From gigawatt to multi-gigawatt wind farms: wake effects, energy budgets and inertial gravity waves investigated by large-eddy simulations
Abstract. The size of newly installed offshore wind farms increases rapidly. Planned offshore wind farm clusters have a rated capacity of several gigawatt and a length of up to one hundred kilometers. The flow through and around wind farms of this scale can be significantly different than the flow through and around smaller wind farms on the sub-gigawatt scale. A good understanding of the involved flow physics is vital for accurately predicting the wind farm power output as well as predicting the meteorological conditions in the wind farm wake. To date there is no study that directly compares small wind farms (sub-gigawatt) with large wind farms (super-gigawatt) in terms of flow effects or power output. The aim of this study is to fill this gap by providing this direct comparison by performing large-eddy simulations of a small wind farm (0.96 GW, 13 km length) and a large wind farm (11.52 GW, 90 km length) in a convective boundary layer, which is the most common boundary layer type in the North Sea.
The results show that there are significant differences in the flow field and the energy budgets of the small and large wind farm. The large wind farm triggers an inertial wave with a wind direction amplitude of approximately 10° and a wind speed amplitude of more than 1 ms-1. In a certain region in the far wake of a large wind farm the wind speed is greater than far upstream of the wind farm, which can be beneficial for a downstream located wind farm. The inertial wave also exists for the small wind farm, but the amplitudes are approximately 4 times weaker and thus may be hardly observable in real wind farm flows, that are more heterogeneous. Regarding turbulence intensity, the wake of the large wind farm has the same length than the wake of the small wind farm and is only a few kilometers long. Both wind farms trigger inertial gravity waves in the free atmosphere, whereas the amplitude is approximately twice as large for the large wind farm. The inertial gravity waves induce streamwise pressure gradients inside the boundary layer, affecting the energy budgets of the wind farms. The most dominant energy source of the small wind farm is the horizontal advection of kinetic energy, but for the large wind farm the vertical turbulent flux of kinetic energy is 5 times greater than the horizontal advection of kinetic energy. The energy input by the gravity wave induced pressure gradient is greater for the small wind farm, because the pressure gradient is greater. For the large wind farm, the energy input by the geostrophic forcing (synoptic-scale pressure gradient) is significantly enhanced by the wind direction change that is related to the inertial oscillation. For both wind farms approximately 75 % of the total available energy is extracted by the wind turbines and 25 % is dissipated.
Viewed (geographical distribution)
The manuscript presents LES simulations of a small and a very large wind farm extending hundreds of kilometers. The PALM code is employed
for the large scale simulations involving billions of grid points. The numerical predictions are compared and discussed in detail.
It is well written and has a potential to contribute to the state of the art in wind farm simulations and flow physics. However some
predictions and the related discussions need further clarification and verification prior to publication:
for the large WF needs further verification. It is also interesting that there is no visible deflection of the upstream flow in the
first 60-70km range (Figs 2&3). A simulation without Coriolis force is suggested.
increased wind speed by about 12% 150km down in the large WF wake similarly need further verification. In addition to the hub height,
the vertical variation of the wind speed should also be presented. In addition, a simulation without the gravitational force is
suggested to identify the cause and to validate the numerical implementation.
unexpected behavior is attributed to the drop in the perturbation pressure. The velocity profile should be extended further up to see
any momentum deficiency and the discussion should be extended to include what causes such a the perturbation pressure drop. In addition,
the momentum deficiency ocaused by WTs should be presented in a plot at the center plane or averaged only across the turbine (not averaged in
the full y range)
presented values in Fig 11 are averaged over all the CVs. Such an analysis gives the distribution of energy components within the CV,
but not the relations between them. For a better understanding, the integrations should be performed at the control surfaces (inflow,
top, outflow) of individual CVs and they should be presented as a series for a turbine row. (inflow of a downstream WT would be the
outflow of the upstream WT)
as suggested in Fig 12. It even acts as a sink for downstream turbines. It definitely needs further validation and explanation.