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• Improve the accuracy of the results obtained in shape optimization. • Adjoint approach applied to chaotic flow. • Integrate large eddy simulations into adjoint shape optimization workflow. • Improve prediction of Reynolds Averaged Navier-Stokes solution. Nowadays, as industrial designs are close to their optimal configurations, the challenge lies in the extraction of the last percentages of improvement. This necessitates accurate evaluations of the performance and represents a significant higher computational cost. The present work aims at integrating Large Eddy Simulations in the optimization framework for an accurate evaluation of the flow field. The number of expensive evaluations is kept to a minimum by using the adjoint method for the evaluation of the gradient of the objective function. Divergence of the gradients due to the chaotic flow motion is avoided by an additional step which decouples the Large Eddy Simulations from the gradient calculations. An adaptation process based on a Reynolds Averaged Navier-Stokes simulation is therefore sought to mimic the more accurate Large Eddy Simulation results. The obtained field is then used in combination with an adjoint shape optimization routine. The method is tested on the design of a U-bend for internal cooling channels by minimizing its pressure loss. Starting from an optimized geometry obtained through a classical approach based on RANS evaluations, further improvements of the design are achieved with the application of the proposed strategy when performances are evaluated by means of LES. [ABSTRACT FROM AUTHOR]