Application of Richardson extrapolation method to aerodynamic and aeroacoustic characteristics of low Reynolds number vertical axis wind turbines

The aerodynamics and aeroacoustics of small scale Darrieus vertical axis wind turbines (VAWT) is investigated at chord-based Reynolds number below 1.5 × 10⁵ . A grid convergence study is carried out for thrust, cross-streamwise force and torque coefficient, and for overall sound pressure level (OSPL). Four levels of grid refinement are used for that purpose. Richardson Extrapolation is used to estimate the continuum value of each parameter by using the three finest grids and calculate the grid convergence level. Four operational points for the Darrieus VAWT are investigated-tip speed ratios (TSR) of 0.37, 1.12, 2.23 and 2.79, keeping a constant freestream velocity of 5.07 m/sec. These values resemble an experimental campaign to validate the numerical results. Commercial software 3DS Simulia PowerFLOW 6-2020 is used, which uses the Lattice Boltzmann/Very Large Eddy Simulation (LB-VLES) method to perform high-fidelity CFD simulations, and the Ffowcs-Williams and Hawkings (FW-H) acoustic analogy to calculate the far-field noise. Results show that thrust, cross-streamwise force and OSPL have better grid convergence than torque. Furthermore, grid convergence is better at TSR = 2.23 than at other TSRs. Blades in the downwind half of rotation are found to always produce less thrust and torque than in the upwind half, due to the effect of VAWT wake on the former. The difference in values between the two halves increased with increasing TSR, in general, due to the wake getting stronger at higher TSR; the ratio of contribution between upwind and downwind halves went as high as 17.6 in case of thrust for TSR = 2.79. In terms of noise, higher TSR produced more noise than the lower TSR configuration due to an increase in unsteady blade loading with increasing TSR. About OSPL directivity on a circular array of points, noise is highest at the most upstream azimuth location corresponding to the location where blade loading is highest in a single rotation.