Developing a digital twin framework for wind tunnel testing: validation of turbulent inflow and airfoil load applications

Abstract. Wind energy systems, such as horizontal-axis wind turbines and vertical-axis wind turbines, operate within the turbulent atmospheric boundary layer, where turbulence significantly impacts their efficiency. Therefore, it is crucial to investigate the impact of turbulent inflow on the aerodynamic performance at the rotor blade scale. As field investigations are challenging, in this work, we present a framework where we combine wind tunnel measurements in turbulent flow with a digital twin of the experimental set-up. For this, first, the decay of the turbulent inflow needs to be described and simulated correctly. Here, we use Reynolds-averaged Navier–Stokes (RANS) simulations with k−ω turbulence models, where a suitable turbulence length scale is required as an inlet boundary condition. While the integral length scale is often chosen without a theoretical basis, this study derives that the Taylor micro-scale is the correct choice for simulating turbulence generated by a regular grid: the temporal decay of turbulent kinetic energy (TKE) is shown to depend on the initial value of the Taylor micro-scale by solving the differential equations given by Speziale and Bernard (1992). Further, the spatial decay of TKE and its dependence on the Taylor micro-scale at the inlet boundary are derived. With this theoretical understanding, RANS simulations with k−ω turbulence models are conducted using the Taylor micro-scale and the TKE obtained from grid experiments as the inlet boundary condition. Second, the results are validated with excellent agreement with the TKE evolution downstream of a grid obtained through hot-wire measurements in the wind tunnel. Third, the study further introduces an airfoil in both the experimental and the numerical setting where 3D simulations are performed. A very good match between force coefficients obtained from experiments and the digital twin is found. In conclusion, this study demonstrates that the Taylor micro-scale is the appropriate turbulence length scale to be used as the boundary condition and initial condition to simulate the evolution of TKE for regular-grid-generated turbulent flows. Additionally, the digital twin of the wind tunnel can accurately replicate the force coefficients obtained in the physical wind tunnel.