| A reaction-rate equation for a composite energetic material was calibrated from two-dimensional steady-state experiment data by using the detonation shock dynamics theory.; From experimental detonation velocities and shock-front shapes at different diameters for an ammonium nitrate-based emulsion explosive at 1.248 g/cm{dollar}sp3,{dollar} the relationship between the detonation velocity normal to the shock-front and the shock-front curvature was obtained. By using this relationship and solving the quasi one-dimensional Euler equations of motion in a problem-conforming intrinsic-coordinate frame obtained from the detonation shock dynamics theory, the reaction rate was determined as a function of pressure and density:{dollar}{dollar}{lcub}dlambdaover dt{rcub} = 20.0 times 10sp6 {lcub}rm exp{rcub}({lcub}-{rcub}14390/sqrt{lcub}P/rhosp{lcub}0.8418{rcub}{rcub})(1 - lambda)sp{lcub}1.889{rcub}{dollar}{dollar}where {dollar}lambda{dollar} is the reaction extent, t is the time in s, P is the pressure in Pa, and {dollar}rho{dollar} is the density in kg/m{dollar}sp3{dollar}.; The reaction-rate equation obtained for this emulsion explosive shows that the rate is very slow and weakly state dependent. These characteristics of the rate indicated that the nonideal behavior of most industrial-type explosives can be attributed to their slow and state-insensitive rates.; By using the above rate equation, one-dimensional initiation experiments (wedge tests) were numerically modeled with a one-dimensional Lagrangian hydrodynamic code. The calculated shock trajectories agreed very well with experimental wedge test data. This agreement also suggested that the small shock-curvature asymptotics may be valid even for a relatively large value of the curvature.; The calibration method developed in this study is independent of the form of the rate. Realistic rate equations for explosives can be obtained in a very systematic way from two-dimensional steady-state experiments. |
