A numerical framework for the aerodynamic characterization of wind turbine airfoils is developed and applied to the miniature wind turbine WiRE-01. The framework is based on a coupling between wall-resolved large eddy simulation (LES) and application of the blade element momentum theory (BEM). It provides not only results for the airfoil aerodynamics but also for the wind turbine, and allows to cover a large range of turbine operating conditions with a minimized computational cost. In order to provide the accuracy and the flexibility needed, the unstructured finite volume method (FVM) and the wall-adapting local eddy viscosity (WALE) model are used within the OpenFOAM toolbox. With the purpose of representing the turbulence experienced by the blade sections of the turbine, a practical turbulent inflow is proposed and the effect of the inflow turbulence on the airfoil aerodynamic performance is studied. It is found that the consideration of the inflow turbulence has a strong effect on the airfoil aerodynamic performance. Through the application of the framework to WiRE-01 miniature wind turbine, a comprehensive characterization of the airfoil used in this turbine is provided, simplifying future studies. In the same time, the numerical results for the turbine are validated with experimental results and good consistency is found. Overall, the airfoil and turbine designs are found to be well optimized, even if the effective angle of attack of the blades should be reduced close to the hub.