  A common model of the explosion mechanism of Type Ia supernovae is based on a
delayed detonation of a white dwarf. A variety of models differ primarily in
the method by which the deflagration leads to a detonation. A common feature of
the models, however, is that all of them involve the propagation of the
detonation through a white dwarf that is either expanding or contracting, where
the stellar internal velocity profile depends on both time and space. In this
work, we investigate the effects of the pre-detonation stellar internal
velocity profile and the post-detonation velocity of expansion on the
production of alpha-particle nuclei, including Ni56, which are the primary
nuclei produced by the detonation wave. We perform one-dimensional hydrodynamic
simulations of the explosion phase of the white dwarf for center and off-center
detonations with five different stellar velocity profiles at the onset of the
detonation. We observe two distinct post-detonation expansion phases:
rarefaction and bulk expansion. Almost all the burning to Ni56 occurs only in
the rarefaction phase, and its expansion time scale is influenced by
pre-existing flow structure in the star, in particular by the pre-detonation
stellar velocity profile. We find that the mass fractions of the alpha-particle
nuclei, including Ni56, are tight functions of the empirical physical parameter
rho_up/v_down, where rho_up is the mass density immediately upstream of the
detonation wave front and v_down is the velocity of the flow immediately
downstream of the detonation wave front. We also find that v_down depends on
the pre-detonation flow velocity. We conclude that the properties of the
pre-existing flow, in particular the internal stellar velocity profile,
influence the final isotopic composition of burned matter produced by the
detonation.
