MULTIPHYSICS MODELLING OF VARIABLE CONFINEMENT COOKOFF TEST (VCCT)
Dr. Charles Dubois
Mr. Pierre Pelletier*
Professor
Chemical Engineering Department
École Polytechnique de Montréal
2900 Boul. Édouard Montpetit
Montréal, QC, Canada
H3T 1J4
Special Project Manager
General Dynamics Ordnance and Tactical
System Canada Inc.
5 Montée des Arsenaux,
Repentigny, QC, Canada,
J5Z 2P4
ABSTRACT
The overall objectives of this project were to built and assess multiphysics finite
elements models for simulating cook-off experiments performed with the small scale variable
confinement cook-off test (VCCT) apparatus. The COMSOL Multiphysics modelling software
was selected to obtain a numerical description of the tests geometry and then employed to
calculate the time evolution of temperature and pressure within the test sample for several
energetic materials composition. This work was achieved by simultaneously solving the
equation of changes for momentum, heat and mass transfer. In the latter case, kinetics
models were incorporated to reflect the early decomposition of the energetic materials found
in the system. Composition B, PBXN-109, CX-85 and IMX-104 high explosive formulations
were simulated and the results were confronted to experimental results from VCCT
conducted in GD-OTS Canada laboratories. Heat losses to the environment were accounted
for by considering natural convection and radiant energy, using COMSOL’s built-in
correlations to estimate the local heat transfer coefficient. Additional details such as solidsolid contact thermal resistance, melting enthalpies and temperature dependant physical
properties were also included in the model. Whenever possible, the specific kinetics of the
decomposition behavior of the energetic materials used was obtained from DSC
measurements using an isoconversional analysis method. Different heating rates were
simulated as part of this project. The analysis showed that simulated temperatures were
close to experimental measurements from thermocouples positioned in the VCCT system.
The estimations of time to onset of runaway reaction were also in good agreement with
experimental data. As a whole, the study tends to confirm that a simulation approach could
eventually be used as a screening tool to reduce the experimental workload associated with
the assessment of thermal sensitivity of energetic materials and could be applied to full scale
munitions following calibration of the model with small scale VCCT test. This simulation work
has also been instrumental in the development of a modified version of the VCCT apparatus.
* Point of contact for paper 16081
Pierre Pelletier
General Dynamics Ordnance and Tactical Systems Canada (GD-OTS Canada)
Tel: (450) 582-6345
Fax: (450) 582-9771
e-mail: Pierre.Pelletier@can.gd-ots.com
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Multiphysics Modelling of Variable Confinement Cook-off Test (VCCT)
1. INTRODUCTION
Studies to reduce the reaction level of high explosives when exposed directly or
indirectly to heat sources has been motivated by major accidents involving undesired
detonation of ordnance and ammunition that could happen at different moments in their life
cycle. The development of the “Insensitive Munitions” (IM for short) concept was the subject
of a sustained level of R&D activities over the past forty years and will remain of interest, as
several countries are implementing IM policies. The means of validating the efforts invested
in IM technologies are not so easily available however for those stimuli due to the elevated
cost to realize them at full scale. In order to ensure that progress is made and could be
assessed, a few reduced sample size protocols have been established to help in energetic
material formulations development and preliminary selection prior to the performance of full
scale standardized IM tests with the munitions of interest. NATO Standardization Agreement
(STANAG) 4491 [1]) describes several explosives, thermal sensitiveness and explosiveness
tests. One of them, “the Variable Confinement Test” (VCCT) has been implemented at GDOTS Canada in Repentigny following discussions with Defence Research and Development
Canada (DRDC) Valcartier regarding their experience with such a test.
No matter the scale however, one of the drawbacks of the cook-off experiments when
medium and slow heating rates (typically 3.3 to 25°C/hr) are considered is the required
duration time that can span over several hours. A numerical technique to estimate the
detonation time in a VCCT assembly would therefore be a useful tool for planning cook-off
experiments and obtain preliminary data. The goal of this work was to establish such
simulation models and assess their accuracy. The simulation work was also instrumental in
the development of an improved version of the test described in a related paper [2].
2. BACKGROUND
Heat transfer is a transit of thermal energy due to a temperature difference. It is
customary to refer to three heat transfer modes: conduction, convection and thermal
radiation. Figure 1 depicts the standard Variable Confinement Cook-off Test (VCCT) [1] setup with arrows representing the heat transfer modes at different locations. In the following
section we will detail the mathematical treatment for each of these modes.
FIGURE 1: Schematic view of the standard VCCT setup and corresponding heat transfer
modes
2
In order to remain general in the treatment of the problem, we refrained from using an
axisymmetric modeling framework, to reflect the fact that experimental conditions (such as
uneven heat source or localized contact with a metallic surface) may bring asymmetry in the
internal temperature profiles.
2.1.
Theoretical framework and simulation approach
The heat diffusion through a solid can be simply expressed by a 3D generalization of
Fourier’s law [2]:
 Cp
T
 k 2T
t
(1)
In this work we considered the density, the heat capacity and the conductivity to be a
function of temperature (T). In order to solve equation (1), appropriate boundary conditions
must be provided [3, 4]. Three scenarios were encountered in our case:
a) For a solid A to solid B interface where the thermal contact resistance can be
neglected, the conditions were continuity of heat flux and temperature:
TA = TB
qA = qB
(2)
b) The contact between two surfaces is never perfect therefore a discontinuity in the
temperature profile of an assembled part may exist. For a solid A to solid B interface
where the thermal contact resistance cannot be neglected; this is expressed by the
following equations [2]:
q
hc 
T1  T3 
xA
1
x

 B
k A A hc A k B A
1  AC 2k AkB AV 

kf 

Lg  A k A  kB A 
(3)
(4)
c) For solid (A) to fluid (C) interface with convection and thermal radiation may take
place:, the Newton cooling law was assumed to apply:
kA
dT
dx
 q  hA(Tw  T )  F FG A TW4  TS4 
(5)
W
In equation (5), the heat transfer coefficient h has to be estimated. This is often done
using correlations considering the following factors [2]:
Nu 
hD
 f Re,Pr   M Rea Pr b
k
(6)
3
The values of M, a and b in (6) are correlation specific and depend on the shape of the
surface, its orientation, etc…In our model, the correlations were taken from the built-in
coefficients library in COMSOL software [5] and were directly calculated based on
geometrical factors and fluid conditions when the boundary condition “convective cooling”
was incorporated in the model. The other circumstance where convection needed to be
considered was when the sample tested in the VCCT experiment was a melt pour explosive
with a relatively low melting temperature such as Composition B or IMX-104. When the
energetic material undergoes a phase change, the computational domain is no longer purely
a solid and also contains a liquid component. Even in the absence of mechanical action or
pressure effect, the fluid can be put in motion due to the temperature induced density
gradient in the sample. If a primary vertical motion is assumed, the general form of the
energy transport equation for a system under natural convection conditions is given by the
following equations [4]:
Z component of the equation of motion
v z
v z v v z
v z
  2u
 vr

 vz
 g  T  T  
t
r
r 
z
 y 2
inertia
(7)
buoyancy
viscous forces
energy equation
T
T v T
T
k
 vr

 vz

t
r
r 
z Cp
convection
1 
 r r

2
2
 T  1  T  T 
 r r   r 2  2  z 2 



(8)
conduction
It is observed that these two partial differential equations (PDE) are coupled through
the variable T. Therefore, under conditions of natural convection, equations (7) and (8) have
to be solved simultaneously. One additional difficulty of considering the convection during
the melting process is the fact that the relative fraction of liquid to solid increases with time.
In order to avoid using advanced meshing techniques, it was decided to solve the equations
of motion over the entire cylindrical shape of the sample, but to depict the non-molten
portion of the explosive as a fluid of very high viscosity, and thus artificially prevent its
movement by effect of natural convection. Therefore, a smoothed step function in the
viscosity was used to approximate the melting process. For example, in the case of
Composition B, the viscosity function used was:
50 for T  80C

 (Pa.s )   7391
 273.15  T  17.6 for T  80C
(9)
In order to account for the large amount of energy involved with the melting process
when a melt pour composition is heated in the VCCT set-up, an approach inspired from the
work of Groulx et al [6] was put in place. This was accomplished by introducing a
discontinuity in the specific heat Cp of the material [7, 8]. In the case of the Composition B
formulation, as used in this study, the enthalpy of fusion with a value of 11.149 kJ/kg (8
cal/g) [7] was used and we assumed that the melting process occurs over a 3K temperature
4
range (from 352 K to 355 K) in order to avoid having strong non-linearity in the system of
equations to solve. The specific heat of the explosive was therefore modified in the following
way:
921.3  3.929T  0.06354T 2 J  kg C 

Cp  11149 J  kg C  for 79C  T  82C

2
1483.9  9.698T  0.1150T J  kg C  for T  82C
(10)
Another melt cast explosive considered in this work, IMX-104, contains about 32% of
DNAN. The latent heat of DNAN has been reported to have a value of 99 kJ/kg [9], and
therefore IMX-104 overall latent heat was estimated at 31.7 kJ/kg. Again, if one assumes
that the melting process occurs over a 3K temperature range (from 365 K to 368 K), the
specific heat of the explosive can be expressed in the following way:
 2.25T  862.5 J  kg C  for 20C  T  94C

Cp  11636 J  kg C  for 94C  T  96C

 2.25T  862.5 J  kg C  for 96C  T  200C
(11)
In order to perform adequately the computer simulations, several physical properties
were required. Those were readily obtained from open sources publications and therefore,
the details are not reported here. Results of cook-off experiments are normally described in
terms of the level of the reaction observed in the sample. This event is a macroscopic
evidence of a process taking place at the molecular level. As the sample is gradually heated
up, the energetic materials begin to decompose. These degradation reactions are
accompanied by thermal effects. As for any chemical reaction, the heat involved in the
process can be released (exothermic) or absorbed (endothermic). In the case of an
exothermic process, the energy released by the chemical reaction will serve to heat up the
material even more. This, in turn, will increase the rate of the degradation and thus liberate a
larger amount of energy. An autocatalytic effect associated to exothermic reactions that may
result in a thermal runaway event (or eventually an explosion) is therefore observed if no
special measures are taken to cool the decomposing sample.
The modelling of a decomposition process can be conducted either as a mechanistic
or an empirical point of view. Empirical models depict the decomposition process as either a
single step or a few steps reaction and no information is sought about the chemical species
involved in the transient states of the materials. For the purpose of this work, we used both
approaches. When available from the literature, data for stepwise reactions involved in the
decomposition process have been used and, in some instances, completed by additional
DSC experiments. It is possible to summarize the use of kinetics and thermal data in the
modelling of a cook-off experiment by considering a hypothetical energetic material that
decomposes in three consecutive steps, as shown in equation (12). Each of these steps will
normally involve a heat of reaction which can be either positive or negative. According to
chemical thermodynamics, when the heat transport equation is applied to an experimental
sample, it needs to be modified to include a source term (W/m3) combining the heat effects
of these three reactions, as shown in equations (13) and (14):
Q3
Q1
Q2
A 
 B 
C 
D
(12)
5
 Cp
T
 k 2T  q
t
(13)
q  1 riQi
(14)
3
where:
Qi = the molar heat of reaction (J/mole)
Ri = reaction rate (mole/m3.s)
The reaction rates are expressed empirically by an “n” order kinetics:
dCi
 k iCini
dt
(15)
and the effect of the temperature on the rate constant is assumed to follow an Arrhenius
relation:
ki  Zi e
 Eai 
  RT 


(16)
Therefore, the first step in attempting to simulate the thermal effects associated with
the decomposition of an energetic material is to obtain a stepwise kinetics model of the
process. Obviously, the number of “i” equations has to be adjusted to a specific formulation
or energetic material. For the purpose of this work, some of these models are already
available in the literature for both melt pour (composition B) and cast cure (PBXN-109)
explosives, while for more recent formulations, such as IMX-104 (melt pour) and CX-85 (cast
cure), we used DSC analysis to characterize the decomposition process. There are different
approaches to obtain kinetics information from DSC data. This method used to obtain the
kinetics models from DSC experiments will be the subject of a future paper since its
applicability and limitations are still being studied.
Table 1 : Kinetics parameter for PBXN-109 decomposition [10]
ln Zi (s-1)
Eai (kJ/mol)
ni
Q/ (J/g)
AB (solid)
43.7
197
1
268
B2C (gas)
38.9
185
1
-803
2C2D (gas)
32.7
143
2
-6560
Table 2 : Apparent kinetics parameters for IMX-104 decomposition process
ln Zi (s-1)
Eai (kJ/mol)
Q/ (J/g)
AB
56
253
-742
BC
34
155
-934
6
3. Experimental studies
For the purpose of verifying and calibrating the simulation and modelling process,
experimental data from VCCT were collected in a large variety of environmental conditions,
materials and sample types. A set of three experiments will be described here and then
compared with the modelling results. The first experiment consisted in heating a Teflon
cylinder inserted in the VCCT thermal sleeve. The cylinder was drilled in order to insert two
thermocouples and monitor the temperature in the sample as a function of time. Two surface
thermocouples were also located on the VCCT endplates while two other surface
thermocouples were positioned at mid-height of two opposite retaining bolts. A schematic of
the thermocouples positions is given in Figure 2 a).
FIGURE 2: Schematic of a) the original VCCT and b) modified VCCT set-up used at GD-OTS Canada –
Repentigny.
The second and third experiments discussed were conducted in a modified VCCT test
set-up shown in Figure 2 b). The second experiment used Composition B as an energetic
material and the sample was submitted to a medium heating rate test using the following
steps: a) a 3°C/min temperature sample pre-heating ramp for 30 minutes, b) a plateau at
108°C for about 1 hour for “soaking” of the sample, and then a 0.5°C/min ramp until
detonation. The third experiment was performed with IMX-104 as the explosive sample and
it was submitted to a fast heating rate.
4. Simulations and results
The calculated values for the temperatures at positions where experimental data were
available are presented in Figure 3 for the VCCT experiment conducted on the inert Teflon
sample. The purpose of this test was to assess the correctness of the COMSOL heat
transfer models in the VCCT arrangement regardless of any other effects such as sample
decomposition or sample melting process. A general examination of the figure shows that
7
there is a fairly good agreement between the calculated values and experimental data, even
though it may seem to be not as good for thermocouples located on extended surfaces of
the set-up, i.e. the endplates and retaining bolts. This can be explained by the fact that these
thermocouples are positioned far from the heating elements. In the VCCT set-up, heat flows
from the confinement sleeves to the endplates, who act as extended surface to dissipate
thermal energy. Several thermal resistances are found along the path of these streamlines:
material thermal conductivities, thermal contact resistances and heat transfer coefficients.
Accordingly, since these resistances are essentially in a serial configuration, all the errors in
estimating them will be cumulative. Therefore, the farther the position of interest is from the
heating bands, the more likely the calculated temperature at this point deviates from the
experimental observation. Another distinctive feature apparent from these data is the effect
of having the VCCT setup standing on a metallic surface. It is clearly seen that the bottom
endplate is always at a lower temperature than the upper endplate.
250
200
Temperature (oC)
150
CH1
CH2
CH3
Probe A
Probe C
Probe B
100
Probe D
paroi
centre
offset
A
50
C
B
0
0
5000
10000
15000
20000
25000
Time (s)
FIGURE 4: Intermediate heating rate experiment conducted on a TEFLON sample: Experimental
(lines) and calculated values (markers)
The comparison between simulated and experimental cook-offs for Composition B is
presented in Figures 5. An inspection of Figure 5 b), where the concentration in
decomposition products of the explosive is presented shows that the initiation point of the
runaway reaction occurs at the mid-height of the sample, near or at the surface of the
sample. When modelling for fast heating rates, the concentration profiles are a better
indicator of the reaction onset than the temperature, since the simulation never converges
when the exponential temperature raise really starts up. A comparison of the calculated and
measured temperatures at three points on the VCCT test arrangement gives a good
agreement between the two sets of data The COMSOL model overestimates the onset time
by about 15 % (Figure 5 a)).
8
FIGURE 5: a) Calculated (line) and measured (symbols) surface temperatures of a Composition B
cook-off experiment under a fast heating rate at t= 115 sec (calculated onset); and b) Calculated
decomposition products concentration at onset
The assessment of the COMSOL models against the experimental data for cook-off
tests on IMX-104 samples is presented in Figure 6 for a medium heating rate. The initiation
point is clearly at the center of the sample, as shown on part b), while part a) indicates that
the calculated time to reach detonation is underestimated by only a few minutes.
FIGURE 6 a) Calculated (line) and measured (symbols) surface temperatures of a IMX-104 cook-off
experiment under a medium heating rate at t= 18700 sec (calculated onset); and b) Calculated midplane temperature profile at onset
The calculated slow cook-off experiment for the 105mm shell is presented in Figure 7.
Only one internal temperature of the sample was experimentally available for comparison
purposes. It is seen that the agreement with the model is rather good in terms of the sample
temperature, while the time to achieve detonation is slightly underestimated.
9
FIGURE 7: Calculated and measured temperatures in a Composition B filled 105 mm shell during a
cook-off experiment (lines end at cook-off event).
5. Conclusion
The work presented in this paper summarizes recent efforts aimed at conducting a finite
elements based modeling exercise of the VCCT experiments and on a standard artillery
projectile. The use of COMSOL simulation environment software proved to be particularly
convenient for this task, mainly because of the built-in heat coefficient library and the
availability of a dedicated Heat Transfer module. The multi-physics capability of COMSOL is
also an asset for carrying out a simultaneous solution of heat and momentum transport
problems, such as the one encountered during the slow heating cycle of a melt-cast
explosive formulation such as Composition B.
The modelling process was successful in predicting the time-dependent temperature profiles
in the VCCT assembly when used with a Teflon sample, as confirmed from experimental
data for medium and fast heating rate cycle. Similar calculations were also conducted on a
virtual Composition B sample, but for these simulations, no experimental temperature values
inside the sample were available to validate the numerical results. A mathematical model
representing the melting process as a pulse in the heat capacity of the sample material is
believed to provide a physically sound approximation of the phase change. When employed
in the simulation of the VCCT experiment, the model provided a description of the transient
melting process along with internal motion due to internal convection.
While the results presented in this paper are encouraging, it must be recognized that a
complete simulation of the cook-off experiment will require additional efforts to include the
chemical reactions associated to the thermal degradation. It is our intend to investigate
these aspects by considering PBXs. For doing so, the heat of reaction should be included as
a source term in the equation energy and the mechanical effect of the gas evolved from the
decomposition process will be considered by a structural analysis of the sample confinement
in the VCCT set-up.
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6. References
[1]
The North Atlantic Treaty Organization (NATO) Standardization Agreement (STANAG)
#4491 Explosives, Thermal sensitiveness and Explosiveness tests, August 2002.
[2] F. P. Incropera, F.P., Introduction to Heat Transfer, 5th edition, Wiley, New York, USA,
2006.
[3] R. W. Lewis R.W., Ken Morgan, K.,, H. R. Thomas H.R., Seetharamu, K., The Finite
Element Method in Heat Transfer Analysis, Wiley, New York, USA, 1996.
[4]
Bird, R.B., Warren E. Stewart, W.E., Edwin N. Lightfoot, E.N.,, Transport Phenomena
(2nd ed), John Wiley & Sons, 2001.
[5] COMSOL - Heat transfer module User Guide
[6] Groulx, D., Ogoh, W., “Solid-Liquid Phase Change Simulation Applied to a Cylindrical
Latent Heat Energy Storage System”, Proceedings of the COMSOL Conf., Boston,
USA, 2009.
[7] Determination of cooling of Comp-B Poured 81mm and 120mm mortar shells by
thermocouples and by finite element thermal model, AMSTA-AR-QAT-T, 28
[8] Vasilakis, J.D., Computer Model for the Solidification of Composition B, Technical
Report ARCCB-TR-85003, December 1985.
[9] Davies, P.J., Provatas, A., Characterisation of 2,4-Dinitroanisole: An Ingredient for use
in Low Sensitivity Melt Cast Formulations, DSTO-TR-1904, Defence Science and
Technology Organisation, Weapons Systems Division, 2006.
[10] McClelland, M.A., Tran, T.D., Cunningham B.J., Weese, R.K., Maienshein, J.L.,
Cookoff Response of PBXN-109: Material Characterization and ALE3D Thermal
Predictions, . JANNAF CS/APS/PSHS Joint Meeting, Monterey, 2000.
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Presenter biography:
Pierre Pelletier
Pierre Pelletier graduated from Laval University in Quebec City Canada in chemical
engineering in 1980 and then worked for Defence Research Establishment Valcartier before
joining Canadian Arsenals in 1987 which changed name over years and acquisition
processes to become General Dynamics Ordnance and Tactical Systems Canada. He
obtained a master in mechanical engineering from Carleton University in Ottawa in 1995.
Along with R&D work on explosives processing and filling of different types of munitions with
melt-pour, cast-cure and pressed explosives, he has been involved in studies related to the
terminal ballistics of fragmentation, shaped charge and EFP cartridges. Since 2005, he is
heading the GD-OTS Canada R&D section involved in insensitive munitions development
studies and development covering energetic materials processing and testing, munitions and
packaging design, IM testing.
His interests out of the job are skiing (alpine and cross-country), jogging, sailing, kayaking,
reading and classical music listening. He enjoys watching Canadian universities football and
is also a keen supporter of the Laval University football team.
12