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Comparison of effects of four subgrid-scale turbulence models in large eddy simulation of a large wind farm

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Abstract

The present study makes predictions of four different subgrid-scale (SGS) models in large eddy simulation (LES) of large wind farms. The considered models are Smagorinsky (SM), dynamic Smagorinsky (DS), dynamic Lagrangian (DL), and wall-adapting local eddy-viscosity (WALE). In all simulations, the atmospheric boundary layer (ABL) is neutral, and wind turbines are modeled using the actuator disk model (ADM). The impact of these subgrid-scale models on the large wind farm simulation is evaluated by studying the mean flow velocity, wake characteristics, wind turbine power extraction, and different mean kinetic energy budget terms. It is observed that various models show different power extraction, and WALE and DL models predict the maximum and minimum power extraction, respectively. Furthermore, the mean kinetic energy budget terms show discrepancies for different models. The dissipation term shows a significant discrepancy in the near-wall and turbine hub regions. This dissipation discrepancy is maximum between the Smagorinsky and dynamic models.

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Abbreviations

A :

Surface area of the wind turbine rotor (m2)

a :

Axial induction factor

C T :

Thrust coefficient

C s :

Smagorinsky constant

C w :

WALE constant

\({\bar E}\) :

Mean kinetic energy (m2 s−2)

f i :

Drag force of wind turbines (m s−2)

H :

Height of ABL (m)

h :

Tip rotor height (m)

K :

Von-karman constant

LW :

Wake length (m)

\({{\tilde p}^ \ast}\) :

Filtered modified pressure (Pa)

\({{\bar S}_{ij}}\) :

Resolved strain-rate tensor

T ij :

Sub-grid stress tensor

\(\hat{\tilde{u}}, \, \hat{\tilde{v}}\) :

Filtered local mean-velocity at twice the grid size (m s−1)

ũ :

Filtered velocity (m s−2)

U ∞ :

Upstream undisturbed (m s−1)

U d :

Velocity at the rotor disk (m s−1)

u r :

Friction velocity (m s−1)

u + :

Normalized mean velocity

z 0 :

Ground roughness (m)

z h :

Wind turbine hub height (m)

z + :

Dimensionless distance from the wall

δ:

Height of the ABL (m)

δ*:

Displacement thickness (m)

θ:

Momentum thickness (m)

δe :

Energy thickness (m)

v t :

SGS eddy viscosity (m2 s−1)

\({\bar \Delta }\) :

Grid filter width

\({\tilde \Delta }\) :

Test filter scale

T :

Turbulent shear stress (Pa)

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Authors and Affiliations

  1. Department of Aerospace Engineering, K. N. Toosi University of Technology, Tehran, Iran

    Vahid Mazidi Sharafabadi & Mani Fathali

Authors
  1. Vahid Mazidi Sharafabadi
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  2. Mani Fathali
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Correspondence to Mani Fathali.

Additional information

Vahid Mazidi Sharafabadi received his M.S. in Aerospace Engineering from Sharif University of Technology (SUT), Tehran, Iran in 2014. He is currently working towards a Ph.D. at K. N. Toosi University of Technology. His research interests are large eddy simulation, wind farm simulation, computational fluid mechanics, and wind urbine simulation.

Mani Fathali received his Ph.D. in Mechanical Engineering at the Katholieke Universiteit Leuven in 2007. Ever since, he has been a faculty member at Aerospace Engineering at K. N. Toosi University of Technology. His research interests are turbulent flow, computational fluid mechanics, large eddy simulation, wind farm simulation.

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Sharafabadi, V.M., Fathali, M. Comparison of effects of four subgrid-scale turbulence models in large eddy simulation of a large wind farm. J Mech Sci Technol 37, 2439–2449 (2023). https://doi.org/10.1007/s12206-023-0420-y

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  • DOI: https://doi.org/10.1007/s12206-023-0420-y

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