Three-dimensional unsteady computational fluid dynamics is applied to the ingestion of fluid from a non-uniform mainstream annulus flow via a rim-seal into a rotor-stator wheel-space. The results provide understanding of the complex flow and information for the development of more efficient computational models and analytical 'orifice models'. The commercial computational fluid dynamics code CFX has been used to carry out unsteady Reynolds-averaged Navier-Stokes computations with an shear stress transport turbulence model. A scalar equation is employed to represent the seeded tracer gas that can be used in experiments to determine sealing effectiveness, and the variation of effectiveness with sealing flow rate is determined for a simple axial clearance seal and one combination of axial and rotational Reynolds numbers. The computational domain comprises one pitch in a row of stator vanes and rotor blades. The rotating blade is accounted for by a sliding interface between the stationary and rotating sections of the model, located downstream of the seal clearance. The unsteady computations confirm that the magnitude of the peak-to-trough pressure difference in the annulus is the principal driving mechanism for ingestion (or ingress) into the wheel-space. This pressure difference is used in orifice models to predict sealing effectiveness; its magnitude however depends on the locations in the annulus and the wheel-space that are chosen for its evaluation as well as the sealing flow rate. The computational fluid dynamics is used to investigate the appropriateness of the locations that are often used to determine the pressure difference. It is shown that maximum ingestion occurs when the static pressure peak produced by the vane combines with that produced by the blade, and that highly swirled ingested flow could contact both the stator and rotor disk when little sealing flow is provided. The relationships between the unsteady simulations and simplified, more computationally efficient steady computations are also investigated. For the system considered here, ingress is found to be dictated principally by the pressure distribution caused by the vane. The effect of the rotating blade on the pressure distribution in the annulus is investigated by comparing the unsteady results with those for steady models that do not involve a blade. It is found that the presence of the blade increases the pressure asymmetry in the annulus. Although the pressure asymmetry predicted by unsteady and steady models have a similar magnitude, the sealing effectiveness is over-predicted considerably for the corresponding steady model. If a 'thin seal' geometric approximation is used in the steady model, however, similar effectiveness results compared with the unsteady model may be obtained much more economically.