Mann turbulence for the IEC Code Comparison Collaborative (OC3)
Kenneth Thomsen, Risø National Laboratory, Update 3 January 24, 2006
Two sets of turbulence fields are created using the IEC Turbulence Simulator in the
WAsP Engineering model1, one at Vhub=Vr=11.4 m/s and one at Vhub=18 m/s. Both
fields are simulated with the Mann model2 using the requirements from IEC61400-1
ed.3:
=3.9 (non-dimensional shear distortion parameter)
iso = 0.55 1
l=0.7 1
With a value of Iref =0.14 the following values of 1 are calculated:
11.4 m/s:
18.0 m/s:
1=1.981 m/s
1=2.674 m/s
1=42m and thus l=0.7 1 = 29.4 m
The Mann model needs the parameter  2 / 3 which can be calculated from l and iso ,
see Appendix A:
11.4 m/s:
18.0 m/s:
1
2
 2 / 3 =0.18
 2 / 3 =0.33
www.waspengineering.dk
Mann, J. Wind Field Simulation, Prob. Engng. Mech., v. 13, n. 4, 1998.
The fields are simulated using 8192 longitudinal points in a 32 by 32 cross-sectional
grid and saved in two different formats:
 Rectangular format 32x32x8192
 Polar format 16x64+1
The fields are simulated in the rectangular grid and afterwards interpolated into the
polar grid with 16 radial points and 64 azimuthal points (and one center point). The
length of fields corresponds to 700 seconds, i.e. for the 11.4 m/s case 7980m and for
the 18 m/s case 12600m.
The file formats is described in Appendix B and the echo output files from the
simulations are given in Appendix C.
For each wind speed, three files are provided: u, v and w component. Note that the
turbulence values are saved in the polar format as scaled zero-mean values with a
standard deviation of 1.0. This means that the actual values must be scaled to the
proper value of turbulence intensity and mean value (for the u-component). Azimuth
zero is down. For the rectangular format, the values are zero-mean (appr.) with the
simulated standard deviation (close to the input value).
Information on the point positions are included in the polar format files. For the
rectangular field files, the distance between the points are given for all three directions
in Appendix C. Note that the outer most points are separated by (Npoints-1)/Npoints *
Fieldsize, i.e. 31/32 * 150 = 145.3m. This corresponds to (Npoints-1)* dL2.
The grid points are the center points of the grid segments, which form the fields.
Plots of center point signals are given in Appendix D.
Appendix A
Note by Hans E. Jørgensen, Risø National Laboratory 2005.
The spectra in IEC61400-1 ed. 3 is in inertial subrange described as
2 / 3
 2 l 
S1 ( f )  0.4754 
f 2 / 3

 Vhub 
In jakob’s model the spectra are described in wave numbers so
V
2
S (k1 ) 
S ( f )  0.4754  iso
l 2 / 3 k12 / 3
2
2
iso
(1.1)
(1.2)
when we compare Mann’s twosided spectra in inertia subrange with (1.2) we have
that :
9
0.4754 2 2 / 3
 2 / 3 
 iso l
55
2
(1.3)
 2 / 3 
55
2
0.4754  iso
l 2 / 3
18
The parameter Alpha in Basic corresponds to  2 / 3
The parameter Gamma is similar to   3.9 in IEC61400-1 ed3
L is corresponding to 0.7-0.8  in IEC61400-1 ed3
Appendix B: From the WasP Engineering Help File
Turbulence fields
Output format to FLEX4
The file output (*.int) is intended for the FLEX program. It has the following file format:
<year>
month>
<day>
<hour>
<min>
5x2-byte integer
<Id>
40x1-byte character
<Ns>
<Na>
<Nv>
<N>
<Ifak>
5x2-byte integer
<r[1]>
<r[2]>
<r[3]>
…
<r[Ns]>
Nsx4-byte real
<dt>
<mean>
<I>
<L>
4x4-byte real
<data>
NxNvx2-byte integer
<Ns>
<Na>
<Nv>
<N>
<Ifak>
<r>
<dt>
<Mean>
<I>
<L>
no. of radial stations
no. of azimuth stations
no. of nodes
no. of data points
scaling factor for data
radial positions [m]
time step
mean wind speed
target turbulence intensity
target turbulence length scale

Stored data are deviations from the target mean value and they are compressed to integers
by the formula:

Turbulence intensity and length scale of simulations may differ slightly from their targets.
For each of batch simulation of turbulence an ASCII file (*.txt) is generated with the simulation
settings. Below is shown an example of such a file:
Output format HAWC and Periodic
Similar to the output format from FLEX4 there is *.txt file containing the information of the how the
simulation has been generated. An example is shown below with the name "Hawc_sim.txt
The corresponding data output files are stored as binary files for each component i.e.
Hawc_sim_xu.bin, where x is the seed number (an integer and) u is the component.
The binary format is stored as a 4 byte real and below is described how the files for the components
are written in the C language:
int NComp; /* is the number of components of the velocity vector to be simulated */
int NPoint[3]; /* NPoint[0] is the number of points in the x-drection, NPoint[1] in the y-direction and
NPoint[2] in the z-direction *
float ***field3d[3]; /* Is a four-dimensional array containing the simulated field */
Memory for that is allocated by
for (i=0;i<NComp;i++) field3d[i] = f3tensor(1,NPoint[0],1,NPoint[1],1,NPoint[2]);
where f3tensor constructs a three-dimensional array of four byte reals with indices running from 1 to
NPoint[0], etc.
FILE *fp[3]; /* three pointers to the binary files */
The statement that writes the simulated fields, both "HAWC" and "periodic", to file:
for (i=0;i<NComp;i++) {
for (i1=1;i1<=NPoint[0];i1++)
for (i2=1;i2<=NPoint[1];i2++)
for (i3=1;i3<=NPoint[2];i3++)
fwrite(&field3d[i][i1][i2][i3],4,1,fp[i]); }
The z-direction index is running fastest, then the y-direction, and the x- (or time-) direction is running
slowest.
C: Echo output
Polar output
11.4 m/s
IECTurbulenceSimulator :
Type of simulation
Mean horizontal wind speed
AlphaEpsilon
l
Gamma
25-01-2006 14:07:36
Basic
11.4m/s
0.18
29.4m
3.9
Simulated turbulence field:
Velocity components (u,v,w)
(1,1,1)
Number of points in each direction 8192, 32, 32
Fieldsize in meters
7980, 150, 150
dL1, dL2, dL3
0.97412109375m, 4.6875m, 4.6875m
Spectrum type Kaimal
Random seed 6
Output type FLEX4
Number of Azimuthal Stations
64
Number of Radial Stations 16
Radii:
4.54m 9.08m 13.62m
18.16m
22.71m
27.25m
31.79m
36.33m
40.87m
45.41m
49.95m
54.49m
59.03m
63.57m
68.12m
72.66m
High frequency compensation applied
18m/s
IECTurbulenceSimulator :
Type of simulation
Mean horizontal wind speed
AlphaEpsilon
l
Gamma
25-01-2006 13:34:48
Basic
18m/s
0.33
29.4m
3.9
Simulated turbulence field:
Velocity components (u,v,w)
(1,1,1)
Number of points in each direction 8192, 32, 32
Fieldsize in meters
12600, 150, 150
dL1, dL2, dL3
1.5380859375m, 4.6875m, 4.6875m
Spectrum type Kaimal
Random seed 7
Output type FLEX4
Number of Azimuthal Stations
64
Number of Radial Stations 16
Radii:
4.54m 9.08m 13.62m
18.16m
22.71m
27.25m
31.79m
36.33m
40.87m
45.41m
49.95m
54.49m
59.03m
72.66m
High frequency compensation applied
63.57m
68.12m
Rectangular output
11.4 m/s
IECTurbulenceSimulator :
Type of simulation
Mean horizontal wind speed
AlphaEpsilon
l
Gamma
25-01-2006 14:07:36
Basic
11.4m/s
0.18
29.4m
3.9
Simulated turbulence field:
Velocity components (u,v,w)
(1,1,1)
Number of points in each direction 8192, 32, 32
Fieldsize in meters
7980, 150, 150
dL1, dL2, dL3
0.97412109375m, 4.6875m, 4.6875m
Spectrum type Kaimal
Random seed 6
Output type HAWC
High frequency compensation applied
18m/s
IECTurbulenceSimulator :
Type of simulation
Mean horizontal wind speed
AlphaEpsilon
l
Gamma
25-01-2006 13:34:48
Basic
18m/s
0.33
29.4m
3.9
Simulated turbulence field:
Velocity components (u,v,w)
(1,1,1)
Number of points in each direction 8192, 32, 32
Fieldsize in meters
12600, 150, 150
dL1, dL2, dL3
1.5380859375m, 4.6875m, 4.6875m
Spectrum type Kaimal
Random seed 7
Output type HAWC
High frequency compensation applied
Appendix D: Center point time series.
11.4 m/s:
18 m/s: