ON THE DIRECT INITIATION OF GASEOUS DETONATIONS BY AN ENERGY-SOURCE

A new criterion for the direct initiation of cylindrical or spherical detonations by a localized energy source is presented. The analysis is based on nonlinear curvature effects on the detonation structure. The se effects are first studied in a quasi-steady-state approximation val id for a characteristic timescale of evolution much larger than the re action timescale. Analytical results for the square-wave model and num erical results for an Arrhenius law of the quasi-steady equations exhi bit two branches of solutions with a C-shaped curve and a critical rad ius below which generalized Chapman-Jouguet (CJ) solutions cannot exis t. For a sufficiently large activation energy this critical radius is much larger than the thickness of the planar CJ detonation front (typi cally 300 times larger at ordinary conditions) which is the only intri nsic lengthscale in the problem. Then, the initiation of gaseous deton ations by an ideal point energy source is investigated in cylindrical and spherical geometries for a one-step irreversible reaction. Direct numerical simulations show that the upper branch of quasi-steady solut ions acts as an attractor of the unsteady blast waves originating from the energy source. The critical source energy, which is associated wi th the critical point of the quasi-steady solutions, corresponds appro ximately to the boundary of the basin of attraction. For initiation en ergy smaller than the critical value, the detonation initiation fails, the strong detonation which is initially formed decays to a weak shoc k wave. A successful initiation of the detonation requires a larger en ergy source. Transient phenomena which are associated with the intrins ic instability of the quasi-steady detonations branch develop in the i nduction timescale and may induce additional mechanisms close to the c ritical condition. In conditions of stable or weakly unstable planar d etonations, these unsteady phenomena are important only in the vicinit y of the critical conditions. The criterion of initiation derived in t his paper works to a good approximation and exhibits the huge numerica l factor, 10(6)-10(8), which has been experimentally observed in the c ritical value of the initiation energy.