Gurney and cylinder wall velocities of explosives: analytical estimates and thermochemical simulations

Gurney velocity (<i>u</i>_G) and cylinder wall velocity (<i>v</i>_s) of energetic materials are calculated using the semi-empirical C<i>γ</i> method, an analytical model previously developed for CHNO high explosives and presently extended to additional elements and to explosives at low loading density. The results are compared to recent procedures based on thermochemical simulations. Regarding <i>u</i>_G, both approaches perform similarly well for organic high explosives, with an average relative error close to 2.6%. However, C<i>γ</i> underestimates <i>u</i>_G for tritonal, an explosive with 20-40 wt% aluminium powder. Regarding <i>v</i>_s, a newly introduced empirical equation is shown to perform better than the Gurney model, although not as well as a recent correlation involving the detonation energy derived from thermochemical simulations, which are still required to predict cylinder wall velocities with optimal accuracy. With regard to the application of present models to the design of new materials, C<i>γ</i> is not recommended for metal-containing compounds. However, for the high-thoughput design of organic high explosives, it is an invaluable tool allowing fast and reproducible calculations of Gurney energies with state-of-the-art accuracy. A very simple, hackable Python script is provided for this purpose as supplementary information.