Sensitivity of the CFD based LIDAR Correction

Céline BEZAULT

(1) METEODYN -celine.bezault@meteodyn.com

(2) LEOSPHERE mboquet@leosphere.fr

Abstract Remote sensing systems are more and more used during campaign of measurements for wind resource assessments. Lidars like the WINDCUBEoffshore conditions, while in complex terrainduring the transformation of measured radial wind speed to horizontal wind speed (in some cases up to 10%). In previous studies, it has been shown that Computation Meteodyn WT, solving the full Reynoldstopographical effects on the wind flow over complex terrain and to bring a corrective parameter to the WINDCUBE (decreasing the bias This post-correction methodology raises however some questions as the influence of the model calibration on the correction performances. In this paper indeed we propose to study the sensitivity of the correction to several model parameters, by varying the topographical data forest density and atmospheric stability which are determinant parameters for CFD modeling. Key words: CFD, Meteodyn WT, CFD Modeling, 1. Introduction Acciona, as a collaborative partnerof the software METEODYN WT and of a WINDCUBE® lidar, has provided data from a met mast and the lidar measuredterrain site, calibrated according to IEC standards. METEODYN has run CFD calculations over the site under various calibrations and provided the corrected lidar data to LEOSPHERE which has analyzed the results. The corrected wind speeds are comparethe anemometer’s measurements at the three heights and mean deviations resulting linear orthogonal regressions performed at every height are compared to each other to study their variation against the model calibration. At the end, the three parties have been able to get results concerning the sensitivity of the WINDCUBE correction module. 2. Description of the case study

a. Met mast descriptionEquipment of the met tower: the meteorological mast is equipped with anemometers at 33.50, 63.90 and 66 m high, vanes at 33.30, 63.70 m high and captors for pressure, relative humidity, and temperature. The period of measurements begins the 14/10/2010 0:00 and finishes the 08/01/

Sensitivity of the CFD based LIDAR Correction

Céline BEZAULT (1) – Matthieu BOQUET (2)

- 14 bd Winston Churchill – 44100 NANTES, FRANCEceline.bezault@meteodyn.com - +33 (0) 240 710 505 - +33 (0) 240 710

LEOSPHERE – 14-16 rue J.Rostand – 91400 ORSAY, FRANCEmboquet@leosphere.fr - +33 (0)181 870 428 - +33 (0)180 810 501 (fax)

Remote sensing systems are more and more used during campaign of measurements for wind resource assessments. Lidars like the WINDCUBE® have a proven accuracy on flat terrains and

conditions, while in complex terrain, the loss of flow homogeneity can create a sensor bias during the transformation of measured radial wind speed to horizontal wind speed (in some cases up to 10%). In previous studies, it has been shown that Computation Fluid Dynamics (CFD), like Meteodyn WT, solving the full Reynolds-averaged Navier-Stokes equations, enables to compute the topographical effects on the wind flow over complex terrain and to bring a corrective parameter to the WINDCUBE (decreasing the bias down below cup uncertainty).

correction methodology raises however some questions as the influence of the model calibration on the correction performances. In this paper indeed we propose to study the sensitivity of

l parameters, by varying the topographical data forest density and atmospheric stability which are determinant parameters for CFD modeling.

CFD Modeling, Lidar correction, WINDCUBE lidar, Remote sensing co

Acciona, as a collaborative partner and owner WT and of a

lidar, has provided data from a met mast and the lidar measured on a complex

, calibrated according to IEC has run CFD

calculations over the site under various calibrations and provided the corrected lidar data to LEOSPHERE which has analyzed the

The corrected wind speeds are compared to the anemometer’s measurements at the three heights and mean deviations resulting linear orthogonal regressions performed at every height are compared to each other to study their variation against the model calibration. At the end, the three parties have been able to

the sensitivity of the

Description of the case study

Met mast description Equipment of the met tower: the meteorological mast is equipped with

at 33.50, 63.90 and 66 m high, vanes at 33.30, 63.70 m high and captors for pressure, relative humidity, and temperature. The period of measurements begins the

the 08/01/2011

14:00. Measurements are given every 10 minutes.

Figure 1 : Mast wind rose:dominant

The main wind direction Southand the table below summarizes the instruments measurement heights and mean deviation:

Table1: Measurement heights and mean deviation at instruments location

1

44100 NANTES, FRANCE 710 506 (fax)

91400 ORSAY, FRANCE 501 (fax)

Remote sensing systems are more and more used during campaign of measurements for wind have a proven accuracy on flat terrains and for

the loss of flow homogeneity can create a sensor bias during the transformation of measured radial wind speed to horizontal wind speed (in some cases up

Fluid Dynamics (CFD), like Stokes equations, enables to compute the

topographical effects on the wind flow over complex terrain and to bring a corrective parameter to the

correction methodology raises however some questions as the influence of the model calibration on the correction performances. In this paper indeed we propose to study the sensitivity of

l parameters, by varying the topographical data such as roughness, forest density and atmospheric stability which are determinant parameters for CFD modeling.

WINDCUBE lidar, Remote sensing correction

14:00. Measurements are given every 10

rose: south-east wind dominant

The main wind direction South-East is studied table below summarizes the

instruments measurement heights and mean

Table1: Measurement heights and mean

deviation at instruments location

2

b. WINDCUBE® lidar description

The WINDCUBE Lidar provides 200m vertical wind profiles on various types of terrains. Every second, it retrieves wind speed, direction and wind shear at 10 different heights selectable by the user between 40m and 200m. Based on a pulsed laser, it allows a constant spatial resolution of 20m. The system contains no inner moving part and is eye safe. The range of wind speed measurements is 0 up to 60 m/s. The WINDCUBE might be positioned as close as a few meters from obstacles as long as the laser beam in not being blocked. (Ref [3] and [4]) In this study, the distance between the met mast and the WINDCUBE® is around 5m.

c. Site characteristics The site characteristics are defined in order to create a model for the CFD computations with Meteodyn WT. The site is qualified by the orographical and roughness data. These data were provided by Acciona with a 10 m resolution. Altitude variations near the site highlighting the terrain complexity are shown on the following pictures:

Figure 2: 3D view of the topography with lidar’s

location

Figure 3: Altitude variation near the site

Figure 4: 2D view of the topography with lidar’s

location The altitude varies from 609 m up to 952 m in a square domain of 6000 m. Values of roughness data correspond to a canopy height between 1 and 15 meters high.

Figure 5: Roughness map on site

Local value of roughness at the instrument’s location varied in order to determine the influence of the roughness value on the lidar correction module. 3. Methodology of the Lidar tool

correction in Meteodyn WT

a. CFD modelling Orographical and roughness data discussed in the previous section are used as input for defining the site in the CFD software Meteodyn WT. A standard resolution is used (4 m in the

3

vertical resolution, 25 m in the horizontal resolution) to model the wind flow over the site. This resolution allows to model the wind flow over complex and forested areas. The minimal horizontal resolution leads the length of calculation cells near the point of interest whereas the minimal vertical resolution drives the length of the calculation cells near the ground. Around the lidar location, the mesh is refined to catch correctly the flow variations. The default horizontal resolution used is equal to 8 m with a horizontal expansion coefficient of 1.1.

Figure 6: Horizontal and vertical mesh for 90°

direction Directional computations with the CFD Meteodyn WT are performed every 5° for several atmospheric stabilities. Meteodyn WT solves the steady isotherm uncompressible Reynolds Averaged Navier-Stokes equations.

• Mass conservation: ������� = 0

• Momentum conservation:

− �(�� ��)�� − �

��� + ��� �� ����

�� + ������ −

� ��′ ��′ � + �� = 0

The non-linear Reynolds stress tensor is modeled by a one-equation closure scheme (k-L model, developed by Yamada and Arritt [1], dedicated to atmospheric boundary layer resolution). The turbulent viscosity is considered equal to the square root of the turbulent kinetic energy multiplied by a turbulent length scale which depends on stability.

�� = �� �� ��

Where the turbulent kinetic energy represents the kinetic energy of the speed fluctuations in a turbulent flow: � = �

� ��′ ��′ Perturbations due to forests usually generate a high level of turbulence and strong wind shears. Meteodyn WT takes these parameters into account by incorporating a sink term in the momentum conservation equations and a turbulence production term in the turbulent kinetic energy equation for the cells lying inside the forested areas [2]. The turbulent kinetic energy transport equation is given by:

�!�!"� = #$ − % + !

!"�&�'�($

� !�!"�

) With % = *+ ,-

.-/ � (dissipation)

#$ = �� 0! �!"� + ! �!"�1 ! �!"�

In the momentum equations, a volumic sink term is introduced for all the cells lying inside (or partially) the forest volume. In the first row of cells, the surfacic sink term is applied. �2 = −� *3 | | Where

• CD is a drag coefficient depending on the forest density. The value of this drag coefficient can be adjusted by users,

• ρ is the air density, • U is the mean wind speed.

The effective drag coefficient CD is moreover linearly decreased in the upper part of the forested volume, from 0.75 times the canopy height up to the canopy height.

The length scale of turbulence LT as well as the C� coefficient are depending on the atmospheric stability through Richardson flux number Rif as follow:

4

�� = √2789 �⁄ ;

Where l is the Monin Obukhov length defined by: 1

; = �1;= + 1

>?� with z = height and >=0.41, l0=100 m.

78 = 1.96 C=.�D��EF�GH(=.�9I�EF�G)C�EF�GH(=.��9�EF�G) if Rif <0.16

78 = 0.085 if Rif >0.16

*+ = 478M� , M� = 16.6

The atmospheric stability can be very unstable, neutral or very stable. In case of an unstable wind profile, thermal effects accelerate the vertical movement of the air. On the other hand, when thermal effects are negligible in terms of the mechanical effects, the atmosphere is considered as neutral. The next picture shows an example of vertical profile of a wind speed in flat terrain with homogeneous roughness for different stability classes.

Figure 7: Thermal stability classes in Meteodyn

WT The results obtained by directional CFD computations are wind speed coefficient, inflow angle, deviation and turbulence intensity.

b. Lidar Correction Tool The WINDCUBE® lidar provided by Leosphere, measures the radial wind speed at several heights, up to 200 m. The lidar can provide radial wind speeds at 4 points located on the scanning cone of measurements, at 10 heights simultaneously.

Figure 8: WINDCUBE® lidar cone of

measurements In order to correct the wind speed estimation at the centre of the cone of measurements, the Lidar correction Tool of Meteodyn WT uses the directional results issued from the CFD modeling that are wind speed up coefficient and inflow angle. The correction automatically uses the coefficients computed at different heights in order to apply a correction on the lidar measurements.

Figure 9: Principle of Meteodyn WT lidar

correction tool 4. Results

11 scenarii have been computed:

Table 2: List of scenarii used for the sensitivity

study

The roughness gives the value that defines the canopy height by canopy height = 30 * roughness. The forest density is characterized by the drag coefficient Cd in the momentum equations (see section 3.a). L corresponds to a low density, N to a normal one, and H correspond to a high density. Finally, the atmospheric stability can vary from 0(very unstable) to a stability parameter equal

to 4 (stable), through neutral conditions (stability parameter = 2). Several analyses are performed:

- Analyses at the vertical of the Lidar location (center of the measurements’ cone).

- Analyses between the East and West points of the Windcube beams.

- Comparison between corrected / uncorrected values and the measurements at the met m

Results are processed at every height as the mean deviation resulting from a linear regression between the lidar and mast wind speeds:

Figure 10: Scatter plots of 10 min (top) and bin-averaged (bottom) horizontal wind speeds measured by the mast (height 66m) and the WINDCUBE® (height 70m) not corrected

Figure 11: Scatter plots of 10 min (top) and bin-averaged (bottom) horizontal wind speeds measured by the mast (height 66m) and the WINDCUBE® (height 70m) corrected with

Meteodyn WT computations with scenario 5.

to 4 (stable), through neutral conditions

analyses are performed: Analyses at the vertical of the Lidar location (center of the measurements’

Analyses between the East and West points of the Windcube beams. Comparison between corrected / uncorrected values and the measurements at the met mast.

Results are processed at every height as the mean deviation resulting from a linear regression between the lidar and mast wind

Scatter plots of 10 min (top) and

) horizontal wind speeds (height 66m) and the

WINDCUBE® (height 70m) not corrected

Scatter plots of 10 min (top) and

averaged (bottom) horizontal wind speeds measured by the mast (height 66m) and the

(height 70m) corrected with with scenario 5.

Table 3 presents the results for the prevailing wind direction South-East:

Table 3: Results obtained for the prevailing direction (South East)

Roughness and density Generally, the roughness value is a parameter which can vary during the CFD calibration. The value of roughness at the lidar location can change from 0.2 (canopy height of 6 m) to 0.4 (canopy height corresponds to 12practice, when a user wants to calibrate his site, he is able to change the roughness value but he never uses such an important difference. The roughness value often varies of ±0.05. Differences in the directional results of the CFD computations become more important (especially for wind speed up coefficient) when the density forest parameter grthe density forest is, the more the flow slows down. At 70 m high, the influence of this parameter is negligible (less than 1%) in comparison with the topographical effects. Influence of the roughness value:

Figure 12: Speed up coefficfor scenario 3

5

presents the results for the prevailing East:

: Results obtained for the prevailing

(South East)

influence Generally, the roughness value is a parameter

during the CFD calibration. The value of roughness at the lidar location can change from 0.2 (canopy height of 6 m) to 0.4 (canopy height corresponds to 12 m). In practice, when a user wants to calibrate his site, he is able to change the roughness value but he never uses such an important difference. The roughness value often varies

Differences in the directional results of the CFD computations become more important (especially for wind speed up coefficient) when the density forest parameter grows. The higher the density forest is, the more the flow slows down. At 70 m high, the influence of this parameter is negligible (less than 1%) in comparison with the topographical effects.

Influence of the roughness value:

Figure 12: Speed up coefficient at 40 m high

for scenario 3

6

Figure 13: Speed up coefficient at 40 m high

for scenario 5

Figure 14: Speed up coefficient at 40 m high

for scenario 11 (right side) Atmospheric stability influence The atmospheric stability parameter is the one which has the more influence on the directional results, both for speed up coefficient and inflow angle. These results comply with fluid mechanics. In fact, the stability parameter determines the wind inlet profile and during the Navier Stokes equation resolution, the stability parameter influences the flow deviation over topography. 5. Conclusion At the vertical of the lidar location, direct results of the CFD Meteodyn WT show that at

a particular location, speed up factors and inflow angles (“absolute” information) are depending on the CFD calibration. The lidar correction tool for WINDCUBE® however uses the difference of inflow angle between two opposite points of the lidar’s beams (“relative” information between for example the East and West point of the cone’s lidar measurements). From this study, we can note that this “relative” information required for the correction is much less sensitive to roughness and atmospheric stability than the absolute values. Also higher the forest density is, smaller the inflow angle gets. CFD computations have been used to correct the WINDCUBE® horizontal wind speeds in complex terrain. This study underlines the quality of the correction whatever CFD parameters are.

6. Acknowledgments Meteodyn and LEOSPHERE would like to express their gratefulness to Acciona Energia for providing all the data necessary for this study. 7. References [1]: Yamada, T, (1983), Simulations of nocturnal drainage flows by a q2l turbulence closure model, Journal of Atmospheric Sciences, vol. 40, Issue 1, pp.91-106 [2]: A.N. Ross, S.B. Vosper; Neutral Turbulentflow over forested hills [3]: M. Courtney, R. Wagner, P. Lindelöw; Commercial LIDAR profilers for wind energy. A comparative guide, EWEC 2009 [4]: Boquet M. et al.: Innovative Solutions for Pulsed Wind LiDAR Accuracy in Complex Terrain, ISARS 2010