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Induction Model

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The latest version of Openwind contains three different induction models show in figure 140 below.

 

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Figure 140: Induction Model Settings

 

Forsting is the induction model by A.R.M Forsting, of which there is more discussion at the end of this section.

Rankine Half-Body (Gribben) is the model published by Gribben and available here

Vortex Cylinder (Branlard) is the model published by Branlard and referenced by Nygaard here

Consider Acceleration Effects - this option models speed-up zones on the shoulder of each turbine in addition to the slow-down in front of each turbine. See the Gribben paper for some nice illustrations of this.

Induction Deficit Combination Scheme - this is the way in which the induction deficit from one turbine is combined with all the others. These options are described in detail in the section on the N.O.Jensen wake model.

Induction Deficit + Wake Deficit Combination Scheme - this is the way in which the total induction deficit is combined with the total wake deficit at each point. Again the options are described in detail in the section on the N.O.Jensen wake model.

Remove turbine self induction effect up to a distance of X RD - this calculates the individual turbine induction effect at X rotor diameters upstream and subtracts this amount of deficit from the induction deficit experienced by that same turbine. This is in order to remove the upwind induction that is assumed and implicitly included in the turbine manufacturer's power curve. To disable this, set X to something large like 10.

 

The following discussion is preserved below, for interest, for now, until we have a more definitive approach.

 

The Forsting induction model in Openwind is based on the work of Dr. A.R.M. Forsting. In particular his PhD thesis which can be found here and is recommended reading for anyone interested in this topic. In his PhD thesis Forsting describes a simple model which closely matches the results of steady state RANS simulations of the flow upwind of a wind turbine. It is this model which is currently available in Openwind as the single turbine induction effect. The term “induction” commonly refers to the slow down as wind approaches a single turbine. Blockage tends to be used to refer to the slow down in front of a wind farm. In this section we use blockage and induction interchangeably due to the way in which we attempt to model blockage as the superposition of induction effects.

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Figure 141:  Induction Zones of 5D Separated Turbines at 8m/s (colour bands every 0.02 m/s)

 

Figure 35.1 above shows the simplified Forsting model with linear induction and wake combination. The circles have a radius of 2.5D.

 

Individual turbine induction effects of multiple turbines can be combined using a variety of simple mechanisms in Openwind including:

RSS (root sum squared) – the overall induction deficit is the square root of the sum of the squares of the induction deficits from all the turbines in the workbook

 

 

Geometric the overall induction is the product of the chaining of the induction efficiency from each individual turbine

Linear the overall induction is the sum of the induction deficit over all turbines

Mixed in which the overall induction is a weighted mix of RSS and Linear described above.

 

Openwind computes an induction effect by comparing the wind speed 2.5D (default) in front of a turbine, to the free speed without induction or wakes.

 

The induction effect can be combined with wake effects in a similar manner to how the induction effects are combined with each other. The current consensus is that the single turbine induction wind speed slow down should be the minimum induction effect across all turbines and should act as a global offset to current wake models. For this reason, the current default combination method for induction with wakes is linear, although geometric gives similar results.

 

 

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Figure 142: Taken from Segalini and Dahlberg (2020)

 

 

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Figure 143: Modelling Figure 3 from Segalini and Dahlberg in Openwind

 

Bleeg (2018) reports that wind speeds 2D in front of a moderately sized wind farm are lower by around 3-5%. Segalini and Dahlberg (2020), in their wind tunnel experiments, show normalised drops in front row wind speed of around 2% in front of an array of 72 closely spaced turbines compared to around 1.5% in Openwind.

Without normalising to the front row this should equate to around 2.5 to 3% at 8m/s. This is because the normalisation to the front row removes the front row induction effect which tends to be at least 1% of wind speed below rated.

 

 

 

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Figure 144: Modelling Table 1 from Segalini and Dahlberg in Openwind

 

The current induction model in Openwind is configured by default to give comparable induction effects to Segalini when using linear induction combination with linear induction-wakes combination. This is the strongest induction effect that it is possible to apply in Openwind at present, but it is still not strong enough to simulate the effects seen in Bleeg and reported to us anecdotally. In particular, the blockage model in Openwind does not currently do a good job of simulating the blockage effects at larger downwind turbine separation distances as seen in Bleeg.

 

As we continue to gather real world and simulated data on how the induction/blockage effect works, we will continue to refine and modify this functionality. In particular, Forsting’s model does not vary with ambient turbulence or stability and we suspect that this is a major shortcoming.

 

At present, use of this model is not recommended and is provided purely for interest and to provoke discussion.

 

 

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