Axial turbine engines consist of a set of stationary and rotating blades. To prevent hot air ingestion into the wheel space and disc cavities, relatively low-temperature air, in the form of bleed air from the compressor, is purged into the mainstream flow. However, the addition of purge flow alters the vortex structures in the rotor blade passage and decreases the turbine's efficiency. Hence, the purge flow should achieve a trade-off between efficiency and the prevention of hot air ingestion. The present study deals with the steady-state analysis of the single radial rim seal of the first-stage high-pressure axial turbine with and without the purge flow passage at different rotor speeds. The working fluid, air, is treated as an ideal gas. Ansys CFX is used for the computational analysis, and SST k-ω is chosen as the turbulence model. Present numerical simulations bring about detailed interaction between the purge and the mainstream flows. The results are discussed in terms of streamlines, pressure and temperature profiles, and efficiencies. As the rotor speed increases, the total-to-total isentropic efficiency and the blade loading decreases. Hence, an optimum rotor speed should be maintained to control the growth of the purge flow passage's boundary layer, thus preventing the blockage effects and minimising turbine losses.