Detonation interaction with a diffuse interface and subsequent chemical reaction

TL;DR: In this article, the authors investigated the interaction of a detonation with an interface separating a combustible from an oxidizing mixture, where the interface orientation and thickness with respect to the detonation wave have a profound effect on the outcome of the interaction.

Abstract: We have investigated the interaction of a detonation with an interface separating a combustible from an oxidizing mixture. The ethylene-oxygen combustible mixture had a fuel-rich composition to promote secondary combustion with the oxidizer in the turbulent mixing zone that resulted from the interaction. Diffuse interfaces were created by the formation of a gravity current using a sliding valve that initially separated the test gas and combustible mixture. Opening the valve allowed a gravity current to develop before the detonation was initiated. By varying the delay between opening the valve and initiating the detonation it was possible to achieve a wide range of interface conditions. The interface orientation and thickness with respect to the detonation wave have a profound effect on the outcome of the interaction. Diffuse interfaces result in curved detonation waves with a transmitted shock and following turbulent mixing zone. The impulse was measured to quantify the degree of secondary combustion, which accounted for 1–5% of the total impulse. A model was developed that estimated the volume expansion of a fluid element due to combustion in the turbulent mixing zone and predicted the resulting impulse increment.

Summary

1 Introduction

• When a detonation wave propagating in a gaseous combustible mixture reaches a concentration boundary, a complex interaction results between the detonation and interface between the two gases.
• In the present study, the interface is a composition gradient between the combustible and non-combustible mixtures.
• The authors have studied this case and the results will be presented in a companion paper.
• It is possible for combustion to occur in the turbulent mixing zone (TMZ) by choosing a combustible mixture such that the combustion products are incompletely oxidized.

2 Experimental setup

• The experiments were carried out using the GALCIT Detonation Tube (GDT) [1, 2] , which is 7.
• Figure 2 is a view of the test section illustrating the location of the end flange of the GDT, the sliding valve assembly, and the test section.
• Detonation velocities were measured to within 5% of the Chapman-Jouguet speed.
• The diffuse interface was made with a gravity current (GC).
• In the PLIF experiments, the combustible mixture in the GDT was replaced with an acetone-helium mixture of matched density.

3 Results and discussion

• The two layer situation was created by allowing a long time to elapse between the creation of the gravity current and detonation initiation (see discussion below).
• As the detonation exits the gravity current, what remains is a transmitted shock followed by the TMZ (c).
• The ture is colored yellow for visibility and flows below the less dense nitrogen gas.
• This translates to a leading shock wave that is for the most part perpendicular to the top and bottom surface along with a reflected trailing shock that is possibly due to slight imperfections in the interface shape.
• 4c except that the gravity current occupies half the height of the test section thus changing the curvature of the leading wave.

3.1 Composition gradient

• Experiments indicate the gravity current heads are out of the field of view and the unsteady motion is minimized.
• The composition gradient is estimated from the gravity current measurements [12, 20] which were carried out specifically to determine the role that the composition profile plays.
• The detonation shape velocities are obtained from the images using EQUATION and considering the detonation to have zero thickness.
• The wave angle β (see Fig. 1 ) is determined numerically from the wave shape.

3.2 Experimental impulse: the role of secondary combustion

• The impulse is calculated from experimental pressure traces to quantify the amount of secondary burning that occurs in the TMZ.
• The integration is carried out using the two-point Newton-Cotes method and the results reported in MPa s.
• The integration of the pressure trace starts at the arrival of the incident shock wave and terminates upon the arrival of pressure disturbances from the GDT approximately 5 ms later.
• The impulse has an abrupt change in slope at the arrival of the incident and reflected shocks.
• It was found that with all factors being equal, the impulse was 1-5% higher with oxygen versus nitrogen as the test gas.

3.2.1 Time scale of combustion

• This section addresses the chemical reaction time scale of the partially oxidized combustion products (CO and H 2 ) and the test gas.
• The initial temperature before the reaction takes place is a weighted average of the detonation products and shocked test gas temperatures and determined during the frozen composition mixing.
• The shear layer displacement thickness changes from being negative to positive causing the surrounding fluid to be displaced and generating compression waves.
• Given the simplicity of the model, only order of magnitude agreement can be expected at best.
• The fact that theory estimates impulses on the same order as the experimental findings indicates that secondary combustion in the TMZ is a plausible explanation for the impulse increment.

4 Conclusion

• The authors have experimentally studied detonation propagation along diffuse interfaces.
• The authors have observed the refraction of the detonation wave through the interface and subsequent creation of a turbulent mixing zone from the remains of the interfacial region.
• By using a fuel-rich ethylene-oxygen combustible mixture and an oxidizing test gas, the authors were able to observe and quantify the effects of combustion inside the turbulent mixing zone.
• The main consequence of the mixture composition gradient through the diffuse interface was to cause the detonation wave to curve: eventually the reaction zone decouples from the leading shock wave when the combustible mixture becomes sufficiently dilute.
• The authors attribute the wave curvature to the decrease in lead shock velocity with increasing dilu-.

Figures

Fig. 4 Four schlieren images from four separate experiments overlaid with the location of the gravity current at the instant of detonation initiation. Ethylene-oxygen (Φ=2.5) is the combustible mixture with pure nitrogen as the test gas. The delay times are 0 s (a), 1 s (b), 2 s (c), and 3 s (d). The vertical height yo is used to estimate the composition profile.

Fig. 5 Estimated mole fraction plotted as a function of vertical distance y in the test section. Two profiles are shown based on Equation (1) for the oxygen dilution case (O2) and the nitrogen dilution case (N2).

Fig. 12 A sketch of a fluid element expanding during chemical reaction at constant pressure and enthalpy.

Fig. 11 Induction time vs. oxygen mass fraction computed using a homogeneous mixing ignition time calculation (HMIT) on the left axis. Temperature and specific volume ratio vs. oxygen mass fraction on the right axis

Fig. 1 The interaction of a detonation with a diffuse interface is illustrated with supporting observations from experimental images. A detonation wave (a) interacts with the diffuse interface and forms a curved wave (b). Upon exiting the combustible mixture, the detonation decouples completely resulting in a transmitted shock and TMZ (c) and (d). When the shock reaches the endwall it reflects (e) and interacts for a second time with the interface.

Fig. 13 Impulse increment (%) for oxygen compared to nitrogen versus delay time. The impulse model prediction is plotted for a range of proportionality factors.

Fig. 8 Detonation velocity plotted as a function of vertical distance (y) in the test section. The profiles are shown for the oxygen dilution case (O2) and the nitrogen dilution case (N2).

Fig. 7 ZND induction time plotted as a function of vertical distance y in the test section. The profiles are shown for the oxygen dilution case (O2) and the nitrogen dilution case (N2).

Fig. 2 A schematic of the test section with the sliding valve assembly and the end flange of the GDT.

Fig. 10 An overlay of pressure and impulse vs. time at pressure transducer P5. The mixture is composed of 2.5C2H4 + 3O2 with O2 as the test gas.

Fig. 9 Estimated wave shape y(x) for the oxygen dilution and the nitrogen dilution cases compared with the experimental results.

Fig. 3 Time sequence illustrating the development of a gravity current using dye visualization. The gravity current head in the dense fluid (at bottom of image) is propagating from right to left. The dark colored fluid is the salt water solution and the clear fluid is de-ionized water. The plate is completely withdrawn at 0.16 s.

Full text

D.H. Lieberman · J.E. Shepherd
Detonation Interaction with a Diffuse Interface and Subsequent
Chemical Reaction
Received: date / Accepted: date
Abstract We have investigated the interaction of a deto-
nation with an interface separating a combustible from an
oxidizing mixture. The ethylene-oxygen combustible mix-
ture had a fuel-rich composition to promote secondary com-
bustion with the oxidizer in the turbulent mixing zone that
resulted from the interaction. Diffuse interfaces were cre-
ated by the formation of a gravity current using a sliding
valve that initially separated the test gas and combustible
mixture. Opening the valve allowed a gravity current to de-
velop before the detonation was initiated. By varying the de-
lay between opening the valve and initiating the detonation
D.H. Lieberman
Graduate Aeronautical Laboratories, California Institute of Technol-
ogy, Pasadena, CA USA
Tel.: +626-437-3192
Fax: +310-754-2799
E-mail: dlieberman@exponent.com Present address: Exponent Fail-
ure Analysis Associates, Los Angeles, CA USA
J.E. Shepherd
Graduate Aeronautical Laboratories, California Institute of Technol-
ogy, Pasadena, CA USA E-mail: joseph.e.shepherd@caltech.edu
it was possible to achieve a wide range of interface condi-
tions. The interface orientation and thickness with respect to
the detonation wave have a profound effect on the outcome
of the interaction. Diffuse interfaces result in curved detona-
tion waves with a transmitted shock and following turbulent
mixing zone. The impulse was measured to quantify the de-
gree of secondary combustion, which accounted for 1-5%
of the total impulse. A model was developed that estimated
the volume expansion of a fluid element due to combustion
in the turbulent mixing zone and predicted the resulting im-
pulse increment.
Keywords Detonation · diffuse interface · secondary
combustion
1 Introduction
When a detonation wave propagating in a gaseous combustible
mixture reaches a concentration boundary, a complex inter-
action results between the detonation and interface between
the two gases. The details of this interaction are dependent
D. Lieberman and J. E. Shepherd "Detonation interaction with a Diffuse Interface and Subsequent
Chemical Reaction" Shock Waves 16(6):421-430, 2007. Preprint, see journal for final version http://
dx.doi.org/10.1007/s00193-007-0080-3

2 D.H. Lieberman, J.E. Shepherd
on the mixture compositions, the relative geometry of the
detonation and interface, and the characteristic thickness of
the interface.
In the present study, the interface is a composition gra-
dient between the combustible and non-combustible mix-
tures. The thickness of the interface is determined by mixing
caused by fluid mechanical stirring and diffusion. We clas-
sified the extent of the mixing at the interface by comparing
the cell size of the detonation with the interface thickness. A
sharp interface occurs when the detonation cell size is much
greater than the interface thickness.
1
A diffuse interface, the
case of the present study, occurs when the detonation cell
width in the combustible gas is much less than the interface
thickness.
The geometry of a detonation propagating in a composi-
tion gradient can be divided into two main categories. The
first is when the detonation velocity is parallel to the direc-
tion of the gradient, and the second is when it is perpen-
dicular. In general, the composition gradient vector and the
detonation velocity vector are not parallel or perpendicular
but at some intermediate angle. The first case has been stud-
ied by numerous researchers investigating the transmission
and successful re-initiation of a detonation across a gap of
non-combustible gas ([3], [8], [15], [16]). Other work [7] has
examined detonation transmission to an inert gas or other
combustible mixture and subsequent reflection off of a rigid
1
We have studied this case and the results will be presented in a
companion paper.
end-wall. The current study will focus to a large extent on
the perpendicular or nearly-perpendicular case.
When the detonation propagation direction is perpendic-
ular to the mixture gradient, a curved detonation wave results
that ultimately decouples into a shock wave and turbulent
mixing zone (TMZ), shown in Fig. 1b. This is due in part to
the dependence of the detonation velocity on the equivalence
ratio. For a detonation modeled as an ideal one-dimensional
discontinuity with no affect of curvature on reaction zone
structure, the normal component of the curved wave will cor-
respond to the local Chapman-Jouguet detonation velocity.
There has been little work done on detonation propagation
perpendicular to a continuous composition gradient. Exper-
iments [10] were carried out that measured concentration
gradients made by diffusion and used soot foils to charac-
terize the detonation propagation. Other work [4] examined
concentration gradients in a numerical study to investigate
the possibility of a flame occurring in the incomplete com-
bustion products. Oblique detonations were observed [5] in
sharp interface experiments where various combustible mix-
tures were separated in parallel channels. It is possible for
combustion to occur in the turbulent mixing zone (TMZ) by
choosing a combustible mixture such that the combustion
products are incompletely oxidized. This allows further re-
actions to take place if the mixture downstream of the inter-
face contains an oxidizer [14]. The aim of the following dis-
cussion is to address the key physical issues that arise when
a detonation propagates in the direction normal to a concen-
tration gradient. Some of the main issues to be discussed are

Detonation Interaction with a Diffuse Interface and Subsequent Chemical Reaction 3
INTERFACE
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Fig. 1 The interaction of a detonation with a diffuse interface is illustrated with supporting observations from experimental images. A detonation
wave (a) interacts with the diffuse interface and forms a curved wave (b). Upon exiting the combustible mixture, the detonation decouples
completely resulting in a transmitted shock and TMZ (c) and (d). When the shock reaches the endwall it reflects (e) and interacts for a second
time with the interface.
the general shape of the detonation wave, and the decou-
pling of the shock wave and reaction zone. The presence of
secondary combustion between the partially oxidized deto-
nation products and oxidizer in the TMZ is also examined.
2 Experimental setup
The experiments were carried out using the GALCIT Deto-
nation Tube (GDT) [1,2], which is 7.3 m long with an inside
diameter of 0.280 m. It is connected to a 0.762 m long square
test section with inside dimensions of 0.15 m by 0.15 m. A
wave cutting device extends 1 m into the end of the GDT to
cut out a square section of the circular detonation front be-
fore entering the test section. A sliding valve assembly sep-
arates the ethylene-oxygen combustible mixture in the GDT
from the oxidizer or inert diluent in the test section during
the experimental preparation.
Figure 2 is a view of the test section illustrating the loca-
tion of the end flange of the GDT, the sliding valve assem-
bly, and the test section. Visualization for the experiments,
using a schlieren system [1], was made through an optical
viewport (BK7 or quartz windows) that could be arranged
in two separate positions. The first position is located 0.275
m downstream of the sliding valve and is referred to as port
1. The second viewport position is located 0.56 m down-
stream of the sliding valve (see Fig. 2) and is referred to as

4 D.H. Lieberman, J.E. Shepherd
port 2. The locations of the pressure transducers and a quartz
window on the end wall used for fluorescence imaging are
also shown. Fuel rich ethylene-oxygen mixtures occupied
the GDT, and either oxygen, nitrogen, or nitrous oxide occu-
pied the test section. The ethylene-oxygen equivalence ratio
Φ
= 2,2.5,3. The initial pressure and temperature for all ex-
periments were 15 kPa and 298 K, respectively. Detonations
'$4
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Fig. 2 A schematic of the test section with the sliding valve assembly
and the end flange of the GDT.
were initiated in the GDT by discharging a 2
µ
F bank of
capacitors charged to 9 kV through a 0.16 mm copper wire.
Detonation velocities were measured to within 5% of the
Chapman-Jouguet speed. The cell sizes of the detonations
were measured using the soot foil technique [19] and were
in all cases below 5 mm.
The diffuse interface was made with a gravity current
(GC). The formation and propagation of the gravity current
was examined in the test section using acetone planar laser
induced fluorescence (PLIF) [12,17], and in a half-scale wa-
ter channel [20] to understand the early time development of
the GC, see Fig 3. The thickness of the diffuse interface,
δ
c
,
was estimated from the thickness of the region of vorticity
obtained from digital particle image velocimetry (DPIV) [9,
20] measurements from the water channel experiments and
then re-scaled for the gas phase experiments. In the PLIF ex-
periments, the combustible mixture in the GDT was replaced
with an acetone-helium mixture of matched density.
The sliding valve, actuated by a falling mass, was de-
signed to completely isolate both the combustible mixture
and test gas, as well as to open sufficiently fast to control
the formation of the gravity current. The sliding valve was
measured to open in 170 ms with an uncertainty of 10 ms.
The mass needed to achieve this opening time was 55 kg.
3 Results and discussion
The general description of this problem, shown as a schematic
in Fig. 1, is of a detonation wave propagating through a dif-
fuse interface. The diffuse interface is composed of ethylene-
oxygen with
Φ
= 2.5 above a layer of pure oxygen. The
two layer situation was created by allowing a long time to
elapse between the creation of the gravity current and det-
onation initiation (see discussion below). The sequence be-
gins with a detonation wave (a) prior to encountering the
diffuse interface. A curved detonation wave (b) results dur-
ing the interaction leading to a decoupled transmitted shock
and TMZ. As the detonation exits the gravity current, what
remains is a transmitted shock followed by the TMZ (c). The

Detonation Interaction with a Diffuse Interface and Subsequent Chemical Reaction 5
Fig. 3 Time sequence illustrating the development of a gravity current
using dye visualization. The gravity current head in the dense fluid (at
bottom of image) is propagating from right to left. The dark colored
fluid is the salt water solution and the clear fluid is de-ionized water.
The plate is completely withdrawn at 0.16 s.
shock wave and TMZ occupy a smaller axial distance than
the curved detonation wave with the distance between the
shock and TMZ (d) increasing with time. When the shock
reaches the endwall it reflects (e) and interacts with the inter-
face a second time. The reflected-shock-interface interaction
is not visible as it occurs in the space between the window
and the endwall. The complex interaction of the shock wave
with the lower experimental boundary Fig. 1b,c produces a
Mach reflection.
Gravity currents of various sizes were formed by vary-
ing the delay time, defined from the time the sliding valve
reaches the open position to the time when a detonation is
initiated in the GDT. The range of behavior is shown in
Fig. 4 where four separate experiments are shown at dif-
ferent stages of the gravity current development. In these
experiments the
φ
= 2.5 ethylene-oxygen combustible mix-
ture is colored yellow for visibility and flows below the less
dense nitrogen gas. Figure 4a is an image of a shock wave
followed by a TMZ. The delay time was 0 s, corresponding
to a planar interface, and consequently explains why there
is no gravity current visible on the overlay. This translates
to a leading shock wave that is for the most part perpen-
dicular to the top and bottom surface along with a reflected
trailing shock that is possibly due to slight imperfections in
the interface shape. As the gravity current grows, the wave
structure becomes more curved. Figure 4b shows the trans-
mitted shock, TMZ, and the location of the gravity current
before the combustible mixture was detonated with a delay
time of 1 s. The leading shock wave is curved with a Mach
stem at the top wall. Figure 4c shows the location of the
gravity current after a 2 s delay time and the presence of a
detonation propagating within 10% of the CJ velocity and
transverse waves visible just behind the detonation front at
the bottom of the figure. At a 3 s delay time, the curved det-
onation (Fig. 4d) looks similar to the detonation in Fig. 4c
except that the gravity current occupies half the height of the
test section thus changing the curvature of the leading wave.

Frequently asked questions

Q1. What have the authors contributed in "Detonation interaction with a diffuse interface and subsequent chemical reaction" ?

The authors have investigated the interaction of a detonation with an interface separating a combustible from an oxidizing mixture. 

Q2. What is the effect of the shear layer displacement thickness on the surrounding fluid?

the shear layer displacement thickness changes from being negative to positive causing the surrounding fluid to be displaced and generating compression waves. 

Q3. How many impulses are used to calculate the increment?

A reference impulse of 1000 kg·m−1·s−1 obtained from impulse measurements at pressure transducer P4 is used to calculate the increment. 

Q4. What is the main consequence of the mixture composition gradient through the diffuse interface?

The main consequence of the mixture composition gradient through the diffuse interface was to cause the detonation wave to curve: eventually the reaction zone decouples from the leading shock wave when the combustible mixture becomes sufficiently dilute. 

Q5. What is the effect of the curved wave on the reaction zone structure?

For a detonation modeled as an ideal one-dimensional discontinuity with no affect of curvature on reaction zone structure, the normal component of the curved wave will correspond to the local Chapman-Jouguet detonation velocity. 

Q6. What is the purpose of the sliding valve?

The sliding valve, actuated by a falling mass, was designed to completely isolate both the combustible mixture and test gas, as well as to open sufficiently fast to control the formation of the gravity current. 

Q7. What is the effect of the rapid increase in induction time with decrease in shock velocity?

The rapid increase in induction time withdecrease in shock velocity results in the decoupling of the reaction zone from the shock and the formation of a gap between the transmitted shock and the turbulent mixing zone. 

Q8. How did the authors measure the effects of combustion in the turbulent mixing zone?

By using a fuel-rich ethylene-oxygen combustible mixture and an oxidizing test gas, the authors were able to observe and quantify the effects of combustion inside the turbulent mixing zone. 

Q9. What is the effect of the vorticity thickness of the interface?

It is evident that the vorticity thickness of the interface is not uniform and exhibits a sinuous shape as a result of the turbulent flow structure present at the interface. 

Q10. What is the color of the ethylene-oxygen combustible mixture?

In these experiments the φ = 2.5 ethylene-oxygen combustible mixture is colored yellow for visibility and flows below the less dense nitrogen gas. 

Q11. What is the effect of a curved detonation wave on the reaction zone?

When the detonation propagation direction is perpendicular to the mixture gradient, a curved detonation wave results that ultimately decouples into a shock wave and turbulent mixing zone (TMZ), shown in Fig. 1b. 

Q12. What is the constant of proportionality C?

The constant of proportionality C is varied from a value of 1 to 10 to account for interface growth after the shock reflection off the end-wall. 

Q13. What is the velocity of the left (u+p) edges of the fluid element?

The velocity of the left (δu−p ) and right (δu+p ) edges of the fluid element are combined to obtain an expression for the growth rate of the fluid elementdx∗ dt = δu + p −δu−p . 

Q14. What was the optical viewport used for the experiments?

Visualization for the experiments, using a schlieren system [1], was made through an optical viewport (BK7 or quartz windows) that could be arranged in two separate positions. 

Q15. What are the details of the interaction between the detonation and the interface?

The details of this interaction are dependenton the mixture compositions, the relative geometry of the detonation and interface, and the characteristic thickness of the interface.