The French collaborative Trio4CLF project aims to understand and control the cryogenic cooling of amplifiers for high power (~1 PetaWatt) and high repetition rate (1-10 Hertz) lasers. In such amplifiers, the fluid evacuates the thermal power absorbed by the solid amplifying plates. A precise knowledge of the heat exchange and thus of the turbulent fluid flow in the amplifier is requested to evaluate its impact on the laser beam quality. As a first step, a Large Eddy Simulation is carried out in air without heating to study the development of the turbulent flow. The CFD code used is TrioCFD, a code developed by the CEA. For validation purpose, the simulation is carried out in the experimental setup configuration: a closed-loop wind tunnel called TRANSAT. Two horizontal plates, separated by 0.05 m, are put in the airflow to represent the amplifier plates. Turbulent boundary layers develop from the plates edges. Numerically, the entrance flow is a homogeneous planar flow with a constant velocity at 10 m/s. The results of this Large Eddy Simulation are presented in this paper as a study of the development of the turbulent boundary layers created by the plates.