/LOAD/PBLAST

The Air Blast incident pressure is fitted from experimental data, then blast pressure is deduced from surface orientation to the detonation point. You must provide detonation point, detonation time and equivalent TNT mass.

This is a simplified loading method because the arrival time and incident pressure are not adjusted for obstacles. It also does not take into account confinement or ground effects.

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Definition

Comments

1. Modeling situation is set with Exp_data flag. You provide explosion data (X_det, Y_det, Z_det), explosion mass (W_TNT) target surface (surf_ID), and detonation time (T_det). All other parameters and flags have default values.
   If Exp_data=3, explosive height must be defined.

   
   
   Figure 1.

   At a given point over the user surface, the corresponding radius $R$ and the explosive mass W_TNT is used to determine characteristic values of the blast wave (arrival time $t_a$ , maximum pressure P_max, positive duration $\text{Δ}{t}_{+}$ , impulse $I_{+}$ , ...) . Both incident wave and reflected wave are to follow Friedlander’s equation:

   • If I_model = 1 (Friedlander model)(1)
     $${\mathrm{P}}_{Friedlander}\left(t\right)=P_{}\cdot e^{\frac{-\left(t-t_a\right)}{\text{Δ}{t}_{+}}}\left(1-\frac{t-t_a}{\text{Δ}{t}_{+}}\right)$$
   • If I_model = 2 (modified Friedlander model)(2)
     $${\mathrm{P}}_{Friedlander}\left(t\right)=P_{\max }\cdot e^{\frac{-b(t-t_a)}{\text{Δ}{t}_{+}}}\left(1-\frac{t-t_a}{\text{Δ}{t}_{+}}\right)$$

   Where, $P_{\max },\text{Δ}{t}_{+},t_a$ are experimentally known at a given scaled distance $\frac{R}{W^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}}$ . ³

   With the modified Friedlander model (I_model=2), ‘b’ is a decay parameter introduced to fit the positive impulse.

   'b’ is solved such as:(3)

   $${\displaystyle \underset{t_a}{\overset{t_a+\text{Δ}{t}_{+}}{\int }}{\mathrm{P}}_{Friedlander}\left(t\right)dt=I_{+}}$$

   
   
   Figure 2. Blast profile from Friedlander equation

2. The fitted time history function ${\mathrm{P}}_{incident}\left(t\right)$ and ${\mathrm{P}}_{reflected}\left(t\right)$ are also used to compute blast loading ${\mathrm{P}}_{BLAST}\left(t\right)$ at a given face centroid Z’ (Figure 3). ²(4)
   $${\mathrm{P}}_{BLAST}\left(t\right)=\left\{\begin{array}{c}{\cos }^2\theta \cdot {\mathrm{P}}_{reflected}\left(t\right)+\left(1+{\cos }^{}\theta -2{\cos }^2\theta \right)\cdot {\mathrm{P}}_{incident}\left(t\right)\text{ if }\cos \theta >0\\ {\mathrm{P}}_{incident}\left(t\right)\text{ if }\cos \theta \le 0\end{array}\right.$$

   
   
   Figure 3. Blast pressure applied on a face centroid Z’ . depends on face orientation

   Where, $\theta$ is the angle between the surface segment (centroid Z’) and the direction to detonation point.

   This means that blast pressure is equal to reflected pressure if segment is directly facing the detonation point, and equal to incident pressure if segment is not facing the detonation point. This modeling is simple because arrival time and incident pressure are not adjusted with shadowing of the related structure. It also does not into account confinement and tunnel effect.

   This also requires the surface to have outward normal vector.

3. If I_z =1, R is constant and computed during Starter at time=0.00. When I_z =2, $R=R(t)$ is updated for each cycle during Engine computation.
4. If W_TNT is not set, the mass is zero and no pressure will be loaded on the related surface.
5. If modeled explosive is not TNT, an equivalent TNT mass must be provided.
6. The experimental data uses the unit system {cm, g, $\mu s$ }. The units defined in /BEGIN will be used to convert the experimental data units to the model units. Therefore, the units defined in /BEGIN must correctly match the units used in the model.
7. It is possible to skip computation time from $T=0$ to $t^{*}=\inf \left(T_{arrival}\right)$ . The shift value is automatically computed during Starter execution. To disable a computation up to $t^{*}$ , the I_tshift value must be equal to 2.

   
   
   Figure 4. I_tshift enables to skip computation time up to first wave arrival time

8. The $N_{dt}$ parameter can impose a minimum time step, if structural one is not large enough. Imposing $\text{Δ}{t}_{blast}=\frac{\inf \left(T_0\right)}{N_{dt}}$ ensures that there are sufficient time steps during positive phase, that is, during the exponential, decrease of the blast wave. By default, $N_{dt}=100$ .

   
   
   Figure 5.

9. Parameter $P_{\min }$ was introduced to keep positive part of Friedlander blast model.(5)
   $${\mathrm{P}}_{}\left(t\right)=\max (P_{BLAST}(t),P_{\min })$$

   Figure 6. Parameter $P_{\min }$ used to keep only overpressure (positive part of the loading)