Aircraft contrails may contribute to the global radiative forcing. In this context, the investigation of contrail formation in the near field of an aircraft may be helpful in developing strategies to reduce undesirable impacts. Contrail formation is also a complex topic, since several physical processes are involved, covering a large range of space and time scales, from the engine exit to the atmospheric global scale. In the near field of the aircraft, contrail formation is mainly dominated by microphysics and mixing processes between the propelling jets and the external flow (the so called jet-vortex interaction). In this study, three-dimensional Reynolds-Averaged Navier–Stokes (RANS) simulations of contrails produced by the Common Research Model wing/body/engine configuration during cruise flights is performed. In the present work, a dedicated internal nozzle geometry has been designed to replace the through flow nacelle of the original CRM configuration. Thus, the engine core and bypass flows are actually computed in the simulations, which allows several parametrical studies and avoids using parameterizations to describe the plume's dilution. The objective is to simulate the early development of contrails in a fresh plume whose dilution is obtained with a spatial simulation of jet/vortex interaction. A coupling is carried out with a chemical and a microphysical model implemented in the unstructured Navier-Stokes CFD code CEDRE to simulate particle growth using an Eulerian approach. The implemented microphysics model can simulate water condensation onto soot particles, taking into account their activation by adsorption of sulfur species. In this context, an adaptation grid mesh procedure has been used in order to generate an optimized unstructured mesh in the fluid zone of interest (i.e. vortex wake and jet exhaust).