The focus of this paper is the numerical prediction of flow trajectories for particles that may be entrained in a bidirectional vortex, a swirling flow that has a reversing axial character. The internal flowfield that we consider is germane to both cylindrical cyclone separators and swirl-dominated thrust chambers that make use of the favorable mixing and centrifugal properties of a bidirectional vortex. To this end, a Lagrangian tracking scheme is employed to determine the motion of inert particles that are subject to the Stokes and Faxen drag in addition to other ancillary contributions due to virtual mass, Saffman lift, Archimedean buoyancy, shear, and gravity. For conditions that correspond to a simulated vortex engine, we find the drag force to be primarily responsible for controlling particle trajectories. Then using a one-way coupling paradigm in a cyclonic chamber, the effects of particle size, geometric inlet parameter, ĸ, particle-to-gas density ratio, θ and initial particle speed are investigated. All but the initial particle velocity are seen to have a significant impact on the particle trajectory. One of the goals of the present model is to assist in identifying fuel injection configurations that promote the optimal confinement of droplets or other injectants to the inner vortex region of a cyclonic chamber, thus reducing hot spots and other losses caused by wall impingement.