Monin-Obukhov similarity theory for modeling of wind turbine wakes under atmospheric stable conditions: Breakdown and modifications

Monin-Obukhov similarity theory (MOST) overestimates the mean vertical velocity gradient in some atmospheric stable conditions, i.e., Richardson number Rf <0.25. To obtain a given hub-height inflow velocity for a certain roughness length, this overestimated velocity gradient underpredicts the friction wind speed and the turbulence intensity, potentially influencing wake modeling of a wind turbine. This work investigates the side effects of the breakdown of MOST on wake modeling under stable conditions and makes some modifications to the flow similarity functions to eliminate these side effects. Based on a field measurement in a wind farm, we first show that MOST predicts a larger velocity gradient for the atmospheric stability parameter ς > 0.1 and proposes new flow similarity functions without constraining Rf to limit the overestimated velocity gradient. Next, different turbulence models based on MOST and a modified one based on the new similarity functions are investigated through numerical simulations. These turbulence models are combined with the actuator disk model (AD) and Reynolds-averaged Navier-Stokes equations (RANS) to model wind turbine wakes under stable conditions. As compared to measurements, numerical results show that turbulence models based on MOST result in a larger wake deficit and a slower wake recovery rate with a root-mean-squared error (RSME) of wake deficit in the range of 0.07 to 0.20. This overestimated wake effect is improved by applying the new similarity functions, and the RSME of wake deficit is reduced by 0.05 on average.