1.2 m.
75
B.25 Shot 104, frames 5 to 34, Φ
= 2.5
.
. . . . . . . . . . . . . . . . . . . .
76
B.26 Shot 104, frames 35 to 49, Φ
= 2.5
.
. . . . . . . . . . . . . . . . . . .
77
B.27 Shot 104. Pressure traces from the pencil gauges located at 0.6 and 1.2 m.
77
B.28 Shot 105, frames 5 to 34, Φ
= 2.5
.
. . . . . . . . . . . . . . . . . . . .
78
ix
B.29 Shot 105, frames 35 to 49, Φ
= 2.5
.
. . . . . . . . . . . . . . . . . . .
79
B.30 Shot 105. Pressure traces from the pencil gauges located at 0.6 and 1.2 m.
79
B.31 Shot 106, frames 5 to 34, Φ
= 2.5
.
. . . . . . . . . . . . . . . . . . . .
80
B.32 Shot 106, frames 35 to 49, Φ
= 2.5
.
. . . . . . . . . . . . . . . . . . .
81
B.33 Shot 106. Pressure traces from the pencil gauges located at 0.6 and 1.2 m.
81
B.34 Shot 114, frames 5 to 34, Φ
= 3
.
. . . . . . . . . . . . . . . . . . . . .
82
B.35 Shot 114, frames 35 to 49, Φ
= 3
.
. . . . . . . . . . . . . . . . . . . .
83
B.36 Shot 114. Pressure traces from the pencil gauges located at 0.6 and 1.2 m.
83
B.37 Shot 115, frames 5 to 34, Φ
= 3
.
. . . . . . . . . . . . . . . . . . . . .
84
B.38 Shot 115, frames 35 to 49, Φ
= 3
.
. . . . . . . . . . . . . . . . . . . .
85
B.39 Shot 115. Pressure traces from the pencil gauges located at 0.6 and 1.2 m.
85
D.1 Outline of balloon geometry
. . . . . . . . . . . . . . . . . . . . . . . .
89
x
List of Tables
1 Volume calculated for different states in the modeled combustion process.
28
2 Shotlist.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
87
3 Shot 109. Initial balloon outline coordinates are given in mm, where x is
the horizontal axis. The initiator tube was located for the center initiation
at the coordinate origin.
. . . . . . . . . . . . . . . . . . . . . . . . . . .
90
4 Shot 109. Initial balloon outline coordinates are given in mm, where x is
the horizontal axis. The initiator tube was located for the center initiation
at the coordinate origin.
. . . . . . . . . . . . . . . . . . . . . . . . . . .
91
5 Shot 114. Initial balloon outline coordinates are given in mm, where x is
the horizontal axis. The initiator tube was located for the center initiation
at the coordinate origin.
. . . . . . . . . . . . . . . . . . . . . . . . . . .
92
xi
xii
1
1 Introduction
We have carried out a series of experiments to study mixing and combustion of fireballs
created by the rapid combustion of rich gaseous explosive mixtures. There are two
combustion events in these experiments. A detonation is used to initiate the primary
(initial) combustion event in propane-oxygen mixtures with equivalence ratios between
one and three. The resulting fireball of combustion products expands and mixes with
the surrounding air, which can result in a secondary combustion event. Blast pressures
were measured at locations 0.6 m and 1.2 m from the center of the balloon containing
the propane-oxygen mixture. The experiments are the first in a series of tests designed
to study the role of fireball composition and gas dynamic interactions on secondary
combustion.
The amount of energy released during the initial combustion event and the secondary
reaction depends on the composition of the balloon mixture and the extent of the mixing
and reaction of the resulting fireball with the surrounding air. Initially, the mixture
inside the balloon was
Φ C
3
H
8
+ 5 O
2
,
where the equivalence ratio is 1
<
Φ
<
3. For a stoichiometric mixture, Φ = 1, complete
combustion occurs during the initial event and the products are fully oxidized
1
C
3
H
8
+ 5 O
2
−→
3 CO
2
+ 4 H
2
O .
In this case, all the energy is released in the initial combustion event and no further
reaction will take place upon mixing of the products with air. There is no secondary
combustion event in this case.
1
The products have been idealized in this reaction equations. Due to the high temperatures, 4000 K,
a substantial amount of dissociation occurs and equilibrium computations indicate that H
2
, CO, and O
are presented in substantial amounts, as shown in Fig.
1
2
1 INTRODUCTION
For Φ
>
1, the products of the initial combustion are incompletely oxidized and
energy will be released both during the initial combustion event and the secondary event
associated with the fireball. For example, at Φ = 3, the initial combustion reaction can
be approximately written as
3 C
3
H
8
+ 5 O
2
−→
9 CO + 11 H
2
+ H
2
O .
As indicated, the partially oxidized species CO and H
2
are created by the initial combus-
tion event in rich mixtures. As the equivalence ratio is increased, Fig.
1
, an increasing
amount of CO and H
2
is produced. When the fireball mixes with the surrounding air,
these can be oxidized to CO
2
and H
2
O,
CO +
1
2
O
2
−→
CO
2
, H
2
+
1
2
O
2
−→
H
2
O ,
releasing energy and creating pressure waves.
3
2 Experimental Setup
The propane-oxygen mixture is contained in a 1.5 liter (equivalent to a 140 mm diam-
eter sphere) balloon. The volume of the balloon was held constant at 1.5 liter for all
experiments. The fireball is initiated by a detonation defracting into the propane-oxygen
mixture out of the initiator tube which emerges from below into the balloon, Fig.
3
a. The
balloon is made of natural rubber latex and, in the inflated state, the wall thickness is
approximately 0.02 mm. The balloon is slightly bulb shaped, see Sec.
D
. The initiation
location of the balloon mixture can be adjusted by sliding the balloon retainer vertically
along the initiator tube. Two configurations are studied, Fig.
2
: a) The initiator tube
end is centered with respect to the balloon and b) The initiator tube end emerges into
the bottom of the balloon. In order to prevent leaking of the balloon mixture, the bal-
loon retainer is sealed with an O-ring against the initiator tube. The initiator tube has
a total length of 440 mm and contains two sections, one of which is equipped with a
equivalence ratio
Φ
absolute mol fraction
1
1.5
2
2.5
3
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
0.55
CO
2
H
2
H
2
O
CO
Figure 1: Major products calculated with
an equilibrium solver (STANJAN) for a
constant volume combustion for a propane-
oxygen mixture as a function of the equiv-
alence ratio. Initial temperature 294 K,
Initial pressure 1.013 bar.
Figure 2: Two initiation locations were
studied. The balloon retainer slides onto
the initiator tube and was locked in posi-
tion with a screw.
4
2 EXPERIMENTAL SETUP
Shchelkin spiral in order to ensure transition to detonation within the tube, Fig.
3
b. The
initiator tube of volume 0.13 l was sealed with a 0.02 mm thick polyethylene diaphragm
and then evacuated to 1 mbar prior to filling with a premixed initiator gas mixture to
atmospheric pressure. Stoichiometric propane-oxygen or stoichiometric acetylene-oxygen
mixtures were used in the initiator, labeled as C
3
H
8
or C
2
H
2
in the plot legends.
After filling the initiator, the balloon was attached and sealed with an elastic band to
the balloon retainer. The remaining air inside the balloon was evacuated prior to filling
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Figure 3: a) The initiator tube is sealed with an approximately 0.02 mm thick diaphragm.
b) Detailed technical drawing of initiator tube. The dimensions are given in mm. The
Shchelkin spiral has a pitch of approximately 25 mm, a wire diameter of 3 mm and an
outer diameter equal to the inner tube diameter.
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dure.
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Figure 5: Plan view of
blast room with location of
fire ball center and blast
pencil gauges.
the balloon by opening valve A and C, Fig.
4
. Since the balloon is elastic, the method
of partial pressures could not be applied directly to mix the propane and oxygen during
the balloon filling. Instead, a vessel of volume 3.8 l was evacuated to 1 mbar by opening
valve B and C and then filled with a premixed propane-oxygen mixture of the desired
stoichiometric ratio by the method of partial pressures through valve D. The premixing
vessel was filled to a final pressure of 1.5 bar and mixed by circulating the gas with a pump
for five minutes. After preparation of the mixture, valves A and B were opened, letting
the pressure in the balloon equilibrate close to atmospheric pressure. Due to tension,
the internal pressure was measured to be 20 mbar above the surrounding atmospheric
pressure. After the pressure equilibrated, the balloon itself contained a volume of 1.5 l
considering the volume of the filling lines. Subsequently, all valves were closed. The leak
rate of the balloon volume was measured to be less than 0.06 l/h, which results in a
volume uncertainty of less than 0.5%, since the charge was initiated within five minutes
after the filling procedure. A discharge system with a stored energy of 30 mJ was used
to ignite the initiator mixture with the spark plug.