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.
