NUMERICAL SIMULATION OF AIRBLAST PHENOMENON IN A BARE PLATE

PROBLEM DEFINITION

A standard rectangular plate of dimensions 2.3×0.5 m2 and thickness 7.56 mm is considered for the analysis. This plate is subjected to 100kg TNT blast at a stand-off distance of 10m. The permanent deformation of the plate is measured. Patran is used as the modeler and post-processor & Dytran is used as the FSI solver.

PLATE MODELLING

Following are the material properties assigned to plate:Young’s modulus = 210 GPaPoisson’s ratio = 0.3Density = 7800 kg/m3

Constitutive model = Elasto-plastic (DMATEP)Mesh type = Uniform

Fig.1 Plate meshed with quad element in Patran

Plate is modeled as a surface and meshed with quad element as shown in Fig1. All four edges of the plate are fixed against rotation and translation.

MODELLING OF EXPLOSIVE AND FLUID DOMAIN

. Air domain is meshed with hexahedron 8 noded element. Uniform meshing technique is used for meshing the fluid domain. Out flow boundary condition is given to fluid domain as the blast wave has to move away from the point of explosion. Explosive is modeled as a sphere of radius 0.25 m at a stand-off distance of 10 m from the plate. A simple formula

(volume=43π r3) is used for finding the radius of the sphere. Where, volume =

mass of explosive /density of explosive.

NUMERICAL RESULTS

The contour for maximum reflected pressure is shown in Fig. 2. Reflected pressure time histories for 100 kg TNT at 10 m stand-off distance is shown in Fig. 3. Maximum displacement contour and displacement time history at the plate centre are shown in Fig. 4 and Fig. 5 respectively. It is observed that the permanent deformation due to 100 kg TNT at 10 m stand-off distance is around 2.15 mm.

Fig 2. Contour for maximum pressure in the plate

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.0450

100000

200000

300000

400000

500000

600000

Time (Sec)

Ref

lect

ed p

ress

ure

(Pa)

Fig 3. Reflected pressure time history at the centre of the plate

Fig 4. Contour for maximum plate displacement

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04

-0.012

-0.01

-0.008

-0.006

-0.004

-0.002

0

0.002

0.004

0.006

0.008

Time (Sec)

Dis

plac

emen

t (m

)

Fig 5. Displacement time history at the centre of the plate

The permanent deformation is found to be 2.15 mm from the numerical simulation which is less than the allowable permanent deformation of 1.5 times the thickness of plate (shown in dotted lines in Fig. 5).

The same analysis is carried out with different plate thicknesses to investigate the change in displacement of the plate. The results thus obtained are minutely scrutinized with a view to confirming the plate thickness required for elastic deformation of the plate for the said conditions. The result for 9.5mm thick plate, being the optimal result, is given below.

Fig 6. Contour for maximum pressure in the plate of 9.5mm thickness

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.0450

100000

200000

300000

400000

500000

600000

Time(sec)

Ref

lect

ed P

ress

ure

(P

a)

Fig 7. Reflected pressure time history at the centre of the plate of 9.5mm thickness

The max pressure is obtained at the centre and its magnitude exactly matches with the empirical value.

Fig 8. Contour for maximum displacement for plate of thickness 9.5mm

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045

-0.0008

-0.0007

-0.0006

-0.0005

-0.0004

-0.0003

-0.0002

-0.0001

0

Time(sec)

Dis

pla

cem

ent

(m)

Fig 8. Displacement time history at the centre of the plate of thickness 9.5 mm

It can be observed that permanent displacement has a negligibly small value of 0.76mm (shown in dotted line). As the displacement tends to zero, it can be conferred that there is no permanent displacement and the plate exhibits elastic behavior at 9.5mm thickness under specified conditions.

Permanent displacement for 10mm plate at zero atm pressure is 0.56mm (Refer Fig. 8).

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045

-0.008

-0.006

-0.004

-0.002

0

0.002

0.004

0.006

Series2

Fig 8. Displacement time history at the centre of the plate of thickness 10 mm(zero atm pressure)

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.0450

100000

200000

300000

400000

500000

600000

Series2

Fig 8. Pressure time history at the centre of the plate of thickness 10 mm