A new k‐epsilon model consistent with Monin–Obukhov similarity theory

Laan, P. van der; Kelly, Mark; Sørensen, Niels N.

doi:10.1002/we.2017

Cited by 30 publications

(39 citation statements)

References 26 publications

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“…In simulations, the disk-averaged velocity U disk is calculated by averaging the local velocity in the disk region, then is applied to estimate the upstream reference velocity U ref based on Equations (16) and (17) and the momentum source S u,i based on Equation 15, respectively.…”

Section: Actuator Disk Model Based On Thrust Coefficient (-Ct)mentioning

confidence: 99%

“…A widely used turbulence model for the thermal stratified boundary layer was developed by Alinot and Masson [15] where a coefficient of the buoyant terms in the ε transport equation is calibrated with atmospheric stability. However, van der Laan et al [16] showed that this model cannot keep the flow homogeneity in a large domain under unstable conditions and thus developed a turbulence model consistent with MOST. In Prospathopoulos et al [13], an additional buoyancy production based on the Richardson number Ri was added to the turbulent kinetic energy equation to model wind turbine wakes under stable conditions.…”

Section: Introductionmentioning

confidence: 99%

“…The present paper aims to investigate these side effects through numerical simulations and to make a modification on MOST to eliminate these side effects. This modification is to propose a new set of similarity functions based on field measurements to limit the wind shear in very stable conditions and to introduce the new similarity functions into the turbulence model proposed by van der Laan et al [16].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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

Han

Liu

et al. 2019

Preprint

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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.

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Section: Actuator Disk Model Based On Thrust Coefficient (-Ct)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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

Han

Liu

et al. 2019

Preprint

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“…In a diurnal cycle stable conditions are typically seen at night with cooler land temperatures while unstable conditions appear in day times with elevated temperatures. Typically, non-neutral conditions dominate for mean wind speeds lower than 15 m s −1 [1] [2]. Non-neutral conditions are thus present during the most prevalent wind speed conditions experienced by commercial wind farms.…”

Section: Introductionmentioning

confidence: 99%

“…Two k − turbulence model modifications for MOST are investigated: the methods of Alinot and Masson [3] and the recently proposed model from M.P. van der Laan et al [1]. The models are applied to the wind farm location, to understand the model accuracy in complex terrain.…”

Section: Introductionmentioning

confidence: 99%

Monin-Obukhov similarity theory and its application to wind flow modelling over complex terrain

Breedt

Craig

Jothiprakasam

2018

Journal of Wind Engineering and Industrial Aerodynamics

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In the wind resource industry Computational Fluid Dynamics (CFD) has gained widespread use to model the Atmospheric Boundary Layer (ABL). These models primarily focus on the neutrally stratified surface layer and ignore physical process such as buoyancy and the Coriolis force. Reductions in uncertainties of turbine suitability and energy production can be achieved if these processes are included. The present work focuses on the development and validation of an ABL CFD model using Monin-Obukhov Similarity Theory (MOST) in which atmospheric stability and the Coriolis force are included. MOST is applied to measured time series data obtained from a commercially proposed wind farm to determine the prevalence and impact of atmospheric stability. The analyses provide the inputs for the CFD model. The CFD model uses the standard k − turbulence model. To account for atmospheric stability modifications based on MOST are introduced to the standard CFD model equations. Two MOST models modifications are investigated. The modifications are successfully validated using the empty domain horizontal homogeneity test of the inlet profiles. The model is thereafter applied to the complex terrain of the proposed wind farm. The models are successfully validated by cross-prediction of the stability-dependent wind velocity profiles between two onsite meteorological masts.

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On a new one‐dimensional k$$ \boldsymbol{k} $$–ε$$ \boldsymbol{\varepsilon} $$ turbulence closure for building‐induced drag

Zonato

Martilli

Santiago

et al. 2023

Quart J Royal Meteoro Soc

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Various urban canopy parameterizations (UCPs) have been developed in the last two decades to take into account the modifications induced by buildings on mean flow and turbulent fields in mesoscale meteorological models, the typical spatial resolution of which cannot resolve urban structures explicitly. In particular, several multilayer UCPs have been proposed, successfully reproducing wind‐flow characteristics in the urban environment. However, they often rely on length scales for the calculation of the eddy viscosity and the dissipation rate, which need to be tuned for various urban configurations. The main objective of this work is to address this shortcoming, by developing a new one‐dimensional turbulence closure that takes building‐induced turbulence into account independently of turbulence length scales. This model directly solves not only the equation for turbulent kinetic energy but also the equation for its dissipation rate (k$$ k $$–ε$$ \varepsilon $$ model). Similar closure schemes have been successfully adopted for vegetated canopies, but their applicability to urban canopies is still unknown. The performance of the new k$$ k $$–ε$$ \varepsilon $$ model, with additional sources and sinks for wind speed, turbulent kinetic energy, and dissipation rate, is tested by means of single‐column simulations in idealized urban areas, using different building packing densities. Results are in good agreement with spatially averaged building‐resolving CFD simulations. In particular, vertical profiles of mean and turbulent variables show better results with respect to simulations using turbulence closures adopting a parameterization of turbulence length scales. The best improvements are obtained for wind speed, reducing errors to half the typical values for standard UCP for high packing densities, and for the dissipation rate. Furthermore, besides the enhancement in the reproduction of the mean flow for urban areas, the proposed turbulence closure does not need additional tuning of coefficients depending on the packing density, resulting in a more general and efficient scheme.

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A new k‐epsilon model consistent with Monin–Obukhov similarity theory

Cited by 30 publications

References 26 publications

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

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

Monin-Obukhov similarity theory and its application to wind flow modelling over complex terrain

On a new one‐dimensional k$$ \boldsymbol{k} $$–ε$$ \boldsymbol{\varepsilon} $$ turbulence closure for building‐induced drag

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