# Infinite Wind Farm Neutral

**Scope**

The benchmark is opened to participants of the Wakebench project using flow models to model wakes of wind turbines aligned in a row in search for an asymptotic deficit state. Two cases are suggested to be modeled:

a) a large (but finite) number of turbines

b) an idealized case with an “infinite” number of turbines, where simulations are made either considering periodic boundary conditions in the streamwise direction, or using analytical models (see e.g. Peña and Rathmann 2013 [1]) to predict the flow in the limit of an infinite number of turbines.

Case a) is compared to case b) to determine how many turbines are needed to reach an asymptotic wake state (and to verify that the same final converged wake state is reached).

**Objectives**

Completion of the benchmark will inform on the number of turbines necessary for an asymptotic deficit state to be reached (which might depend on the quantity that is analyzed), as well as on the flow characteristics associated to this state. The dependency on the distance between the turbines as well as the ambient level of turbulence intensity will be investigated.

Comparing the modeling of a finite number of turbines with that of an infinite line of turbines will also allow to validate assumptions made when modeling the latter case. This study is aimed as well at helping the development and validation of engineering models intended at modeling the flow deep inside wind turbine farms.

**Data Accessibility**

The benchmark is offered to participants of the IEA Task 31 Wakebench

**Input data**

The geometry of the turbine and corresponding airfoil data to be used are the ones associated to the 5MW 126-m rotor-diameter model turbine defined in Jonkman et al., 2009 [2]. The file IWFN_NREL-5-126_Geom.txt includes the geometry of the blades, while the files IWFN_NREL-5-126_AD.txt, with AD the airfoil section considered, include these airfoil data. Note that these airfoil data were corrected for stall delay as mentioned in [2].

The conditions for simulating the flow along the line of turbines are:

-The inflow axial mean velocity at hub height (90m) is 8m/s (note that the coordinate system used below is defined as: (x,y,z) = crosswise, vertical and axial directions).

-The atmospheric conditions are considered neutral.

More information about the different model runs is found below.

**Validation data**

Comparisons will be made of the output data provided by each of the participants, as well as between cases a) and b).

**Model runs**

6 different model runs are suggested in each of the cases a) and b), for a total of 12 runs, considering the simulation conditions below:

Please note that the spacing of 6D is optional. This spacing is intended in helping to evaluate if a trend can be obtained in the results. The benchmark is then constituted of 8 basic model runs.

The turbulence intensity (TI) level is defined at the position of the first turbine (at hub height) when this turbine is not present, and is to be averaged over 10 real-time minutes (for transient codes). It is calculated using the axial component of the velocity. Dist is the axial spacing between the turbines in rotor diameters (*D*).

In all cases, an infinite wind farm is to be considered in the transversal direction (normal to the incoming wind) with a spacing of 10D between the turbine rows.

**Output data**

**General considerations:**

In the finite case (a), the flow should pass through the domain at least two times before data can begin to be used to perform averages.

In the infinite case (b), the participants should let their simulations run long enough so that they judge it has converged.

**Mean velocities and turbulent kinetic energy (averages and standard deviations):**

Data are to be provided in the format described in the file IWFN_UserID_ModelID_run#_profvertUTKE.txt. Please note that this file will contain 9 + (n-1)*8 columns, with n the number of turbines (n is chosen by the user for runs A1 to A6, while n=1 for runs B1 to B6).

Data are to be provided in the format described in the file IWFN_UserID_ModelID_run#_profaxUTKE.txt.

*The mean velocities (*Ūi=x,y,z*) are first determined by calculating 20 averages (RMS) in bins of 10-minutes performed from the end of the simulation in the last 30 minutes of the simulation, moving in steps of 1 minute from the end of the simulation. The final result to be provided is the average of the bin averages as well as the corresponding standard deviation

20 TKE values are first calculated in bins of 10-minutes from the end of the simulation in the last 30 minutes of the simulation, moving in steps of 1 minute from the end of the simulation. The final result to be provided is the average of the bin values as well as the corresponding standard deviation.

.

**Power (average and standard deviation)**:

Average power values are first determined by calculating 20 averages (RMS) in bins of 10-minutes performed from the end of the simulation in the last 30 minutes of the simulation, moving in steps of 1 minute from the end of the simulation. The final result to be provided is the average of the bin averages as well as the corresponding standard deviation.

Data are to be provided in the format described in the file IWFN_UserID_ModelID_run#_profPower.txt. Please note that this file will contain n data points, with n the number of turbines (n is chosen by the user for runs A1 to A4, while n=1 for runs B1 to B4).

**Remarks**

The participants are asked to provide information about the resolution of their grid as well as the type of forcing that is used to sustain the flow in the case where periodic boundary conditions are used in the streamwise direction.