Simulation of the Effects of an Air Blast Wave - ELSA - Europa

4 Investigations with Explosives as a Charge (Solid TNT)The aim of the RAILPROTECT project is to contribute to alleviating the vulnerability of Europe'spassenger transport infrastructures. The effects of a terrorist attack should be simulated numerically,and for a numerical investigation the knowledge of the loading of the structures is necessary. Thereare different approaches and possibilities for the calculation of a detonation inside buildings, asdiscussed in chapter 3.A detonation releases a large amount of energy in a very short time. This results in an air shockwavewhich is spread outwards from the charge. Then, the air blast wave reaches the structure,which, depending on the size of the charge and on the distance, will respond to this wave loading.A calculation of the behaviour of the air blast wave requires the knowledge of the behaviour of theexplosive and of the air around the explosive. The results of the numerical investigation can becompared for the validity of the calculations with existing experimental-analytical data. As will beshown in this chapter, the experimental-analytical results of Kingery [14] will constitute the basisfor these comparisons.4.1 Modelling of the explosiveThe explosive for the numerical investigation can be built up e.g. with the Jones–Wilkins–Lee(JWL)-equation. This equation of state (EOS) is widely used because of its simplicity and due to thefact that most high explosives are well modelled by this equation. According to it, the value ofpressure is given as⎛ ω ⎞−RV⎛ ω ⎞1 −R2VEpEOS= A⎜1− ⎟e + B⎜1− ⎟e+ ω⎝ RV1 ⎠ ⎝ RV2 ⎠ V(15)In this equation A, B, R1, R2 and ω are the model parameters, V is the ratio ρ sol /ρ, where ρ=currentdensity and ρ sol =density of solid explosive, and E is the internal energy per unit volume of theexplosive. It is noted that E=ρ sol e int , where e int is the current internal energy per unit mass. Theparameters of this equation for most explosives are shown in Dobratz [10]. Different authors useslightly differing parameter values for this equation, as shown in Table 2. Note that the equationwill be reduced only to its last term if the solid explosive is exhausted and the resulting gases fullyexpanded. The last term of equation (15) is the EOS of an ideal gas that can be used e.g. for the air.pEOSE= ω (16)V20