This paper presents a numerical study of the effects of rotor induced swirl velocity on the performance of brush seals. Such effects have been studied experimentally by Ferguson (1988), but this paper is apparently the first to obtain an enhanced understanding from the detailed flowfield distributions. The analysis involves the solution of the full Navier-Stokes equations in a two-dimensional, idealized configuration using a strongly conservative finite volume method developed by the authors in conjunction with the QUICK differencing scheme. The present computations have demonstrated excellent agreement with measurements for the similar flow across tube banks. An enhanced understanding of decreasing leakage with increasing shaft speed was obtained in terms of the various flow features. Specifically, the cause and effect relationship of certain interactions between the axial and tangential flows was identified. Computer-drawn pathlines show how increased leakage resistance results from large rotor-induced lateral motion of leakage fluid particles. In addition, a first-order streamwise periodic boundary condition treatment which facilitates numerical convergence has been proposed for essentially any flow which is streamwise periodic in two orthogonal directions.