Linearized simulation of flow over wind farms and complex terrains

Area of Science:

• Fluid dynamics
• Renewable energy engineering
• Computational science

Background:

• Accurate wind flow modeling is essential for wind farm efficiency, especially over complex terrains.
• Existing models often require boundary-layer approximations or are computationally expensive.

Purpose of the Study:

• To develop an efficient and accurate numerical model for wind flow over complex terrains and wind farms.
• To investigate the impact of terrain and wind turbines on wind flow characteristics.
• To reduce computational cost compared to traditional methods.

Main Methods:

• Numerical solution of linearized Navier-Stokes equations around a logarithmic wind profile.
• Application of the Boussinesq approximation for Reynolds stress modeling.
• Inclusion of terrain as vertical coordinate shifts and turbines/forestry as body forces.

Main Results:

• A computational cost reduction by a factor of 8 compared to primitive-variable formulations.
• Demonstrated speed-up of wind upstream of a Gaussian hill and decreased speed downstream.
• Identified an additional spanwise velocity component introduced by the hill affecting turbine operations.

Conclusions:

• The developed linear model provides an efficient estimation of wind flow over complex terrains and wind farms.
• Terrain significantly impacts wind speed and introduces spanwise flow, affecting turbine performance.
• Further investigation into parabolic equations for turbulent kinetic energy shows promise.