  We present a numerical study of detonation propagation in unconfined
explosive charges shaped as an annular arc (rib). Steady detonation in a
straight charge propagates at constant speed but when it enters an annular
section, it goes through a transition phase and eventually reaches a new steady
state of constant angular velocity. This study examines the speed of the
detonation wave along the annular charge during the transition phase and at
steady state, as well as its dependence on the dimensions of the annulus. The
system is modeled using a recently proposed diffuse-interface formulation which
allows for the representation of a two-phase explosive and of an additional
inert material. The explosive considered is the polymer-bonded TATB-based LX-17
and is modeled using two JWL equations of state and the Ignition and Growth
reaction rate law. Results show that steady state speeds are in good agreement
with experiment. In the transition phase, the evolution of outer detonation
speed deviates from the exponential bounded growth function suggested by
previous studies. We propose a new description of the transition phase which
consists of two regimes. The first is caused by local effects at the outer edge
of the annulus and leads to a dependence of outer detonation speed on angular
position along the arc. The second regime is induced by effects originating
from the inner edge of the annular charge and leads to the deceleration of the
outer detonation until steady state is reached. The study concludes with a
parametric study where the dependence of the steady state and the transition
phase on the dimensions of the annulus is investigated.
