CFD wake modeling using a porous disc - WindSim

CFD wake modeling using aporous discGiorgio Crasto

Actuator disc• Single wakes over flat terrains are modeled withWindSim•The tower and the nacelle of the wind turbine aremodeled by solid cells• The rotor is modeled by a porous disc providing aresistive force which is calculated from the thrustcoefficient C T• Comparisons of CFD results are presented againstexperimental data, wind tunnel tests from Vermeer et al.[1]. The numerical results are further compared againstthree analytical models for wakes [2,3,4].

Actuator discThe thrust, momentum sink for the axial flow, is supposed unformlydistributed on the swept area (uniform pressure drop):1t T T 22/ A C uAxial induction factor:u u1 aBy definition1a u1 1 C T 2Betz’s theory

Actuator discFigure 1. Perspective view of the actuator disc, streamlines and isosurface of turbulent kinetic energy (1,4 m 2 /s 2 , U e 10 m/s at 500m a.g.l.).

Height [rotor diamaters]Actuator disc10TNO WT TNO WT TNO WT TNO WT-15D CFD 2D CFD 6D CFD 8D CFD8D downstream2D downstream6D downstream10.10 0.2 0.4 0.6 0.8 1 1.2Velocity ratioFigure 2. Vertical profiles of normalized velocity from TNO Wind Tunnel tests(solid black lines), from Vermeer et al. [1], predicted by the actuator disc CFDmodel (coloured lines).

Comparisons with analytical models• Analytical models:• 1. Jensen model [2]• 2. Larsen model [3]• 3. Ishihara et al. model [4]Cases: z 0 0,03m z 0 0,0001mC T 0,80 a bC T 0,31 c d

Comparisons with analytical modelsCT0.90.80.70.60.50.40.30.20.100 5 10 15 20 25 30undisturbed velocity [m/s]

Normalized-Wind-DeficitComparisons with analytical modelsCase a: C T = 0,80; z 0 = 0,03 m (onshore)10.90.8case a (Ct 0,8; z0 0,03m)Wake model 1Wake model 2Wake model 30.70.60.50.40.30.20.10-20 -10 0 10 20 30

Normalized-Wind-DeficitComparisons with analytical modelsCase b: C T = 0,80; z 0 = 0,0001 m (offshore)1case b a (Ct (Ct 0,8; z0 z0 0,0001m) 0,03m)Wake model 110.9Wake model 22Wake model 330.80.70.60.50.40.30.20.10-20 -10 0 10 20 30

Normalized-Wind-DeficitComparisons with analytical modelsCase c: C T = 0,31; z 0 = 0,03 m (onshore)1case c a (Ct 0,31; 0,8; z0 0,03m)Wake model 10.9Wake model 2Wake model 30.80.70.60.50.40.30.20.10-20 -10 0 10 20 30

Normalized-Wind-DeficitComparisons with analytical modelsCase d: C T = 0,31; z 0 = 0,0001 m (offshore)1case case d (Ct a (Ct 0,31; 0,8; z0 0,0001m) 0,03m)Wake model 1 10.9Wake model 2 2Wake model 3 30.80.70.60.50.40.30.20.10-20 -10 0 10 20 30

Turbulent Intensity [%]Comparisons with analytical modelsCase a: C T = 0,80; z 0 = 0,03 m (onshore)1009080706050403020100-20 -10 0 10 20 30

Turbulent Intensity [%]Comparisons with analytical modelsCase b: C T = 0,80; z 0 = 0,0001 m (offshore)1009080706050403020100-20 -10 0 10 20 30

Turbulent Intensity [%]Comparisons with analytical modelsCase c: C T = 0,31; z 0 = 0,03 m (onshore)1009080706050403020100-20 -10 0 10 20 30

Turbulent Intensity [%]Comparisons with analytical modelsCase d: C T = 0,31; z 0 = 0,0001 m (offshore)1009080706050403020100-20 -10 0 10 20 30

Conclusions• An actuator disc concept is applied to model awind turbine in RANS simulations of a singleWECS wake. A uniform pressure drop is appliedon the disc; the value of the pressure drop iscalculated from the thrust coefficient and axialinduction factor. From comparison with WT [1]tests the wind deficit predicted by the CFDsimulations is the under predicted in the nearwake (2D diameters downstream), the level ofwind deficit is instead correctly predicted at 6Ddownstream while in the far wake the winddeficit is overestimated. When comparing thepresented actuator disc to some analyticalmodels the best match is found to the Larsen[3].

Future steps• Automatization of the process:– Reading of the layout of the wind farm fromthe .ows file– Automatic generation of the grid– Reading of the thrust curve from the .pwsfile• Investigation of:– Rotational effects (swirling)– Introduction of turbulence sources in theactuator disc– Possible nesting technique to improve thegrid design

References[1] VERMEER L.J, SØRENSEN J.N., CRESPO A.(2003). WIND TURBINE WAKE AERODYNAMICS.PROGRESS IN AEROSPACE SCIENCES 39(2003) 467–510.[2] KATIC, I., HØJSTRUP, J., JENSEN, N.O. "ASIMPLE MODEL FOR CLUSTER EFFICIENCY."EWEC PROCEEDINGS, 7-9 OCTOBER 1986,ROME, ITALY.[3] LARSEN, C. G. "A SIMPLE WAKECALCULATION PROCEDURE." RISØ-M-2760,1988.[4] ISHIHARA, T., YAMAGUCHI, A., FUJINO, Y."DEVELOPMENT OF A NEW WAKE MODELBASED ON A WIND TUNNEL EXPERIMENT."GLOBAL WIND POWER 2004.