Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

# Monin-Obukhov Similarity Theory for Modeling of Wind Turbine Wakes under Atmospheric Stable Conditions: Breakdown and Modifications

Version 1 : Received: 14 August 2019 / Approved: 16 August 2019 / Online: 16 August 2019 (07:52:44 CEST)

How to cite: Han, X.X.; Liu, D.Y.; Xu, C.; Shen, W.Z.; Li, L.M.; Xue, F.F. Monin-Obukhov Similarity Theory for Modeling of Wind Turbine Wakes under Atmospheric Stable Conditions: Breakdown and Modifications. Preprints 2019, 2019080175 (doi: 10.20944/preprints201908.0175.v1). Han, X.X.; Liu, D.Y.; Xu, C.; Shen, W.Z.; Li, L.M.; Xue, F.F. Monin-Obukhov Similarity Theory for Modeling of Wind Turbine Wakes under Atmospheric Stable Conditions: Breakdown and Modifications. Preprints 2019, 2019080175 (doi: 10.20944/preprints201908.0175.v1).

## Abstract

Monin-Obukhov similarity theory (MOST) overestimates wind shear in some atmospheric stable conditions, i.e. Richardson number $R_f<0.25$. The overestimated wind shear that leads to an under-predicted friction wind speed and a lower ambient turbulence intensity for a given hub-height reference wind speed and a given roughness length, could influence 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 firstly show that MOST predicts a larger wind shear for the atmospheric stability parameter $\zeta>0.1$ and proposes new flow similarity functions without constraining $R_f$ to limit the overestimated wind shear by MOST. 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 larger wake deficits and slower wake recovery rate with a square root of the mean-squared-error (RSME) of wake deficit in the range of 0.07-0.18. This overestimated wake effect is improved by applying the new similarity functions and the RSME of wake deficit is averagely reduced by 0.05. Finally, we check the role of the under-predicted turbulence intensity playing in the larger wake deficit predicted by models based MOST. Additional numerical simulations using the modified turbulence model are carried out, in which the roughness length is reduced to impose a hub-height ambient turbulence intensity equivalent to the MOST case. Simulation results show that reducing turbulence intensity enhances wake effects, however, it cannot reproduce the large wake deficit predicted by models based on MOST, which suggests that the overestimated wake effect by MOST could be also related to the overestimated wind shear.

## Subject Areas

wind turbine; wake; atmospheric stability; MOST; turbulence models

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