The present work focuses on the problem of aerothermodynamics of space vehicles with rounded edges on the hypersonic segment of the flight trajectory. Firstly, the in-house Navier-Stokes solver, UNIC-UNS code, with the slip boundary condition is used to simulate the flows around a spherical-nosed cylinder at different Knudsen numbers and Mach numbers, and compared with DSMC computations for validation. The Navier-Stokes simulations are in good agreement with that of DSMC. The hypersonic flows over the European eXPErimental Re-entry Test-bed (EXPERT) model are then simulated for a wide range of flow regimes, which correspond to the expected descent trajectory with allowance for rarefaction and thermochemical nonequilibrium. Three dimensional CFD analyses are presented for the complete geometry of the capsules considering the air dissociation and its effects on the flow structure and on the force and thermal loads for the hypersonic segment of the flight as a precursor to the future studies and to provide the scientific community with quality data that can be used to improve tools for the design of hypersonic vehicles.