Hot gas ingestion into the wheel space can reduce the lifetime of vulnerable components in gas turbine like the turbine disk. Rim seal structure at the periphery of the wheel-space is designed to protect the turbine disk from hot gas. This paper describes the steady and unsteady Reynolds-averaged Navier-Stokes (RANS and URANS) computation method with Shear Stress Transport (SST) turbulent model using commercial CFD code and the validation of grids. The RANS and URANS computation have been carried out in a one stage turbine model with different rim seal configurations: fish-mouth rim seal and double rim seal. A 10.91° sector computation model comprises one pitch in a row of stator vanes, and rotor blades is set up and simulated with different sealant flow rate. Results show that the fish-mouth rim seal can achieve higher sealing effectiveness with low sealant flow rate by installing the inner shell at high radius on the stator disk. The comparison between the steady and unsteady results indicates that the RANS computation underpredicts the level of the hot gas ingestion, especially in the double rim seal configuration. It can be found in the URANS computation results at different time steps that, when the rotating effect is considered, the interaction between the vane wake and the wave of the blade leading edge can lead to more serious pressure asymmetry, which worsens the hot gas ingestion. The counter-rotating vortex induced at outer wheel space and the Kelvin-Helmholtz-like vortices caused by velocity difference of mainstream and sealing flow can further aggravate the ingress.