Abstract
Utilizing fluid scaling laws of idealized wind farm and wind resource simulations can reduce the computational effort and increase the understanding of the corresponding numerical model. However, not all fluid scaling laws are fully appreciated in the wind energy community. In this work, we employ dimensional analysis and Reynolds-averaged Navier-Stokes simulations of interacting wind turbine wakes and a Gaussian hill, and large-eddy simulations of a single wind turbine, to show that idealized wind farm simulations including terrain, subjected to a non-neutral atmospheric surface layer following Monin-Obukhov Similarity Theory, are independent of the inflow wind speed and wind turbine size due to Reynolds number similarity.
Highlights
Understanding the flow in and around wind farms is key to the development and improvement of numerical models that support reduction of levelized cost of wind energy
An idealized atmospheric surface layer (ASL) corresponds to an implementation of Monin-Obukhov Similarity Theory (MOST), whereby effects of atmospheric stability are parameterized via analytical expressions of properly normalized wind speed gradient (i.e., Reindependent)
For a given stability state, the turbulence length scale implied by MOST does not depend on the wind speed1, and the velocity deficit and wake turbulence intensity of a single wind turbine are independent of the inflow velocity scale
Summary
Understanding the flow in and around wind farms is key to the development and improvement of numerical models that support reduction of levelized cost of wind energy. Numerical simulations of a wind turbine wake can be made to be independent of Re, using an idealized atmospheric inflow representing the atmospheric surface layer (ASL). An idealized ASL corresponds to an implementation of Monin-Obukhov Similarity Theory (MOST), whereby effects of atmospheric stability are parameterized via analytical expressions of properly normalized wind speed gradient (i.e., Reindependent). The wind speed independence can be used to simplify and expedite calculations of the annual energy production of a wind farm using Reynolds-averaged Navier-Stokes (RANS) solvers [1]. The wind turbine size is not an independent parameter as long as the Obukhov length, roughness length, and terrain height are scaled by the wind turbine size
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