Similarity Deviation of Diameter and Thickness Effects

Abstract

One way to characterize the similarity of detonations (in the sense of their reaction rate) is through size effect tests. Using cylinders (rods), they’re called diameter effect tests, and using slabs, they’re called thickness effect tests. From the steady state equations of motion of these configurations it follows that they scale as r(D)=h(D), where r=rod radius, h=slab thickness, and D=steady detonation velocity. But tests show deviations from such scaling. Here we propose an explanation to these deviations. The explanation is based on a previous work in which we show that a boundary layer of partial reaction usually forms when a detonation wave is grazing along a free boundary. We suggest and show via computer simulations that those scaling deviations are related to this partially reacted boundary layer effect.