1. The Mann uniform shear turbulence model

The IEC Turbulence Simulator is an implementation of the Mann method recommended in IEC61400-1 Ed. 3. It is distributed with Wasp Engineering and, since February 2009, it is also available as a separate tool without a license. The IEC Turbulence Simulator simulates standard turbulence over flat uniform terrain. The simulated turbulence can be used as input to aero-elastic turbine simulators, which in turn can calculate fatigue loads, e.g. as part of the requirements for obtaining an IEC turbine certificate.

The method is based on rapid-distortion theory. For the present application, atmospheric turbulence is modelled as an initially isotropic spectral tensor deformed by the shear of the mean wind profile.

A free Command-Line version of MANN 64bit turbulence generator version 1.0 release date 19.03.2014, may be downloaded from the web site: http://www.hawc2.dk/download/pre-processing-tools

1.1. Direct input

The following input arguments are required to execute the turbulence generator:

\(\Delta x\),\(\Delta y\),\(\Delta z\)

Distance between grid point in X-direction (wind direction), Y-direction (horizontal and normal to wind direction) and Z-direction (vertical)

\(Nx\),\(Ny\),\(Nz\)

Number of grid points in X, Y and Z direction (power of 2)

\(\gamma=3.9\)

Gamma is the non-dimensional shear distortion parameter

\(l\)

Length Scale parameter, normally in the range \(0.7\cdot\Lambda_1\) to \(0.8\cdot\Lambda_1\) where \(\Lambda_1\) is the longitudinal turbulence scale parameter which for a hub height \(z\) is given by

image

\(\alpha\epsilon^{2/3}\)

AlphaEpsilon is a parameter in Mann’s model. For best agreement with IEC61400-1 it can be calculated according to

image

where \(\sigma_{iso}^2\) is the un-sheared, isotropic variance. The relation between \(\sigma_{iso}\) and the standard deviation of the wind velocity in the mean wind direction. \(\sigma_{1}\) is to be taken as: \(\sigma_{iso}=0.55\cdot\sigma_{1}\)

HF Compensation

If HF compensation is applied, point velocity represents local anemometer measurements. Else, point velocity represents average in grid box.

The necessary input data are described in IEC61400-1, third edition, ch. 6.3 Wind conditions and Annex B - Turbulence models.

Note that

1. The duration [\(T\)] of the generated turbulent wind is related to the point distance in X, number of points in X and the Mean Wind Speed at hub [\(U\)] as

image

2. The dimensions of the wind box, e.g. the length, width and height are given by
table(borderlessWhite).
| \(Lx=Nx\cdot \Delta x\)|
| \(Ly=Ny\cdot \Delta y\)|
| \(Lz=Nz\cdot \Delta z\)|

1.2. Derived input

The select box Derived input may be used for easier input specification. In this select box the following applies:

1. The relation between the Length Scale parameter [\(l\)] and the Longitudinal Turbulence Scale Parameter [\(\Lambda_{1}\)] is given by the Length Factor [\(f_{L}\)], i.e. \(l=f_{L}\cdot \Lambda_{1}\)

2. The length of the generated wind box [\(Lx\)] is calculated based on Wind Series Duration [\(T\)] and Mean Wind Speed [\(U\)] by the equation

\(Lx=T\cdot U\)

3. The un-sheared, isotropic variance is calculated according to

image

4. The AlphaEpsilon parameter is thus calculated according to

image

1.3. Scaling of generated wind field

The specified Turbulence Intensity [\(TI\)] is used to scale the generated turbulence series. The scale factor is established based on the averaged standard deviation of the wind series in the X direction of the 4 grid points closest to the turbulence box center (at the hub) and the specified standard deviation: \(\sigma_{1}=TI\cdot U\). All wind components are then scaled using the established scale factor.