Validation of a Theoretical Model for Large Turbine Array Performance Under Realistic Atmospheric Conditions

Theoretical models, capable of approximating the performance of large wind turbine arrays, are valuable tools for exploring a wide range of parameters and to guide the design of more expensive and detailed numerical experiments. The two-scale momentum model of Nishino [1] is a simple analytical model for estimating the efficiency of very large wind turbine arrays under idealised conditions. It suggests that the primary factor controlling array efficiency is the non-dimensional parameter λ/C_f0, where λ is the ratio of the rotor swept area to the land area (per turbine) and C_f0 is the friction coefficient of the surface prior to array construction. The Nishino model has been found to perform well against CFD experiments employing simple boundary layer velocity profiles. The aim of this study is to test the model’s validity under more realistic atmospheric conditions.

Large-eddy simulations of a periodic turbine array were carried out using the Met Office – NERC Cloud model (MONC) [2]. Individual turbines were represented as distributed momentum sinks following actuator disk theory. The simulations were forced using velocity profiles taken from the Met Office 1.5km operational NWP model (UKV) at an offshore location in the North Sea. A total of five simulations were carried out, including 2 stable cases, 2 unstable cases, and 1 neutral. The Nishino model predictions for the turbine coefficient of performance, C_p, were found to agree with the simulations to within 3% in all but one of the cases. The worst case prediction was within 10% of the simulations.

[1] Nishino, T., 2016. Two-scale momentum theory for very large wind farms. Journal of Physics. 753

[2] MONC: https://code.metoffice.gov.uk/trac/monc/