Determination of the Velocity-curvature Relationship for Unknown Front Shapes

Detonation Shock Dynamics (DSD) is a detonation propagation methodology that replaces the detonation shock and reaction zone with a surface that evolves according to a specified normal-velocity evolution law. DSD is able to model detonation propagation when supplied with two components: the normaldetonation-velocity variation versus detonation surface curvature and the surface edge angle at the explosiveconfiner interface. The velocity-curvature relationship is typically derived from experimental rate-stick data. Experimental front shapes can be fit to an analytic equation with an appropriate characteristic shape to examine detonation velocity-curvature variation computed from that analytic expression. However, in some complex explosive-confiner configurations, an appropriate functional form for the detonation front shape may be difficult to construct. To address such situations, we numerically compute the velocity-curvature variation directly from discrete experimental front-shape data using local rather than global fitting forms. The results are then compared to the global method for determining the velocity-curvature variation. The possibilities and limitations of such an approach are discussed.