A Complete Equation of State for TNT-Air Mixtures

摘要

A complete equation of state is proposed for TNT-air mixtures up to 15,000 K. Three components are recognized: (ⅰ) pure TNT, (ⅱ) pure air, and (ⅲ) a mixture of TNT and air; each component is assumed to be in thermodynamic equilibrium. The thermodynamic states were calculated with the Cheetah code. Figure 1 depicts the specific internal E_r(T,R) as a function of temperature T and density ratio R = ρ/ρ_0 . Cheetah has been extended (exp6.v7.0.1.chi library) to include to include ionized species of air an electrons: N+, O+, O-, N2+, N2-, O2+, O2-, NO+, CO+, C+, Ne+, e-; results agree with Gilmore's calculations. This figure illustrates the strong dependence on density at high temperatures. Figure 2 depicts the specific internal energy u(T,R) as a function of T and R for pure TNT. Again one finds a strong dependence on density at high temperatures. Discontinuities in the curves at high density correspond to phase changes. Previous numerical simulations by Brode used an equation of state for TNT as developed by Jones and Miller. Figure 3 presents the specific internal energy E_r(T, R = 1, Y_(air)) as a function of temperature and mass fraction of air: Y_(air) = m_(air)/m_(mixture). At high temperatures there is a monotonic variation in temperature from pure TNT (Y_(air) = 0) to pure air (Y_(air) = 100%) at constant energy. At lower temperatures, there appears a fold in the thermodynamic equilibrium surface (below 1,200 K). The thermodynamic Equation of State (EOS) functions for pure TNT are shown in Figure 4. Illustrated there are the pressure function: p(u,ρ), the sound speed function: a(u,ρ) and the isentropic gamma function: Γ(u,ρ); again jumps come from phase changes. In our Godunov code, the algorithm requires pressure, sound speed and gamma in each cell, which are computed from these aforementioned EOS functions. Figure 5 presents the specific internal energy u(T, ρ) of pure TNT in the low temperature regime. Also shown there is the CJ isentrope which was used to define the u-T relationship for TNT in previous studies; it illustrates the complexity introduced by density variations in TNT over the range: 0.001 ≤ ρ(g / cc) ≤ 2.16.