SeaTwirl : wind farm layouts analysis

SeaTwirl's wind farm layouts analysis

Report developed by Dr Pablo Ouro, Senior CFD consultant

Dr Pablo Ouro - Senior CFD consultant in offshore renewable energy

Prepared for:

SeaTwirl AB

Lilla Bommen 1, floor 13,

411 04 Göteborg (Sweden)

[phone]

Prepared by:

Dr Pablo Ouro

Senior CFD consultant

19 Melrose Gardens, Cardiff, UK.

T: [phone]

1. [e-mail]

This document has been prepared by Dr Pablo Ouro ("PO") for sole use of our client SeaTwirl (the "Client") in accordance with generally accepted consultancy principles, the budget for fees and the terms of reference agreed between PO and the Client. Any information provided by third parties and referred to herein has not been checked or verified by PO, unless otherwise expressly stated in the document. No third party may rely upon this document without the prior and express written agreement of PO.

SeaTwirl wind farm layout design

Wite paper, SeaTwirl AB (publ)

Abstract

This report presents estimates of the energy generation from wind farms comprising 25 10MW vertical axis turbines using SeaTwirl's design. Comparisons with analogous farms adopting 10MW horizontal axis turbines show that the former yield notably higher energy generation due to reduced wake effects. The presented results outline that the aspect ratio of the vertical axis turbine rotor is essential to increase their performance.

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Dr Pablo Ouro - Senior CFD consultant in offshore renewable energy

1. Background information

Offshore wind farms consider the deployment of several turbines in multiple rows in order to make the most use of the consented sea region. Discarding restrains due to bathymetry features, the best wind farm layout needs to balance the increase in costs from cabling or moorings when turbine spacing is large, with the consequent reduction of wake effects that can decrease the energy yield when turbines are in close proximity.

SeaTwirl wind farm layout design

Wite paper, SeaTwirl AB (publ)

2. Wake modelling

The wake developed behind wind turbines is highly complex, characterised by a region of low velocity behind the rotor that eventually recovers the free-stream velocity further downwind. This recovery depends on the acting thrust of the turbine as well as the turbulence intensity of the oncoming wind. To date, most research characterising the wind turbine wakes focused almost exclusively on horizontal axis turbines (HAT) as they dominate the market. These wakes can be reasonably well represented in their time-averaged sense using analytical wake models based on either experimental or field data or high- fidelity simulations. Ouro and Lazennec (2021) developed the first analytical wake model for vertical axis turbines (VAT) considering their geometric and operational particularities, which was well validated against high-fidelity simulations.

The first models considered a so-called"top-hat" velocity deficit distribution as proposed by Jensen and then by Jansen but this approach failed to represent the wake shape. More recently, Gaussian wake models provide a notable improvement as they conserve mass and momentum together with capturing the wake shape over its cross-section and in the downwind direction. Equation (1) presents how the velocity wake deficit (defined as the difference between velocity decay in the wake region and that in the free-stream) for a HAT (ΔUH) has two components, one accounting for velocity deficit magnitude (CH) that depends on the thrust coefficient (CT) and wake expansion (σH, Eq. (2)) and its shape (fH) which has an exponential distribution in the radial direction. It is important to note that the wake expansion is a linear function that scales with kH known as the wake expansion rate that is kH = 0.35·Iu, with Iu denoting turbulence intensity. Thus, higher turbulence intensity levels (normally occurring at low velocities) leads to a faster wake recovery.

(1)

(2)

The shape of the wakes developed behind HATs and VATs are depicted in Figure 1. This shows that a Gaussian model provides a physically sound representation of the HAT wake as only the rotor diameter is the scaling geometry feature with a circular cross-section. Conversely, VATs have a rectangular cross-section with their diameter (D) and height (H) meaning that the wake shape over the vertical and horizontal planes differ, with Gaussian models failing to capture this. Ouro and Lazennec (2021) proposed an anisotropic super-Gaussian model that allows to represent with a super-Gaussian distribution the wake distribution over the two spatial directions independently, i.e. ΔUV(z) and ΔUV(y). Considering the aspect ratio ξ = H/D, the super-Gaussian VAT wake model reads:

(3)

(4)

(5)

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