Problem Statement:
Figure-1 Blast wall configuration
Solution:
General settings:
Ø In Run Geometries both Spherical
geometry and Cylindrical geometry are checked because the solution will
maintain both spherical geometry and cylindrical geometry since there is ground
and a centrally detonated spherical charge.
Ø The Checkpoints-At end of phase box
is ticked so that a solution check point is stored at the end of the
spherically symmetric phase. This permits changes to be made to the definition
of the cylindrical phase and rerun without having to rerun the spherical phase.
Ø The switch time was calculated as
suggested in the user guide as switch time = 1.2 x 10-3 x
= 1.2 x 10-3 x
Since the density of the TNT can be taken as
1600 kg/m3 this gives a volume VTNT of explosive,
VTNT =
and then the
radius of the spherical charge is rTNT =
Ø The switch time (for second order
accuracy) is taken as 21 milli seconds
Ø Standard atmospheric conditions are
taken as 101325 pa atmospheric pressure and 288 k temperature.
Ø In the display settings a white
Background is ticked and the checkpoints at the end of phase are ticked so as
to save the checkpoints data after each solution phase.
Spherical Geometry settings:
Ø We are going to plot Overpressure as
a variable with an interval of 10 time steps, show targets are ticked for
convenience.
Ø In the detonation parameters, the
Explosive type is taken as TNT with charge mass 815 kg.
Ø A problem time of 0.06s will be
sufficient to gather information on the positive phases of all target points
out to 5m. This value is calculated by taking the 18m domain size, dividing by
the atmospheric sound speed 330m/s to give 0.0545s and increasing by a little
for a good measure.
Ø The default safety number of 0.5 is
taken.
Ø A nominal cell size of 10mm is used
for an accurate simulation, fit to charge radius is chosen. So the cell size
will be internally adjusted by ProSAir to ensure the charge surface exactly
aligns with a cell boundary.
Ø A domain size of 2m is chosen, the
distance from the charge to ground.
Ø The boundary has been set to stop so
the spherical computation will stop as the blast wave reaches 2m (the domain
size) from the centre of detonation.
Ø There are no target points in
spherical Geometry.
Cylindrical Geometry settings:
Ø We are going to plot Overpressure
variable in contour plot type with a interval of 50 timesteps.
Ø A scale factor of 10 is chosen and
the option "Show targets" is ticked for convenience.
Ø Problem time of 0.05s is taken
considering the cylindrical domain size of 16m.
Ø The height of blast is 2m and the CFL
safety number is 0.5, the boundary types both in the radial as well as axial
directions are chosen to be transmissive since the shock waves as to pass into
the outer domain freely.
Ø A cell size of 0.03m is chosen.
Ø Domain size of 18m in radial
direction and 16m in axial direction is taken.
Ø Obstacles:
·
Since
there's a blast wall of width 0.5m and height of 3m next to the explosive the
geometry data for the blast wall is taken as 2 2.5 0 3 with material type as
solid
·
The
building is 15m in height and 5m in width and 12m away from the explosive so
the Geometry data for the building is taken as 12 17 0 15 with material type as
solid.
Ø Target Point Grids:
15 target point grids are defines for which the associated target points
will correspond to those of Figure namely a grid(column) of 15 points in the
radial direction, at r=11.99 and 15 points in vertical from h=0 to h=15.
Ø All the above settings are applied to
the simulation by clicking "Ok" at the right bottom.
Running Simulation:
On running the
simulation the spherical solution phase starts and ProSAir displays a plot
overpressure with radius, evolving in time, until the shock reaches the outer
boundary at radius R= 2m as shown in Figure
Figure-2 : Overpressure
versus radius after at the end of the spherically symmetric solution phase
(about 7.3ms)
Solution then switches to the cylindrical phase. There is a
small pause in computation as ProSAir transfers the spherical symmetric
solution onto the cylindrical symmetric grid given the initial plot of Figure 3
Figure-3 : Overpressure
contour plot at the start of the cylindrically symmetric solution phase (about
0.45ms
Figure-4 : Overpressure
contour plot as the blast wave reaches target point 6,7 and 8 at 9.37ms
At 10.131ms, the blast wave impacts at target points 7,8,9.
Again these target points have yet to feel the effect of the reflected shock
and so the peak pressure, time of arrival and, most likely impulse will not be
affected by the reflection.
There after a cycle of shock wave reflections and shock wave
vents are seen.
Results:
The maximum peak pressure is estimated on the wall-facing
side of the building as 2002.37 kpa at the target point 11 and the
positive phase impulse is estimated as 5219.05 kpa and the plots for all the
target points is shown below
Discussion:
The overpressure is plotted using excel for the target point
11 using the data from pt_cylindrical_11.csv, the sharpness of the peaks
indicates that the mesh is fully resolved and the first peak at 11.3588 ms creates
a maximum over pressure on the wall of the building for the design of the
building this data is useful and there's another blast wave at 44.4 ms which is
reflected from the blast wall and ground, more over the blast wall has a big
influence on the overpressure on the building, the blast wall obstacle blocked
the substantial amount of pressure energy.
Convergence study:
At first the simulation was performed at 0.05 nominal cell
size in Cylindrical phase where the maximum peak pressure is 1935.49 kpa estimated
at the target point 11,
then the cell size is reduced to 0.03m in the cylindrical
phase then, the results are obtained as mentioned in the results.
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