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Contents
1 Introduction .............................................................................................................. 3
2 Simulation setup ...................................................................................................... 4
2.1 Background on the nature of blast ............................................................................. 4
2.2 Definition of simulation elements ............................................................................... 4
2.2.1 Warhead .................................................................................................................... 4
2.2.2 Aircraft ....................................................................................................................... 5
2.2.3 Atmospheric air .......................................................................................................... 6
2.3 Numerical procedure ................................................................................................. 6
2.3.1 Near-field development of the blast wave ................................................................. 6
2.3.2 Interaction of the blast wave with the aircraft ............................................................ 7
3 Simulation results .................................................................................................... 9
3.1 Near-field development of the blast wave ................................................................. 9
3.2 Interaction of the blast wave with the aircraft .......................................................... 10
3.2.1 Blast loading on the fuselage .................................................................................. 10
3.2.2 Blast loading on the left nacelle ............................................................................... 14
4 Conclusions ........................................................................................................... 16
5 References ............................................................................................................. 17
Appendices
A Grid convergence of the near-field blast wave
B Verification of the re-mapping procedure
C Grid convergence of the 3D simulation

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2 Simulation setup
The AUTODYN software version 14.5 [2] was used to simulate the propagation of
the blast wave from a warhead near the aircraft and its interaction with the aircraft.
The simulation does not account for the response of the aircraft to the blast loading.
The software simulates the complete flowfield around the aircraft and the spatial
and temporal description of the blast loading on the aircraft is retrieved.
The CFD calculation is built from three elements in order to properly represent the
blast loading, namely the warhead, the aircraft and the surrounding atmospheric air.
These elements are described in Section 2.2 and the numerical procedure followed
for the blast loading simulations is described in Section 2.3. First, in Section 2.1,
some introductory information on blast is given.
2.1 Background on the nature of blast
High Explosives (HE) are solid materials with the ability to detonate. During
detonation the state of the HE changes extremely rapidly into a hot gas. Typical
detonation pressures inside the explosion position are in excess of 20 GPa with a
temperature of about 3000 K. A blast wave is formed due to this sudden and large
amount of released energy.
The front part of a blast wave is the shock front which causes an instantaneous rise
in pressure. This is called the peak pressure. The shock front of the blast wave
propagates supersonic, compresses the air and gives a particle velocity increase in
same direction as the wave. The mathematical integral over the pressure – time
history is called the impulse.
With increasing distance from the detonation position the peak pressure decreases
and the duration of the pressure increases for constant charge mass. As long as the
propagating blast wave does not hit a body the pressure is called the incident
pressure. When the blast wave interacts with a body a reflection occurs giving a
local rise in pressure that becomes several times the incident pressure. The loading
on a body due to blast differs significantly from static loading:
• The blast loading gives a sharp rise in pressure which is not the case for a
slowly applied pressure.
• The duration of a blast loading of a conventional warhead is significantly
shorter than for a slowly applied pressure.
• The dynamic behaviour of the blast wave requires obtaining the pressuretime history at specific locations in order to describe the loading.
2.2 Definition of simulation elements
2.2.1 Warhead
In consultation with the DSB, the modelled warhead is type 9N314. The warhead,
with a total mass of 70 kg, consists of a steel casing with preformed fragments and
a High Explosive (HE) charge [3]. The geometric charge mass shape is
approximated by a cylinder. The energy contained in the HE charge is used to
break-up the casing, accelerate the fragments and generate an explosive
overpressure called blast. Hence, only a certain portion of the total HE energy is

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The time required for the blast wave to propagate along the aircraft is much shorter
than the typical time at which the aircraft starts to deform. This allows the aircraft
body to be modelled as a rigid body since any material deformation is negligible in
the blast timescale. The thus calculated blast load on the outer contour of the
aircraft is the maximum load.
2.2.3 Atmospheric air
The warhead detonated at an altitude of approximately 10 km (flight level 330). At
this altitude the ambient air properties used in the CFD simulation are as follows:
• Density: 0.41 kg/m3
• Pressure: 26.21 kPa
• Temperature: 223 K
2.3 Numerical procedure
The complete blast event is simulated in two stages, namely the near-field
development of the blast wave close to the warhead, and the interaction of the blast
wave with the aircraft. In the first stage the blast is simulated over the distance that
separates the warhead from the aircraft. The flowfield of this simulation is then remapped in a larger domain that includes the complete aircraft. This procedure
allows a fine numerical grid (small CFD elements) to be used close to the warhead.
This is necessary to properly describe the large pressure gradients across the initial
development of the blast wave. The numerical grid of the second stage is made
coarser in order to encompass the complete aircraft.
2.3.1 Near-field development of the blast wave
Initial conditions for the near-field blast wave are summarised in Figure 2.3. The
warhead is moving at a velocity of ~600 m/s [1] and travels through quiescent air.
The warhead is detonated from the centre of the charge. The CFD simulation is
two-dimensional axisymmetric around the axis of the cylindrical charge mass. The
numerical grid used for this simulation is 2000 × 1000 cells and covers a distance of
8 m longitudinally and 4 m radially. Therefore the cell size used is 4 mm. The 4 mm
cell size is sufficient to properly resolve the pressure profiles (see Appendix A). The
simulation is carried out until the blast front reached a radial distance of 3 m.
The flowfield at that stage is then imported into the larger numerical grid for the
second stage including the interaction with the aircraft. The ideal gas equation of
state is used for the air and the HE detonation products are modelled using the socalled Jones-Wilkins-Lee (JWL) equation of state. The parameters for air and
Composition B are provided in Table 2.1

Figure 2.3 Initial conditions for the blast wave development near the warhead. The HE charge
mass is shown in green and moving at an initial velocity of ~600 m/s whereas the
quiescent air is shown in blue. The detonation initiation point is shown with a red circle
and the simulation is axisymmetric around the axis of the cylindrical warhead

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Note that warhead design I at the initial position and orientation results in a match
with the observed fragment hit pattern at the time this blast study was performed
(April 2015). In July 2015, new data enabled the exploration of different warhead
designs, resulting in a “best match” on a slightly offset location [1]. The different
warhead designs affect mainly the fragmentation. The best match is ~1 m closer to
the aircraft, resulting locally in a somewhat higher blast loading than presented in
this report. The blast loading further away from the point of detonation remains in
the same order of magnitude.
At every time step during the simulation the loading applied on the aircraft is
recorded by virtual “pressure gauges” on the aircraft. The location of these pressure
gauges is presented in Figure 2.6 and Figure 2.7 with red symbols. In the CFD
simulation three groups of pressure gauges are defined:
• Top gauges (69 in total), positioned horizontally on the left-hand side of the
fuselage at the shortest distance from the warhead position at the time of
detonation.
• Lateral gauges (64 in total), positioned horizontally on the left-hand side of
the fuselage and closest to the wing attachment to the aircraft.
• A single bottom gauge, located on the right-hand side of the fuselage at the
position of panel AAHZ3112NL, which showed damage that is suspected to
stem from blast [1].

Figure 2.6 Location of the lateral and top pressure gauges on the left-hand side of the aircraft.

Figure 2.7 Location of the bottom pressure gauge on the right-hand side of the aircraft.

The three-dimensional numerical grid consists of 533 × 267 × 200 cells (along the
x, y,  and z axis, respectively) covering a distance of 160 × 80 × 60 m centred
around the warhead detonation point. Non-uniform cell sizes were used in order to
provide a finer grid (cell size of 50 mm) at the detonation point and a coarser grid
(cell size of approximately 1 m) farthest from the detonation point. This is allowed
because the pressure gradient across the blast wave becomes smaller when
moving further away from the point of detonation.

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accuracy of the pressure profiles is verified by means of a grid convergence study
that is provided in Appendix A.

Figure 3.2 Pressure profile (positive phase shown) of the blast wave from the warhead at 0.91 ms
after detonation along four directions: upwind, downwind, 45° downwind and radial
(see Figure 3.1 for the definition of directions). The peak pressure along these four
directions are approximately 1600 kPa, 1100 kPa, 600 kPa and 1400 kPa,
respectively.
3.2 Interaction of the blast wave with the aircraft
3.2.1 Blast loading on the fuselage
The flowfield presented in Figure 3.1 and Figure 3.2 is the input for the simulation of
the interaction between the blast wave with the aircraft. The transfer of the flowfield
conditions from the first stage of the simulation to the second stage is referred to as
the remapping procedure. The correct execution of the procedure is verified by
tracing the pressure profiles from both stages (see Appendix B for details). The
blast loading on the fuselage can then be determined until the blast reaches the tail
of the aircraft, or until the magnitude of the blast becomes negligible.
The blast wave is visualised at four different times in Figure 3.3 through Figure 3.6.
Viewed from the front (left figures) and the top (right figures) the blast wave is
shown using lines of constant pressure. The maximum (red) and minimum (blue)
pressures are displayed on each figure. Features that can be observed from the
front view is the reflection of the blast from the fuselage (see Figure 3.4) and the
propagation of the blast around the fuselage (see Figure 3.5). Features that can be
observed from the top view is the blast propagation towards the nose (see Figure
3.4) and towards the leading edge of the wing (see Figure 3.5 and Figure 3.6).
The pressure-time history is provided in Figure 3.7 at four locations along the
fuselage: 0 m (at the nose), 2.5 m (at the shortest distance with the warhead), 10 m
and 25 m (at the root of the wing’s leading edge). The highest calculated peak
pressure is 2500 kPa occurring at 2.5 m from the nose. At 10 m and 20 m from the
nose the peak pressure decreases to 88 kPa and 41 kPa, respectively. The
duration of the blast varies between approximately 3 ms and 7 ms.
The accuracy of the pressure evolution shown in Figure 3.7 is addressed in
Appendix C. It is explained that the peak pressure at 2.5 m is underestimated due
to a numerical artefact (choice of cell size) whereas the other peak pressures are

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Figure 3.5 Lines of constant pressure 7.2 ms after detonation from the front view (left) and the top view (right). The blast
interacts with the entire front section of the fuselage including the right-hand side. Views include the numeric
values of maximum (red) and minimum (blue) peak pressure.

Figure 3.6 Lines of constant pressure 23.3 ms after detonation from the front view (left) and the top view (right). The
blast front reaches the leading edge of the wing at the wing root. Views include the numeric values of
maximum (red) and minimum (blue) peak pressure.

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impulse along the fuselage is presented in Figure 3.9. The highest impulse occurs
at 2.5 m from the nose and reaches 1600 Pa·s. The impulse decreases for
increasing distance from the nose to approximately 180 Pa·s at the root of the wing.
Beyond a distance of 35 m the impulse drops below 100 Pa·s

Figure 3.8 Peak pressure along the aircraft measured with the top, lateral and bottom gauges.
The highest peak pressure is obtained at 2.5 m from the nose and reaches up to
5000 kPa (see Appendix C). The peak pressure decreases for increasing distance
from the nose and drops below 75 kPa (according to [1] a threshold for blast damage)
at 12.5 m. At the root of the wing the peak pressure is 40 kPa. Beyond 35 m the effect
of the blast wave is negligible.

Figure 3.9 Impulse along the aircraft measured with the top, lateral and bottom gauges. The
highest impulse is obtained at 2.5 m from the nose and reaches at least 1600 Pa·s. At
the root of the wing the impulse is approximately 180 Pa·s. Beyond 35 m the impulse
decreases below 100 Pa·s.
3.2.2 Blast loading on the left nacelle
The blast loading on the left nacelle has also been investigated, as illustrated in
Figure 3.10. The estimated pressure evolution applied on the left nacelle is shown
in Figure 3.11. The blast interacts with the nacelle between 20 ms and 35 ms and
the pressure reaches a maximum value of 65 kPa.

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4 Conclusions
The Dutch Safety Board (DSB) wants to provide a clear picture of the cause of the
crash of flight MH17. A possible cause is fatal damage to the aircraft due to the
fragmenting warhead of a guided weapon. A detonating warhead causes damage
to the aircraft due to impacting fragments and explosive overpressure (blast). The
damage potential of blast is of interest to the DSB, so that TNO investigated the
local blast loading on the aircraft as a result of a warhead detonation.
A Computational Fluid Dynamics (CFD) simulation was performed with AUTODYN
to determine the blast pressure evolution over time, hence the blast load on the
aircraft. The CFD simulation accounts for the altitude, warhead properties, velocity
of the aircraft, velocity of the warhead, and shape of the aircraft. The position and
orientation of the detonating warhead relative to the aircraft was taken from
previous work [1].
The highest peak pressure is approximately 5000 kPa with a duration of 3 ms
(corresponding with an impulse of at least 1600 Pa·s), at a distance of 2.5 m from
the nose of the fuselage. Beyond a distance of 12.5 m from the nose the peak
pressure drops below 75 kPa. This means that beyond this distance the occurrence
of blast damage to the aircraft structure is unlikely.
At the root of the wing the peak pressure and impulse are 40 kPa and 180 Pa·s,
respectively. Beyond 35 m from the nose the effect of the blast wave is negligible.
The interaction between the reflecting blast wave and the left engine nacelle is
noteworthy. The peak pressure in front of the nacelle is estimated to be 65 kPa.

Appendix A | 1 / 1

A Grid convergence of the near-field blast wave
A grid convergence study is performed to ensure that the blast profiles and peak
pressures are properly resolved numerically. This was done for the CFD calculation
stage involving the near-field development of the blast. The blast wave was
simulated using different cell sizes and the resulting blast profiles were compared.
Figure A.1 shows the blast profiles at different times after detonation for different
cell sizes. A cell size of 8 mm overestimates the peak pressure in the near field
(within 1.5 m from the warhead). The peak pressures obtained with the 4 mm and
2 mm cell sizes are quite similar and representative for the blast loading. Therefore,
a cell size of 4 mm is chosen for the simulation of the near-field blast from the
warhead.

Figure A.1 Pressure profile of the blast from the warhead at different times after detonation using
a numerical cell size of 8 mm, 4 mm and 2 mm. The peak pressures obtained with a
cell size of 4 mm and 2 mm are very similar. Therefore, calculations have been found
to converge at cell size 4 mm

Appendix C | 1 / 2

C Grid convergence of the 3D simulation
A grid convergence study for the 3D simulation is performed to ensure that the blast
profiles and peak pressures are properly resolved numerically. The aircraft shape
was not included for the purpose of this investigation. The flowfield of the 2D blast
wave development simulation is incorporated into a 3D numerical grid of cell size
varying between 15 mm and 100 mm. The blast is initially located at 3.2 m from the
warhead and propagates in the 3D grid up to a distance of 6 m.
Figure C.1 presents the pressure profiles at different times for different cell sizes.
The initial profiles show that the peak pressure is well preserved for cell sizes of
15 mm, 25 mm and 50 mm. A substantial loss of peak pressure occurs for a cell
size of 100 mm. After the blast propagates for 0.5 ms the discrepancy in peak
pressure obtained from the different profiles becomes larger, varying from 720 kPa
(15 mm cell size) to 357 kPa (100 mm cell size). The 0.5 ms corresponds to a
distance of approximately 4 m from the warhead. At this distance, although a grid
convergence is still not fully obtained for a cell size of 15 mm, the finest grid
certainly provides the highest accuracy. The discrepancy in peak pressure is
considerably less significant at larger distances, as shown by the profiles at 1.5 ms
and 2.5 ms. A cell size of 50 mm is considered permissible at distances larger than
5 m from the detonation point.
In the complete 3D simulation, including the aircraft, a cell size of 50 mm is used
near the warhead. A cell size of 1 m is used at a distance of 65 m from the warhead
for a total of nearly 30 million cells, being the maximum number of cells for this
study. This implies that the peak pressure is most likely underestimated only in the
near field (up to a distance of 4.5 m from the warhead), but is well-resolved at larger
distances.
Since the distance separating the warhead and the aircraft is approximately 4 m,
the pressure measured from the gauge located at the shortest distance from the
warhead is likely underestimated. For that reason the value of the 15 mm mesh is
used for only that location. The pressure measured by the other gauges is
sufficiently well-resolved.
The pressure-time profiles from the large 3D simulation (including the aircraft) are
shown in Figure C.2 for different distances from the nose of the aircraft. It can be
seen that the pressure rise is much steeper close to the warhead than far to it. The
pressure profiles at large distances are in contrast with the expected shock wave
profile where a discontinuity takes place to reach the peak pressure. The relatively
slow rise in pressure is a result of numerical dispersion which is inevitable with CFD
simulations. Smaller cell sizes would improve the quality of the pressure profile, but
the available resources did not allow such finer numerical grid. The loss of
“sharpness” in the pressure profile affects the peak pressure (see figure C.1), but
not the impulse: the area under the pressure curve is preserved even if the
sharpness is lost.