The objective of the present work is to improve numerical predictions of unsteady turbulent swirling flows in the draft tubes of hydraulic power plants. We present Large Eddy Simulation (LES) results on a simplified draft tube consisting of a straight conical diffuser. The basis of LES is to solve the large scales of motion, which contain most of the energy, while the small scales are modeled. LES strategy is here preferred to the average equations strategies (RANS models) because it resolves directly the most energetic part of the turbulent flow. LES is now recognized as a powerful tool to simulate real applications in several engineering fields which are more and more frequently found. However, the cost of large-eddy simulations of wall bounded flows is still expensive. Bypass methods are investigated to perform high-Reynolds-number LES at a reasonable cost. In this study, computations at a Reynolds number about 2 $10^5$ are presented. This study presents the result of a new near-wall model for turbulent boundary layer taking into account the streamwise pressure gradient (adverse or favorable). Validations are made based on simple channel flow, without any pressure gradient and on the data base ERCOFTAC. The experiments carried out by Clausen et al. [1] reproduce the essential features of the complex flow and are used to develop and test closure models for such flows.