The interaction of inflow turbulence with an airfoil is significant for low Reynolds number applications, as it generates leading edge noise, but also strongly modifies the airfoil boundary layer properties and thus the produced noise. Inflow turbulence impact still demands to be better understood and is also a numerical challenge. Large Eddy Simulations are here carried out with both incompressible and compressible solvers. The Synthetic Eddy Method and the Random Fourier Modes method, used to generate synthetic turbulence, are studied in this work. In order to eventually perform airfoil simulations, the second method is modified to take into account spanwise periodic boundary conditions, to reduce spurious noise level in compressible simulations. First, properties of the methods are studied with a spatially decaying turbulence academic case. Even if the decay is not well represented, the methods show satisfactory properties in terms of isotropy, homogeneity and one-dimensional spectra. Furthermore, spurious noise levels are reduced thanks to the modified method. Preliminary airfoil simulations are then carried out with inflow turbulence for flow validation in presence of a laminar separation bubble. The drag coefficient is in very good agreement with experimental results. However, there are some discrepancies between simulations and experiments on the lift coefficient, which is extremely sensitive to perturbations. These discrepancies are attributed to a lack of experimental turbulence characteristic information, such as isotropy or integral length scale and to too short simulations at high angles of attack. * The Einstein convention is used : subscript repetition implies summation, subscript between brackets avoids it.

The present work is dedicated to turbulence synthesis tailored to lateral periodic boundary conditions for direct noise computations through compressible large eddy simulations. Synthetic turbulence can be essential for aeroacoustic applications when computing airfoil turbulent inflow noise or for accurately capturing the behavior of boundary layers. This behavior determines both trailing edge noise and complex flow structures such as laminar separation bubbles. For airfoil simulation purposes, spanwise periodic boundary conditions are usually considered. If synthetic perturbations are injected without observing the periodicity rule, strong spurious pressure waves are emitted and pollute the entire computational domain. In this work, the random Fourier modes method for turbulence generation is adapted in order to respect the spanwise periodicity constraint right at the computational domain inlet. This approach does not affect the turbulence properties such as the spectral shape and the turbulent kinetic energy decay. Since the emphasis is put on the generation and convection of the turbulence, only the turbulence convection region between the inlet and the airfoil is considered in this paper, without the airfoil. Two geometrical configurations are tested: the first one is a simple box with a constant mesh size, and the second one concentrates the fine cells on the area in front of the airfoil. In the second configuration, the computational cost is reduced by up to 25%, but more spurious noise is present because of interpolation areas between different grids using the Chimera method. Finally, the results’ reproducibility is assessed using different turbulence realizations.