Experimental and numerical detonation cell in H2-N2O-Ar mixtures

Experimental and numerical detonation cell in
H2-N2O-Ar mixtures
R. Mével 1,2,∗ ,D.Davidenko 1 ,F.Lafosse 1 , G. Dupré 1,2 and C.-E. Paillard 1,2
1 Institut de Combustion, Aérothermique, Réactivité et Environnement
2 University of Orléans
Abstract
The investigation of detonation in hydrogen-nitrous oxide mixtures is related to several important industrial
safety issues including nuclear waste storage and semi-conductor production. Because of a limited number of
detonation cell size data available in the literature, the present study aims at providing additional experimental
data and estimating several methods to predict detonation cell size. Detonation cell size is measured at
different argon dilution and initial pressures, for mixtures with equivalence ratios from 0.3 to 2.5. It is shown
that even at low initial pressure, H2-N2O-Ar mixtures are very sensitive to detonation. Using a detailed
chemical kinetic model, the semi-empirical correlation by Ng has been shown to give accurate prediction of
cell size. After a specific reduction of the detailed scheme and the adjustment of the detonation velocity to
match the experimental one, a 2-D Euler simulation has been shown a capability to provide reliable cell size
data for stoichiometric mixtures.
Introduction
Detonation in hydrogen-nitrous oxide mixtures is
related to several important safety issues. The first
one is related to some nuclear wastes storage at
Anford site since these wastes periodically release a
gaseous mixture mainly composed of hydrogen and
nitrous oxide [1–5]. The second one is the safety
of semi-conductor manufacturing processes since
hydrogen-nitrous oxide kinetics play an important
role in the oxidation of silane by nitrous oxide [6].
Among explosion hazards, the detonation is the
most dangerous one since it can result in large scale
destructions. Direct initiation of detonation is rarely
taken into account in risk assessment because the
required energy is high compared to that inducing a
deflagration. Nevertheless, it has been shown that
confinement conditions can facilitate the deflagration
to detonation transition (DDT) [7].
A fundamental parameter for risk assement is the
detonation cell size. Effects of the equivalence ratio,
initial pressure and dilution on the detonation cell
size of H2-N2O(-diluent) mixtures have been studied
[8–10] but the available data are quite limited
if compared to more common mixtures such as
hydrocarbon-air or hydrogen-air mixtures.
Specific Objectives
The objective of the present study is, first, to provide
additional experimental data on the detonation cell
∗ Corresponding author: mevel@cnrs-orleans.fr
Proceedings of the European Combustion Meeting 2009
1
size for hydrogen-nitrous oxide mixtures and, second,
to evaluate the accuracy of cell size prediction using
both a semi-empirical correlation (based on chemical
kinetics) and 2-D numerical simulations.
Materials and Methods
Materials
Hydrogen-nitrous oxide-argon mixtures are prepared
from high purity grade gas supplied by Air Liquide.
Each gas is introduced in a 10 L Pyrex tank using the
partial pressure method and mixed by a magnetic
stirrer for at least half an hour prior to experiments.
The initial conditions are varied within the following
ranges: equivalence ratio (Φ) between 0.3 and 2.5,
dilution from 20 to 60 mol% Ar, and initial pressure
between 7 and 35 kPa. Detonations are initiated in
a shock tube behind an incident shock wave. The
shock tube is made of stainless steel. The driver
section is 0.9 m long and has an inner diameter of
128 mm. The driven section is 4.6 m long and has
an inner diameter of 78 mm. The two parts of the
tube are linked to vacuum pumps and separated by a
double membrane system which allows a good control
of the driver section pressure, P4. Four pressure
transducers are mounted flush to the driven section
inner wall and allow to measure the shock velocity
with an accuracy of 1%. The measurement of the
wave velocity permits to calculate the temperature
and pressure conditions behind the shock wave. The
classical soot record method is used to evaluate the
sensitivity to detonation of different mixtures. An

example of soot record is shown in Figure 1.
Soot records are digitised and analysed using
the Visilog software. The cell size, λ, reported
in the present study corresponds to the mean of
the largest and smallest cells measured on a given foil.
Figure 1: Experimental soot record of detonation cells in
aH2-N2O-Ar mixture. Initial conditions: Φ = 1; XAr =
0.2; P1 =10kPa;T1 = 295 K.
Methods
The presently used chemical kinetic model, constituted
of 203 reactions and 32 species, was previously
described and validated against numerous experimental
shock-tube, flow reactor and flame speed
data [11, 12]. Since it is too large to be directly
applied to multidimensional detonation simulations,
it has to be reduced to the minimum number of
reactions describing the heat release dynamics in
the detonation wave. The reduction was conducted
using an automatic procedure [13] for the elimination
of redundant chemical reactions. This procedure is
based on the simulation of an autoignition process in
a homogeneous adiabatic constant-pressure reactor.
The importance of each reaction is evaluated from
an error criterion based on the following macroscopic
characteristics of the oxidation process: ignition
delay time (time interval to the thermicity peak),
maximum thermicity, profiles of temperature and
mean molar mass. The errors are determined with
respect to the same characteristics obtained with the
detailed kinetic model. Reactions are eliminated one
after the other, starting from the least important one
until none of the remaining reactions can be deleted
without exceeding the imposed error tolerances,
resulting in a reduced kinetic scheme.
For cell size prediction, two methods are used. The
first one corresponds to the classical correlation, λ
=A.Δi, withΔi, the induction distance and A, the
ratio of the cell size to the induction distance. The
second one is the use of a 2D Euler code to simulate
2
the detonation wave propagation.
Instead of using the A ratio obtained from previous
experiments, A is calculated using the Ng’s method,
described in details in Refs. [14, 15]. Briefly, A is
obtained from the reduced activation energy, ɛi, as
defined by Schultz and Shepherd [16], a stability
parameter, χ, which corresponds to the ratio of the
induction distance to the reaction distance, and fit
coefficients. This method allows the use of detailed
kinetic schemes within the ”Shock and Detonation
Tool Box” from Caltech to determine induction
distances.
A high-resolution Euler code for a reactive flow,
based on the shock-capturing, Weighted Essentially
Non-Oscillatory (WENO) scheme of the fifth order
[17], is applied to a 2-D detonation simulation.
To avoid restrictions on the time step, the time
integration is performed with the semi-implicit
additive Runge-Kutta scheme ASIRK2C [18]. The
convective terms are included in the explicit operator
whereas all source terms are treated implicitly. The
global time step is controlled by imposing a Courant
number equal to 0.7. The code is parallized using
MPI library.
2D simulations are made on two rectangular domains
whose dimensions are 150 mm in the direction of
the detonation propagation and 39 mm or 78 mm in
the transversal direction. The computational mesh
is structured and orthogonal. In the longitudinal
direction, it consists of 500 points uniformly distributed
with a step of 50 μm and 500 points with
progressively increasing spacing. The detonation
front is kept within the first mesh portion. In the
transversal direction, the mesh consists of 400 or 800
equally spaced points.
To obtain a nearly standing detonation front,
a uniform flow at the Chapman-Jouguet (CJ)
detonation velocity is imposed on the inlet boundary.
CJ conditions are considered on the outlet
boundary. Symmetry or perfectly reflecting conditions
are imposed on the two remaining boundaries.
Results and Discussion
Experimental results
As a first step, the evolution of wave velocity as
a function of the pressure ratio of driver to driven
sections (P4/P1) is measured. This ratio (P4/P1)
is linked to the shock strength. Stoichiometric
mixtures, 50 mol% Ar diluted, at initial pressures
of 10 kPa and 20 kPa are used. Figure 2 shows the
results obtained at initial pressure of 10 kPa.
In the left part of the graph, the velocity of the
incident shock increases linearly with (P4/P1) ratio.
Then, for a critical ratio around 55, the coupling
between the shock wave and the reaction zone

ecomes effective inducing a large jump in the
measured velocity. Finally, as the (P4/P1) ratio
continues to increase, the wave velocity tends to
stabilize at the self-sustained CJ velocity. It can be
noted that the critical pressure ratio is significantly
reduced at higher initial pressure ((P4/P1)≈35 for
P1 = 20 kPa) due to the decrease of the critical
energy for detonation onset. Critical conditions
for the detonation onset have been estimated at
several initial pressures from the ideal 1-D shock
wave theory, using the velocity measurements as a
function of the (P4/P1) ratio. For P1 =10kPa,the
critical temperature and pressure are 904 K and 127
kPa, respectively. For P1 = 20 kPa, the critical temperature
is 750 K and the critical pressure is 188 kPa.
Wave velocity (m/s)
2400
2000
1600
1200
800
400
Experimental data
CJ velocity
20 40 60 80
P 4/P 1
Figure 2: Wave velocity in H2-N2O-Ar mixture as a function
of the (P4/P1) ratio. Initial conditions: Φ = 1; XAr
=0.5;P1 =10kPa;T1 = 295 K
λ (mm)
10
80
70
60
50
40
30
20
X Ar = 0.2
X Ar = 0.4
X Ar = 0.6
1
Equivalence ratio
Figure 3: Detonation cell size in H2-N2O-Ar mixtures
as a function of equivalence ratio at different dilutions.
Initial conditions: Φ = 0.3-2.5; XAr = 0.2-0.6; P1 =10
kPa; T1 = 295 K
3
λ (mm)
100
10
1
P 1 = 7 kPa
P 1 = 10 kPa
P 1 = 35 kPa
1
Equivalence ratio
Figure 4: Detonation cell size in H2-N2O-Ar mixtures
as a function of equivalence ratio at different initial pressures.
Initial conditions: Φ = 0.3-2.5; XAr =0.2;P1 =
7-35 kPa; T1 = 295 K
As a second step, detonation cell size has been
measured at various equivalence ratios, dilutions
and initial pressures. Figure 3 and Figure 4 present
the evolution of the cell size as a function of the
equivalence ratio at different dilution levels and
initial pressures, respectively. As it can be seen, the
cell size dependence on the equivalence ratio presents
the classical U-shape with a minimum value around
stoichiometry: stoichiometric H2-N2O mixtures are
the most sensitive to detonation. It can also be
noted that λ decreases with the decrease of dilution
and with the increase of initial pressure, both being
typical features.
Numerical results
The reduced kinetic model presented here has been
obtained for a stoichiometric mixture with the following
molar composition: XH2 =0.3,XN2O =0.3,XAr
= 0.4. The same mixture is considered for the 2D
simulations of the detonation wave.
The reduction is performed on a 1-D parametric grid
defined in terms of post-shock conditions (P and T) in
the range of shock velocity from 0.8 DCJ to 1.6 DCJ,
DCJ being the CJ detonation velocity. The following
7 reactions are identified as important:
O + H2 = H + OH (1)
OH + H2 = H2O + H (2)
OH + H + M = H2O + M (3)
N2O(+M) =N2 + O(+M) (4)
N2O + H = N2 + OH (5)

NH + NO = N2O + H (6)
NH + NH = N2 + H + H (7)
By analyzing the reduced model, it is found that the
role of the reverse reaction R6 and forward reaction
R7 consists to limit the consumption of H radical by
the forward reaction R5. Further reduction could
be achieved by eliminating the two last reactions
and reducing the rate constant of reaction R5. The
reduction of the preexponenial factor of reaction
R5 by 45 % allows to compensate the effect of
reactions R6 and R7 and to delete 2 species, NH and
NO, among the 10 remaining species. Finally, the
partially globalized version of the reduced model,
noted as globalized model, includes reactions R1-R5.
More details on the reduction procedure can be
found in [19]
Several tests have been performed to validate the
reduced kinetic schemes. Their applicability to
detonation simulations is tested using the constantpressure
reactor model. The initial conditions are
determined behind a shock wave propagating in a
fresh mixture at P1 = 10 kPa and T1 = 297 K.
The shock velocity, D, is varied within the range
(0.8-1.2) DCJ, whereDCJ = 1897 m/s, yielding the
following variations of the post-shock conditions: P2
= 241-546 kPa and T2 = 1316-2465 K. Figure 5
presents a comparison of the maximum thermicity
and of time to maximum thermicity, predicted with
the three kinetic schemes: detailed, reduced R1-R7,
globalized R1-R5. From Figure 5, one can see that
the results given by the three reaction mechanisms
are in good agreement. The predictions provided by
the last one are as accurate as those given by the
reduced scheme R1-R7.
Maximum thermicity (s -1 )
1x10 7
1x10 6
Time to maximum
Thermicity
Maximum
Thermicity
Detailed scheme
Reduced scheme
Globalized scheme
0.8 0.9 1 1.1 1.2
D/DCJ
Figure 5: Maximum thermicity and time to maximum
thermicity in a H2-N2O-Ar mixture as a function of
D/DCJ: comparison between the detailed, the reduced
and the globalized chemical schemes. Initial conditions:
Φ=1;XAr =0.4;P1 = 10.1 kPa; T1 = 297 K.
1x10 -4
1x10 -5
1x10 -6
1x10 -7
Time to maximum thermicity (s)
4
Other tests were conducted using the ZND model.
Figure 6 shows spatial profiles of temperature and
thermicity computed with the detailed and globalized
kinetic schemes for D = DCJ. The latter gives
a slightly higher detonation velocity DCJ = 1908
m/s. This example proves that the reduced scheme
provides correct profiles of macroscopic quantities
during the entire oxidation process. 2D detonation
simulations discussed below have been conducted
with the globalized kinetic scheme.
Temperature (K)
3200
2800
2400
2000
1600
Detailled scheme
Globalized scheme
Temperature
0.0004 0.0008 0.0012
Distance (m)
Thermicity
1E+006
8E+005
4E+005
0E+000
Figure 6: Temperature and thermicity profiles in a H2-
N2O-Ar mixture: comparison between the detailed and
the globalized chemical scheme. Initial conditions: Φ =
1; XAr =0.4;P1 = 10.1 kPa; T1 = 297 K.
For the cell size prediction, first, the correlation of Ng
has been tested against the experimental data from
the present study. Figure 7 shows an example of the
results obtained.
λ (mm)
100
10
0.2
T 1 = 295 K
X Ar = 0.2
0.3
P 1 = 7 kPa
P 1 = 10 kPa
P 1 = 35 kPa
0.4
0.5
0.6 0.7 0.8 0.9
Equivalence ratio
1
Thermicity (s-1)
2 3
Figure 7: Comparison between Ng’s cell size correlation
and the experimental detonation cell size of H2-N2O-Ar
mixture. Initial conditions: Φ = 0.3-2.5; XAr =0.2;P1
=7-35kPa;T1 = 297 K.
It can be seen that the correlation allows a good
quantitative prediction of the cell size with a mean
error around 40 %. The evolution of cell size as

a function of the equivalence ratio, initial pressure
and dilution is well reproduced by the correlation.
As important parameters of the correlation (the
induction distance and the reaction zone length)
are derived from the detailed scheme, it can be
concluded that the accuracy of the predicted cell
size is directly related to the quality of the kinetic
scheme. Thus, the correlation of Ng can be used as a
reliable tool as long as a carefully validated detailed
chemical model is used.
Further, 2-D numerical simulations have been performed.
Figure 8 and Figure 9 show a Schlieren picture
of the detonation front and a numerical soot
record, respectively.
Figure 8: Numerical Schlieren picture of a simulated detonation
in a H2-N2O-Ar mixture. Initial conditions: Φ =
1; XAr =0.4;P1 = 10.1 kPa; T1 = 297 K.
The numerical soot foils are used to estimate the cell
size. The mean cell size in the simulations presented
in Figure 8 and Figure 9 is 9 mm, that is almost
two times smaller than the experimental one. As the
velocity of the simulated detonation is 50 m/s higher
than in the experiment, it was decided to adjust the
propagation velocity in the simulation. The desired
effect can be achieved by modifying the enthalpy
of formation of H2O, the most important oxidation
product. Based on computational tests, the modified
enthalpy of formation must be -221.1 kJ/mol instead
of the standard value of -241.8 kJ/mol. Additionnal
simulations have been performed and a mean cell
size of 18 mm was derived, perfectly matching the
experimental data. Figure 10 sums up the results
of the different numerical simulations and compares
them with the experimental results and Ng’s correlation.
5
Figure 9: Example of numerical soot foil obtained in a
H2-N2O-Ar mixture. Initial conditions: Φ = 1; XAr =
0.4; P1 = 10.1 kPa; T1 = 297 K.
λ (mm)
100
10
Experimental data
λnum-adjusted
λnum
λNg
1
Equivalence ratio
Figure 10: Dependence of the cell size on the equivalence
ratio in H2-N2O-Ar mixtures: comparison between experimental
data and different predictions. Initial conditions:
Φ = 0.3-2.5; XAr =0.4;P1 =10kPa;T1 = 295 K.
Theoretically, the most reliable method for cell size
prediction would consist in deriving the detonation
cell size from numerical simulation. In practice, such
simulations are very costly and require a drastic
reduction of the chemical kinetics so that it is often
taken into account as a single irreversible step.
In detonation waves, instabilities result from the
coupling between chemistry and gasdynamics. Consequently,
it is not surprising that the use of a single
reaction results in poor cell size prediction. In the
present study, although the detailed scheme has been
strongly reduced, the chemical mechanism consists
of 5 reversible reactions. The cell size predicted
using this approach is within the experimental range
of measurement. However, the obtained value is

almost two times smaller than the experimental
one. This difference can be explained by the high
propagation velocity of the simulated detonation.
The detonation wave never reaches the theoretical
CJ velocity, even after several meters of propagation,
and keeps a speed excess of 10 m/s compared to CJ
velocity. Experimentally, self-sustained detonation
waves exhibit a speed deficit ranging between 2
% and 10 % of the CJ velocity according to their
stability level. In case of a detonation onset, one can
observe very small detonation cells which increase in
size with distance, since the overdriven detonation
is weakened by rarefaction waves. Consequently,
the cell size is strongly related to the propagation
velocity of the detonation, so that the faster simulated
detonation exhibits smaller cells than that
experimentally observed. In order to obtain a more
reliable cell size data from the 2-D simulations,
the heat reaction can be decreased to simulate
energy and momentum losses responsible for the
velocity deficit observed in experiments. This later
approach provides a good estimation of the measured
cell size, which seems to validate the present analysis.
Conclusions
Detonation cell size of H2-N2O-Ar mixtures has
been measured over a wide range of equivalence
ratio, initial pressure and dilution: it exhibits typical
behaviour.
Using a detailed kinetic model, the semi-empirical
correlation of Ng has been tested with respect
to available data and showed good results. After
a specific reduction of the detailed scheme, cell
size prediction has also been performed from 2-D
Euler simulations. It has been demonstrated that
a good agreement with experimental data can be
achieved by adjusting the propagation velocity of the
simulated detonation with the experimental one.
Efforts will be carried on, using this approach
and specific reduced chemical schemes, in order to
check if the evolution of cell size as a function of
equivalence ratio can be accurately described.
Acknowledgements
This work was partly supported by a grant
from the French ”Ministère de l’ Éducation et de
l’Enseignement supérieur”.
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