/BEM/DAA

Format

Definition

Comments

1. The entire structure must be modeled. Symmetric analysis is not supported.
2. The surface normal $n$ should be pointed into the fluid.
3. Standoff point defined with (X_s, Y_s, Zs) is the location where the incident pressure wave is given at time t=0:

   
   
   Figure 1.

4. A plane wave can be simulated using a spherical wave and putting the explosive charge far enough away.
5. Pressure at the standoff point as a function of time is:(1)
   $${\mathrm{P}}_i\left(t\right)=P_m{e}^{-\frac{t}{\theta }}$$
   Where,

   $P_m$

   Maximum pressure

   $t$

   Time

   $\theta$

   Decay time

   The maximum pressure and decay time can be calculated using:(2)

   $$P_m=K{\left[\frac{W^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}}{R}\right]}^a$$

   (3)

   $$\theta =K_{\theta }{W}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}{\left[\frac{W^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}}{R}\right]}^{a_{\theta }}$$

   $W$

   Explosive mass.

   $R$

   Distance to the explosion.

   $K$ , $\alpha$ , $K_{\theta }$ and $a_{\theta }$

   Constants depending on the explosive.

   If $W$ in kg, $R$ in meter, $P_m$ in MPa and in ms.

   	$K$	$\alpha$	$K_{\theta }$	$a_{\theta }$
   TNT	52.12	1.180	0.0895	-0.185
   PETN	56.21	1.194	0.0860	-0.257
   HBX	53.51	1.144	0.0920	-0.247

6. A free surface is a plane defined by a point and its normal vector.
7. The afterflow normal velocity is calculated as:(4)
   $$v_{afterflow}=\frac{\cos \gamma }{\rho R}{\displaystyle {\int }_0^{t}P\left(t\right)dt}$$

   P

   Fluid point.

   C

   Explosive charge point.

   S

   Standoff point.

   
   
   Figure 2.