Giorgio CRASTO, Francesco PARAGGIO

giorgio.crasto@gmail.com

fparaggio@gmail.com

Third Symposium on OpenFOAM® in Wind Energy. Politecnico di Milano 15-17 June 2015

RANS Simulations of Askervein hill with OpenFOAM®

The Askervein Hill project

• Askervein is a well known test-site where extensive wind measurements were carried out in ‘82 and ‘83.

• Is considered to be an Isolated hill

– Althought some other hills are close at NE ... Map A and Map B are available (thanks to Prof. P.Taylor)

• Neutral stratification ... Run TU03-B

• Homogenous roughness? (z0 0.03m or what?)

2

• Map A: 257x257 – 16km x 16km => 62.5m

• Map B: 257x257 – 6km x 6km => 23.4375m

Askervein Hill: an isolated hill?

3

Askervein Hill: resolution consequences

4

• Askervein, a 116m high hill: Map A Map B

115.108m 116.837m

Askervein Hill: measurements points

• HT Hill Top

• CP Center Point

• RS Reference Site

• Line A through HT

• Line AA through CP

• Line B main axis

• TU03-B (210°)

5

Askervein Hill: homogeneous roughness?

6

Negligible?

Simulations 2D, rectangular domain

7

• Reynolds Averaged Navier-Stokes (RANS)

• Standard k-e turbulence model

• Effects of model constant se on the wall-functions

• Periodic BC

– Mass flow given

0,000

0,005

0,010

0,015

0,020

0,025

0,030

0,035

0,040

0 5 10 15 20 25

z0 o

bta

ine

d b

y in

terp

ola

tio

n h

/2-1

00

m]

ratio first cell over roughness length (h/z0)

se 1.44

se 1.30

se 1.11

~11.8

Height of first (ground adjacent) cell ~ 11.8 * 0.03m = 0.354m

3D simulations on a cubic domain

8

• The snappyHexMesh applied directly to the orography of the site gave a poor quality grid.

terrainBlockMesher (TBM) + SHM

9

• snappyHexMesh only NO!

• terrainBlockMesher => boundary-fitted grid ok

• terrainBlockMesher + SNM ... More promising

• ZephyTOOLS prismatic cells over a cylindrical domain (mesher M1)

TBM + snappyHexMesh

10

1. terrainBlockMesher (body-fitted) 2. 1° level snappyHexMesh 3. 2° level snappyHexMesh

PRO: reduced height first cell; increased resolution close to the ground CON: expansion ratio 2, generally accepted <1.2

Further settings

• Standard k-e model

• simpleFoam (incompressible)

• First cell height 2m (= 66.67*z0) - not 0.354m!! – Non-orthogonality alarms reducing the grid size

• Convergence criteria:

11

OF 2.3.1 default (for ABL test-case) ZephyTOOLS default

p 1e-3;

U 1e-4;

"(k|epsilon)" 1e-4;

p 5e-4;

U 1e-5;

"(k|epsilon)" 1e-5;

ZephyTOOLS vref 15 m/s href 500 m

CUBIC GRID vref 16.016 m/s href 1008 m

ut = 0.63 m/s

1 and 2 cells per sHM level (Speed)

12

1 and 2 cells per sHM level (TKE)

13

- 2 cells for each level - More was not accepted by my and

the grid generated had only one cell per level!

Discretization schemes (Speed)

14

Residuals:

p 5e-4

U 1e-5

"(k|epsilon)" 1e-5

Discretization schemes (TKE)

15

Residuals:

p 5e-4

U 1e-5

"(k|epsilon)" 1e-5

Discretization schemes

16

Discretization schemes

17/21

Discretization schemes and RMSE

map Grid generation Scheme (divSchemes) RMSerr. Speed RMSerr. TKE A TBM + 2 levels of SHM bounded linearUpwind 1.239643 0.766631 B TBM + 2 levels of SHM bounded linearUpwind 1.253133 0.748267 A TBM + 2 levels of SHM b. skewCorrected linearUpwind 1.293558 0.781646 B TBM + 2 levels of SHM b. skewCorrected linearUpwind 1.309883 0.777852 A TBM + 2 levels of SHM b. linear (2nd ord. Central) 1.290942 0.899257 B TBM + 2 levels of SHM b. linear (2nd ord. Central) 1.474857 0.92132 A TBM + 2 levels of SHM bounded linearUpwindV 1.321186 0.799412 B TBM + 2 levels of SHM bounded linearUpwindV 1.350313 0.801742 TBM terrainBlockMesher SHM snappyHexMesh A ZephyTOOLS (OF 2.3.0) linearUpwind; upwind for k|e 0.993898 1.034235 B ZephyTOOLS (OF 2.3.0) linearUpwind; upwind for k|e 0.973765 0.995486

18/21

gradSchemes laplacianSchemes TBM + 2l of SHM Gauss linear Gauss linear limited corrected 0.333 ZephyTOOLS cellMDLimited Gauss linear 0.5 Gauss linear limited 0.5

Speed [m/s]: TBM+SHM vs. ZephyTOOLS

19/21

TKE [m2/s2]: TBM+SHM vs. ZephyTOOLS

20/21

Conclusions & Future Steps

21

Highlighted the grid sensitivity (vertical and horizontal) SHM not satisfying; TBM + SHM promising

Need to improve the code to automize the gridding while satisfing the h/z0 rule; some limits due to PC;

No substantial difference between cubic and ZT in terms of results (speed&tke) ... Probably differences due to the SHM

ZT slightly underestimeted the speed-up at HT and the step raise of TKE;

Both methods understimated significantly the peak of TKE (due to turbulence modelling?);

Improve (automize) the gridding; Test cases with roughness maps (Bolund); Compute the production of a Wind Farm.