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CFD tips for a traditional windmill environment

CFD tips for a traditional windmill environment by Victor Reijs is licensed under CC BY-NC-SA 4.0

Introduction

This page gives some requirements how to configure one's own CFD simulation. It is built around the 10 tips of Blocken [2015] and feedback from others.
There is a slight bias for SIMSCALE (based on OpenFOAM) in these tips (but it is written in such a way that one can figure it out for other CFD software).

Several questions are outstanding, see below purple text. If you have input, please let me know.

The wind mill environment

On this web page we will be looking at a traditional wind mill (normally a diameter of ~7m, height of ~25m and sails pan of ~12m; there are of course many variations;-) in a urban environment (although a more pastoral environment migth also be the case). So not many high buldings around (say up to 12m high) and hopefully also no high trees (say an z0 around 0.5 to 1m), but the build and green environment can be changing. And here CFD will be helpful to simulate the influence of new buildings and/or growing trees.
At present a circle with a radius of 400m around the mill is chosen to evaluate the wind mill biotope. This will also be proposed for the CFD simulation.
An anemometer could be placed on/near the wind mill to record wind speed/direction. The space for the rotating sails is of importance as this will provide an impression of the available power.
The space for the rotating sails could be evaluted using Rotating Zone, but no experience yet has been gained on this.

Requirements

Building model

Some six different regions can be defined (between square brackets, the location and recommended grid size):

The Building model will be rotated (in model editing mode) to simulate changing wind direction. If the CFD software supports PWC [Pedestrian Wind Comfort), the rotation will be done within the CFD machine.

CFD External Flow Volume (EFV)

There are two types of guidelines that need to be obeyed when looking at the described wind mill environment: (Franke's rule set [2007] is not needed for this specific environment [due to large influence area]):
  1. Minimum distances between the Building model and the surfaces of the EFV (domain):
  2. Blocking ratio (Hmax is height of the highest building; if Hmax is height of the mill cap height then add the sail length to Hmax):
    1. Height blocking ratio (Zmax): Hdomain>6*Hmax [Blocken, 2015, formula 14]
    2. Blocking ratio: Adomain>3*Abuilding [Gool, 2025, pers. comm & Blocken, 2015, formula 12]

Turbulence model

CFD solver must have minimum capability of solving the Navier-Stokes fluid flow equations for a three-dimensional incompressible flow analysis of steady state [Green Mark Department, 20016, section A2].
RANS is being used and this provides a time-averaged stream. This provides relative good results for wind velocities used for turning/operating traditional wind mills (>2.5Bft).
Allowable turbulence models: one-equation Spalart-Allmaras model, the standard k-ε model and its many modified versions, such as the Renormalization Group (RNG) k-ε model and the realizable k-ε model, the standard k-omega model and the k-omega shear stress transport (SST) model [Blocken, 2015, page 229].
Recommendation: minimally standard k-ε mode, while RNG and realizable k-ε model provide good solutions for an PWC environment (assuming that a mill is a tall person;-) [Gool, 2025, pers. comm.].

LBM solvers would allow a good time vayring solution of the wind mill environment. No experience has been gained yet with this.

Atmosphere conditions

Temperature

Isothermal condition at 15°C air temperature [ISA 1976] at steady state condition:
Kinematic viscosity: 1.470e-5 m2/sec
Density: 1.225 kg/m3

Atmospheric Boundary Layer [ABL]

The equations for the inlet ABL can be found at Blocken [2015, section 5.4] (see also at SIMSCALE).
Remember that the z0 can be different for different wind directions (as it depends on the roughness of the wind [upstream from the flow region] from that direction). The (average) wind speed varies also with the wind direction.
Recommendation: use formula as given by SIMSCALE

A quality mesh grid

Using the earlier described regions (without the functional space[s]), the areas of different meshing sizes are depicted here:
Grids aroudn a mill

Some recommendations by Green Mark Department [2017, section A5]:

Some gathered recommendations by Blocken [2015, page 232-233]:

Others (e.g. SIMSCALE):

A grid convergence study is recommended if no previous experience has been gained.

<In the future an example of a bad and good mesh will be presented on this page>

The roughness parameters

There are two types of roughness specifications:

For software based on OpenFOAM (such as SIMSCALE) and ANSYS/Fluent, the conversion between z0, ks and Cs is:
ks~9.8*z0/Cs and using Cs=0.9 gives ks~10.9*z0

For ANSYS-CFX based software, the conversion between z0 and ks is:
ks=29.6*z0

Different roughness araes

Different roughness areas
Figure 16 of Blocken [2015].

In SIMSCALE:
Also check that the stream is reacting properly to changing ks.

Remark: Still need to find out how to make several areas of different Roughness height ks and Cs for the EFV in SIMSCALE. This needs to be done in the CAD program: SketchUp is not able to do this: Better to use OnShape. For now: for all areas 2, 3, 4 and 5 the same (z0,) ks-x and Cs are used.

Remark: SIMSCALE seems not to provide real different velocity output when changing the Roughness Height considerable (like a factor of 100). This is important to get working/uderstanding!

Horizontally homogeneous in empty computational domain

When one removes all objects (but keep roughness heights/lengths as wanted), a horizontal homogeneity in speed and turbulent kinetic energy should be achieved. And example is here (-13.6m to 68m):
Empty Flow Volume

Also check that the stream is reacting properly to changing ks.

Higher-order discretization schemes

Don't use 1st order gradient schemes; 2nd order (such as Gauss) should be ok.
SIMSCALE uses default Gaussian integration.

Evaluation of convergence

Check in the convergence plots if the solution converges smoothly and converges to a stable end (so no oscillations). Termination threshold preferrable around 10-4.
Recommendation: Check in SIMSCALE: Simulation Runs -> Convergence plot -> Residuals

Grid convergence study

The grid resolution should be varied using a linear refinement factor of at least 1.5 in each direction (so that is around 3.4 [~1.53] for 3 directions). The results should not change significantly. At least three refinements checks need to be done (reduce and increase the recommended grid sizes with factor of 1.5).

What do we measure

Wind speed (perpendicular to the plane of the sails) and the turbulence intensity.

Validating the results

One needs to validate the results using scientific articles.
Areas to be covered:

Conclusions

If one compares two or more environments, the relative valuee become important. If the aerodynamic system is relatively linear, all unknown method parameters will be divided out, and thus the values of these parameters become a little less important (again: as long as we are in a linear environment)!
<Can only provide text for this section when things are fully understood, reviewed and tried>

References

Blocken, Bert et al.: Modification of pedestrian wind comfort in the Silvertop Tower passages by an automatic control system. In: Journal of Wind Engineering and Industrial Aerodynamics 92  (2004), pp. 849-873.
Blocken, Bert et al.: CFD simulation of the atmospheric boundary layer:wall function problems. In: Atmospheric Environment 41  (2007), issue 3, pp. 238-252.
Blocken, Bert: Computational Fluid Dynamics for urban physics: Importance, scales, possibilities, limitations and ten tips and tricks towards accurate and reliable simulations. In: Building and Environment 91  (2015), pp. 219-245.
Franke, Jörg  et al. COST Action 732: Best practice guideline for the CFD simulation of flows in the urban environment. Brussels, COST Office 2007.
Green Mark Department: BCA GREEN MARK FOR RESIDENTIAL BUILDINGS: Technical guide and requirements. In: (2017), issue GM RB: 2016.
Townsend, Jamie, F.  et al.: Roughness constant selection for atmospheric boundary layer simulations using a k-ω SST turbulence model within a commercial CFD solver. In: Advances in Wind Engineering 100005  (2024), pp. 1-10.

Acknowledgements

I would like to thank people, such as Frank van Gool, Ezra van de Elst and others for their help, encouragement and/or constructive feedback. Any remaining errors in methodology or results are my responsibility of course!!! If you want to provide constructive feedback, please let me know.
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Major content related changes: January 8, 2025