In gas turbines, rim seals are fitted at the periphery of the wheel-space between the turbine disk and its adjacent casing; their purpose is to reduce the ingress of hot mainstream gases. A superposed sealant flow, bled from the compressor, is used to purge the wheel-space or at least dilute the ingress to an acceptable level. The ingress is caused by the circumferential variation of pressure in the turbine annulus radially outward of the seal. Engine designers often use double-rim seals where the variation in pressure is attenuated in the outer wheel-space between the two seals. This paper describes experimental results from a research facility that models an axial turbine stage with engine-representative rim seals. The radial variation of CO2 gas concentration, swirl, and pressure, in both the inner and outer wheel-space, are presented over a range of purge flow rates. The data are used to assess the performance of two seals: a datum double-rim seal and a derivative with a series of radial fins. The concept behind the finned seal is that the radial fins increase the swirl in the outer wheel-space; measurements of swirl show the captive fluid between the fins rotate with near solid body rotation. The improved attenuation of the pressure asymmetry, which governs the ingress, results in an improved performance of the inner geometry of the seal. The fins also increased the pressure in the outer wheel-space and reduced the ingress though the outer geometry of the seal.